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Progress Over Time- Part 4- Curriculum Design Implications

In this series of blog posts, I will share with you memos that I am issuing to all teaching staff at my school, to update them on a whole-school ‘Progress Over Time’ teaching & learning development initiative. The teachers at Wyvern are a talented, highly-committed and special group of people. I’m sure you will agree, the work they are producing in exploring how to effectively implement retrieval practice, spacing and interleaving is quite inspirational…

Earlier posts in this series:

Part 1 -Using Research- How Robust is the Effect

Part 2- Individual Practice Implications for Teachers

Part 3- Social and Motivational Factors Involved in Using Desirable Difficulties

Progress Over Time- Part 4- Curriculum Design Implications

What are the benefits of having high levels of fluency with certain knowledge and skills? I.e. having them retrievable ‘automatically’ and ‘without thinking’?

Another theme to emerge from the Curriculum Leader meetings so far is that the Retrieval, Spacing and Interleaving Effects are factors that have implications for the design of our subject curricula and schemes of work across the college. Furthermore, these conversations are timely as we are all navigating our way through incorporating the different and challenging exam specification requirements and writing our new schemes of learning for the 9-1 GCSEs.

In this memo, I want to share some fascinating discussions we have had so far, and in particular, a number of the ideas that I think may have relevance across subjects in specific areas. However, I want to be transparent and candid here- this is unchartered territory. To my knowledge, there is not a comprehensive literature base that looks at curriculum sequencing to take advantage of Desirable Difficulties within secondary school contexts. At best we have but a handful of individual papers. We must tread cautiously, think carefully and make sure we evaluate impact as we go.

Planning for distributed study

In 2015 Prof Doug Rohrer, University of South Florida completed a meta-study review of research into the effects of distributing practice over more extended time periods than is usually the case. He states, “In many academic courses, students encounter a particular fact or concept many times over a period of a few weeks and then do not see it again during the remainder of the course. Are these brief instructional periods sufficient, or should the same amount of instruction be distributed over longer periods of time?”

Doug found only nine papers in the literature which met the criteria of being experimentally sound and relevant to our context. The studies varied across subjects including foreign languages, history, science and trivia. In short, the answer is ‘yes’. These studies consistently found that if you take the same amount of instruction, but distribute it across longer periods of time, retention is significantly increased.

Above- Results from Bird (2010) study where English-learning students were learning three kinds of verb tenses. Both groups studied on five occasions, but the study was scheduled to occur over 2 and 8 weeks for the short and long groups respectively.

Thus, I think it is reasonable to say the work that has been done in this area, albeit limited, is suggestive that there may be benefits of trying to build spacing into our mid-and-long-term planning if our goal for doing this is to maximise progress over time.

Matt’s innovative and superb work to explore building distributed practice into the formative assessment cycle (discussed in part 2) came to mind when I read this meta-study. If you take that study>-space->essay->space->feedback->space->test approach which distributes the study of an individual topic over a more extended time period, it does require the teaching of a few topics simultaneously. This approach necessitates that in any one fortnight’s worth of lessons you could be switching between two or more topics each at different stages. Mid-term-planning has to be rigorous if that model is to be efficiently delivered, but that is well within the capabilities of any Wyvern-calibre teacher. I think Matt’s intuitions are spot on here and it will be fantastic to hear how this approach goes in practice as the year progresses.

Plan time to build fluency before starting higher-order skills

If you ever get a chance to see Bryan’s organisational skills in action, do take it; they are quite something to behold! The level of detail and thought put into the sequencing in the Music Department’s schemes of learning is remarkable. As Bryan and his team consider how to adapt these to match with the new Music GCSE specification, Alan, Bryan and I had a stimulating discussion about how Desirable Difficulties could help in specific areas.

Focusing on the Special Study (Haydn’s Clock Symphony and other works etc.) as discussed in a part 2, the following questioning path arose, ‘do you teach all the basic content of the Clock Symphony then go straight into the higher-order ‘apply-style’ questions on the same symphony, or do you need to spend time building the fluency of the basic content and thus move the apply-style lessons for Haydn’s symphony into Y11 towards the end of the course? Good question!

As different as our subjects are, there is a perpetual debate in the maths teaching world of whether you should teach problem-solving simultaneously with content or whether you focus on building fluency with the basics first then back-load your course so that students focus on problem-solving empowered by fluency with the knowledge they need to solve the problems. I have always been inclined to do the latter as I cannot see the benefits of being asked to solve problems that you do not have tools to solve. Some argue that you can acquire these skills by learning them simultaneously while problem-solving. That goes against all of my experience as a teacher of maths and what I know about Working Memory overload. However, I can see that in some subjects this would be entirely feasible.

It was a privilege to talk through with Bryan whether the same ideas are transferable to this new Special Study content in music and what Desirable Difficulties would tell us, in theory, would be optimal. Theory-optimal versus real-world optimal can sometimes be different things, and I look forward to hearing how this thinking develops and gets put into practice on the new 9-1 Music GCSE scheme of learning in due course.

Maybe these ideas will be of use in your subjects, maybe not…

Project-based learning

In our meetings with Katherine and Steve, it was clear how Art and Technology lend themselves as subjects to project-based learning approaches. Discussing to what extent Desirable Difficulties can enhance curriculum planning in these subjects certainly pushed me out of my comfort zone, which was fantastic (!), but I think there are a few points worthy of sharing from our conversations that may be of interest to other subjects.

Firstly in Art, as a subject, it has significant creative and expressive elements. The criteria against which students are assessed are deliberately very generalised and open to interpretation to allow them to reach the pinnacle of GCSE-level artistic skill in many different ways. The majority of work is portfolio and iterative-based, allowing students to improve previous works incrementally. The GCSE Art exhibition is always a highlight in the calendar year at Wyvern which showcases not only students’ skill, but also the skills of Katherine and her team in nurturing and developing their students to such a high degree of competency.

The project-based approach is undoubtedly highly effective for Art, and Katherine talks about how as students work on projects, for example drawing a personal item in Year 7, they are taught shading skills which they are then expected to transfer to future projects. Katherine talks about generally seeing this transfer and retention from project-to-project which again demonstrates project-based learning approaches work so well for Art. From a Desirable Difficulties perspective, I have been considering how these apply using project-based methods and I think they certainly do. I think Katherine and her team are in fact already utilising them.

Consider the Year 7 project to sketch a personal item. Students will typically work on this project over a period of a few weeks, first drawing the object without prior instruction. They then get feedback and instruction regarding shading techniques before repeating the exercise applying their newly studied techniques. Subsequent projects then expect the application of these techniques in new contexts. Project-based learning done this way can certainly fit well within the framework of distributed practice discussed at the start of this memo. Their training and retrieval on shading techniques, for example, will be spread over more extended time periods precisely because they will be required on subsequent projects.

Steve in Technology is keen to reinforce a culture with students that while they may be building, for example, a fire alarm, they entirely understand what this project is the vehicle for regarding transferable knowledge and skills. He has many great ideas for how to get this message across to students so that their first thought when starting a new project is to think of previously acquired transferable knowledge and skills.

It has taken me a few weeks of deliberation to understand why the project-based approach is so successful in Art and Technology, yet I have never seen a successful implementation of it within Maths. I think I know this now and hopefully, through sharing the ideas involved you can think about how they may or may not apply to your subject.

Firstly, finding projects in a maths context which pull from right across the curriculum content is at best difficult, if at all possible. It is hard enough to find a real-life setting for algebraic completing the square, let alone to design subsequent projects which will provide sufficient distributed opportunities to retrieve it. Whichever projects you selected for a maths curriculum and however ‘rich’ they are in terms of content, you can’t get sufficient coverage to ensure enough distributed retrieval opportunities across a series of projects to build retention. For example, if we ran a personal finance project on loans and mortgages, students could learn and use many percentages skills, but they would not learn many algebraic or shape skills which would need to be visited in a subsequent project. In a later project, say designing a garden, students could learn many shape and arithmetic skills, but the project would not lend itself to revisiting the previous project’s percentage skills unless you did it in a very contrived manner.

For project-based learning to be effective, a couple of factors seem to be that the projects provide sufficient curriculum coverage, and also they provide distributed practice opportunities to build retention with previously studied skills. Art and Technology are subjects in which with careful and skilful planning from colleagues of Katherine and Steve’s calibre, this is absolutely possible and desirable.

An interesting thought to come from our meetings with Katherine and Steve was the notion that rather than trying to ‘atomise’ a curriculum and design it from ‘bottom-up’ with planned spacing and interleaving, there is an equally-valid and alternative approach. Instead, if you use a project-based approach, but specifically monitor whether students are transferring skills and knowledge from one project to the next, then you can infer from that if they are getting sufficient distributed practice to build retention and transfer. Monitor that the learning is being retained and transferred from project-to-project and if it is not then tweaking your schemes of work. If the transfer is not happening, perhaps there is a need to adjust the scheduling of the projects or to put in some specific retrieval practice activities. If it is happening, great, press on!

One final issue I needed to get to the bottom of was, ‘why are students so limited by Working Memory overload in Maths, but this seems less of an issue in some other subjects?’ I think the reason is down to the notion that during assessment in maths there is a ‘threshold’ over which students either can or cannot cross. 3 X 8 equals 24. They do not get half marks for saying 12. To solve a problem in maths requires significant cognitive resource and lack of automaticity with the prerequisite skills required to solve the problem consume this resource and prevents them getting over the threshold to progressing with the problem. In other subjects, a lack of automaticity with prerequisite skills does not prevent them from scoring marks. They still produce something of assessment value, even if it could be improved. Because the nature of some subjects’ assessment criteria is more subjective and continuous, there are no ‘thresholds’ to get over (or not), there is instead a continuous scale of relative success. In this case, students regulate themselves from going into Working Memory overload, i.e. their ‘best effort’ produces something that scores marks- there is no threshold over which they need a definitive level of fluency with prior skills to pass.

Apologies for making these last few paragraphs so Maths-centric, but I firmly believe articulating professional learning and ideas within our contexts then passing over to colleagues to process within their subject domains is the respectful, civilised approach for which we should adopt in schools. From hearing how I have reflected on the ideas regarding similarities and differences between other subjects and my own, I hope you feel able to consider how they may or may not be relevant in your subjects.

Could I finish this update on our Progress Over Time work by sincerely thanking you all for your efforts and professionalism in engaging with this college thrust. There is already a wealth of inspiring and impactful work going on across the college towards this thrust. We have many gifted and highly committed teachers and CLs in the college, and it has been a real privilege to work with you and showcase your T&L developmental work with Progress Over Time thus far. I look forward to the upcoming meetings with other CLs and also the next phases of professional learning and putting this into practice with everyone.

What are the benefits of having high levels of fluency with certain knowledge and skills? I.e. having them retrievable ‘automatically’ and ‘without thinking’?

It makes it easier to complete ‘higher-order’ and ‘challenging’ tasks by preventing Working Memory going into overload

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mathqed · 7 years ago

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Progress Over Time- Part 3- Social and Motivational Factors Involved in Using Desirable Difficulties

In this series of blog posts, I will share with you memos that I am issuing to all teaching staff at my school, Wyvern College, to update them on a whole-school ‘Progress Over Time’ teaching & learning development initiative. The teachers at Wyvern are a talented, highly-committed and special group of people. I’m sure you will agree, the work they are producing in exploring how to effectively implement retrieval practice, spacing and interleaving is quite inspirational…

Earlier posts in this series:

Part 1 -Using Research- How Robust is the Effect

Part 2- Individual Practice Implications for Teachers

Progress Over Time- Part 3- Social and Motivational Factors Involved in Using Desirable Difficulties

To assess learning, assessments should be t……………….-d…………………. and c…………………..-v………………………..

One of the fundamental ideas relating to Desirable Difficulties is that the teaching strategies which build deep, long-lasting learning are more challenging and ‘slower-wins’ than teaching that aims for rapid performance-boosting, but short-lived progress gains. ‘No pain, no gain’, ‘delayed gratification’, however you want to frame it, this is a finding that has been highly replicable in the research.

As teachers know all too well, in general terms, humans in many contexts are often not wired to choose the more challenging option! For example, rereading through some revision notes is much easier to do than creating a quiz on the same content then taking it yourself a number of times. Rereading, particularly if you do it a few times quickly, builds up a sense of familiarity that is easy to mistake for learning. Retrieval practice is much more effortful, and it quickly highlights specific areas where you don’t yet have sufficient retention.

So in summary, ‘consumption’ strategies such as rereading and watching videos that quickly build a ‘feeling of knowing’ feel good because they give rapid, short-term performance gains which can be highly motivating. Conversely, ‘retrieval’ strategies such as low-stakes quizzing, flashcards etc. suppress early performance gains to maximise learning (which cannot be seen by the student until a later date). The instant gratification, buy today-pay tomorrow society in which we live undoubtedly makes the ‘efficient learning is effortful’ a hard-sell to students. The now widely discredited ‘learning styles’ theory was based on just the opposite: easy learning is the best learning. I think it’s more than just social conditioning though. We seem to have a natural sub-conscious tendency to gravitate towards decisions in which we get instant and positive feedback.

When it comes to motivation, particularly with students of an age where they are still developing the ability to make judgements about their learning metacognitively, I think it is an essential factor for teachers to consider when implementing retrieval, spacing and interleaving etc. We have some exploration and ideas surfacing within the college for how to do this efficiently, but in schools and academia, I think this is still very much in its infancy. Managing student motivation while delivering retrieval, spacing and interleaving is a real priority area where we need both more research and more practical experimentation, evaluation and sharing amongst teachers in schools.

As already discussed in a previous memo, Craig noticed that he could deliver retrieval practice quizzes on a daily basis rather than a weekly basis if he used multiple-choice rather than free-recall answer formats. Interestingly, during their cluster research work this year, Emma and Karen noticed motivation benefits from using a multiple-choice format answers with students too.

Retrieval practice requires somewhat of a ‘Goldilocks’ approach. If the spacing between retrievals is too long then there is a high likelihood that during a free-recall test you won’t be able to retrieve the information successfully, and that is pointless; it is an undesirable, rather than desirable difficulty. Particularly during the first or second time that we ask students to retrieve something, to have a successful retrieval the time intervals need to be relatively short. The intervals should expand out quite quickly after that. We are constrained by our timetable and curriculum structures of course; if you see a class once per week, you can’t quiz any shorter than a week spacing at the start. There is no doubt in my mind that in real-world classrooms there is a time, place and context in which using multiple-choice questioning is appropriate because it boosts students’ likelihood of having a successful (partial) retrieval during the first couple of times they are expected to recall some information. This scaffolding has a positive effect, not only just for learning, but also for motivation too. Students are more inclined to engage with tasks in which they score better.

So while in theory we’d all be doing free-recall tests all the time and quizzing students just before the point at which they forget information, in the real world of education we are influenced by timetabling constraints and student motivation etc. Consequently for us, I think there is a strong argument that the best implementation of retrieval practice in some contexts would be to start with scaffolding strategies such as multiple-choice questions, cued answers (first letters given etc.) and then transition to free-recall quizzing (no cues given) after the first few attempts when students can retrieve the information successfully after a spacing gap of a few weeks etc. This is all getting rather deep! Let’s summarise…

From Emma’s work so far and my experience of using Desirable Difficulties (including seeing significant benefits) for a few years now, I think it’s reasonable to offer students some strategies, particularly early on in low-stakes quizzing etc., that support their performance. Things such as multiple-choice answer formats, giving first letters of answers etc. do support students’ motivation and thus their retrieval success later on down the line. However, these strategies should transition towards pure free-recall (no cues) after students have shown you they can successfully retrieve the scaffolded information over a period of a few weeks.

The skill and judgement of the teacher are essential here, and you are balancing theoretical optimum strategies versus students’ motivation factors which work against these strategies, and it is just that, a balance. You know better than anyone else where Goldilocks sits in your classes’ learning journeys.

There is research going on as we speak into these ideas in Prof Jeff Karpicke’s lab at Purdue University, Indiana. However, I think this is an area where real insights could come from the coal face and teachers sharing their findings such as Emma and Karen’s ongoing great work…

Next up, let’s look at we’ve learned so far about designing our curricula and schemes of work using Desirable Difficulties such that they can enhance student outcomes.

To assess learning, assessments should be time-delayed and contextually-varied.

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mathqed · 7 years ago

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How To Use Retrieval Practice To Improve Learning guide

The terrific www.retrievalpractice.org website has released an outstanding practical guide to using retrieval practice effectively in your classroom. Click the link to download.

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mathqed · 7 years ago

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Progress Over Time- Part 2- Individual Practice Implications for Teachers

Earlier posts in this series:

Part 1 -Using Research- How Robust is the Effect

Part 2-Individual Practice Implications for Teachers

The differences between ‘performance’ and ‘learning’ are …

Factors that ‘prop up’ students’ performance in lessons, but that are not there on delayed tests include…

In which knowledge and skills do students need to build high-levels of fluency?

Across the college and our taught subjects, it was clear from meetings with CLs that one notion that seemed to resonate significantly was that in order to perform well on the respective ‘higher-order’ exam-style questions, there is a ‘foundational base’ of knowledge within in each subject that students need to develop high-levels of fluency in.

Fluency alone is not enough, of course; students still need to be taught the higher-order skills. However, if students lack fluency with the prior foundational knowledge from which the higher-order abilities build, teaching those higher-order skills becomes much less efficient. Making an analogy- teaching factorisation of quadratics to a student that doesn’t know their timestables is near impossible.

In our meetings with CLs thus far it has been fascinating to explore what these particular skills and knowledge looks like across the taught curriculum. Here is a non-exhaustive sample of what CLs have expressed to date about their subjects:

Laraine (Languages)– More than just vocabulary, it is tenses and common phrases too. Laraine has done excellent work looking in detail at what this knowledge is for the year 7 Languages curriculum and has already put strategies into action to build students’ fluency.

Emma (Religious and Personal Studies)– Religious teachings- the central beliefs, ideas and instructions of each religion (including atheism!). Essential vocabulary associated with the content and also English translations of Hindu words.

Bryan (Music)– While there are many foundational skills with regards to performance, of particular interest was recent additions to the Music GCSE in the form of a Special Study. Within this students are expected to study Haydn’s Clock symphony and other pieces in great depth. To do this successfully, students need fluency with understanding the composer, other works, elements of sonata form, instruments that form a ‘Classical Orchestra’, dynamics, harmony, melody, rhythm and metre, timbre, structure and the related associated vocabulary.

Craig (Science)- Key definitions of vocabulary, fundamental concepts in the periodic table, conceptual understanding of energy types, significant areas of fluency with maths such as area and unit conversions, cause and effect relationships, fundamentals of atomic structure, fundamentals of reactions.

Matt (Media)– Key vocabulary such as enigma codes and action codes. Camera concepts such as crabbing, extreme close-up, tracking, jump cuts and crash-zoom.

Steve (Technology)– The new 9-1 Technology GCSE is first examined next academic year, a year behind most subjects’ first 9-1 sitting and two years behind English & Maths. Accordingly, issuing of the new exam specifications and indicative sample papers is still relatively in its infancy. Steve quite rightly is holding back from attempting to fully ‘atomise’ the knowledge students need to be fluent in within his subject until the government and exam boards have put a little more ‘meat on the bone’ with regards to specifics of what the exams will assess. Nonetheless, there will certainly be a whole raft of technical vocabulary in which students need to be fluent such as ergonomics, thermo-polymer, anthropometric data, environmental impact etc. Material properties are another fundamental knowledge base. Furthermore, students need fluency with contemporary trends, including ’emerging technologies’. Finally and similarly to science, the mathematical demand has dramatically increased, and fluency with calculating missing angles, areas and so on is an essential prerequisite.

Katherine (Art)– What makes a great artist? Do you need an understanding of the artistic genres to be a great artist yourself? What difficult questions these are to answer! With regards to fluency, there are elements of technical ability, understanding of colour theory and use of composition etc., but there is also a purely creative, expressive dimension too. Katherine and I had a fascinating discussion exploring these ideas which are challenging to pin down. Katherine talks about students who ‘can see’ and students who ‘can do’ and all variations of these- those that can do but can’t see etc. Concerning fluency, there are elements associated with both ‘seeing’ and ‘doing’.

There is, of course, more work that CLs want to do with their teams in this area and all of them that I’ve met with over the last few weeks expressed the desire for Wyvern to plan time for them to do it. Indeed, one of the messages I will be passing on as a result of this work will be a request for dedicated time in future INSET days for further exploration and documenting of the knowledge and skills within each of our subjects in which we want to focus on developing high-levels of student fluency.

Which knowledge and skills makes the ‘fluency priority list’? Once we have that defined, to build the fluency we plan within our lessons to retrieve, space and interleave…

How are different teachers putting retrieval practice, spacing and interleaving into action?

It is clear from our discussions with CLs and many teachers across the college that there is a healthy level of understanding amongst the teaching staff of the importance of using retrieval-based strategies for building retention of learning. In simple terms, recalling previously studied information is the very process that builds retention. ‘Consuming’ information multiple times with strategies such as highlighting and rereading are much less impactful in this regard.

While retrieval practice is essential, of course, it is only one part of effective teaching and learning. There are naturally questions about where the correct balance lies in lesson planning between learning new content, deepening understanding of that learning or building retention and fluency with the previously studied material. All ships need to rise simultaneously. Academic-based research does not give us many clues here, and I’m confident there are no silver bullets, one-size-fits-all solutions. Your professional judgement, experience and intuitions as experts in your subject pedagogy are essential in deciding where the correct balance is for your students and your subject.

There are many ways in which Wyvern teachers have been incorporating retrieval, spacing and interleaving into their practice right across the college. With great excitement, I am pleased to share some examples with you now.

Laraine has put in place Knowledge Organisers for her Y7 French course based on essential vocabulary, common phrases and tenses that relate to the content of each taught unit.

The language she is using with students for these resources is ‘non-negotiables’ which does emphasise the importance with which she wants students to treat them. Students are currently getting a weekly retrieval practice quiz on this content whereby columns in one or more of the tables are blanked, and students fill in the blanks. To interleave, sometimes blanks are made in different tables, getting the students to jump between thinking about vocabulary to thinking about common phrases or tenses.

Laraine and her colleagues have some challenging questions to consider concerning time to devote to this type of retrieval practice quizzing versus covering new content, delivering assessments and feedback etc. I don’t envy them! While it may be desirable to quiz on a daily basis, is weekly the practical and realistic frequency taking into account the many factors a languages teacher has to consider? This question was indeed a common theme expressed by CLs across the subjects, not just languages. It’s certainly something we had to weigh up due to the increased content demands of the new Maths GCSE. One way around this point that I know some other schools use is to set daily, short Look-Cover-Write-Check retrieval practice as homework for students based on their Knowledge Organisers as supplementary to the more in-depth homework tasks. Things for us all to think on.

Bryan has taken a similar, Knowledge Organiser approach to building the fluency of his students’ knowledge for the new ‘Special Study’ part of the music GCSE.

In this exam, students will be expected to apply the knowledge Bryan has identified in these Knowledge Organisers in context. For example, students need to describe how Haydn used particular musical devices to create specific effects and so on. An important and challenging consideration for Bryan is the vast quantity of information with which students need the fluency to answer this exam versus the relatively small proportion of the Music GCSE exam grade towards which it counts. Again, the question is raised, ‘what time should we be devoting to fluency-building retrieval practice?’ I don’t think there is an easy or obvious answer. It is something that is very subject-specific, and you are all the experts in your own subjects. Using this memo as a vehicle for sharing common themes and ideas etc., in addition to the previous point about scheduling retrieval practice in student homework, I think Bryan and myself explored some interesting ways of using mid-and-long-term planning with the scheduling of the curriculum to make this more efficient. We’ll look at this in a future memo.

Emma and her colleagues have been conducting regular retrieval practice ‘revision quizzes’ with their GCSE classes based on their fluency priority knowledge.

Interestingly, for their research cluster project this year, Emma and Karen are looking into the difference between giving retrieval practice quizzes in free-recall or a multiple-choice answer formats. They are comparing quizzes with the same questions, but varying the answer format and looking at the impact on student outcomes etc. A fascinating project and I look forward to hearing their findings later in the year.

Also, Emma has already noticed some effects on student motivation; more about that in a future memo.

Craig and his colleagues in science have been delivering retrieval practice multiple-choice starter questions to GCSE classes at the start of every lesson. Craig has found that by making these multiple-choice, it has made the quizzes much faster to deliver in class as the answers can be reviewed by reading out a list of letters rather than needing to cite sentences and then decide if individual students’ responses were close enough to the correct answer.

In theory, multiple-choice questions are not as effective at building retention of learning as real free-recall questions because they don’t require a retrieval on behalf of the student, only a logical selection or elimination. However, the upshot is that if retrieval practice activities in some contexts, can be delivered much faster and therefore with higher frequency if they are in a multiple-choice format, then it may indeed be the format that is most pragmatic and beneficial in a real classroom context in your subject. Is multiple-choice daily more beneficial that free-recall weekly? This question is undoubtedly a professional judgement call for individual CLs and teachers.

There are ways to improve the retention-building benefits of multiple-choice questions; the Bjorks have done a significant amount of work in this area. Firstly, it is crucial that incorrect answers are plausible ‘competitive alternatives’ with the correct answer. Secondly, if a wrong answer on one question is the correct answer to a later question, students will perform better on the following question for having to effortfully eliminate it as an answer to the former question previously. Finally, the Bjorks have shown that it is possible to set up scoring procedures whereby students indicate not only their response but their degree of certainty which can be used to guide them into the elimination thinking processes which cause a partial-retrieval and thus still build retention. This later technique currently requires computer programs to deliver at scale and so at this stage is not ready for secondary school environments.

Simon Watson in PE has also created some retrieval practice quizzes for GCSE PE theory content which he and colleagues are now using at the start of PE theory lessons. What is particularly impressive about this work is how he has planned the sequencing of the questions such that they incorporate the Spacing and Interleaving Effects.

As the year goes on, the questions in the quizzes include not only content from the current topic, but also previously studied subjects from half-terms before. The number of items devoted to current versus previous content changes each half-term and thus Simon makes sure that each question is visited many times over the year in a spaced (and interleaved) way. See how the proportions change in his diagram above- 6 Qs on each half-term, 4 Qs on each half-term etc.

I know some colleagues have expressed that now they have incorporated regular retrieval practice into their lessons, they are starting to think about ways of scheduling it to get the benefit from the Spacing and Interleaving Effects. I think Simon’s work in this area is tremendous and I’d thoroughly recommend a chat with him if you’d like to explore this further within your practice.

Matt has been experimenting this year with implementing the Spacing Effect in a particularly novel way. He realised he could build spaced study opportunities into the formative assessment cycle! Within his media lessons, he has taught students a topic and got them to write an essay. Then he has moved on to new topics again with students learning and writing an essay on that content. After approximately three weeks after writing the first essay he then gives students their marked work on the first essay, he gives them feedback, and they make corrections and improvements. Another week after that they then sit a test.

This approximately 4-5 week schedule of study>-space->essay->space->feedback->space->test is followed across the media topics and so lessons from day-to-day can transition from looking forward to looking back etc.

Matt’s approach is impressive, and one of the reasons I like it is that it builds spacing and interleaving into mid-term planning, thus ensuring it definitely happens rather than it being reliant upon day-to-day planning and the ebbs and flows of daily workload. To refine and maximise impact even further there are things to consider which I know Matt has in hand such as optimising the spacing gaps (in theory these should expand each time) and also ensuring that the feedback phase includes retrieval-based strategies as well as imparting the feedback. What a creative solution and well-thought-through implementation this is!

To finish with, if you are Twitter-inclined, there are many teachers currently sharing their journey and findings of implementing these ideas in practice. I’ll end with a couple of images of designs that looked different to what I’ve seen within Wyvern so far, just to seed some thought…

Are there engagement benefits to be had by attributing scores to low-stakes quizzes, incentivising with higher marks for content from further back…?

Next time we’ll take a look at what we’ve learned across the college about the social and motivation factors that influence putting Desirable Difficulties into action…

The differences between ‘performance’ and ‘learning’ are …

Learning is retention over time and transfer of knowledge to new contexts. Performance is just a snapshot of what students can do at some point during instruction. Performance is often a poor predictor of learning

Factors that ‘prop’ up students’ performance in lessons, but that are not there on delayed tests include…

Recency, mimicry, cues, scaffolding and differing response formats

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mathqed · 7 years ago

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Progress Over Time- Part 1- Using Research- How Robust is the Effect?

Part 1- Using Research- How Robust is the Effect?

Desirable Difficulties- “Conditions that create difficulty for the learner, slowing the rate of apparent learning, but actually lead to better long-term retention and transfer of knowledge”- R. A. Bjork

Examples of Desirable Difficulties: R………….. Effect, S………….. Effect, I………….. Effect

After the Progress Over Time INSET session last October, a number of colleagues commented to me that the content resonated with their intuitions gained from their many years of experience in the classroom. ‘Rapid and sustained’ progress always felt oxymoronic, they said; in learning as in life, there are no shortcuts. ‘Rapid or sustained’ would be closer to the mark… Progress that is sustained rarely grows from learning techniques which emphasise rapid, superficial acquisition of knowledge or skills.

When learning about Desirable Difficulties myself for the first time, I certainly remember feeling as though these ideas gave me a vocabulary and conceptual framework to articulate what my teacher instincts were telling me; to learn something to meaningful depth and longevity, students need study schedules that look far beyond just delivering them the information just once…

The same is true in our own professional learning, of course. When we identify adaptations to our practice that we want to embed, it takes considerable sustained, conscious effort and deliberate practice to ingrain the change to the point of automaticity.

When Alan asked me to lead the Progress Over Time thrust on behalf of the college, I agreed under the condition that we scheduled the training such that it modelled the ideas it advocated. A one-off INSET session and a few posters around college would be somewhat hypocritical! The twilight INSET had a follow-up delayed quiz, and there’s another one coming later in the year! Furthermore, I insisted on time for colleagues to digest the ideas and reflect upon any implications for their own practice. For Curriculum Leaders, we scheduled follow-up meetings to harvest and share best practice from across the college and also to explore ways in which the leadership of the college could empower and support CLs with follow-up amendments they wanted to make in their own departments. A good number of these meetings have now happened, the rest will be scheduled soon, and it now seems timely to share with all teaching staff a ‘progress update’ on Progress Over Time…

Firstly, I would like to effuse about three things: the tremendous amount of good practice with regards to Progress Over Time already within the college; the professionalism and expertise of CLs in reflecting on the implications of Desirable Difficulties etc within their own subject curricula; and also the open-mindedness of so many staff across the college to think about and act on these ideas. Given the talent, and competence already in the college, along with the considerable thought already having been given to how we plan for and deliver Progress Over Time, I very much see my role as a ‘facilitator and sharer’, rather than just a ‘pollinator’… This series of memos is a means through which to share what I have been privileged to learn from many of you thus far.

In this first memo, I would like to focus on reflections more broadly about applying Desirable Difficulties within 11-16 teaching and what I’ve learned about trying to implement lab-based research in school environments. Future memos will then focus on updates about practical Wyvern examples regarding implications for individual teacher practice, social factors involved in implementing Desirable Difficulties, curriculum design implications and also updates from the Y9 Learning Leaders project.

One of the most important questions I have learned that you should ask anyone advocating ideas from educational research for use in classroom teaching is, “how robust is the effect and what evidence do you have with regards to this?” You see, much of the research out there was conducted with undergraduate students in laboratory-based environments. Undergraduates have, by their very position, demonstrated they are effective learners and they don’t represent the spread of academic attainment that we have within our school populations. They are also typically developmentally more mature.

In the vast majority of laboratory-based studies, the experiments are specifically designed to maximise the impact of the phenomena they are trying to observe. Any factors that could interfere with or reduce the impact size of the results are eliminated from the experiment by design.

If only we were in such a privileged position! The takeaway point is that many of the effects that are observed in the research-world are ephemeral and/or ethereal, fragile things that can be hard to replicate in a reliable, predictable way in real-world classrooms. Perhaps there is no better example in recent times than Dweck’s Growth Mindset…

To my knowledge, there has not been a single longitudinal study run in a school environment which has shown an implementation of Growth Mindset which has led to better student academic outcomes. Furthermore, according to some sources, the theory itself is in somewhat of a ‘replication crisis’ in academia. Allegedly, few research teams outside of Dweck’s own lab can replicate the findings, even under laboratory conditions.

The point, I believe, is that whilst people don’t doubt that Growth Mindset is real, at this stage it is too fragile, perhaps too little understood, to be a finding that we are able to implement in real-world 11-16 classrooms in reliable ways with predictable impact. Martin K and myself learned this the hard way in our cluster research study a couple of years ago!

Replicability and predictability under a broad range of contexts (robustness) is the first criterion one should have in mind before we invest time and energy into bringing any research finding into our classrooms. Show us the evidence…!

There is still much work to be done with Desirable Difficulties, but one of the reasons I feel confident in making it the foundation for our whole-school Progress Over Time thrust is precisely the replicability and predictability of the effects. The academic research into spacing, interleaving and retrieval is decades-old and well-understood. As Nick Soderstrom PhD, a researcher and graduate from the Bjork lab recently said in a conversation with me, “it’s very hard to design a study where you don’t observe the retrieval, spacing or interleaving effects.” These effects have also been shown not just in knowledge domains, but also physical skill domains too. Also, whilst I think there is a long way to go to build a research base of using these effects to their maximum in real-world 11-16 classrooms, researchers such as D Rohrer, J Karpicke, H Roediger, M McDaniel, S Carpenter and more have all published school-based studies showing impact.

Having set out these thoughts, I would like to finish this first memo by acknowledging from my work with CLs so far just how diverse the knowledge structures are across our subjects. It is remarkable to learn about how different the contexts and constraints are within which we all work. Skills-focus versus knowledge-focus, practical versus abstract, project-based versus cumulative knowledge-based, our subjects are certainly very different! I am delighted to share that in our Progress Over Time work so far we have been able to find some strategies and ideas that are useful across this great divide!

Next, we’ll take a look at what we’ve realised so far…

Examples of Desirable Difficulties: Retrieval Effect, Spacing Effect, Interleaving Effect

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mathqed · 8 years ago

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How has the introduction of department-wide interleaving affected students’ rates of learning?

Two years ago we took the decision to introduce department-wide interleaving (and spaced practice) through the introduction of Numeracy Ninjas, weekly skill quizzes (on a mixture of topics) and delayed end-of-unit testing. This was in response to our learning about Desirable Difficulties and the impact university laboratory studies had shown these can have on learning. For more information about Desirable Difficulties, read a summary here.

Previously, our department typically delivered blocked practice teaching from the start of year 7 until Xmas in year 11. We then switched to interleaved practice, giving students a weekly practice GCSE exam paper and feeding back on their performance in class, modeling solutions etc. Approximately 3 times per year we gave all students in KS4 a summative assessment which was a full previous GCSE exam paper and recorded their A*-G grade performance against the real grade boundaries for that paper. For the 2013-14 cohort we plotted their progress flight path across KS4 as shown below:

Cohort mean A*-G grade over time versus minimum expected progress on maths summative assessments

In those days, ‘minimum expected progress’ was the important currency and thus the vertical axis shows how many GCSE grades the mean average student needed to progress to achieve their minimum expected progress GCSE grade (remember 3LOP?!). The important point is that units on the vertical axis are in whole GCSE grades (A, B, C etc).

What struck us was how little retained-progress students made for 2.3 years on the course whilst they were studying using almost exclusively blocked practice methods, approximately 0.5 GCSE grades. We were teaching them a skill, they were reproducing it in their books, but they could not retain and apply it on a delayed assessment. Once they switched to interleaved practice their rate of progress greatly increased, approximately 1.4 GCSE grade over 0.7 years.

Significant differences in rates of progress observed during blocked and interleaved practice phases of the Maths GCSE course for the 2013-2014 cohort

The flight path highlighted how critical students fully engaging with the practice papers was in the final few months of the GCSE course. This was a time when they were being pulled in many different directions as they had to balance their intense and peaking workload across their GCSE subjects.

Naturally, the flight path led to the question being raised, “what if we brought the interleaving forward to earlier in the course? Would their rate of progress through years 9 and 10 increase so by the time they reached year 11 it was either more secure, and/or would lead to greater final attainment?” Relatively speaking, we thought the potential benefits significantly outweighed the consequences if it was ineffective and so introduced interleaving across the department’s practice through Numeracy Ninjas in year 7, MathsBox Weekly Skill Checks in years 8 to 11 and delayed (3 week after finish teaching) end-of-unit testing in all year groups. These 3 initiatives ensured that students would be getting interleaved practice right the way through their 5 years with us, rather than just in the final 7 months.

This year we sat all year groups on exactly the same assessments during each term which allowed us to plot a flight path across the 5 years under the assumption that each year group is of similar ability; this is fairly reasonable, looking at prior attainment. We used the Edexcel Practice Set papers which were created by combining questions from previous GCSE papers. The benefit of this was that they came with national performance data (ResultsPlus) for each question and so we were able to back-calculate A*-G grade boundaries for each paper and put them onto the 9-1 scale by using the grade 1-G, 4-C, 7-A equivalencies.

Now that we’ve been delivering interleaving at a department-wide level for 2 years, what impact has it made on students’ rates of progress?

Progress flight path after introduction of department-wide interleaving throughout full 5 year course

The first thing to note is that the two flight paths cannot be compared on the same axes. There are more 9-1 grades that A*-G grades and thus you can’t do a 121 mapping onto similar axes. Nonetheless, the differences in shape between the flight paths is striking. Since the introduction of interleaving the flight path has changed from a hockey-stick to almost perfectly linear.

Even though the ‘width’ of 9-1 grades are narrower than A*-G grades, the rate of progress in years 9 and 10, even with a conservative estimate is at least twice, if not more, than it was before.

Students are retaining what we are teaching them and able to apply it on assessments cumulatively through the course much better than previously. There is now much less pressure for students to make the rapid progress gains in the final few months of year 11.

Of course, what ecological validity brings, unavoidable confounding variables undermine… I certainly believe however that the changes to introducing interleaving throughout the course and department wide are the most siginificant changes, by far, that we have made between these data sets which could explain the differences in shapes (and gradients) of progress flight paths.

This adds further weight to recent studies in real-world maths classrooms of the learning benefits of interleaving and suggests that simple free and commercially available resources such and Numeracy Ninjas, MathsBox Weekly Skill Checks and Edexcel End-of-Unit Tests are enough to fascilitate these benefits.

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mathqed · 8 years ago

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Putting ‘mastery’ into practice: impact videos from the MathsHubs’ Secondary Mastery Specialists programme

In the school year 2016-17, all Maths Hubs participated in a national project to start exploring teaching for mastery approaches in secondary schools. Between two and four teachers from secondary schools in each Maths Hub took part in a programme, with three residentials over the course of the year, developmental work back at school, and ongoing communication and discussion in online communities.

In the 2017 summer term, we asked some of the teachers for some examples of what was changing at their schools as a result of their participation in the programme, both in their own classrooms, and in their work with colleagues in maths departments.

The programme is continuing into 2017-18.

Click here to see some great short videos about the impact the programme had on these maths teachers’ practice

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mathqed · 8 years ago

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An interview with Robert and Elizabeth Bjork

Craig Barton’s brilliant maths podcast has hosted some inspirational and influential education thought-leaders in its time including Dylan William, Bruno Reddy and Dan Meyer. His most recent episode takes it to a new level, having secured a 2-hour interview with Robert and Elizabeth Bjork! In a wide-ranging interview about learning, forgetting and memory, Craig and the Bjorks explore both the theory and what it all means for classroom practice.

A great in-depth piece for anyone interested in learning vs performance and desirable difficulties.

Listen here:

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mathqed · 8 years ago

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Spaced and interleaved retrieval practice using flashcards

I’ve never understood the ‘drill-and-kill versus teach-for-conceptual understanding’ argument. In that, I mean it’s not a dichotomy. Both reinforce each other. Students who try to problem solve with fluency but no conceptual understanding can’t apply their knowledge to new contexts. Students who try to problem solve with conceptual understanding but no fluency fall into working-memory overload in doing the basics and lose sight of, or can’t form, the strategy for solving the problem.

Clearly, students need both- conceptual understanding and fluency. How then do we teach to ensure students get an appropriate balance between each?

In this post, I want to focus on the fluency element. Regular retrieval practice following a spaced and interleaved schedule is a highly effective strategy for building retention and fluency. What teaching strategies promote this type of practice? One is flashcards…

I have been working on creating sets of topic-based flashcards for students to facilitate regular retrieval practice. Going forwards, I intend to give each student a set of flashcards at the start of each unit of study. I will advise them to do retrieval practice with these for 10 minutes each day at home whilst we study the unit. As their sets of flashcards build up over time they can regularly revisit previous sets to ensure they retain earlier learning. As time goes on they can shuffle the older sets to ensure they are getting interleaved retrieval practice. I may do occassional low-stakes quizzes in class to gamify the strategy and reward the students who put most into it. Perhaps a parental log could be filled in? Perhaps students will benefit from a schedule explaining which sets to practice each day?

Download this set of flashcards on the topic of negative numbers. Print double-sided.

It’s early-doors with this idea and I’ll keep you updated with how it progresses. I have high-hopes, particularly for students who typically can follow lessons in class but then struggle to retain their learning over time.

If it shows early promise we could certainly do a within-subjects cross-over study to demonstrate its impact.

Watch this space…

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mathqed · 8 years ago

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Preparing Y11 students for the new 9-1 GCSE exams- meet the WAFF!

Hi everyone! I write to share what we’re doing at Wyvern College this year in the final six months to prepare our Year 11s for the new 9-1 exams. This may or may not be of interest to you. As HOD at Wyvern, I have been very preoccupied with putting this preparation schedule together this year. I think it’s more important than ever that this absolutely right as the students go into the new 9-1 exams.

You have to rely on your preparation. You got to really be passionate and try to prepare more than anyone else, and put yourself in a position to succeed, and when the moment comes you got to enjoy, relax, breathe and rely on your preparation so that you can perform and not be anxious or filled with doubt.

-Steve Nash

Trial exams feedback

Firstly, our 11s sat the Edexcel Secure Mock during their Christmas Trial exams. This was a very useful exercise and reinforced the message to both students and their teachers that this new GCSE is a whole new world in many regards. Our teachers are busy marking the papers and entering the score that each student attained on each question into a in-house built question-level-analysis spreadsheet.

On trial results day in late January students are going to receive a personalised summary of their performance. This will show their performance on each question, the topics they relate to and importantly, advice on what they need to do to act on their weaknesses in the form of a clip number on MathsWatch that relates to that topic. We call this the ‘WAFF’, short for ‘Wyvern Assessment Feedback Form’. This is a tounge-in-cheek nod to PiXL who seem to want to give everything an acronym!

The WAFF for each student is generated in Excel by some macro code that I wrote. It’s all automated using the question-level-analysis data input by teachers. Here is a draft example of one of the personalised summaries the students will receive:

We had to estimate the grade boundaries as Edexcel did not release any when the Secure Mock paper was published. There is an Edexcel ResultsPlus service this year where you can submit your results and compare them to others nationally. I’m not sure if they are going to give indicative boundaries once they have a representative national sample, but if they do it will provide a good check on our own assumptions regarding grade boundaries.

The feedback sheets will be shared via hardcopy and email with students. Parents are also going to receive an email with their child’s feedback sheet attached. Other stakeholders such as tutors and mentors will be sent the sheets by request.

Students are expected to work their way through their amber and red topics, watching the relevant MathsWatch videos, making notes and then completing the excellent new interactive questions that have been added to the platform recently.

In addition to the feedback sheets, students and parents will also be emailed full annotated solutions to the mock papers and expected to make corrections on their own papers. I cannot share that here for obvious reasons…!

Practice Paper Revision Programme- Churchill Maths Papers

One of the most important components of our department’s historical success is the practice paper revision programme that we run between Xmas and the May exams each academic year with our Y11 students. I inherited this departmental approach from my talented and wise predecessor and it will certainly never change under my tenure!

Students complete a full GCSE practice paper for homework each week. These are not assessments, but ‘guided learning tools’ aimed at developing students’ ability to jump between topics and not only execute the right strategies, but also to select them. The papers are marked on a fast turnaround (typically over 2-3 days such as a weekend) and fed back to students in class. Key questions that the class struggled on are gone through with students making green pen corrections. As they work their way through paper-after-paper the scores pick up and we find that the average student typically improves by 1 and 1/3 grades in terms of formal exam performance during the 6 months they do the weekly papers. Many do much better than this.

After-school and lunchtime sessions are offered by teachers to support students in working on their papers.

The students who get the most from the programme are the ones who can learn independently, looking things up as necessary. This is a mantra that is repeated regularly to students. ‘No blanks’ is the message along with ‘it’s ok not to know it yet, but it’s a call to action to look it up rather than an excuse not to do it.’

To support students in knowing where to look for help on a question, this year we are replacing the front covers of our practice papers with bespoke ones that link every question to the MathsWatch video related to that topic. Here is an example:

After the papers are marked students will be expected to fill in the number of marks they scored on each question in the table on the cover sheet, thus making them aware of their strengths and weaknesses identified on that paper.

Personally, after marking each paper I do a quick email to all students and copy in all parents to give praise to the students who performed well and/or made excellent progress that week, report whether the class average has risen, report which students did not submit papers on time etc. I try to build a ‘we’re in this together as a team’ feeling using colloquial language. For me it’s important parents see the quality of feedback their child is receiving and also know what they can do to support.

Which papers are we using? For me the choice is an obvious one- I believe the Churchill Maths practice papers are by far the best product out there to prepare students for the new-style 9-1 papers.

The Churchill Maths papers are tremendous and certainly capture the increase level of challenge, expectations for problem-solving and additional content of the new spec. If anything, they go beyond, but that’s a good thing… ‘train them with a pack on their backs’ etc…

I really cannot talk highly enough of the Chruchill Papers which are very reasonably priced and Shaun Armstrong, their creator, is a very accommodating and caring experienced examiner, teacher and top man.

There are sample papers to download from the Churchill Maths site if you’d like to check them out. They also do practice papers in the style of the OCR and AQA papers, not just for Edexcel.

CorbettMaths Revision Postcards

Finally, I couldn’t end this post without mentioning the outstanding CorbettMaths Revision Postcards. All our Y11 students will be given the opportunity to purchase a set of these tremendous revision resources. The QR code link to video lessons and exam practice questions on the back of each postcard is a very neat touch.

Do feel free to share what you’re doing with your Y11s in the comments section. Also, feel free to get in touch if you’d like to chat about the WAFFs or our bespoke practice paper front covers.

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mathqed · 9 years ago

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Project Euler- get students coding to solve maths problems

Could your students code a simple program to solve this maths problem?

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

ProjectEuler.net is a website that proposes maths problems of varying difficulty which can be solved by developing simple computer programs. For example, here’s some Javascript code I wrote in https://repl.it to solve the first problem:

var n; var total = 0;

for (n=1; n <= 999; n++ ) { if(n%3===0) { total = total + n; } if(n%5===0) { total = total + n; } if(n%3 ===0 && n%5 ===0) { total = total – n; } }

The 550+ problems start relatively straight-forward, such as above and increase in difficulty as you move through them. You submit your solution to each question and it tells you that you are the nth person to solve it etc.

As coding is part of the National Curriculum these days, students should have the skills to access the problems in Project Euler.

A fun cross-curricular link? An extra-curricular maths club?

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mathqed · 9 years ago

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Help us build Numeracy Ninjas, the app…

We are looking for a developer to partner with to build iOS and Android apps of Numeracy Ninjas. With over 2500 schools now using Ninjas worldwide, we want to take the project to the next level, giving students the opportunity to improve their maths skills on their smart phones and tablets.

If you are a full-stack developer yourself, or if you know someone who is please take a look at our job information page.

Email enquiries to [email protected].

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mathqed · 9 years ago

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Biteable for making videos featuring animations

We want to set the right tone in the first few minutes with our year 7s with a bit of ‘visioneering’. We used Biteable to make the following video to welcome our newest students into our maths department. We used iMovie to add the voice over:

youtube

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mathqed · 9 years ago

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A week working at UCLA in the Bjork Learning and Forgetting Lab

Dear readers,

Over the summer I was privileged to visit UCLA in Los Angeles to work with a number of educational researchers looking into how cognitive science can be used to improve teaching. In a highly stimulating week I learned about both the historical and contemporary research findings relating to our thrusts and was also able to share some of the work we have done at Wyvern College with the academics.

I thought that many of you may be interested in hearing about what I learned during the visit and so have summarised it in this blog post in order that it might provide some ideas and inspiration for your own professional learning this coming year.

I am not an expert in the minutiae and detail of all the following content. At UCLA there are fulltime researchers spending years of their career looking into specific, narrow phenomena. In my visit I tried to capture the main concepts and ideas of many people’s research across the breadth of the department and will summarise them forthwith. To provide you with some direction for further reading if you are interested, I have hyperlinked papers and articles to this post.

I spent a week working in a research group of the UCLA Psychology Department called the Bjork Learning and Forgetting Lab. This has been led by heroes of mine, Professors Robert (Bob) and Elizabeth Bjork since they both got tenure 37 at UCLA 37 years ago. Bob is a Distinguished Research Professor and is considered one of the top two experts in the world on memory and cognition. He has been President of the American Psychological Society and is also a previous winner of that institution’s Distinguished Service to Psychological Science Award and also their Lifetime Achievement Award. Elizabeth is a Fellow of the Association for Psychological Science and is a previous winner of UCLA’s Distinguished Teaching Award.

Performance versus learning

The Bjorks’ research is focussed on understanding the way in which human memory works and the implications for learning and teachers’ classroom practice. I’ll summarise the main points, pulling out their key ideas and laying down some context before then sharing their most important findings in terms of implications for classroom practice. It is important that the learning-enhancing strategies later discussed are seen through the prism of the context that underlies them in order to prevent subsequent misinterpretation or people inferring they are ‘universal silver bullets’; they most certainly are not.

The Bjorks say that any definition of learning needs to include both an element of knowledge needing to be retained and accessible over time and also that the knowledge needs to be transferable to different contexts to that in which it was acquired. They talk of learning as ‘retention and transfer’.

In any observation you make of a classroom they argue that what the students are demonstrating at a particular point in time is performance, not necessarily learning. Their mantra is that performance is often a very poor proxy for learning. If a student gives you a correct answer during a lesson, can you infer from this whether they will be able to give a correct answer on this topic in six months’ time and when the question is worded in a different context? That correct answer today may in fact just be the result of the students’ mimicry of the teacher, the recency with which the student was given the information or other factors that can ‘prop-up’ performance. It is refreshing to know that Ofsted also now understand this point having seen the Bjorks’ and others’ research in this area, facilitated by people such as David Didau, which was a big influence in them deciding no longer grading individual lessons and becoming much more focussed on exam performance data.

However, rather than interpreting this notion as entirely futile, it does have some strong positive implications for the way in which we conduct summative assessment. Alan, my Headteacher speaks regularly about the need for college assessment to be accurate and reliable. If mimicry and recency can desync performance from learning, by ensuring summative assessments of learning are time-delayed and contextually-varied (to the way in which the knowledge was taught) we can be more confident in what students have retained and transferred (learned) from what we taught them. If students can apply the knowledge from today’s lesson on an assessment independently in a few weeks from now in a context that is different to the lesson then we can be reasonably confident we are measuring learning and not performance.

We experimented with this approach to assessment in maths last year by doing time-delayed end-of-unit assessments with Year 9 students. It was sobering to see the significant difference between what students could do in their exercise books during their lessons versus that they then couldn’t do on a delayed and contextually varied end-of-unit assessment. Formative assessment is an excellent in-lesson tool to manage the pace of learning, but is often near-useless for measuring retention and transfer– learning. Time-delayed, contextually-varied summative assessment certainly has its place if you want to accurately track learning…

In this video Bob discusses these ideas in more detail: dissociating learning from performance (GoCognitive, 2008a).

Memory– if you measure it you change it

A common misconception people have about memory is that it ‘operates like a video recorder’, i.e. information is somehow ‘recorded’ in its entirety and in the format in which it was input. The Bjorks’ work has shown this is a very poor analogy.

Memories typically become less accessible over time and the drop-off is significant. If you are to retain access to new knowledge over time periods of months and years you need to retrieve it a number of times after it was first learned. The gaps between retrievals need to be of the order of days and weeks to be effective. If this is done, by retrieving previously learned information, what the Bjorks call a retrieval event, you are in fact boosting its accessibility in future retrieval events. Perhaps a metaphor of a seed ben of plants and only regularly watering only the ones you want to grow would be a better analogy than that of a video recorder?

For more details, see this video: using our memory shapes our memory (GoCognitive, 2008c).

The New Theory of Disuse

The Bjorks are perhaps most well-known for their theory of memory called The New Theory of Disuse. Since its publication it has been rigorously tested with empirical studies and is widely accepted amongst cognitive scientists as capturing important behaviours. I will summarise The New Theory of Disuse as concisely as I can for your interest below. If you are interested, you can read the original article here (Bjork and Bjork, 1992) or a more detailed summary I have written previously here (Emeny, 2015). Bob also explains it in this video: the theory of disuse and the role of forgetting in human memory (GoCognitive, 2008b).

The theory says that everything committed to memory, each memory representation, has two strengths, a retrieval strength and a storage strength. The retrieval strength corresponds to how easy it is to access the memory representation; how easy it is for you to retrieve it into your working memory. Memories with high retrieval strength are highly accessible. Storage strength relates to how deeply you have learned the memory representation, in particular how linked and connected it is to other memory representations. Memories with high storage strength are deeply learned and conceptually well understood.

The theory specifically uses the word disuse in its title as the Bjorks’ research has shown that memories are never completely forgotten, you just loose access to them over time. In the context of their theory, they have shown that gains in storage strength are entirely cumulative; you never lose storage strength. So when you learn something, over time you will lose access to it (a loss of retrieval strength) but you won’t lose the depth of understanding for which you learned it.

Consequently, you can end up with memory representations that have high storage strength and low retrieval strength. For example, if I asked you to name everyone in your primary school class you would struggle. If instead I showed you a list of names and asked you to pick out the ones that were in your primary school class, you could probably get them all. This high storage strength memory is still retained by you, but its accessibility (retrieval strength) was low through disuse. The cued recall would be sufficient however to increase the retrieval strength.

There is a relatively more challenging part of the theory to understand which relates to the gains in retrieval and storage strength each time you retrieve something from your memory. Please do not worry if you do not fully follow this; the main messages to take from it are:

You need to retrieve learning a number of times with a spacing gap to build storage strength

Gains in storage strength (depth of understanding) are much greater if done so after you have had time to forget your previous learning (i.e. done from low retrieval strength). Conversely, if you try to get gains in conceptual understanding by retrieving something from the point when it is already ‘automatic’, the gains are minimal; you do it ‘without thinking’ and because you don’t think, you don’t link it to other things in your memory. As Bjork puts it, ‘teachers need to realise forgetting is the friend of learning’.

The implication of these ideas (which have been verified experimentally) is that if you want ‘deep learning’ (high storage strength), you need to build it over time through revisiting topics a number of times when you find them difficult, but not impossible, to retrieve from your memory. Put bluntly, sustained learning is not a rapid gain, but instead requires a number of revisits over time. Mid-term planning to revisit concepts a number of times is essential if you want your students’ learning to be sustained. Telling them once and expecting them to remember it is futile.

For completeness, I’ll describe how these observations relate to the theory. Please feel free to skim over the next two paragraphs if you are happy just to know the findings and are less concerned about their theoretical foundations.

The Bjorks showed that each time you retrieve a memory representation into your working memory you it gets a gain in both retrieval and storage strength. The growth in each of the strengths depends upon the current relative strengths. They found that gains in retrieval strength are positive correlated to the current storage strength. Put simply, the deeper you have learned something, the faster you gain access to it when you have lost access to it. ‘You never forget to ride a bike’, is the cliché. You lose access to it over time, but it comes back quickly if you spent a lot of your childhood riding your bike.

They then showed that gains in storage strength are negatively correlated with current retrieval strength. In simple terms, you get a greater gain in the depth of learning if you retrieve something after you have lost some access to it. Effortful retrievals are great for new learning and making connections to previous learning. Retrieving things that are already automatic see minimal gains in learning (storage strength).

The Bjorks realised that to get the greatest gains in learning (storage strength), teachers need to introduce techniques in their instruction that limit gains in retrieval strength. By keeping this low, the gains in storage strength, making connections and links, the gains in learning are maximised. They called these teaching techniques desirable difficulties. There has been considerable research effort put into understanding desirable difficulties in the ensuing years and they are still very much the focus of contemporary research in the Bjork Learning and Forgetting Lab and in other research institutions around the world.

Before I discuss desirable difficulties and share with you both the historical and contemporary findings, it is important to emphasise the desirable part of desirable difficulties. These techniques make learning seem more effortful and challenging, certainly at the superficial level. The gains are long-term and in fact lead to lower performance during the early stages of learning. Their message is certainly not ‘make learning more difficult’, the increased challenge and difficulty must be desirable ones– specifically ones that potentiate learning. The Bjorks have shown that students often prefer to take the easier path than engage in desirable techniques that make their learning seem more challenging; their intuition for what maximises their learning is often very wrong. Desirable difficulties seem counter-intuitive for many people, teachers and students alike.

Bob and Elizabeth Bjork in their lab at UCLA that has been conducting cognitive science research for 37 years.

Desirable difficulties

The following are the main desirable difficulties that have a strong research base and are currently or previously the focus of study in the Bjork Learning and Forgetting Lab.

Spacing

Building storage strength (learning) is a cumulative process that takes time. Each time your retrieve something you get a gain in its retrieval strength. However, the more times you retrieve it, the rate at which the retrieval strength falls (the speed at which you lose access to it) decreases. The more times you retrieve previous learning, the longer it will be retained for the future. The result of this is that spacing students’ practise activities leads to greater retention of their learning over time. If they are going to complete 20 questions on a topic their retention in the long run will be better if they do 10 today and 10 in a fortnight than if they do all 20 today.

The spacing effect has been experimentally verified many times and with a broad research base stretching back over the last century. Doug Rohrer, a Professor at the University of South Florida has published many papers on the spacing effect. He has summarised much of the main ideas and research base in a literature review, Student Instruction Should Be Distributed Over Long Time Periods, (Rohrer 2015).

In an impressive study, Spacing effects in learning: A temporal ridgeline of optimum retention, Cepeda et al (2008) explored the effect of varying both the time intervals between each time some learning was retrieved (the spacing interval) and between the last time some learning was retrieved and the test (the testing interval). They found there is an optimum spacing interval which, if you are aiming for long-term retention (a long test interval) is of the order of 3 weeks. In this study which involved over 1350 subjects (!) they were still only able to look at retrieving learning on two occasions. We know in practice that maximising storage strength is likely to take more than two retrievals and so current research in the lab is looking into whether fixed 3-week spacing intervals is optimum if more retrievals are done. Recent findings suggest that expanding spacing intervals are even more effective, particularly if informed by formative assessment (based on students’ response times) (Mettler, Massey and Kellman, 2016).

Whilst the retention benefits of spacing have been shown many times in the literature, these are mostly laboratory studies typically performed on undergraduate students tested on semantic, list-type information. Currently, there is little more than testimonial evidence for impact of spaced learning in secondary school classrooms. A number of colleagues in the maths department and myself have been experimenting with spaced learning the last couple of years and we believe we it can certainly be applied and benefit learning in secondary maths. I’m personally in the process of working with Bob to publish the impact study for Numeracy Ninjas which incorporated spacing principles and had a strong impact on students’ numeracy. In the coming year I’m going to do some collaboration studies with Bob and his team hopefully to demonstrate strategies for successfully applying spacing in secondary maths classrooms.

A number of maths colleagues have tried various approaches to spaced learning. I will include a variety here in case they are of interest to you and something you might like to adapt and make the subject of your own professional development work in the future:

Spaced starters. Beginning lessons with a small number of question on previously taught topics. Repeat the topics of the starter questions until students are getting them right over a period of days, then move onto different topics

Lagged homeworks. Make homework topics based on what was taught a few weeks ago

Staggered revision schedule. Giving students a revision schedule where each topic gets revisited at least 3 times by staggering the tasks. See an extract below of the staggered revision schedule many of our class of 2016 cohort followed:

In addition to teachers incorporating spaced learning ideas into their practice, Bob is also keen for students to understand these principles and to realise that by incorporating them into their own independent study that they can get significant learning gains without an increase in study time. At present, I am not aware of any good case studies of schools who have got this working in practice. This may be something you would like to look into?

Interleaving

Interleaving is the second main desirable difficulty for which there is a significant research base to support. In principle, interleaving is simply giving students questions on a variety of topics, rather than ‘blocked practise’ on single topics. Put simplistically:

Blocked practise Interleaved practise Study A

Practice AAAAAA

Study B

Practice BBBBBB

Study C

Practice CCCCCC

Study A

Study B

Study C

Practise ACBBCAABACBABCCABC

There are different competing theories about why interleaving leads to greater retention and context-transfer benefits over time. Some researchers believe it is because students have to learn to select the strategy in addition to executing the strategy. In blocked practise they effectively have already been given the strategy. Others believe interleaving somehow captures ‘higher-level processing and linking’ than blocked practise.

An important thing to understand about using interleaving in practice, which is typical of many of the desirable difficulties, is that students will find doing interleaved practise much more challenging and difficult than blocked practise. Their performance, quantity of work produced and accuracy in lessons will be lower. However, the gains in the longer term can be highly significant. In a 2007 paper, The shuffling of mathematics problems improves learning, Rohrer and Taylor (2007) showed that students who undertake interleaved practise in maths lessons perform lower in end-of-lesson tests, but that they outperform students who did blocked practise on a delayed test 1 week later. The effect was highly significant; the interleaved group performed with 3 times greater accuracy on the delayed test!

The mixers (interleaved group) performed lower in end-of-lesson assessments (practice performance), but out-performed the blockers group by 3:1 on a 1-week delayed test (test performance)

These findings, which have been replicated, raise profound questions about pitch and challenge in lessons, whether work sampling, lesson observation etc can accurately judge and quantify students’ learning or whether we should focus ourselves more on outcomes and progress over time, as Ofsted now do. Interleaving and many of the other desirable difficulties that lead to better outcomes in the long run will see lower ‘in-lesson performance’ in the short term as students work on activities which are ‘desirably more difficult’ than they would traditionally have worked on.

We incorporated spacing and interleaved principles into our Numeracy Ninjas programme and ran a year-long study of its impact with 470+ Year 7 and 8 students in 2015-16. We found that it increased the average students’ retention of mental numeracy strategies and important KS3 topics by at least an additional 70% when compared with a control cohort who did not have Numeracy Ninjas the previous year.

The testing effect

Testing can be used for many reasons. Traditionally we think of it in terms of assessing students’ level of attainment and tracking their progress. Around the turn of the millennium, Dylan William (1998), strongly advocated using assessment formatively, not just to assess learning that had happened, but to then use it to guide and design future instruction through Assessment For Learning strategies. The community of researchers associated with desirable difficulties have highlighted a different way in which we can use testing, one that is a learning event in itself.

Before we go any further, I should clarify that when I say ‘testing’, I really mean a ‘retrieval event’. In what follows think of testing within a ‘low-stakes’ format, perhaps as a ‘quiz’ rather than a ‘test’. A test is one way of getting students to retrieve previously learned information from their brain (rather than giving it to them); there are others.

The desirable difficulty community of researchers want teachers and students to understand that testing, i.e. low-stake quizzing, cannot only be used for assessment purposes (both summative and formative), but as a learning event itself. The process of students having to retrieve the information during the test is a highly-effective memory-modifier and enhances their learning.

In a study, Test-enhanced learning: Taking memory tests improves long-term retention, Roediger and Karpicke (2006) gave students prose passages from “The Sun” and “Sea Otters” to learn. However, they instructed students to follow different study schedules:

True to the typical desirable difficulties format, the students that undertook the STTT schedule performed lower in a test 5 mins after studying, but higher in a delayed 1-week test.

One of the most remarkable findings in this study was that the STTT schedule was even more effective than SSSS even though on no feedback was given on the tests during the learning period. In the 3 ‘tests’ (T) that the STTT group took during the learning period students answers were not marked.

Bob and Elizabeth talks about this study showing the significant benefits of students undertaking learning activities where they have to repeatedly retrieve previously learned information. To clarify, this isn’t talking about the misconception many people have that ‘if they discover it for themselves they’ll learn it better’; there is no research foundation for this. The point is that to build retention of previously learning, students will get better results if they undertake learning activities, such as low-stakes tests, which require them to retrieve the information themselves rather than simply re-reading it or passively receiving it from the teacher.

The message for teachers, as the Bjorks put it, ‘input less and get students outputting more’. Using frequent low-stakes quizzing of previously taught topics is very effective at building retention, certainly in comparison with techniques such as re-reading and copying notes. The old cliché of getting students to teach their parents/peers is another effective strategy that captures this message, but only if they generate the lesson themselves by retrieving previously learned information. In the ‘Brain, Book, Buddy, Boss’ strategy that we give students in maths to follow when they are stuck, it is very important they have engaged with the ‘Brain’ strategy first before turning to the others!

The Bjorks are also keen on students understanding the impact the testing effect should have on their own study habits. They believe most students engage in revision techniques that are not retrieval-based, such as highlighting, re-reading and re-copying notes. One effective strategy for students to know from the testing effect is that a very effective way to study is to generate their own quizzes based on previous lessons and to test themselves on these at regular intervals until their performance on them is high after a long delay. They should also ensure they can answer questions when they jump between quizzes (interleaving).

Alan talks often about getting students following ‘active learning strategies’ for their revision. Within this context, the desirable difficulties research suggests we these should include strategies incorporating high-levels of retrieval.

The pre-testing effect

Giving students a test or challenging activity on the topic of a lesson they have not yet been taught can enhance their learning of the content in that subsequent lesson. Even though students will perform very poorly on the pre-test, their learning in the lesson that follows can be greater than it would otherwise have been.

In one maths-based study, Designing for productive failure, Kapur and Bielaczyc (2012) showed that pre-testing students, a process they called ‘productive failure’, led to greater learning in the subsequent direct instruction lessons as evidenced by delayed test performance. Direct instruction was more effective if they were given a pre-test first. They demonstrated the effect across question types that ranged from recall to abstract problem solving and transfer to different contexts. Their findings suggest that fears that some teachers (myself included!) have about students embedding errors if you give them free-reign on a topic before some instruction may be counter-productive to students’ learning. It may be that the links and intuitions generated during the ‘productive failure’ pre-testing then make the subsequent learning from the subsequent direct instruction more effective.

I did not get a chance to speak with the Bjork researchers in depth about this desirable difficulty and so am not clear myself if there are particular caveats and limitations to this strategy or how best to implement it in a secondary school environment. Perhaps this might be something that you would like to look into in your own projects? Would giving students pre-reading to do before lessons enhance their learning?

For further reading on pre-testing studies see: Productive failure in learning the concept of variance (Kapur, 2012), The benefits of generating errors during learning (Potts and Shanks, 2014), Why does guessing incorrectly enhance, rather than impair, retention? (Yan et al, 2014) and The Pretesting Effect: Do Unsuccessful Retrieval Attempts Enhance Learning? (Richland, Kornell and KAO, 2009).

Checking out Santa Monica Pier (end of Route 66) with Bjork Lab researchers Dr Veronica Yan and Dr Courtney Clark. Both have done research work on the benefits of pre-testing and other desirable difficulties

Disfluency- fonts etc

During my visit I got the opportunity to meet with Danny Oppenheimer, Professor of Marking and Psychology, for a brief 45 discussion. Although his research interests are mainly outside the domain of desirable difficulties, he has contributed to this field via an interesting result around the concept of ‘disfluency’.

In a study, Fortune favors the bold (and italicized): Effects of disfluency on educational outcomes, Diemand-Yauman et al (2011) found that giving students learning resources which had fonts that were more difficult to read led to better performance on delayed tests on that information. The disfluency caused by an increased subjective experience of difficultly led to deeper processing of the information. The study demonstrated the effect first under laboratory conditions, but then also replicated it in a secondary school environment.

Before you start changing your worksheets to Curlz MT size 8 font, there have been a number of issues in replicating the original study findings and it would be fair to say how context-dependent the learning conditions need to be for this the effect to enhance learning. More research is needed to understand specific disfluency strategies that teachers can use to get students to process information presented to them more deeply.

For further reading on the concept of using disfluency to increase depth of processing see, Thinking, Fast and Slow (Kahnemann, 2011).

Other research

There was other research projects going on in the lab that show promise in enhancing learning, but at this stage are relatively impractical to put into practice in schools without developing software platforms and particular ICT infrastructure to help their delivery. For this reason, I will not go into depth about them here but am happy to discuss them with you in person if you have a particular interest. In particular, these areas relate to confidence-weighted multiple choice testing and perceptual learning. The paper, Perceptual Learning Modules in Mathematics: Enhancing Students’ Pattern Recognition, Structure Extraction, and Fluency, (Kellman, Massey and Son, 2010) gives you a flavour of the ideas involved in perceptual learning. The impact is quite impressive!

Identity-based motivation theory

One morning during my visit I got to meet Daphna Oyserman, Dean’s Professor of Education and Communication at the University of California. During a walk along the beautiful Manhattan Beach, Daphna explained to me her work into mindsets and how changes in context can change students’ mindsets and subsequent behaviours and outcomes.

Manhattan Beach, LA

Importantly, Daphna explained in detail why Dweck’s growth mindset work is an incomplete theory. Essentially, it’s a good idea, but flawed because it doesn’t incorporate human motivation factors. It is more of an observational theory than a theory of action. Yes, people with growth mindsets get better outcomes, but the theory doesn’t explain the motivations, strategies and so on that tell us why some people have growth mindsets and others have fixed mindsets. It is an observable symptom rather than a root cause and as such, teachers are not informed about what to do with it. Some colleagues and myself were frustrated with exact this point when we tried to do some work on growth mindsets last academic year.

Ultimately, Daphna argues that a mindset theory needs to start by considering human motivation and decision making that then moves onto giving tangible actions and strategies which influence mindset. Without starting at this point, any theory that focusses only on the observable outcomes of mindset, rather than the driving input factors isn’t likely to yield interventions and strategies that can be acted upon. You need to look under the bonnet to see what is wrong with a car…

Daphna has spent a considerable number of years deriving and then rigorously testing her own theory of mindset that starts from a motivational standpoint. Her Identity-Based Motivation theory, (Scott and Kosslyn, 2015) argues that people’s perception of their ‘self’, their identity strongly influences the way in which they react to both easy and difficult tasks and situations. Both their perception of their current identity and their future identity are important drivers in people’s mindsets and consequent actions. What kind of person they think they are now and what kind of person they think they will be in the future strongly governs their mindset. Their mindset is centred around their current and future perceived identities.

I have been thinking about this a lot anecdotally and the more I consider it, the more I think the concept of identity seems important in so many instances surrounding motivational decisions. The concept of branding is about buying a new identity for yourself. In high-performing and motivated sports and other professional teams people often talk about the ‘team spirit’ and people buying into something (an identity) bigger than themselves. The antithesis of this are the ‘lost souls’ as I sometimes think of them, the students without a plan, without a future identity to work towards. Even Dan Pink’s (2010) big three drivers of motivation, autonomy, mastery and purpose seem to be coherent and relevant when you view them through the lens of being components of a strong perceived identity. It seems to encompass my own intuitions and observations about real intrinsic motivation.

Daphna has shown that students’ identities are dynamically constructed, meaning they are highly dependent upon the environmental conditions and the ‘possible future identities’ students have in any given moment. Within the growth mindsets theory this manifested itself in the observation that students could be ‘growthy’ about some parts of their lives and ‘fixy’ about others. She has shown that by changing the perceived possible future identities the current ones that come to mind can be changed.

Next, her work has shown that in order to be motivated to take actions students need to see the relevance between taking the current action and it helping them work towards their future identity. The current task has to feel related to the long-term goal. There are a number of factors that Daphna has shown are important to achieve this:

The action needs to be one that is consistent with important social identities. For example, if their future identity is based on a career as a doctor, the action needs to be consistent with the ethos and values of being a doctor. The flip side of this observation is for students who have a low-aspiration future identity, their current actions will reflect this as they try to fit in with the social identity they are working towards.

Students need to feel that the actions are relevant behavioural strategies that are achievable. If they perceive the action you are asking them to take is not achievable they are unlikely to be motivated to take it.

Students need to feel that the actions will help them achieve their goals. They need to seem relevant. Daphna has even done some experimental manipulations (Lewis and Oyserman, 2015) to make students feel like their future goals are closer than they really are and she saw resulting increased student motivation.

If the above action readiness conditions are met, as Daphna calls them, she argues that students’ interpretation of perceived difficulty will be different. Students who believe the task is relevant and consistent with their future identity will perceive a difficult task as being important and engage with it. Conversely, students who believe the task is not relevant with their future identity will perceive a difficult task as being impossible, ‘not for people like me’ and not engage with it. The defining factor in whether they are motivated to take actions to engage in difficult tasks, which under Dweck’s theory we would call ‘growthy’, is down to whether they believe the actions are relevant in helping them work towards their perceived future identity.

Fortunately, Daphna is as much a pragmatist as much as a theorist. She has developed a complete programme called Pathways to Success (Oyserman, 2015) that can be run over 12 sessions in schools to put her Identity-Based Motivation theory into action to boost students’ academic outcomes. She is currently developing a website that includes all the resources and even videos of her delivering the sessions in US high schools herself. Although not formally published yet, she has very promising impact data from schools right across the socio-economic spectrum.

Potential implications for maths teaching

One way to view desirable difficulties are that they are specific high-impact strategies for incorporating challenge into lessons. This is productive challenge that leads to better retention and transfer of learning over time. These are challenge strategies that are in addition to pitching high from a conceptual standpoint which are effective at consolidating learning for the long term.

Whilst the benefits of desirable difficulties have been replicated many times in laboratory studies, knowledge of how to implement them and maximise their benefits in real classrooms is still relatively in its infancy. In your own research projects and professional development, you may like to explore some of the desirable difficulties ideas.

Desirable difficulties enhance learning in the long term by making it more challenging in the short term. In order to get students to engage with desirable difficulty strategies and embrace the increased challenge you might like to explore how this fits within the Identity-Based Motivation theory ideas. Do we need to explain desirable difficulties to students to get their ‘buy-in’? Should we talk about them wanting to become someone who ‘studies short and smart’, not ‘studies long and poorly’? Perhaps you would like to get involved in delivering the Pathways to Success programme?

I hope this has provided you with some ideas for your own professional development and that it has been of interest. On a personal note, I feel as though I learned so much from the Bjorks and their colleagues who were so welcoming and generous with their time. They are very interested in what teachers do to put their research into action. I plan to collaborate with them myself in the future once I’ve had time to think in more detail about what all this means for maths teaching.

Bibliography

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Cepeda, N.J., Vul, E., Rohrer, D., Wixted, J.T. and Pashler, H. (2008) ‘Spacing effects in learning: A temporal Ridgeline of optimal retention’, Psychological Science, 19(11), pp. 1095–1102. doi: 10.1111/j.1467-9280.2008.02209.x.

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Rohrer, D. and Taylor, K. (2007) ‘The shuffling of mathematics problems improves learning’, Instructional Science, 35(6), pp. 481–498. doi: 10.1007/s11251-007-9015-8.

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Yan, V.X., Yu, Y., Garcia, M.A. and Bjork, R.A. (2014) ‘Why does guessing incorrectly enhance, rather than impair, retention?’, Memory & Cognition, 42(8), pp. 1373–1383. doi: 10.3758/s13421-014-0454-6.

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