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30 x 13, oh dear me

Mathematical equations can seem quite daunting for children if they are yet to learn the concept or strategies (Singer, Ellerton & Cai, 2013). For example, look at the equation above, it may be straightforward for us as we’ve been learning mathematical concepts for years and have developed a range of strategies and knowledge for answering this concept (Swan, Pead, Doorman & Mooldijk, 2013). Yet, for most children, particularly younger children this problem can look complex as it requires the multiplication of larger numbers. I, personally disliked long multiplication because I could easily get confused with what numbers required multiplication and the step of adding the two numbers.  I believe one of the key reasons why I couldn’t grasp the concept of large number multiplication was because I was not stimulated enough to learn it. I felt defeated and unengaged each time I went through the learning process. Fortunately, I’ve come to learn that this is normal behaviour. Emotions are one of the major issues influencing cognitive learning, the result of mathematical interpretation comes from physiological arousal (McLeod, 1988; Tofade, Elsner & Haines, 2013). The point of teaching is to provide rich learning experiences that capture the attention of children (Tofade, Elsner & Haines, 2013). We want to provide experiences that stimulate the minds and activates mathematical thinking processes (Way, 2011).

Using questions throughout lessons is a teaching technique that assesses students’ knowledge, support their comprehension, and stimulate critical thinking (ACARA, n.d. ACMNA057; Tofade, Elsner & Haines, 2013, Way, 2011). Using appropriate and well-constructed questions leads to rich discussions, new insights, and supports the comprehension of content (ACARA, n.d., ACMNA076; Tofade, Elsner & Haines, 2013; Singer, Ellerton & Cai, 2013). Through inquiry-based experiences such as questioning, children can begin to rationalise the direction of the steps in order to achieve an answer (Singer, Ellerton & Cai, 2013). Reflect back to when you were younger, in order to learn you questioned experiences and ideas and when you received the answer you stored that into your memory for later reference. In reference to the equation above the following questions are used to stimulate children’s thinking process:

Closed questions:

Which is the larger number? (ACARA, n.d., ACMNA052, ACMNA072, Does it make a difference if we calculate the higher number first? (ACARA, n.d., ACMNA060) Can we break this down? (ACARA, n.d., ACMNA057, ACMNA074 Can we make the numbers smaller? (ACARA, n.d., ACMNA073)

Open-ended questions?

How else could we display this so we can count it? (ACARA, n.d., ACMNA081) How are these numbers different? What strategies do we use for normal multiplication? (ACARA, n.d., ACMNA074, ACMNA075) What else could we do rather than draw it out?

References 

Australian Curriculum, Assessment and Reporting Authority. (n.d.) Australian Curriculum: Mathematics, Year 3 to Year 5. Retrieved from: https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/?year=11754&year=11755&year=11756&strand=Number+and+Algebra&capability=ignore&capability=Literacy&capability=Numeracy&capability=Information+and+Communication+Technology+%28ICT%29+Capability&capability=Critical+and+Creative+Thinking&capability=Personal+and+Social+Capability&capability=Ethical+Understanding&capability=Intercultural+Understanding&priority=ignore&priority=Aboriginal+and+Torres+Strait+Islander+Histories+and+Cultures&priority=Asia+and+Australia%E2%80%99s+Engagement+with+Asia&priority=Sustainability&elaborations=true&elaborations=false&scotterms=false&isFirstPageLoad=false

Fessesha, E. & Pyle, A. (2016). Conceptualizing play-based learning from the kindergarten teacher’s perspective. International Journal of Early Years Education. Retrieved from: DOI: 10.1080/09669760.2016.1174105

McLeod, D. B.. (1988). Affective Issues in Mathematical Problem Solving: Some Theoretical Considerations. Journal for Research in Mathematics Education, 19(2), 134–141.

Singer, F.M., Ellerton, N. & Cai, J. (2013). Problem-posing research in mathematics education: new questions and directions. Educational Studies in Mathematics, 83(1). https://doi.org/10.1007/s10649-013-9478-2

Swan, M., Pead, D., Doorman, M., Mooldijk, A. (2013). Designing and using professional development resources for inquiry-based learning. ZDM Mathematics Education, 45(945). https://doi.org/10.1007/s11858-013-0520-8

Tofade, T., Elsner, J., & Haines, S. T. (2013). Best practice strategies for effective use of questions as a teaching tool. American journal of pharmaceutical education, 77(7), 155. doi:10.5688/ajpe777155

Way, J. (2011). Using questioning to stimulate mathematical thinking. NRICH enriching mathematics. Retrieved from: https://nrich.maths.org/2473

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Learning geometry through real life connections

Through the study of geometry and spatial awareness, children learn location, structure, shape, and transformation (Horne, 2003; Newcomb & Stieff, 2012). Children use this knowledge make sense of the geometry components including features and properties of shapes and objects (ACARA, n.d.). The study of geometry and spatial thinking is highly valuable to children’s mathematical learning as it can be applied in other areas (Horne, 2003).

Geometry and spatial awareness are one of the mathematical areas that can be utilised and benefit from visual imagery (Spelke, Ah Lee & Izard, 2010). During a practical experience last year, I observed year three children engaging in a geometry lesson, the properties of shape. The teacher has used the smartboard to show a 3D image of shapes. She used an app that allowed her to use her cursor to move the shape into different angles. She then extended the activity by allowing children to use the cursor themselves and take notes of the different orientation, turns, and properties of the shapes. I really enjoyed viewing this experience as I witness the classroom become extremely engaged, they were able to comprehend the content through the support of technological media.

For my stimulus in this module, I wanted to use the context of visual imagery in relation to geometry and mapping. I have decided to use a google maps image of a school, in the context of this module I have used a random google image school, but for the real-life experience, I would use the actual school of attendance. I used this image because it allows children to conceptualise an understanding of length, shape, size, scales, true size and comparison (MacDonald & Lowrie, 2011; Spelke, Ah Lee & Izard, 2010). Throughout this experience, I would use open-ended questions that allowed children to make sense of the image in relation to geometry.

Note. This experience is designed for a year two or year three classroom.

What does this image tell us?

This allows children to make connections to their everyday environment by locating key features relating to geometric shapes. Children will build awareness towards angles and measurement within their everyday environment (ACMMG064), identify and locate symmetry within the image (ACMMG066) and locate shapes, structures, and measurement (MacDonald & Lowrie, 2011).

What can we compare this scale too?

This will allow children to consider ratio in terms of geometry reasoning. Using a physical item for comparison, place the item next to the image and ask this question (Copley, 2010). It allows children to compare the size, is this realistic? (ACARA, n.d., ACMMG064). How do they know it’s not true to size? What can we do to compare? Then extend the learning by inviting children to think what we use to measure this large area surface (ACARA, n.d., ACMNG061)

If we are guiding a new student around the school, how can we direct them to the library (or any given location)?

Children will have the opportunity to observe for location, positions, and pathways (ACARA, n.d., ACMMG05). This question will allow children to make comparisons of measurement with their peers. It will allow a rich discussion of transitivity and conservation (MacDonald & Lowrie, 2011)

References

Australian Curriculum, Assessment, and Reporting Authority. (n.d.) Australian Curriculum: Mathematics.

Copley, J .V. (2010). Geometry and spatial sense in the early childhood curriculum. In J. V. Copley (Ed.), The young child and mathematics (2nd ed.), (pp. 99-117). Reston, VA: National Council of Teachers of Mathematics

Horne, M. (2003). Properties of shape. Australian Primary Mathematics Classroom, 8(2), 8. http://ezproxy.acu.edu.au/login?url=http://search.informit.com.au/documentSummary;dn=408130323462644;res=IELHSS

MacDonald, A., & Lowrie, T. (2011). Developing measurement concepts within context: Children’s representations of length. Mathematics Education Research Journal, 23(1), 27-42. http://ezproxy.acu.edu.au/login?url=http://dx.doi.org/10.1007/s13394-011-0002-7

Spelke, E., Ah Lee, S., & Izard, V. (2010). Beyond core knowledge: Natural geometry. Cognitive Science, 34(5), 863.

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A peer within my course included the role of technology in learning, particularly for number lines. This intrigued me enough to make me research for others.  I came across an internet source that incorporates number lines and number patterns. The source is called ‘Hoppity, hop! Help Hopper hop Whole Numbers on the number grid’. This interactive allows children to examine the location of the numbers upon the number line and identify how the pattern can represent an answer (Bobis, 2007). The source also. Allows children to view the frog leap upon the number line positions, allowing children to visually see the patterns and number sets. Please, take a look!

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Number Lines & Mental Computation

I found the research completed by Bobis (2007) to be so intriguing. I was almost memorised to reflect upon where I had fallen short within my years of learning maths. A key paragraph that captured my attention the most:

"The worry with an early emphasis on standard algorithms is that students will shift their focus to executing convenient procedures rather than on understanding the mathematics." - Bobis (2007)

Thinking back to when I would be completing maths tasks, I felt so lost and confused which resulted in me writing and using an algorithm, even if wasn't related to that mathematical area. This piece of computational knowledge would have served as a strength throughout the development of my mathematical knowledge (Grover & Pea, 2013; Bobis, 2007). Fortunately, these reflections of my own experiences allow me to realise where I struggled and what key information I missed that lead me to struggle. It allows me to consider how am I providing the right information in the most engaging and mind stimulating way.

Number Line Strategies to Support Mental Computation:

The introduction of strategies such as number lines promotes children's awareness of multiple relationships among numbers, understanding of mathematical procedures, the examination of assumptions and opportunity for visual references for mental computations (Kaminski, 2002; Cheeseman, 2010). Number line strategies include:

Patterns Placement:

Research explains that the development of number sense supports the ability to build upon the mental computation of children (Yadav, Mayfield, Zhou, Hambrusch & Korb, 2014) Through pattern placement, children learn number sense by adding and subtracting numbers through numerical value (Bobis, 2007).

Empty Number Lines:

The procedure of an empty number lines allows for children to access and use conceptual thinking processes, such as logical reasoning, decomposition, a recreation of patterns and abstract thinking (Berry & Csizmadia, 2016). By using an empty number line, children are able to map out visually techniques to build upon sophisticated strategic thinking by using different methods of sequencing by number groups (Cheeseman, 2010).

Number Line Addition and Subtraction:

Number lines can be used to exercise children left-to-right spatial-numerical representations of numbers (Aulet & Lourenco, 2018; Kaminski, 2002). Number lines allow children to map out numbers and the spaces between them when adding or subtracting (Aulet & Lourenco, 2018). Children are able to make a relationship between algorithms and spatial organisation (Aulet & Lourenco, 2018; Kaminski, 2002).

References:

Aulet, L., & Lourenco, S. (2018). The Developing Mental Number Line: Does Its Directionality Relate to 5- to 7-Year-Old Children's Mathematical Abilities? Frontiers in Psychology, 9, 1142.

Bobis, J. (2006). From here to there: The path to computational fluency with multi-digit multiplication. Australian Primary Mathematics Classroom, 12(4), 22- 27.  http://ezproxy.acu.edu.au/login?url=http://go.galegroup.com/ps/i.do?&id=GALE|A170817120&v=2.1&u=acuni&it=r&p=AONE&sw=w&authCount=1

Cheeseman, J. (2010). Empty number lines: How can we help children to use them? In J. Mousley, L. Bragg, & C. Campbell (Eds.), Mathematics-Celebrating achievement 100 (Proceedings of the 42nd annual conference of the Mathematical Association of Victoria pp. 49-58) Melbourne, Vic: MAV. http://ezproxy.acu.edu.au/login?url=http://search.informit.com.au/documentSummary;dn=998640761921722;res=IELHSS

Grover, S., & Pea, R. (2013). Computational Thinking in K-12: A Review of the State of the Field. Educational Researcher, 42(1), 38-43.

Kaminski, E. (2002). Promoting mathematical understanding: Number sense in action. Mathematics Education Research Journal, 14(2), 133-149.

Yadav, A., Mayfield, C., Zhou, N., Hambrusch, S., & Korb, J. T. (2014). Computational Thinking in Elementary and Secondary Teacher Education. ACM Transactions on Computing Education, 14(1), 1-16.

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Child’s Play

In the child-initiated dramatic play of Jabil, Elle, and Joey, they show to be using discussion and analysing to comprehend mathematical concepts (Touhill, 2013). The mathematical concepts which they are trying to understand are division, addition, subtraction and shape, and size. To further define in line with the Mathematical for Kindergarten, these children are investigating the concepts of subtilising small collections (ACARA, n.d., ACMNA003), sorting and describing shapes (Queensland Studies Authority, 2006; ACARA, n.d., ACMMG010), data representation and interpretation (ACARA, n.d., ACMSP011). The Australian Curriculum suggests that as Jabil, Elle, and Joey are in Kindergarten and they should be learning to understand the concepts of quantities and numerals using problem-solving skills using materials and using the discussion to identify a reasonable answer (ACARA, n.d.). 

Through my recent teaching experiences in both an early childhood and primary setting, I've come to believe that children learn best through inquiry learning and play-based experiences. I strongly believe that it allows children to hypothesise, experiment, question and conclude an understanding. This mindset is supported through the consideration of what kind of learner, I am. I am not a theoretical person but rather a practical learner. I need to observe and use my senses to make a theory in which I can put into practice. This learning strategy is highly common for many people, especially children. Our attention spans can be easily distracted and bored if we are not engaged, this is also common for children with Attention Deficit Disorder (ADD). What I believe and what is supported by theory is that, teaching of the curriculum should be a sum of engaging, interest-based and rich content activities (Zeki, 2017; Ginsberg & Amit, 2008). Therefore, my teaching approaches with Jabil, Elle and Joey would be: 

• A deep discussion of the possible outcomes, allowing children to use counting skills and subtraction strategies 

• Experimenting by using a practical use; playdoh (one for each child) • Allowing children to create and cut shapes then discussing why they chose that particular shape (ACARA, n.d., ACMMG010)

 • Discuss with children how many times that shape could be cut inside of the pizza to make an equal amount for all three people (ACARA, n.d., ACMMG010, ACMSP011) 

• Discussing with the group to find out what shape works best and how many pieces they could provide each person 

• Capturing the thinking process and outcomes through photographs that can be displayed through the classroom 

• Then coming together for a final discussion to draw up our conclusion and physical drawings to display our new learning

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Interesting read in light of our previous module ‘The Growth Points of Subtraction’. What could be the reason children feel this way? Sense of failure when reaching challenges? That was something I felt growing up. I gave up before I started. 

Is Math the Most Hated Subject?

A recent survey of over 20,000 U.S. 9th graders found that the academic subject in which the highest percentage of students reported as being their least favorite was indeed mathematics.* Yet, behind gym, mathematics also had the highest percentage of students who indicated that it was their most favorite.

So maybe more appropriately, math is the most polarizing subject. Why do you think this is?

Least Favorite School Subject:

Most Favorite School Subject:

*Ingels, S.J., Pratt, D.J. Herget, D.R., Dever, J.A., Fritch, L.B., Ottem, R., Rogers, J.E.,Kitmitto, S., and Leinwand, S. (NCES 2014-361). High School Longitudinal Study of 2009 (HSLS:09) Base Year to First Follow-Up Data File Documentation. National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC.

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The Growth Points of Subtraction

The domain of subtraction features several growth points that are required to extend on children’s learning (Gervasoni, 2011). These available growth points allow educators to identify children’s skills and especially children who may be vulnerable in particular areas. The Early Numeracy Interview (ENI) was a strategy used to identify children’s vulnerability within mathematical domains. Below, I have provided a sample of growth points required for subtraction as stated by the Victorian Government Education and Training and the research of Gervasoni (2011): 

1. Early stages: Unable to combine and count collections 

2. Counting all through physical representation – using perceptual strategies to subtract with numbers from ten 

3. Counting on from one number to find a total of two collections 

4. Using appropriate strategies to count down or count back 

5. Using new (basic) strategies: doubles, adding 10, ten facts

6. Derived strategies: near doubles, build to next ten, family facts, intuitive – more sophisticated strategies and using them to solve larger number problems. 

7. Extending and applying subtraction strategies using basic, derived and intuitive strategies – Solving mentally while using appropriate strategies and understanding key concepts.

Personally, I struggled with Mathematics. I struggled to grasp basic concepts, possibly because I was unable to identify what I did not understand. Then as I continued throughout school, because I never addressed those issues and it became harder and harder to acquire new knowledge. Reflecting upon the growth points presented, I wish my teachers had looked upon this because as I read through, I can already identify what I struggled with. For example, until late Year 4, I still used counting based strategies when calculating addition or subtraction. In the Early Numeracy Interview (ENI) created by Gervasoni (2011) up to 30% of Grade 4 children were still using counting based strategies. Research shows, that this could possibly be related to children’s limitation of number sense or a short knowledge on the understanding of that mathematical procedure (Powell & Fuchs, 2012). It’s sad to say, but my learning could have been salvaged if my teachers had tried implementing customised teaching strategies according to my limitation. This realisation encouraged me to research appropriate strategies like using reasoning and calculating, teaching children the procedural knowledge rather than understanding just the concept of subtraction. It allows children to understand the method required to produce the answer. In reflection, I want to be a teacher that is aware of children’s struggles so I can research and provide the appropriate strategies.

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When I introduce a new topic and students groan

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What do you need in a good maths lesson? (Part Two)

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What do you need in a good maths lesson? (Part One)

Please Note: I’ve copied and pasted my own work from MAC word document, so Tumblr is displaying my writing like a journal article. Quite stylish, if you think about it. 

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The value of assessment

Throughout school, I have experienced some sort of assessment, whether it be a test, an assignment or even feedback. I understood the idea of assessment as a form of gaining knowledge on what children are learning, but through my current studies, I have come to understand that is more of a reflection of what knowledge has been acquired (Clark, Mitchell & Roche, 2005). Assessments are highly vital and important in supporting children’s mathematical understanding. It allows educators to gain awareness of current development and knowledge children already acquire (Tan, 2013; Clark, Mitchell & Roche, 2005). Reggio Emilia, an educational philosopher, approached documentation as a sophisticated procedure required to explain a child’s response to learning environments (McNally & Slutsky, 2016). Supporting literature by Tan (2013) identified that encouraging feedback practices enabled children to improve their work and also provided clarity for standards required for previous and desired performance. Through an informative analysis of assessment, the next step required is in-placing new appropriate goals for children. The Australian Curriculum Assessment and Certification believe that assessment is a ‘purposeful and systematic collection of information about children’s learning’ (ACARA, 2017).  ACARA states that assessment must be used to continuously improve the educational practices, ensuring common achievement standards and using assessment for summative purposes (ACARA, 2012, as cited by Klenowski, 2012). In absorbing this new knowledge, I have taken into action implementing assessments for when I’ve completed learning activities. In my current job, I write up an evaluation sheet on what each child learnt and where they need further coaching. I then plan my next activity which will be appropriate for their current learning. With older children, I will often discuss and ask their opinions on whether they have been able to gain knowledge. I ask them, “What have you learnt that you may not have have known before? Did you find this activity enjoyable?”, I then take the time to reflect on their answers and then take notes of what I observed that could be better. For example, I decided to introduce children to a mathematical worksheet, appropriate for kindergarten and year one. Children had to colour the image according to the shape, directed in the key above. I then assessed child’s ability to follow the key and colour the items appropriately, I came to identify some children don’t care and are happily creating their own rules. Note Taken. I am now appreciative of assessment in my teaching, I want to constantly be aware of children’s progressions and their level of learning. I want to ensure that they receive the utmost appropriate and exciting activities so they can continue a successful mathematical development.

References

Australian Curriculum, Assessment and Reporting Authority. (2017). Mathematics. Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/

Clark, D., Mitchell, A., & Roche, A. (2005).  Student one-to-one assessment interviews in mathematics: A powerful tool for teachers. MAV Annual Conference. Retrieved from: https://www.mav.vic.edu.au/files/conferences/2005/doug-clarke.pdf

Klenowski, Valentina (2012) The Australian curriculum : implications for teaching and assessment. Primary English Teaching Association Australia, 186, pp. 1-8.

McNally, S. A. & Slutsky, R. (2016) Key elements of the Reggio Emilia approach and how they are interconnected to create the highly regarded system of early childhood education. Early Child Development and Care, 2(193). Retrived from: https://doi.org/10.1080/03004430.2016.1197920

Tan, K. (2013). A Framework for Assessment for Learning: Implications for Feedback Practices within and beyond the Gap. ISRN Education. Retrieved from: https://doi.org/10.1155/2013/640609.

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Technology support

Reminiscing back to when I was learning maths, I struggled with applying the correct equations to the appropriate questions and as a result, it affected my development in mathematics. I remember when I found it difficult to understand I would become frustrated and unmotivated. McLeod (1998) identified that many students can face the same frustrations and due to their emotions they often resort to the easiest equations rather than the correct one. Due to my learning and experiences, I’ve come to recognise the importance of mental-emotional management in the classroom. Sutton, Mudrey-Camino & Knight (2009) suggest that teachers should have a relationship with children which builds on communication and confidence, which is valuable for supporting emotional regulation. Wright (2017) also suggested that frustrations can be limited through significantly engaging and relevant curriculum based activities. I understand that I hold a high responsibility of providing the best learning experiences while using optimising a variety of resources. Previously, I had minimal knowledge of the role technology and media in the classroom. During my childhood, the concept of technology-based lesson wasn’t introduced until I was in high school. It is now common that the modern primary school child is brought up and surrounded by the world of technology. I’ve come to witness this at my current job, supervising at an after school care, the frequent amount of children who bring and use their iPads at school. I’m now considering the idea of using technology to support emotional regulation. Children show great responses to technology and connecting ICT to mathematical curriculum shows strong success in content absorption (Back, 2013). This is definitely be something I would like to further explore in my future role as an educator. I’ve also noticed at my work that children with autism often enjoy learning through iPad media, they tend to pay attention to the visuals in front of them and the interactive technology allows them to absorb educational information (Allen, 2016). Allen (2016) shows theoretical support for my theory, in which stating that apps are able to reach characterised mediums which are supporting their needs and help cater to their ability levels. I have now come to appreciate the role of technology in my classroom, through a positive aspect rather than pessimistic. I am looking to further introduced more strategic and appropriate educational apps when teaching children with disabilities.

References

Allen, M. L., Hartley, C., & Cain, K. (2016). iPads and the Use of “Apps” by Children with Autism Spectrum Disorder: Do They Promote Learning? Frontiers in Psychology, 7(13). Retrieved from: http://doi.org/10.3389/fpsyg.2016.01305

Sutton, R. E., Mudrey-Camino, R. & C. Knight (2009). Teachers' Emotion Regulation and Classroom Management. Theory into Practice, 2(48), 130-137. Retrieved from: https://doi.org/10.1080/00405840902776418

Back, J. (2013). Manipulatives in the Primary Classroom. NRICH Enriching Mathematics. Retrieved from: https://nrich.maths.org/10461

Wright, P. (2017) Critical relationships between teachers and learners of school mathematics. Pedagogy, Culture & Society, 4(25), 515-530. Retrieved from: https://doi.org/10.1080/14681366.2017.1285345

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Visual Learning in Maths

I want you to think back to your memories in school. You may not have realised how abundant your classroom was in unsuspecting resources of measurement and space. I didn’t realise either, but now I’m reflecting and I can remember the large play mats with centre-metres values across it, weight scales, rulers and large tubs where we would fill up blocks and even the blocks themselves. Children are active learners, constantly acquiring information through playing and exploring resources, even items that are scaffolded by their teachers (Back, 2013). McDonough, Cheeseman & Ferguson (2013) noted that children are able to reflect on the different attributes of shape through creative visual images. I’ve attempted to encourage this teaching of children through visual learning in my work, by asking children to explore shapes and geometry through colouring worksheet activities (provided to kindergartens and pre-schoolers). As children retain information better when they are relatable, they also absorb this information through colour and vibrant learning (Vlach & Sandhofer, 2012). The Early Years Learning Framework has a strong focus on visual learning, children are encouraged to learn and become through an active involvement in art. The EYLF suggests that the curriculum learning should focus on learning through appropriately design art environments (DEEWR, 2009). The Australian Curriculum focuses on the first few years of schooling to be high in visual learning. Examples of visual learning are found in Foundational years in assisting mathematics learning of words, numbers, and symbols (ACARA, 2017). I can support this visual learning through open question discussion. Questions will allow me to draw attention to mathematical concepts within images and support chidrens understanding of the versatility of maths (McDonough, et al., 2013).

References:

Australian Curriculum, Assessment and Reporting Authority. (2017). Mathematics. Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/

Australian Government Department of Education, Employment and Workplace Relations (2009) Early Years Learning Framework: Being, Becoming and Belonging. Commonwealth of Australia: ACT.

McDonough, A. (2003). What does effective teaching of measurement look like? ERNP experience. Prime Number, 18(4), 4-8.

McDonough, A., Cheeseman, J., Ferguson, S. (2013). Young children’s emerging understandings of measurement of mass. Australasian Journal of Early Childhood, 38(4), 13-20. 

Vlach, H., A., & Sandhofer, C., M. (2012). Fast Mapping Across Time: Memory Processes Support Children’s Retention of Learned Words. Frontiers in Psychology, 3(46). Retrieved from: http://doi.org/10.3389/fpsyg.2012.00046

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Old but Gold!

I remember using these clocks in mathematical lessons during year three and four! Could these be used in year one or year two? Why?

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Mental about Learning

Through my previous experiences of completing psychology subjects prior to my masters, I’ve learnt that children show better memory retention when concepts, labels or topics are relatable (Vlach & Sandhofer, 2012). I’ve also come to learn that children will also use this memory retention invaluable computational strategies when solving mathematical problems (Bobis, 2007). Reading through an article by Bobis (2007), I noticed she stated that educators often assumed that fluency in written and mental computation require separate instruction, I will admit, I was one of them. When children are faced with mathematical equations under high cognitive demand they can often become frustrated and bored, resulting in the easiest, but may not be correct, strategy (Bobis, 2007). Thinking back to when I was younger, I see myself doing exactly that. I became less intrigued therefore less motivated and I would give in to do the simplest equation, if the answer was wrong I wouldn’t revert to using different strategies I would just call quits. From my past experiences, I can understand that Children’s minds are wondrous and require attention and excitement therefore as a teacher, I will face the struggle of trying to ensure that ALL children are engaged and learning.   The new knowledge that I have acquired is that children can often solve mathematics problems by inventing their own algorithms (Bobis, 2007). Referring to when I was younger, I recall myself doing that when I struggled with certain mathematical questions. As a teenager, I would continue that strategy even if it was wrong. It’s possible if my teachers had realised my method, they could have stirred me towards algorithms that would work for me. In learning and reflecting upon this, I’ve come to the mindset that I would like to constantly be aware of the algorithms children are making and how I can guide or scaffold their way of thinking into a quicker or correct technique.

References: Vlach, H., A., & Sandhofer, C., M. (2012). Fast Mapping Across Time: Memory Processes Support Children’s Retention of Learned Words. Frontiers in Psychology, 3(46). Retrieved from: http://doi.org/10.3389/fpsyg.2012.00046 Bobis, J. (2006). From here to there: The path to computational fluency with multi-digit multiplication. Australian Primary Mathematics Classroom, 12(4), 22- 27.  Retrieved from: http://ezproxy.acu.edu.au/login?url=http://go.galegroup.com/ps/i.do?&id=GALE|A170817120&v=2.1&u=acuni&it=r&p=AONE&sw=w&authCount=1

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Appreciating Teaching Strategies

Prior to reading through the literature of Module four, I had minimal knowledge on what possible teaching strategies I would be implementing. I had assumed that it would be already structured, an A to B plan that was enforced by the teaching curriculum or my supporting teachers. I’ve now come to learn the greater power I have on the influence of programs and activities that I can implement in my classroom. In a reflection of my goal as a teacher, I have now come to take into account the importance of knowing what activities will best support learning while considering children’s abilities and prior knowledge (Swinkles, 2016). Before reading the provided literature, I had never really taken into account the amount of mathematical knowledge that children consume over the first few years of their early stages. I was aware of the simple activities of counting and shapes but never realised that daily routines could contain a variety of early mathematics skills (Mulligan & Mitchelmore, 2009). I have also been assisted in this understanding by starting in an early child care centre which has helped me to visualise and observe what theories I am learning. Children can begin to learn the concept of measurement and space with the simple act of filling up a cup or even emptying and refilling baskets of blocks (Mulligan & Mitchelmore, 2009). From the theoretical work of Trawick-Smith et al. (2017), I have now come to respect and support the role of active social learning through block play. I’ve come to understand the role of block play, a simple activity that doesn’t require teacher support but can be further scaffolded, by introducing appropriate resources. I can scaffold this learning by introducing children to problem solving and experimentation situations such as weight scales for measurement and rulers for measurement and also creating questions like asking children to make an estimation of the number of blocks required to create a small tower the height of a classmate.

In reference to the Early Years Learning Framework, I would like to plan activities for my future classroom that encourage self-learning and social learning experiences (DEEWR, 2009). My goal is to ensure that children gain knowledge through their own experimentation and experiences involved in active and social learning (Trawick-Smith, Swaminathan, Baton, Danieluk, Marsh & Szarwacki, 2017; Samuelsson & Carlsson, 2008).

Do you have any classroom activities suggestion that will assist in mathematical learning?

What mathematical resources could I implement in my new position, caring for young babies?

References:

Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2). Retrieved: https://link-springer-com.ezproxy2.acu.edu.au/content/pdf/10.1007%2FBF03217544.pdf

Samuelsson, I., P. & Carlsson, M., A. (2008). The Playing Learning Child: Towards a pedagogy of early childhood. Scandinavian Journal of Education Research, 52(6). Retrieved from: https://doi.org/10.1080/00313830802497265

Swinkles, K. (2016). Mathematically rich interactions in early childhood. The Spoke. Retrieved from: http://thespoke.earlychildhoodaustralia.org.au/mathematically-rich-interactions-early-childhood/

Trawick-Smith, J., Swaminathan, S., Baton, B., Danieluk, C., Marsh, S., & Szarwacki, M. (2017). Block play and mathematics learning in preschool: The effects of building complexity, peer and teacher interactions in the block area, and replica play materials. Journal of Early Childhood Research, 15(4), 433-448.