calcyoulaterteach

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Final Make

Miller’s Meaningful Math

For my final make, I decided to gather all of the resources I had as well as search for new resources that can be used to make mathematics meaningful.  The site is intended for both teachers and students.  There are several sections to the site and I would like to add a couple more as well as expand upon the resources that I have gathered thus far. The sections include Art, Formulas, Motion, Nature, TV and Movies, Careers in Mathematics and Other.  Thanks to suggestions made at the virtual meeting with ED677 on Thursday 5/3 for our final share, I have added a new section for music. I would also like to add a section for comments and/or feedback.  I really enjoyed pulling this all together and see more opportunities to gather even more meaningful resources now.  I would love to share this collection with other math teachers as well.

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Blog post - Week 12 - 4/9 Shared Purpose

Geometry in Construction

I absolutely LOVE this story! A math teacher and industrial technology teacher came up with this idea and it seems to be highly sucessful! “To Burke, the program really is about providing a valuable experience to students and a service to the community.” The students really seem to want to connect their learning!  “The students conducted a survey of some members of the Loveland community, asking if they are interested in helping the homeless and trying to determine where that desire to help ends.”

Arcadia Public Art Project

Kickstarter

For several years, I commuted through the Glenside train station.  It’s really great to see a positive change in the community lead by Arcadians.  The project does need more funding in order to achieve the goal of including LED lighting which looks REALLY COOL!  I will be donating to this project and would encourage others to do the same.  

The College March

The students of Washington Heights Expeditionary Learning School in New York City marched to the post office together to mail their college applications.  The streets are closed and the student body as well as the community outside the school are there to show their support for the seniors in their quest to go to college.

Purpose is good.  Shared purpose is better.

This article was written for a business audience, but the concepts can certainly be applied to the classroom if you substitute students for customers.  The main idea is that having a shared purpose is more important than simply having a purpose.  “Most leaders think of purpose as a purpose for. But what is needed is a purpose with.” When the purpose is shared, the engagement is stronger.

When students and teachers can work together towards a shared purpose, the sum of their work is greater than the parts.

I really like this quote as a reminder that small changes can sum to a large impact.  This helps me to not feel overwhelmed by trying to take on too much at one time.  

[calcyoulaterteach]

Blog post - Week 11 - 4/2 Openly-Networked

1. Re-Crafting Mathematics Education

This site shows some ways that crafting such as knitting, sewing, weaving and quilting employ mathematics.  

2. Re-Crafting Blog The link to this blog was embedded in the ReCrafting Mathematics Education site.  It provides more information regarding the making of things and also discusses how mathematics and mathematical concepts are an  integral part of the making process.

3. When will we stop teaching kids to memorize math?  This essay really gets at the heart of what I aim to do with my teaching. I want students to comprehend what they are doing, not simply compute answers.  “The important part of math is understanding how to represent a real world problem using mathematical symbols. How math connects to everyday things. What math symbols mean.”

4. Here’s how to get kids to stop saying they hate math. This article also really gets at why it is important to teach mathematics in a meaningful way in order to promote understanding. ”Teaching this way is a critical first step if students are to begin recognizing mathematics as meaningful. Conceptual understanding is a key ingredient to helping people think mathematically and use mathematics outside a classroom. ”

5. Problems

https://twitter.com/mashupmath

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Blog post - Week 10 - 3/26 Production - Centered: Academic, Civic, Community and Career  Connections

Say What? Math Edition

I have done a lot of thinking about an app that is both educational and useful.  I wanted the app to help students in a real and concrete way.  One of the areas I try to gradually help students with is mathematical language and literacy.  I encourage them to speak and use mathematical language with accuracy.  For example, when presenting a group project on limits of rational functions, I have found that students often use the words “top” and “bottom” as opposed to “numerator” and “denominator”.  I do not mark off their grades provided they (as a group) can come up with the mathematically accepted terminology which they inevitably do.  

The “Say What? Math Edition” app would be a tool for all levels of math students to practice and improve their math language skills.  My app will provide the user with an image of a mathematical construct such as a geometric figure, equation, graph, inequality, etc.  The user will then need to put into words what the construct portrays.  The app will then interpret the words exactly as they are said and create a new image.  The app will then let the user know if the two images match or not and depending on the settings, give the user a chance to adjust or correct as needed.  It could also include different modes such as fill in the blank and multiple choice.  I would also like the app to give users the option to share a “brag badge” on social media or via email.  This will allow for students to connect with one another.  This app has the potential to be utilized in many different ways.  

This app provides an opportunity for equity in that users are working to level the playing field regarding the use of mathematical terminology.  It is also equitable in that there are settings to allow for a different number of attempts for the user.  Perhaps a teacher or parent can set the number of tries based on the users ability.  The app should also provide information (written and/or video) regarding missed questions so the user can learn and then correct any errors on subsequent trials.  

There is great importance in speaking with mathematical accuracy.  I interviewed several people regarding this app idea and most said that it is important in some contexts, however in the opinion of some students, it is not as relevant in others.  For example, in places of business it is important to speak with mathematical accuracy.  Students cited examples of errors such as buildings and bridges collapsing and the consequences of injury to people as well as the expense of such tragedies to people in addition to the cost to rebuild.  One student also commented that errors in mathematical language could cause confusion which could prevent someone else from completing a task.  

Another important point was raised by an adult I interviewed regarding voice recognition.  There are many voice recognition tools available for modern convenience and as we look to the future, it is quite possible that voice recognition will become a more integrated part of everyday living.  As such, students should grow in their understanding and practice with speaking to a computer in a mutually understood language.  

According to the students I interviewed, the primary use of their phones is to connect with others.  As such, I wanted the app to match this student interest and provide students with a means to connect to others.  Allowing students the opportunity to share the “brag badge” not only allows them showcase their skills, but notifies students that someone else is able to help them.  If a student has posted their brag badge, they are letting others know that they understand the selected topic and are able to help.  The app can suggest potential helpers to a student in need of additional help.  The brag badge should have a setting that also indicates that the student is interested in helping their classmates, or perhaps the teacher can set that expectation for the class.  

I think it would be interesting for students of all ages to be able to see how the words they use can be interpreted (or perhaps misinterpreted) into a geometric figure, equation, graph, inequality, etc.  By allowing students to correct their work and visualize the misunderstandings, they are able to better understand how to communicate mathematically.

[calcyoulaterteach]

Academic, Civic, Community & Career Connections

Desmos

Desmos is a wonderful tool for mathematics education.  While I have been using desmos for several years, I have not explored the premade resources.  Through the blog of Dan Meyer (dy/dan) I came across the following resource on the Intermediate Value Theorem.  I introduce this theorem in PreCalculus and like many theorems, it may seem obvious (it does to me).  This interactive exploration leads students to the (arguably) critical component of the IVT which is that the function must be continuous! I have studied and taught this topic multiple times in multiple courses (precalculus/calculus), but the way this activity navigates through the possibilities is beyond anything I have experienced with this topic.  I can’t wait to have my Calculus and PreCalculus students explore this topic!

Interactive Geometry - Here are two geometry tools that students can use to interact with geometric shapes and figures.

Geogabra

Geometer’s sketchpad

These two resources give students the opportunity to manipulate geometric constructs in order to better understand theorems, algorithms, and properties in geometry.

Poll Everywhere

This free tool is a great way to get student responses in real time.  I recently set up a multiple choice poll.  They also offer free response, clickable images, ranking, and word clouds.  The paid version includes reporting features as well as reporting and grading features. There are many ways to leverage this interactive tool in ANY classroom and beyond!

TI Nspire

One of my go to mathematical resources is Mr. Tarrou.  On his website Tarrou’s Chalk Talk, there is a section for TI-Nspire tutorials. Students (and teachers) can use these videos to learn how to effectively utilize this dynamic calculator to help visualize the functions, geometric figures, statistical analysis and more!

Texas Instruments also offers tutorials and other resources.

Extra Practice with IXL

IXL is a good tool for students to practice skills.  Students work toward mastering a skill by solving problems of increasing difficulty as they get problems correct.  Incorrect responses offer students an explanation so that they can improve and hopefully solve correctly on the next attempt. Teachers have access to a dashboard showing how many and which students are currently practicing.  The dashboard also suggests students that may need help.  I have utilized this feature to assist students while circulating the room during in class practice.  This site does require a membership

The above resources all help students become college, career and community readied.  By giving students the tools to visualize and practice their mathematical skills on both an individual and group level, their understanding is enhanced and increased.  Poll Everywhere in particular is a resource that can be utilized in presentations in college as well is into the workforce and even beyond into the community to gather information that can be used to help others.  IXL may be the one example that presents an issue in regards to equity as it does require payment to fully utilize this resource. I recognize that I am fortunate my school has a subscription, but if I did not have this resource available, I would consider trying to obtain the funds as this site is useful for practice and skill mastery.

Keep on connecting!

[calcyoulaterteach]

Week 6 - 2/19 Practitioner Knowledge and Networked Inquiry

As I continue to work through my pose/wobble/flow, I would like to consider how math can become more meaningful to students.  I can find beauty and wonder in math and thoroughly enjoy many topics and skills I teach, but the same is not true for students.  My goal is to make more of the math I teach meaningful to more students. Some ways are to have students teach each other, provide real world/practical applications and show connections between mathematics and other subjects such as art and physics.

Find 6  1. When am I ever going to use this? As I continue to work on my pose, woble and flow, one of my aims is to help bring meaning to our work.  Meaning may come through understanding and/or appreciation for the beauty and wonder of math.  What some students may see as beautiful, others may not appreciate.  While I have told students that they may not use this (particular math skill) in their future, skills such as logical reasoning are valuable in other contexts of education as well as life.  While I value perseverance highly, I had not considered that as part of the skill set I am trying to develop within students.  This video provides an excellent response to students seeking purpose for learning in mathematics. 

2. Growth Mindset

This video helps to explain what is needed for teachers to make effective changes based on professional development.  While the intended audience is administrators, it is still helpful for teachers to consume this information in an effort to be able to accept feedback from administration.

3. Kialo - a debate platform powered be reason

This site is a great platform for hosting an organized debate.  Debates can either be private or public.  Rather than having a thread organized by time, arguments are ranked according to importance by invited users.  While there are not many opportunities for in depth debate in the mathematics classroom, I would love to incorporate this into my end of semester calculus project.  There is dispute as to who should be credited with discovering calculus.  Both Isaac Newton and Gottfried Wilhelm von Leibniz are said to have discovered it independently, however they each say the other stole their ideas.  

4. How to raise a lifelong learner

As I wobble towards making math meaningful, I found this site interesting.  While it is mainly directed to the parents of young children, there are some suggestions that are appropriate for any school age child.

5. Danny C - Connected Learning

5. As I was scrolling back through the class blog, I noticed that Danny C (also a math teacher) is working towards making math meaningful to students. In this blog post, he gives an example of a word problem that seems to be irrelevant.  While I do find this example to be rather unlikely to occur in the real world, this type of problem (system of equations) is very useful when placed in a more realistic context.  The skill can also be extended and applied in later courses.  But the questions remains, how can we make it meaningful now and at this level (algebra 1). 

6. 

[calcyoulaterteach]

Week 5 - 2/12 Learning (and Wobbling) in Connected Community

1. “What I Wish I had Known”   

This article lists some great general advice from experienced teachers.  Some of my favorites are:

Find a mentor

Ask for help, and learn from your mistakes

Continue learning to better yourself

Keep up with the times

Always remember your motivation

2. An opportunity/encouragement to wobble  Sage on the Stage

A business school expert explains why and how the role of the teacher is changing from lecturer to facilitator of information.  While I do occasionally offer my AP students the opportunity to lead the class in learning, I would like to create more opportunities for them as well as start allowing my other classes to do the same.

3. Can’t is not an answer

This blog post has some real examples of things educators can do to promote change within oneself as well as the community at large.  The author, Starr Sackstein has, “pushed forward, focusing on what [she] believed to be best for kids even when [she] felt [she] was swimming against a tide of no”.  She also lists some actions to make ourselves and our schools better.  Three of my favorites are:

Remember anything is possible, perhaps it just hasn’t happened “yet”

Be vulnerable...publicly

Make a mistake and learn from it

There are many more helpful suggestions and I plan to print this out and hang it up near my desk.

4. Knowing the Why

I was browsing around on storri and read this post and loved it! I really connected with the sentiment of not following in a predecessors footsteps simply because of how something had been done in the past.  I worked in benefits administration for seven years and during that time, I encountered this type of situation on a regular basis.  When there is meaning to one’s work, there is more joy.  I want my students to always question and ask why.  I want them to find their own joy and fulfillment in their lives both in and beyond school.

5.  Connecting with a Critical eye

It’s always important to read and interpret critically, considering the vast amount of information and arguably more importantly, misinformation available on the internet as well as social media.  However, this article provides reason to not just read and think critically, but to be your own fact checker.  It’s made me wonder if/how many false items I have read and/or spread.

Link to the original study http://science.sciencemag.org/content/359/6380/1146

6. Strong Roots

I thought this quote/graphic were perfect for finding the strength to wobble. The stronger your roots, the more secure you are in your pose and wobble.  

As a scrolled down, I was excited to learn that the author is Kira Baker-Doyle!  

[calcyoulaterteach]

Ok...catch up time! Blog post - Week 4 - 2/4 Playing with Playful Ways of Knowing and Learning

1. Women in gaming

I found the following video to be very encouraging for women to get into gaming.  It depicts several women each sharing the unique reason they enjoy gaming.  I especially liked that Frances said she was, “introduced by [her] mom and grandmother”, showing that games can span generations.  Another interesting point was made by YuXin who said, “I hope that the gaming world can be more encouraging, friendly and inclusive to all kinds of different experience and artistic expressions.”

2. Mastermind!

There are many logic games available, but my favorite at the moment is MasterMind (Codebreaker) .  The modern game was invented in 1970 by Mordecai Meirowitz, however there was a paper version of this game called bulls and cows.  This is a two player game where one player sets a code and the other has eight tries to break the code by guessing.  There are 6 different colored pegs and four locations to place the pegs.  The code maker then indicates how many pegs are the correct color and position.  The guesser continues until the code is solved or they run out of guesses.  This game teaches logic in a fun way.  While I prefer the Iphone app by Peaksel, the following websites have similar versions.  

https://content.jwplatform.com/previews/09Dpe0yC-avTupidD

http://www.archimedes-lab.org/mastermind.html

http://smart-kit.com/s5102/mastermind-logic-game/

http://www.app-types.com/en/app-type/549/mastermind

3. Blocks Rock!

Intuitively, I knew playing with blocks is great for child development.  The article, “Why toy blocks rock: The science of building and construction toys” by Gwen Dewar synthesizes research as to why and how this type of play impacts the brain.

4. Scavenger Hunt

In the article “All I Really Need to Know (About Creative Thinking) I Learned (By Studying How Children Learn) in Kindergarten”  Mitchel Resnick points out that, “teamwork is more important than ever before” and that schools are placing, “more emphasis on collaboration to help prepare students for their future jobs”.  I recently read the article (linked above). This inspired me to want to create a scavenger hunt.  A lesson like this may take more time and effort to create, but it is more memorable for the students and hopefully more effective as well.

5. Let the big kids play too!

Much of the research around educational play is focused on young children, however the following article shows that play is important for this age group.

“ One of the casualties of current education reform efforts has been the erosion of play, creativity, and joy from teenagers’ classrooms and lives, with devastating effects. Researchers have documented a rise in mental health problems—such as anxiety and depression—among young people that has paralleled a decline in children’s opportunities to play. “

6. Play and mindfulness

Here is an article on some very interesting work that was being done with Childhaven, a group that works with young children who have been abused or neglected.  I found it interesting that the interventions worked best when a mindfulness exercise using a chime was integrated into the classroom routine.

[calcyoulaterteach]

Blog post - Week 3 - 1/29 Seeking Equity

1.  The majority of the time I was reading through the piece by Craig Froehle, I kept thinking back to a unit from ED678 about appropriation and stealing Navajo designs.  It sounds like Craig Froehle didn’t mind and even seemed pleased that some artists such as Angus Maguire picked up his idea and improved the artistry or reworked the idea.  There were however, some exceptions and he did seem to mind when others added boxes, indicating that resources were increased but there was no mention of how that occurred.  In regards to equity, it is important for educators to be aware of cultural differences.  “We have a responsibility to listen to people of marginalized cultures, understand as much as possible the blatant and subtle ways in which their cultures have been appropriated and exploited, and educate ourselves enough to make informed choices when it comes to engaging with people of other cultures.”

The Difference Between Cultural Exchange and Cultural Appropriation

Also, in the Reich and Ito article “From Good Intentions to Real Outcomes”, the authors state that, “Lack of awareness of learner’s specific social and cultural contexts can lead to unanticipated outcomes”  and so there is a need to increase awareness.

2. Here is a great article to get started with the topic of equity in education!

3. The Educon panel discussion indicated that it is important for students to have experiences like that of the real world.  Educators should try to “[connect]...the world of work and the future of careers...break down this barrier between school and the rest of the world. (1:43:34)   The following excerpt from the New York Times indicates the importance and value of working within a group.  The article continues to discuss the investigation into why some groups are more successful than others and provides meaningful insight into the conditions for successful groups.

What Google Learned From Its Quest to Build the Perfect Team

“In Silicon Valley, software engineers are encouraged to work together, in part because studies show that groups tend to innovate faster, see mistakes more quickly and find better solutions to problems. Studies also show that people working in teams tend to achieve better results and report higher job satisfaction. In a 2015 study, executives said that profitability increases when workers are persuaded to collaborate more. Within companies and conglomerates, as well as in government agencies and schools, teams are now the fundamental unit of organization. If a company wants to outstrip its competitors, it needs to influence not only how people work but also how they work together.”

4. Also during the Educon panel discussion, the term “gamer-gate” came up (1:37:17) and as I was unfamiliar with this, I wanted to investigate further. While I am not much of a gamer at this point in time, I have some experience with coding and am very much an advocate for increasing female participation in typically male dominant areas such as coding and chess club.  

Here is the wikipedia entry on the topic

Gamergate Controversy

There is much controversy surrounding gamergate and without getting into too much detail, one of the lead advocates, Anita Sarkeesian is a highly polarizing figure. I was considering posting her interview with Stephen Colbert, but decided not to.  If you choose to look into this issue, I would encourage you to do so with a critical eye and suggest looking for a variety of perspectives.  After spending a bit of time looking into this, I will admit that I am more unsettled than when I began.

5. I was highly intrigued by a section of Reich and Ito’s “From Good Intentions to Real Outcomes” which sited a 1990’s study by Harold Wenglinsky which found that, “ low-income, nonwhite children more often used technology in math class for drill and practice, while affluent, white children were more likely to use technology for graphing, problem solving and other higher-order exercises” (Pages 6 and 7). Teaching teachers how to effectively utilize technology is an important component in the quest for equity.  

I have access to a set of TI Nspire calculators which I am familiar with, however I know they are capable of much more than I know how to do.  I have looked up a few things here and there over the past four years, however I would really like to spend more time learning how they can be leveraged to a higher degree in all of my classes.  The following youtube channels are great resources.

Texas Instruments

TI Calculators

6. Desmos! I have always loved Desmos for graphing and so to see it listed in Reich and Ito’s “From Good Intentions to Real Outcomes” (Page 15) brought me much joy.  Desmos offers a four function calculator, a scientific calculator, a graphing calculator and much more!  They also offer classroom activities and you can even save files for demonstrations within your own lessons!  They even have animations illustrating concepts such as how to graph the sine function from the unit circle which I use in my PreCalculus course. 

7. #The4thBox

I created two very different scenarios for #The4thBox.  First is a positive spin where the three people sit down together and build a community through conversation.  The boxes allow the people a place to sit and discuss equity and equality.  The second depiction is of the tallest person taking all of the resources and greedily taking advantage of the situation.  Rather than caring for the other two hopeful spectators, this person has wielded their physical power to exclude the others.  This situation does occur in the real world.  Perhaps only the tallest/strongest person was able to lift the heavy boxes and so felt that they alone deserve to use them.  Perhaps only they had the financial means to purchase the boxes and for this reason decided to maintain full control without giving either of the other two hopeful spectators an opportunity to make a purchase.  Regardless of the reason, it certainly does not seem fair to me.   

[calcyoulaterteach]

Blog post - Week 2 - 1/22 Democracy and Participatory Culture

It’s been a little while since I have blogged and I am finally able to get caught up a bit.  I’d like to start by sharing my “find five” from Week 2.

1. During the video “Critical Literacy and Our Student’s Lives”  Kevin Hudson brought up the idea of visual annotations which reminded me of an info-graphic on visual note taking that I wish I had saved.  Here is a link to something similar. 

 https://www.edweek.org/tm/articles/2016/12/28/the-power-of-visual-notetaking.html

2, I follow “Teacher2Teacher” on Facebook and occasionally screenshot some of their posts.  While listening to the “Critical Literacy and Our Student’s Lives” video, I was reminded of the following screenshot as Andrea Zellner said, “the way that we grow as educators is by...noticing where we’re falling short and that it’s not a failure but rather an opportunity to grow.  

3. The video representation of the John Seely Brown keynote “The Global One Room School house” - highlights from “Entrepreneurial Learner”mentioned Andrew Sullivan and his article, “Why I Blog”  I found this video https://youtu.be/SnU900s1A70 which is an interview of Andrew Sullivan explaining the origins of his blogging.

Video link

4. Also in the John Seely Brown video representation, at 7:12, he states, “NOBODY AGREES ON ANYTHING”  This reminded me so very much of my first experiences as a mother.  Frequently, parenting advice is quite contradictory and so as a new mom, I had no choice but to navigate through the conflicting and vice and information available.  I found it helpful to join a local community group of moms where I learned invaluable information about caring for baby and self.  Most importantly, I was reminded to trust in myself and my own instincts.  No one has all of the answers and it is our job as educators to take in as much information as we can, synthesize it and decide what is best for the learners.

5. At 7:43 of the John Seely Brown video, he state, “ Fail, fail, fail and then get it right”.  I instantly looked over to a Mary Engelbreit magnet on the side of my cabinet near my desk with the following image on it.  I use this image and quote as a reminder to myself to keep trying and not worry about my mistakes and failures, because the next class is coming soon and there is no time to dwell on them.

[calcyoulaterteach]

My Interest in Gymnastics

I admit that the initial reason I wanted to begin gymnastics class was so that I could use the leotard as a swimsuit.  I knew another girl that had taken gymnastics then quit and was using her leotards as swimsuits.  Since I did not have many swimsuits and wanted more, I convinced my mom to sign me up for gymnastics but did not tell her my reasoning until several years later.  I was rather upset that I did not get a leotard when I began gymnastics as we used regular clothes in my first class and the first recital leotard had sequins and thus was not suitable for swimming.  

After one term at the first school, we switched to a gym that was farther away, but ran a much better program.  I was fortunate that my mother was willing to spend the extra time and money to support my interest.  By this time, I had become better at gymnastics and wanted to keep my leotards for gymnastics only.  I enjoyed the challenge of the balance beam and appreciated the focus and concentration required to be successful in this event as well as the uneven bars.  I also really enjoyed practicing on the trampoline.  In addition to the weightless feeling at the vertex of a jump, we used a harness to assist with learning flips which was another really cool sensation.

Gymnastics was not something that was practiced in school.  We were not even allowed to do cartwheels at recess nor in gym class.  However, when I moved to a new school in the middle of 6th grade, the next unit in gym class was gymnastics!  I was beyond thrilled to show off some of my skills. I continued practicing gymnastics, but stopped at the end of 7th grade.  I was able to use some of my gymnastic skills again in 10th grade.  I had joined the track team in high school and at the end of 9th grade began trying the field event high jump.  As I continued practicing high jump and improving, my technique began to improve.  One of my coaches commented that while jumping over the bar, my body moved in a snake like pattern as I maneuvered over the bar.  I was able to clear higher heights than other athletes who were taller than myself.  I attributed my unexpected ability in part to the flexibility I had developed through my earlier years of gymnastics.  

Music and arts are being diminished in many schools.  Funding for these programs can be a challenge and many people do not see the benefits of including these topics in education any longer.  Physical education is also being reduced in many schools due to budget cuts and an increase in academic focus.  Physical activity is very important to the health and well-being of our students.  In addition to the obvious physical benefits of physical education, studies have shown that student’s learning ability is in increased when they are physically active.  The brain receives more oxygen and thus performs better when the body is active.