Oct 122016

I had the opportunity to read a preprint edition of Malke Rosenfeld’s new book, Math on the Move, and here are my thoughts.

First off, let me start off with what this book is not. As educators we have probably sat through a professional development where someone told us that in math class, we can appeal to the “kinesthetic learning style” by having the learners up and moving around the classroom. We can appeal to “kinesthetic learners” by having them move their arms, or by doing gallery walks. I have sat through several of these. [yes, I put that phrase in quotes on purpose. I do not believe in ‘learning styles’. Multiple Intelligences, yes, learning styles, no.]

Rosenfeld’s book is not this. No where near this. This book is not about “kinesthetic learning” this is about making connections in mathematics through motion, body, and dance for elementary school learners. It is an amazing concept to think about. I really appreciate that on page 2, she says, “not all of dance is mathematical and not all math is danceable.” That sets the tone for the entire book. Rosenfeld looks for the strengths in using movement, and using the body as a thinking tool. This is a powerful idea, and the first chapter of the book is about what doesn’t and does count as using the body as a thinking tool. I loved the deep thinking this chapter provoked, because it made really think about dance and movement with respect to math.

And, let me be honest. My knowledge of math through motion is very limited. My idea of dancing is more aligned with this guy than anything that someone else would consider “dancing.” Honestly, I wondered for a moment if someone had recorded me actually dancing when I saw this gif.

dancing-gif via

But, despite the fact I am both musically and rhythmically challenged, I have always thought there was opportunity to connect math and movement. I have never figured out how, but I have been intrigued by the idea. After reading the table on page 17 I realized why.

table of nouns and verbs about math movement

The verbs of math are aligned with the verbs of dancing. The nouns of math are also aligned in large part. Looking at the list, and knowing, intellectually, about the ideas of dance, it is easy to understand how strong the connection is. Through examples of learner work, QR codes showing video of learners moving, multiple lesson examples, pictures, role playing examples, and well developed explanations, Rosenfeld shows me how to implement dance in a very constructive way in the elementary classroom. By the end of chapter 3, I was willing to try it with elementary kids tomorrow. That takes a lot for me to say, because I am secondary through and through. Little kids scare me. But I am so excited by the opportunity I see after the first three chapters of lessons that I am willing to try them. They are so interesting!

I think the real power comes later in the book when the 6 stages are developed further.

  1. Understand
  2. Experiment
  3. Create
  4. Combine
  5. Transform
  6. Communicate

These stages allow learners to move from the understanding of a concept and goal to the creation of a multi-step dance pattern and ending with the discussion and communication of the idea through a presentation of the dance. The last half of the book has QR Codes on almost every single page with video link examples. The depth of knowledge these can provide is stunning.

All in all, the more I read and find the joy in mathematical dancing, the more opportunity I see to push this into the upper levels. There is so much more that can be done with this idea beyond the boring and basic. It might even make me a better dancer! Well, no. It isn’t a miracle book, just a really good math book. It is authentic movement, not the usual fake stuff we see.

I think it is time to bring real motion in to math class, get learners moving in purposeful, meaningful ways, and leverage that motion into strong mathematical knowledge.

If you want to read a chapter for yourself, check it out on Heinemann’s website.


Aug 192014

Want to watch an ap stats classes eyes glaze over? Start talking to them about stratified vs. cluster vs simple random sample vs judgement sampling.

sleeping learner photo via

Really. Pull the powerpoint from the book, throw it on the screen, and watch the light dim from their eyes.

I didn’t do that. …. This year. I didn’t do it last year either, but I was not totally successful in this endeavor. Last year I did some activities AND showed the powerpoint. Not this year at all.

Last week on Thursday and Friday I showed the powerpoint I created that had the theory, the background and the why we are learning the vocab, then they looked up the words themselves.

Today we did the Jelly Blubbers activity. Jelly Blubbers teacher handout and the Learner Notes and a  Stratified Blubber Colony stratified blubber page I don’t hand out.

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It drove the point home that judgment sampling is wrong because it creates bias, and that for certain things, stratified is terrific! We had a short discussion of why we need different ways to do the sampling, and what benefits are achieved by sampling.

This was the progression and order we did it in. The bias in the judgement sample is clear. They really liked the larger blubbers over the smaller ones.

All in all, it was a great day in AP Stats.

Algebra 2 was more … difficult.

There is a lot of vocab to go through, ie. Domain, Range, function notation, set notation and interval notation, etc etc etc.

We spent the entire period learning those. I really feel like it was not successful, HOWEVER, they were involved and active in the discussion about what the different ways of representing domain, range and the other ideas were. I think they learned useful things today, it just was not as an active day as I would want.

I will work on that tomorrow.

Aug 182014

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These two pages are representative of the MASSIVE vocab we are wading through in my AP Stats class today. I snapped a couple of pics as I was walking the classroom answering questions. It was a successful day, I think. …. Maybe.

I finalized a diagram I had in my head and that I have drawn by hand several times over the last couple of years.

statscycle Stats is about taking the population, extracting a sample correctly, and constructing an appropriate, useful model.

That reminds me of a quote I read today:


Anyway, I took the learners through my short ppt on the theory behind the journey we are starting. After that, they had to start looking up the vocab in the textbook and start developing the definitions for the 8 types of sampling, the 4 types of bias, and the other vocab associated with sampling.

Next up, the sharing of the vocab they found (which will all be the same, they all figured out how to use the book quickly). I will do that quickly, answer questions, and immediately move to “On the River” exercise. More on that later.

My Learners:

I was really struck today by the different ways the classes jumped into this exercise. Period 2 was very helpful to each other. They started discussing the vocab right away and were very animated. By contrast, Period 3 was silent. I don’t mean they whispered. I mean they were absolutely silent. It really freaked me out. I just wandered around and it took about 20 minutes before they started asking questions. That was highly odd.

By contrast, my 5th period had a table that not only was really thinking, but they determined what stratified sampling was without consulting the book. They asked me if it was legitimate to sample via strata (although they did not use that vocab, it was exactly their question.)

The level of their thinking really impressed me. It was the first day of week 2, and they are naturally coming up with the ideas of  stats on their own. Pretty cool.

Jan 282013

Last week I posted research and articles on vocabulary in math, this week I have a topic of reading and writing in math class, including some mathematical poetry. Sounds interesting, right?

by James Henle

This paper offers six different versions of mathematical poems, both traditional and modern. I really liked the fact that it offers Pascal’s Triangle as a modern mathematical poem. A very different way to look at it.

by Patrick Bahls

While the author uses examples from Calculus in this paper, the justifications, descriptions, and everything else about the concepts are applicable to any math classroom. Very well thought out and very thorough treatment of why we should use some poetry in our writing assignments in math class.

by Vicki Urquhart and McREL (an organization)

This 24 page document goes through the research on using writing in math class and then gives strategies and methods to incorporate more writing in the math curriculum. There are some good ideas here, although most of the content is geared towards elementary school concepts.

Finally, some websites that have content related to this topic.

Pat’s blog, (which I love because of the ongoing “this day in math” series) had a posting on Math, Shakespeare and some good ol’ Limericks. Great article, expecially when combined with the poetry articles above.

A college professor, Derek Bruff, had a great posting on How to read a math textbook. This is a skill that is too often not taught, just assumed. Although we all know reading a math textbook is radically different than reading other textbooks.

An entire website dedicated to Writing in Math Classes by Dr. Annalisa Crannell has lots of good resources for the math teacher. Again, it is geared to Calculus, but there is enough there to figure out how to use it in other classes at the high school level as well.

That is all for today. Hopefully, as always, it will help someone.

Jan 202013

I think like most teachers, I read a lot. When I say I read a lot, I mean a freakin’ lot, and I save articles that I think will have an impact on my teaching either now or later. This means I have an folder with a couple of hundred research reports and articles. Over the weekend the question was posted on Twitter whether or not anyone has anything to share on vocabulary in math class.

I has some articles and emailed them to the couple of people who requested, but it made me think that a terrific #Made4Math series would be to post some of the articles. It will be doubly good because it will force me to re-read the articles.

So today, I start with vocabulary in mathematics.

by Kathryn Sullivan

This article is short, and it gives a good introduction to many of the “little” words that we use in math class often that really does create problems for many learners. What surprised me was that it wasn’t words like add, subtract, etc. It is words like “the,” “each,” “how,” etc.

by Suzanne Irujo

This article is short (6 pages) and breaks down the different parts of English that are used in math class. It definitely makes you think about the difference between Academic and Informal uses of language. In math, it is almost entirely Academic use, which causes problems for the learner (especially the ELL learner.)

by Dr. Madeline Kovarik

This 20 page research paper gives some great insights into how important the use of and development of vocabulary is in the math classroom, and then it gives some curriculum insights into how to achieve good vocabulary learning. I need to study this paper some more, because I have only recently found this paper, but on first reading it seems a valuable addition.

is by the AISD Elementary Mathematics Department.

It is an elementary level research paper, but that is okay because it has some great insights into learning vocab and bridging the Academic vs non-academic language usage. It included black line masters, ideas for helping ELL and below level learners. It is completely of use to the secondary level teacher as well.

In addition, I found a book online and downloaded it. It is a good book on the issue, but there is no way I will post the pdf file. It is still copyrighted and would be a HUGE violation.

The book is “Teaching and Learning Vocabulary: Bringing Research to Practice” by Elfrieda H. Hiebert and Michael L. Kamil. I have found some great ideas in the book, but it is a little long and very dense reading. Here is a short review of the book to see if it is something you would like to purchase.

I hope this helps someone.