A while back John Stevens asked me if I would write a guest post for Table Talk Math. Of course I was happy to do so. I knew I wanted to share the process of exploring a trick to figure out the math behind it so parents would be encouraged to engage their kids in asking why and building on conceptual knowledge rather than being tempted to tell kids a procedure. After some considering I opted against any of the tricks in the book and I decided on the nines trick. You know the one where you use your fingers? This one:

I had a great time figuring out why it works and I don't want to rob you of that opportunity to explore! After you've played feel free to read my guest post and leave a comment if you explained it differently.

# Drawing On Math

Ponderings of a high school math teacher.

## July 14, 2017

## July 13, 2017

### Box of Books

On my last post Michael commented: "I'd be interested to hear your take on something like the junior high activities book, the one with the soccer ball on the cover. It just seems to me that all these math edu books essentially recycle the same core group of tasks. We're going to have a visual pattern. We're going to have the area model. We're going to have that thing with the sultan and the penny and the chess board. It's not like there are THAT many different types of tasks. That's how it seems to me, at least. But I'd be interested to see whether anything in the book of activities feels 'new' to you."

This post comes in two parts:

Part 1) I'm on the publishing committee for NCTM, let me tell you about the beginning of the process of reviewing books from NCTM's catalog

Part 2) Do you want some books? I have a variety of thoughts on how to get them to you cheap!

**Part 1:**

For my first task as a committee member I reviewed old books (5n years old where n is a whole number) to decide if they should continue printing, update and print a new edition, or retire the book.

What the review process looks like |

Interestingly that book was the oldest one I reviewed, published in 1999. And Michael was right, flipping through I saw the locker problem, foxy fives, cryptograms and M&M data. All excellent problems, ones I've used and great to have in your repertoire. But while reviewing this book (and some others in the pile) I wondered, how often do people use books like this now that the internet exists? NCTM has a ways to go to get their website running at full capacity (I got a secret preview of a proposed upgrade that looks awesome!) but even still people can search the NCTM site to find the journal articles that this book is composed of. Plus they can search all the blogs and other lesson compilation sites. I don't turn to books for lesson ideas but there must be others who do because the catalog has a variety of updated versions of this book and around 40 people bought this one in 2017.

In reviewing my comments I noticed I wrote a contradictory note about another book, saying, "quality intro based on research, filled with tasks (bonus- people might pay more attention to journals since many tasks are from journals)." I wonder which is true? Maybe both? If people buy a book referencing journal articles will they be more likely to look to NCTM journals next time rather than a book?

Surrounded by books! |

But in reading the outline it sounds like DNR means remove from the catalog no matter how many are left in stock and maybe sell them on clearance at conferences. I'm hoping some of them go on clearance online first as we have lots left in stock, as a print on demand author this idea of ordering thousands of books at a time and hoping for the best is a new one to wrap my hear around. I can't wait to find out what the rest of the committee thinks in August!

**Part 2:**

Books I reviewed (the other 9 were eBooks):

- Activities for Junior High School and Middle School Mathematics, Vol. 2
- Learning and Teaching Measurement: 2003 Yearbook with Classroom Activities Companion Book
- Thinking and Reasoning with Data and Chance: Sixty-eighth Yearbook of the National Council of Teachers of Mathematics (2006) (Book and CD-ROM)
- Learning of Mathematics, The: Sixty-ninth Yearbook of the National Council of Teachers of Mathematics (2007)
- Mathematics Teaching Today: Professional Standards for Teaching Mathematics, revision (Claimed by Peg)
- Making Sense of Mathematics: Children Sharing and Comparing Solutions to Challenging Problems
- Mathematics Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction, and Learning (Claimed by Nita)
- Professional Collaborations in Mathematics Teaching and Learning: Seeking Success for All- 74th Yearbook (2012)
- The Common Core Mathematics Standards: Transforming Practice Through Team Leadership
- Bridging the Gap Between CCSS and Teaching Statistics
- Eyes on Math: A Visual Approach to Teaching Math Concepts

Books published this year I've received:

- Unpacking Fractions (Claimed by Casey)
- Reasoning and Sense Making in the Mathematics Classroom: Grades 3-5
- Reimagining the Mathematics Classroom
- Reflective and Collaborative Processes to Improve Mathematics Teaching (Claimed by Glenn)
- Taking Action Grades 6-8 (Claimed by Casey)
- Taking Action Grades 9-12 (Claimed by Peg)
- JRME: Children's Measurement
- Good Questions, Third Edition
- Access and Equity Grades 6-8 (Claimed by Marian)

If you would like a book that isn't on my list or one that someone else claimed we can order another box of books to be delivered to TMC! Shipping is expensive from NCTM but not much more expensive for several books than a single book. Megan has graciously offered to receive the package since she's nearby, just comment here with what books you'd like and I will order them. Since shipping takes time I will place the order on Monday July 17, so spend your weekend picking out books!

I plan to suggest to NCTM that something like this service be made available via coupon code for other small conferences, I'm imagining you would enter the code and the cost of shipping is drastically reduced and the address automatically changed to the conference organizer's choice of address. No idea if this is doable but it would be cool to allow small conferences the chance to sell books like NCTM conferences do without having to send merchandise back and forth. And of course you can always do this with your local network of friends, tweet out to anyone nearby that you're about to place an order and see if they want to split the cost of shipping with you. Not sure who is nearby? Check out the map! Not on the map? Add yourself!

Don't forget to comment with what book(s) you'd like. If you're not attending TMC feel free to claim books too, I'm happy to ship via media mail. Also leave a comment if you have any ideas I can share with the publishing committee next month! [Edit: comments are having trouble making it through, feel free to tweet instead

## July 5, 2017

### Welcome Blankets (Crochet With Me!)

Kathy Henderson shared this article on Facebook a while back. I shared it and some people were interested in making some #MTBoS blankets and learning together at TMC. So here's the info! The same people who made the pink pussy hats for the women's march are making welcome blankets for immigrants. They are partnering with multiple refugee and immigrant resettlement agencies to coordinate distribution, but first there will be a display at an art museum in Chicago.

Project info: https://www.welcomeblanket.org/

Pattern: https://www.welcomeblanket.org/patterns/ It's so mathy! There are so many possible configurations! It's just like the pattern blocks at math-on-a-stick. It would be really fun if lots of us made squares and then played with them at TMC before sewing them all together into blankets. Could we make all possible orientations as a team? (No Tina, there must be thousands, someone get nerdsniped and report back on that exact number please.)

If you want to start now, grab supplies and start crocheting. This is the crochet pattern pdf to make the two color square pattern but they are accepting any pattern blanket so long as the dimensions are 40x40" A good place for beginners would be solid 10x10" squares (with easy horizontal rows) since they would fit right in with the other two color squares. A good place to check out is http://www.lionbrand.com/learn/how-to-crochet.

If you want to learn at TMC I'll have supplies but you'll probably get hooked (pun intended) so you'll want your own hook and yarn so you can continue crafting on your way home. Traveling is a great time to crochet and this pattern is excellent since it's made in pieces! If you want to learn grab a J hook and some worsted weight yarn (any craft store will have them). If you want to connect your squares to mine get Bernat Super Value yarn (it was on sale and it's washable so I bought true red, navy and white).

Can't wait to craft with you!

"The proposed border wall between the United States and Mexico is almost 2000 miles long. Imagine if the massive distance of this wall was re-conceptualized and re-contextualized not to divide, but to include. Instead of wall, a concrete line, to keep people out, what if lines of yarn became 3,500,640 yards of blankets to welcome people in?"

Project info: https://www.welcomeblanket.org/

Pattern: https://www.welcomeblanket.org/patterns/ It's so mathy! There are so many possible configurations! It's just like the pattern blocks at math-on-a-stick. It would be really fun if lots of us made squares and then played with them at TMC before sewing them all together into blankets. Could we make all possible orientations as a team? (No Tina, there must be thousands, someone get nerdsniped and report back on that exact number please.)

If you want to start now, grab supplies and start crocheting. This is the crochet pattern pdf to make the two color square pattern but they are accepting any pattern blanket so long as the dimensions are 40x40" A good place for beginners would be solid 10x10" squares (with easy horizontal rows) since they would fit right in with the other two color squares. A good place to check out is http://www.lionbrand.com/learn/how-to-crochet.

Can't wait to craft with you!

## June 27, 2017

### Please Nix the Tricks: Grad School Edition

I am taking a grad class on students with ADHD. I'm not loving the book (

I was dismayed to see a study on “Memorize in Minutes” included in the articles. I appreciated that the article stated up front “we were not trying to build conceptual knowledge... we were solely concerned with the act of memorization” (Mahler, 2011, p. 5). However, I think this is a poor choice of skills to prioritize. The article did address this concern as well “some have suggested that students be given calculators or multiplication charts instead of asking them to memorize the facts. However, students with insufficient working memory already have a tendency to lose track of what they are doing, forgetting one part of a task while working on another; thus it is even more important that these particular students attain automaticity with multiplication facts” (Mahler, 2011, p. 6). I will allow this as a possibility but I am far from convinced that spending time teaching stories is more effective than any other option. In fact, “needing to translate a story made his retrieval slower than if he had memorized the numerical answers” which sounds just as bad if not worse than the distraction of picking up a calculator (Mahler, 2011, p. 7). In discussing the growth from the post test to the delayed post test the author states, “it is speculated that participants were finally using the facts in their everyday classrooms, and were now engaged in the natural practice in which they previously could not participate“ (Mahler, 2011, p. 20). This ‘natural practice’ could have been occurring from the start if these students were allowed a calculator. With no control in this study there is no way to tell if the stories are more or less effective than any other intervention strategy. I believe the intervention time would have been much better spent on teaching mathematical strategies for how to calculate new facts from ones students have memorized. To practice such strategies students could play games or solve problems that included multiplication facts to get the ‘natural practice’ that was so effective. Even focusing the intervention time on practice using a calculator or reading a multiplication chart would have been much more applicable in the long term than learning stories that do not apply to any other area of mathematics.

Mahler, J. (2011). When multiplication facts won't stick: Could a language/story approach curriculum. The Education Therapist, 32(1), 5-8, 20-21. ERIC doc. no. ED527570.

http://files.eric.ed.gov/fulltext/ED527570.pdf

*Nowhere to Hide*) because it's rather chatty and there aren't many strategies that I can use so I was interested to read the articles which are supposed to supplement the book. I was excited to see one specifically about math until I started reading and was appalled it studied this book of tricks! Here's what I wrote as part of my larger essay, I hope it doesn't impact my grade to express dismay!I was dismayed to see a study on “Memorize in Minutes” included in the articles. I appreciated that the article stated up front “we were not trying to build conceptual knowledge... we were solely concerned with the act of memorization” (Mahler, 2011, p. 5). However, I think this is a poor choice of skills to prioritize. The article did address this concern as well “some have suggested that students be given calculators or multiplication charts instead of asking them to memorize the facts. However, students with insufficient working memory already have a tendency to lose track of what they are doing, forgetting one part of a task while working on another; thus it is even more important that these particular students attain automaticity with multiplication facts” (Mahler, 2011, p. 6). I will allow this as a possibility but I am far from convinced that spending time teaching stories is more effective than any other option. In fact, “needing to translate a story made his retrieval slower than if he had memorized the numerical answers” which sounds just as bad if not worse than the distraction of picking up a calculator (Mahler, 2011, p. 7). In discussing the growth from the post test to the delayed post test the author states, “it is speculated that participants were finally using the facts in their everyday classrooms, and were now engaged in the natural practice in which they previously could not participate“ (Mahler, 2011, p. 20). This ‘natural practice’ could have been occurring from the start if these students were allowed a calculator. With no control in this study there is no way to tell if the stories are more or less effective than any other intervention strategy. I believe the intervention time would have been much better spent on teaching mathematical strategies for how to calculate new facts from ones students have memorized. To practice such strategies students could play games or solve problems that included multiplication facts to get the ‘natural practice’ that was so effective. Even focusing the intervention time on practice using a calculator or reading a multiplication chart would have been much more applicable in the long term than learning stories that do not apply to any other area of mathematics.

Mahler, J. (2011). When multiplication facts won't stick: Could a language/story approach curriculum. The Education Therapist, 32(1), 5-8, 20-21. ERIC doc. no. ED527570.

http://files.eric.ed.gov/fulltext/ED527570.pdf

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