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Issue 2, Fall 2008

On Schools of Education, Theodore Sizer
Opening up to Math, Sarah Strong
In Over Our Heads, Stacey Lopaz
African Bushmeat Expedition, Jay Vavra
Learning as Production,
      Critique as Assessment
, Elisabeth Soep
Speeding Race Cars
      & Dying Embers
, Ashley Bull-Carrico
Messy Business: A Student's Perspective
      on Project-Based Learning
, Mollie Davis
The Great Lego Caper, Zoltan Sarda

1: Writing on the Walls
2: San Diego/Tijuana Crossed Gazes
3: Blogging is Writing
4: Public Service Advertising Campaign
5: Science Friction
6: I Am an Artist

HTH GSE » UnBoxed » Issue 2 » field notes

Explorer students playing a group math game.

Speeding Race Cars
& Dying Embers:

My Journey Toward a More
Engaging Math Curriculum

Flash back. It’s the exciting beginning of a new school year. For the next six weeks I have the simple goal of getting to know these new personalities and figuring out how to teach 24 very different little beings. I turn on the cheesy UB40 song “The Way You Do the Things You Do.” It is my anticipatory set to a review lesson on analogies. I have decided to kill two birds with one stone, and do a little assessment of how these kids write figuratively and how they feel about math. We listen…You got a smile so bright you know you could have been a candle. I’m holding you so tight you know you could have been a handle... They quickly catch on to the comparisons and we brainstorm analogies in the form of similes and metaphors. The goal today is for each student to figuratively describe themselves as mathematicians using an analogy. I model expectations, and off they go.

As I walk around the room, pencils diligently writing (it’s the beginning of the year and they are still trying to impress me) I am intrigued by the variation in their analogies. Victoria is like the ocean tide. Jose is like a wolf hunting prey. There is a racehorse, a sandcastle being built, a harsh flame scattered through unvoiced trees (I’m not joking), a helicopter, and a river. There is also a snail, a sloth, a crashing airplane, and a runner in last place. Beyond this initial opening statement the assignment asks that they explain their analogy. One student, Nick, wrote the following:

“As a mathematician I am like a speeding racecar. The track I race on is the problem I must overcome and solve. The wild turns and curves are the crucial info to crack the problem. My first lap I gather my info as I read over the problem. I start to solve it on my second lap as I zoom past the other cars at the speed of sound. I go to the pit stop to refuel and rethink my answer to the question. On the final lap I check my answers so I don’t make any mistakes. I shoot over the finish line, the checkered flag waves and the crowd roars with wonder as I finish my problem. I have won 1st place, Problem Solved!”

This makes a lot of sense. Nick scored advanced on his state math test. Also, when I asked students to look at the seven intelligences and describe what kind of learner they were, Nick chose logical /mathematical. I would say he had a knack for the verbal/linguistic too after reading his analogy—not bad for a nine year old.

At the other end of the spectrum is the student who is the runner in last place, who describes how everyone is passing him and how that makes him feel like giving up. I also have those in the middle, like Victoria, who described herself as the ocean tide; sometimes the tide was moving fast and sometimes sitting still. My favorite part—I was her moon, directing lessons and providing her with help and guidance.

I knew before the year started that I would have a class of students who ran the gamut in ability levels in every subject. We all do, every year. But the most significant reminder I came away with was this: I had students who loathed math and some who probably dreaded it on a daily basis. Add to this the hour of math in class and the 20 - 30 minutes of math homework each day, and I was sure that math was not going to be the only thing they hated by the end of the year. So what should I do?

I began by questioning my math practices. For the past eight years, my annual planning process at the end of each summer has looked almost identical. I lug the enormous Everyday Math box to the middle of my ridiculously colorful US rug in my classroom. I sit with my standards, my prior year’s Math-at-a-Glance calendar and my notes. I take out all of the teacher’s manuals and references—there are over ten in this program—and flip through them looking at my shorthand comments. These comments, which I usually can’t make out, consist mostly of timelines and reminders of things to not “waste” too much time on.

I wish I could say that my focus has been on how I was going to build mathematically powerful students who could solve problems and communicate their understanding. But every year I am stricken with accountability anxiety as I look through all of the concepts I am supposed to teach. Hours later I end up in the center of a mathematical rainbow of teacher’s manuals, student workbooks, and supplemental materials. I finish with another Year-At-A-Glance calendar. This time it moves even faster than the prior year and cuts out all of the “fluff” units such as the fun tessellation project and the US driving project, or it saves them until the end of the year, post-testing.

Realizing this was a gigantic red flag. I needed a more important purpose in teaching math than covering content, a central focus more significant than making sure my students ended up proficient and advanced on state tests. What did I really want for these kids, especially those who had been through five years of school and still hated math? When I reflected on this question I realized I not only wanted all of my students to enjoy math, but I wanted them to feel secure and confident in their ability to tackle math problems. I also wanted to make sure they were challenged and thinking critically.

I began searching for ways to achieve these goals by leaving my teacher’s manuals behind, and picking up books like Five Easy Steps to a Balanced Math Curriculum (Ainsworth, 2000), How Social and Emotional Development Add Up (Haynes, Ben-Avie, & Ensign, 2003), and The Homework Myth (Kohn, 2006) among others. The great thing about is its magical ability to know what books are good for you based on your previous purchases. One of the books it suggested was Jack Frohlichstein’s Mathematical Fun, Games, and Puzzles (1962). The book began by asking questions such as, “Have you ever wondered why the number 13 is considered unlucky? Did you know that many hotels eliminate the number 13 in marking their floors and numbering their rooms? Have you ever heard that odd numbers are considered masculine and even numbers in many cultures are feminine? Can you think why?” I couldn’t put down this little old relic of a book. The history of arithmetic and numbers was intriguing, and the games and puzzles sections were fascinating. As I read, I couldn’t help thinking, “Michael, my last place runner, would love this” or “Marshall, my mathematical sloth, would think this was cool.” Then I thought, what if I started bringing in these games and puzzles and trying them out as a way of teaching math to everyone, not just as an option of what early finishers could do?

I began to feel like I was on the right track when I attended a conference held by the California Association of the Gifted (CAG) a month later. I teach at a school that uses strategies developed for gifted children with all our children, so I was hoping to find ideas on how to meet the needs of my confident and not-so-confident math students. At the conference, it seemed that almost every hour there was another workshop focused on math games. I went to Double Dare You Math Games, Marvelous Math Games, Math Games for the Gifted, and more. Not only was I enjoying attending a conference on a weekend, but I was excited about bringing these ideas back to my students. In each session, there was another reason for integrating games into my math curriculum. Presenters described math games as engaging for all, naturally differentiated, and open-ended; math games encouraged strategic thinking, planning, and communication; and perhaps most importantly, they promoted positive attitudes toward math.

So, what all began as a figurative writing review lesson became the driving force for rethinking how I approach math in my classroom. I am eager to see what happens for my students as I integrate more math games into the curriculum. I hope that those students who saw themselves as dying flowers or dried up rivers will find other analogies to describe themselves as mathematicians. We’ll see. . .

Resources and References

To learn more about how to integrate math games and interactive math tutorials into your teaching, check out the following website:
Ainsworth, L (2000). Five easy steps to a balanced math program for upper elementary teachers. Inglewood, CO: Advanced Learning Centers.

Assouline, S. & Lupkowski-Shoplik, A. (2003) Developing mathematical talent: A guide for challenging and educating gifted students. Waco, TX: Prufrock Press. 

Assouline, S. & Lupkowski-Shoplik, A. (2005). Developing math talent: A guide for educating gifted and advanced learners in math. Waco, TX: Prufrock Press.

Frohlichstein, Jack (1962). Mathematical fun, games, and puzzles. New York: Dover Publications.

Haynes, N. M., Ben-Avie, M. & Ensign, J. (2003). How social and emotional development add up: Getting results in math and science education. New York: Teachers College Press.

Johnson, David & Johnson, Roger (1991). Learning mathematics and cooperative learning lesson plans for teachers. Edina, MN: Interaction Book Company.

Johnson, S. (2005). Math education for gifted students (Gifted Child Today Reader). Waco, TX: Prufrock Press.

Kohn, A. (2006). The homework myth: Why our kids get too much of a bad thing. Cambridge: De Capo Press.