1.3: Learning Materials
One of the first reflective questions I recall responding to when considering CoT was during the interview process. It was the easiest interview question I have every been asked. “Have you given any thought to what your classroom might look like?” I have always envisioned a classroom full of manipulatives, and not just traditional ones. In addition to standard geometric solids, balls, building blocks, giant cardboard boxes, life-sized nets (geometric patterns one can fold oneself into), knots, hoola hoops, books, puzzles, games, art, and all sorts of mathematically stimulating things will adorn the walls and ceiling of my room. Not only for decoration, but they will all have purposes in various demonstrations and serve as objects of inquiry, conversation, and constant reminders of mathematical ideas and applications. When I consider learning materials used in the classroom, I think about tools, toys, texts, brains and bodies.
In the mathematics classroom, tools can range from standard pencil and paper to compass and ruler to the computer (see expectation 4.3: Technology for examples of Geometer's Sketchpad and Microsoft Excel) or the dreaded or co-dependent calculator, but they are all mathematical in nature. I have begun to collect many of these tools for use in the classroom in quantities enough to distribute to an entire class as needed. When students are encouraged to use the tools of mathematics in an appropriate and exploratory way, their practicality becomes more clear and forges deeper understanding of the mathematics. We have cut and folded nets and conjectured about surface area of both two and three-dimensional figures. If you thought dissection was only for biology and anatomy, you are wrong. I think a fun exercise for next year will be to dissect a ball. I'm not sure yet whether this will fall into tools or toys, but the learning will deeper than it was this year.
Toys will play a large role in my mathematics classroom as well. From content-related Web-based games to those designed for pure entertainment value, games can be an appropriate way to explain and practice mathematical concepts (see expectation 4.2: Variety in Instruction for examples) . In the short time I was student teaching, I developed two different games from lesson content that helped engage the students in cooperative discussions about the lesson. The Radical Game is a simple card game for which I prepared cards with equivalent simplified and unsimplified radical expressions on them. I divided the cards among the students. They were instructed to first decide whether their expression was in simplest form. If so, they were to find the classmate with an unsimplified form of their radical. If theirs was not simplified, they had to find the classmate with the simplest form of their expression. The game was fun, got the kids out of their seats, and caused them to make some determinations about math both individually and collectively.
Another game I created this year is called The Business of Symmetry. I have copied 70 (and still growing) corporate logos and trademarks. The class made their own teams, and as the slides progressed, each team discussed and recorded how many lines of symmetry they saw in each trademark. At the end of the game, the students added their total lines of symmetry, and each team got to choose a prize (drop a homework, etc.) in the order of the closest to the actual total. I have chosen logos that the kids are used to seeing and will recognize. This makes the game more enjoyable and hopefully causes them to remember symmetry the next time they see it around town. I plan to develop this game a little more thoroughly over the next year.
This year I have also used Legos, magnets, collapsible and non-collapsible shapes (applications of triangles), Tried to make triangles from assorted segment lengths and implemented lots of other fun stuff to engage, explain, and more effectively demonstrate the mathematical concepts. Jumbo playing cards, dice and Rubik's Cubes have also been added to my collection of mathematically relevant "toys" to use in the classroom.
Reading and writing cause students to think and apply topics of mathematics to the world around them (see expectation 1.4: Teaching Reading and Writing). When mathematical relationships are expressed in words, it often translates the confusing and intangible symbols into a language much easier to understand or express. The expectation that students should read and write mathematically in English trains their brains to digest the concepts more explicitly and is an important part of assessing their level of understanding.
Brains and bodies should be active in the mathematics classroom, keeping students engaged and involved in the learning. On the first day I took over the maternity leave at Lawrence North, I had each class undo their own
human knot. This served two purposes for me. It got the students moving and engaged, but it also helped me establish a rapport and begin to learn names in an interactive setting. I had prepared some mathematical materials about knots (theory and coloring) for them to read after the activity and answer some questions about the activity.
When students experience mathematical concepts through investigation, experimentation, conjecture, and discussion, their learning is more meaningful and retention is stronger. Students should have sensory opportunities to succeed and fail while touching, feeling, moving and sharing mathematics just as they would in a pottery class--learning from their mishaps and messes. Making mathematics real and connected to fun associations from their world is the key to overcoming much of the math anxiety that troubles adolescents and impedes their success.
