Ten Ways to Use Puzzles in Math Education

Scott Kim, April 22, 2002 • From http://scottkim.com/education

**Puzzles make math fun**

Chances are that you already use puzzles in your classroom. After all, a puzzle is nothing but a problem that is fun to solve. Primary level teachers commonly use puzzle manipulatives like tangrams to teach concepts like sahpe, fractions and area. Secondary and high school teachers often use puzzles to introduce concepts and spice up homework. College entrance exams and math competitions are mostly collections of puzzles.

As a professional puzzle designer and math educator, I would like to see puzzles used more widely at all levels of math education. Here are ten ways you can use puzzles in your math classrooms, with links to web resources. Most of the products mentioned work with upper elementary through high school students.

**1. Classroom Resource**

Display a collection of physical puzzles that students can play with before class and as a reward when they have finished their work. Physical puzzles are especially good for tactile learners, who often can’t absorb traditional educational methods. Some of the best classroom puzzles include *Rush Hour*, *Hoppers*, and *Math Dice* from ThinkFun, each of which include a graded series of 40 puzzles.

The *Problem of the Week* book and posters from Dale Seymour Publications (part of Pearson Learning) is a colorful collection of entertaining puzzles that you can hang on your wall. I plan to create similar puzzles on the web.

**2. Arts & Crafts**

Having students build puzzles themselves both saves money and involves them in a creative crafts activity. *Exploring Math Through Puzzles*, by Wei Zhang (Key Curriculum Press), includes pieces for building 54 puzzles involving wire, string and beads, plus notes on 3D visualization and problem-solving techniques.

* Creative Puzzles of the World*, by Pieter Van Delft and Jack Botermans (Key Curriculum Press) explores the multicultural artistic and historical side of puzzles, with extensive instructions for making the puzzles.

**3. Introduce Ideas**

Martin Gardner, author of the *The Colossal Book of Mathematics* (Norton) and dozens of other classics in recreational mathematics, recently wrote in Scientific American that puzzles are a great way to get students excited about learning new ideas. A good collection of warmup exercises for high school math topics is Thought Provokers, by Doug Rohrer (Key Curriculum Press).

I write a monthly puzzle column called Bogglers in the popular science magazine Discover. Many of the puzzles teach concepts from contemporary math and science. Recent topics include Fermat’s Last Theorem, cryptography and topology.

**4. Illustrate Strategies**

Books on creative thinking often use puzzles to illustrate thinking strategies, and the ways that we can get stuck in mental ruts. Lateral Thinking proponent Edward De Bono’s books include De Bono’s Thinking Course (Checkmark) and Six Thinking Hats (Little Brown).

**5. Physical Manipulatives**

Physical manipulatives like pattern blocks and tangrams make abstract ideas tangible, and encourage open-ended exploration. Manipulatives are most common in elementary schools, but work at all levels.

**6. Livelier Homework**

English teachers often spice up their vocabulary exercises by working words into crossword puzzles, created with the aid of software like Crossword Wizard. To learn more about software for creating crossword and word search puzzles for the classroom, see http://www.cogix.com/cw/CW20.htm.

**7. Public Events**

For elementary students, the Family Math Program uses math puzzles and activities to create a carnival-like event for both students and parents to enjoy.

For secondary and high school math clubs and competitions there are many books of contest puzzles, such as 50 Mathematical Puzzles and Problems, edited by Gilles Cohen (Key Curriculum Press).

**8. Skill Testing**

College entrance exames like the SAT use puzzles to evaluate mental skills. The best way to prepare for such tests is to work through books of puzzles. Mensa (www.mensa.org) publishes many excellent books of puzzles.

**9. Problem Posing**

As teachers, we all know that the best way to learn something is to teach it. One teacher told me that he challenges students to invent questions that will appear on the exams. The questions from students are frequently quite hard, and involve students more deeply in their own learning.

**10. Original Research**

Rebecca Wahl at Butler University has found that puzzles are an effective way to get undergraduate students to do original mathematical research. Unlike advanced mathematical topics, most puzzles require no special background, yet are rich with unsolved challenging problems.

Here are other things I'm thinking of doing to support puzzles in math education:

- Create a "puzzle of the week" on the web. Probably a few different versions for different age levels.
- Cite evidence that puzzles are good for testing and developing mental skills.
- Create teacher support materials for the most useful puzzles.
- Create an index that correlates puzzles with mathematical topics in particular grade levels.
- Invent new puzzles to accompany curriculum areas that lack puzzles.
- Develop a web site with unsolved research-level puzzles that students can solve and get credit for. Should include a directory of major unsolved problems in mathematics for which there are cash prizes.

If you have comments, ideas, things you would like to see, or other references, you can contact me at:

Scott Kim

scott@scottkim.com