Monday, May 23, 2011

First Day of Math - Let's Start With a Puzzle!

Summer school begins tonight. Two nights a week for three hours each night I will be teaching preservice teachers how to teach math. This is perhaps my favorite class to teach. I get folks who are often quite nervous about taking a course with the word math in the title and have just eight short weeks to develop their confidence in and love for a subject for which many willingly express a dislike. Hey, I love a good challenge.

Unlike many instructors, I do not begin by handing out the syllabus or even by giving introductions. I ask students to clear their desks and then working in teams, I give them a math problem or puzzle to solve. In past semesters I have started off with tangrams, attribute block trains, and pentominoes. The puzzles they solve are challenging. I ask them to keep a list of all the math concepts and skills they are using while working towards their solutions. It may sound odd, but I want them jump headfirst into thinking mathematically and realize quickly that they need to become comfortable in their "mathematical skin." I also need them to understand that to teach math they need to know math--really KNOW math. In fact, this is how my syllabus begins.
You cannot teach what you do not know. There is a large body of evidence from which educational researchers have concluded that the quality of teacher subject matter knowledge directly affects student learning. Nowhere is this more apparent than in the teaching of mathematics. We also know that “a teacher’s subject matter knowledge of school mathematics is a product of the interaction between mathematical competence and concern about teaching and learning mathematics (Ma, 1999).” As a result, this course is focused on developing your mathematical competence so that you will not only know the mathematics you will teach one day, but also feel utterly confident in discussing and explaining it.
It is only AFTER they get this message that I hand out the syllabus and allow introductions, though having started with a group task they have already begun to know one another.

So, what task am I starting with today? This time around I'm going with some Kakuro puzzles. Like Sudoku, the object of filling in a kakuro grid is to fill the boxes with numbers so that no number is repeated in a column or row. However, kakuro puzzles are based on finding sums. Here is what one looks like.
After introducing the puzzle and explaining the rules, I solve a sample problem with them and model strategies. Then they are given a few problems to solve with a partner.
If you are interested in trying some kakuro puzzles yourself, here are a few useful resources.
When students get to work, I get to observe. What will I learn about my students by listening and watching them solve puzzles? A lot! I will learn how flexibly they think. I'll learn something about their number sense. I'll learn how they approach problem solving and something about their ability to deal with a challenge. I will also learn how well they work with others, what their mathematical discourse sounds like, and a whole lot about their feelings towards math.

Once we've finished solving and discussing the puzzles, then we get down to business, but not before I read a poem and a book or two. (You can read more about this at the post The Importance of Math in Our Lives.)


  1. This is critical stuff you're doing, Tricia, particularly when you read research like this about math anxiety. Plus, ya know, poetry is always good :-)

  2. That sounds like a fantastic class! My primary memory of eighth grade math (or, truly, any math I took in my K-12 years) was that the teacher that year had a bulletin board full of logic and number puzzles in the back of the room. Consequently, I spent that whole year in the back of the room not paying much attention to whatever he was talking about in favor doing the puzzles. He didn't bother me about it, but I always felt like I had to be sneaky. It didn't occur to me until I was grown that he did that intentionally for students such as myself. I wish more teachers had--those puzzles were highly motivating.

  3. Tricia, I'm thrilled that you're going to be posting more about math! I love everything you write. :)

    I'm especially interested (personally) in learning more about how you teach teachers. So post away!!! (P.S. My class may be cancelled due to low I may have to save what I learn from you for the next class. But I will soak up what you say for workshops...I teach tomorrow and the quote you use is a great one to include. :) )

    THANK YOU FOR POSTING at Math Monday!