Math Inquiry

Math Inquiry is a classroom strategy that I've modelled several times for the teachers in our division.  I've heard many different ways to use it with students, but here is how I use it in a Gr. 1-4 classroom.

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1. The first step is to choose a really rich problem, one that has many different ways to approach the problem solving aspect, or has many steps, or has more than one correct answer. I've been collecting these problems over the years.  When I find a good one, I save it. 
   
2. Present the problem to the class as a real world problem that needs to be solved.  Make sure that everyone fully understands what must be determined.
3. Pair the students.  Obviously, as their teacher you will know who to pair up.  You want students who work well together.
4. The problem is printed on a large sheet of paper (I usually use 11.5 x 17), with lots of room for figuring.  Then students each get a fineline marker to use.  I don't allow pencils, because I tell them that I want to see their mistakes, and I hope they make some, because that's how they learn.  Give the students 20-30 minutes to solve.  (Note: I often add an extension to the problem at the bottom of the worksheet for those early finishers, but this is an optional part of the problem.)
5. Students must decide how they are going to present their work to the rest of the class.  Each person must have a role in the presentation.

Pairs of students show the rest of the class how they solved the problem.  Some teachers call the presentation part of the process Math Congress. This is THE most important step in the whole process. Make sure you draw out the different strategies students have used.  Allow the rest of the students to comment and ask questions. Ask other students to paraphrase what each pair of students presented.

For older students (Gr. 5-8) I spread out the process over a few days.  Here is the variation:

1. After presenting the problem orally to the students, have students work independently on the problem.  Collect the students' work and that's it for Day 1.
2. After class, review each student's work.  Pair up students according to the strategy they have chosen to use (make a diagram, addition, multiplication, work backwards, etc).  If you see students who are struggling to find a strategy to use, put them in a group together and this is your small group that you work with over the next few days.
3. On Day 2, put students into their pairs/group and have them discuss how they will solve the problem. The teacher works with the small group.  Students make a rough copy of their solution on 11.5 x 17 printer paper.
4. On Day 3, students' papers are put up on the wall and students go on a gallery walk to see the various strategies that are being utilized.  Hand out poster paper. Then students have the rest of the class to create a polished copy of their solution. Small group does the same.
5. On Day 4, hold Math Congress, similar to the younger students.  Again, this is a very important step in the process.  Paraphrasing and questioning is vital.

Depending on the number of students, and the richness of the problem, Math Inquiry for older students may take from 2-4 days.

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One of the best resources I have for Math Inquiry is Math Expressions: Developing Student Thinking and Problem Solving Through Communication by Cathy Marks Krpan.

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