Inquiry or Problem based learning in math is not new. It is the math pedagogy advanced by the Ontario Ministry of Education (2005) and is based on the belief that “…by learning [math] through problem solving, students are given numerous opportunities to connect mathematical ideas and to develop conceptual understanding” (Ontario Ministry of Education: 2005, p. 11).
If you are reading this post, then you probably already buy into this. You might also be starting your math transformation by locating websites to help you generate the “mother of all inquiry questions”.
Generating your own inquiry question is a skill that needs to be developed, over time.
If I had to suggest an alternative starting point in preparing for math inquiry or problem based learning, then it would be to instead focus on developing the math talk community, within your classroom. Specifically, each student’s ability to defend, and prove their own thinking, while at the same time questioning and reflecting on the math thinking of others. This being done with a view to enhancing the understanding of math concepts, for each member of the talk community.
There are many resources that already contain well crafted inquiry questions and could be used as a starting point for familiarizing oneself with how an inquiry question is framed. Fosnot’s math kits, websites like math researcher Dan Meyer’s 101 questions, and some textbook problems contain excellent inquiry contexts for students to work through. Math inquiry questions or engaging math contexts tend to satisfy the following criteria:
- The solution is not immediately obvious.
- The problem provides a learning situation related to a key concept or big idea.
- The context of the problem is meaningful to students.
- There may be more than one solution.
- The problem promotes the use of one or more strategies.
- The situation requires decision making above and beyond the choosing of a mathematical operation.
- The solution time is reasonable.
- The situation may encourage collaboration in seeking solutions
(Guide to Effective Instruction in Mathematics, vol. 2, p. 26)
Simply taking a question from any of these resources and using it within your classroom is fine. Don’t feel like you are only doing inquiry if you make your own question.
Here are some ideas that might help a reader consider how to start preparing for math inquiry by developing a math talk community.
Develop math norms of working with a partner
Provide a common experience for learners where they work with a partner to problem solve a given math context. By engaging with the task in a problem based way, students develop a sense of what solving math problems with a partner “looks like”, “sounds like”, and “feels like”. Students also start getting into the habit of using their intuitive math sense to develop new understanding. From there, have students develop class norms around working with a math partner and record their ideas on chart paper.
(Norm exemplar courtesy of Carrie Byer)
Develop question starters
Develop question starters with students that help them probe into their partner’s thinking, in constructive ways. Record these question starters on chart paper. This provides students with a useful framework for questioning that ultimately gets the class community into the habit of ‘showing and proving their thinking’. Over time, you will notice students devising their own questions, and an increase in peer to peer discussion about their math thinking.
(Question prompts courtesy of Ashleigh McIntosh)
Institute regular math meetings (math congress)
According to the Ontario Math Curriculum (2005) document, “One of the best opportunities for students to reflect is immediately after they have completed an investigation, when the teacher brings students together to share and analyse their solutions” (p. 14). In this larger group setting, “Students then share strategies, defend the procedures they used, justify their answers, and clarify any misunderstandings they may have had” (Ontario Ministry of Education: 2005, p. 14). To help sustain this important aspect of developing the math community, it would be important to create math meeting (or math congress – Fosnot) norms, like in the case of working with a partner. Again, record the norms on chart paper and post in the classroom for students to review prior to math meetings.
(Math meeting norms courtesy of Carrie Byer)
Keep these norms and question starters posted throughout the year, and revisit them regularly – even if you feel the students “have it”.