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Mathematizing Mathematics

Students making sense of a real world problem in Ms McAlear’s grade 6 math class.

“As teachers do we see our role as initiating learners into mathematical communities, speaking and inquiring with young mathematicians at work? Or do we speak to them, trying to transmit a of skills and concepts…developed by previous mathematicians? Are we teaching the history of mathematics rather than mathematics?      ~Cathy Fosnot~

It’s encouraging to see the enthusiasm with which our Park Ave. P.S. team has embraced our whole school focus on mathematics teaching and learning~not only because this is an area of personal and professional passion for me; but also because we are, as a staff, uncovering some powerful and important insights about the nature of mathematics and networked learning.

In stressing the importance of inclusion, inquiry and  innovation my role has really been that of catalyst and coach; providing resources, structures and guidance for this learning. In our conversations so far, we have discovered that our students have a wider range of skills and, deeper understandings, than the tools that we were previously using; revealed. In our case, all our students, including those students who have been identified with learning disabilities, are  revealing capacities and communicating ideas in ways that are both surprising and encouraging.

The problem shown in the photo above (The Sold Out Show)  is a great example. In designing the task for her students, Ms M considered the models and strategies her students were using as they solved multi-step multiplication and problems. She created a problem that would push her students to better understand the relationship between these two operations as well as the important mathematical processes of reasoning and proving how they know their solution is accurate.

Rather than demonstrate and have her students memorize the steps toward an accurate solution, Ms M has crafted a problem that will help her students to build and communicate their understanding. The culmination of this task will see the students analyzing and questioning each other’s proofs with  Ms M taking the time to highlight the mathematical relationships, ideas and terminology as they are doing so.

For many of us,this is a reversal of the model of instruction we experienced as students; one where the teacher demonstrated the singular procedure and skills that would be needed to complete a task, then assigned a similar task with the expectation that all the students would replicate what had been demonstrated.  This model worked, for about half of us.

In our classrooms, we are asking students to show us what they know about mathematics and how they are able to apply this knowledge in context; then using these contexts to push them to a deeper understanding of how mathematics allows us to make sense of our world, communicate about our world and work to solve problems in our world~ a process that the Dutch mathematician Hans Freudenthal describes as ‘mathematizing’.

Creating classrooms where our students mathematize, rather than memorize, is our ultimate goal; as always, your comments and questions are welcome!

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