## descriptive vs explanatory thinking in mathematics

Posted on: February 2nd, 2014 by jnovakowski

On Wednesday morning, I made my monthly visit to Quilchena to take part in a collaborative inquiry with the intermediate teachers looking at alternative ways to assess students’ mathematical thinking.

In Una Simpson’s grades 4 and 5 class, the students had been studying various aspects of geometry. The day before I visited, Una listed a series of geometry-related topics on the board and pairs of students were assigned a topic to highlight in a “ShowMe” screencast. Students were asked to both describe the shapes they were using by their attributes and to explain the concepts involved such as what makes a prism a prism, what is a polygon, what is the relationship between two and three-dimensional shapes?

The students took several photographs that could be used to explain their topic.

And then used the ShowMe screencasting app to record their descriptions and explanations.

In Tanya Blumel’s grades 5 and 6 class, we looked at the two types of division (sharing/partitive and grouping) and then the students worked through some three digit divided by one digit questions using the grouping method. As students shared their work, we focused on how they explained their thinking and the mathematical language they used to support their reasoning.

In Andrew Livingston’s grade 7 class, the student have been learning about the relationship between fractions, decimal numbers and percentages. He gave the students a task from their textbook but instead of writing their responses in their math journals, the students were asked to explain their reasoning orally using the ShowMe app. The students coloured in the various shapes on the grid and then had to determine the fraction, decimal equivalent and percentage of the total grid for each space. The students’ reasoning for the triangular shapes was the most interesting to listen to.

This is ongoing work and we hope to see the benefits of focusing on oral explanations when we ask students to write about their thinking…hoping that the metacognitive writing will be easier for them with these background experiences.
~Janice