Providing a Math Experience

Hi All,

This week in Math class we discussed different ways of providing a meaningful experience for students. One of the main themes that we discussed was understanding the difference between knowing, doing, and understanding in mathematics. To me, knowing is about being able to know specific conventions when being given a particular problem. Doing involves actually being able to use those conventions in completing a task. Whereas, understanding involves actually understanding why you are using those conventions and reflecting on the problem. Although all are important, to me, it is the understanding that is essential for the Math learner. Being able to question these conventions and look deeper in order to gain understanding is more valuable for the learner. I think that making mistakes and communicating with peers is essential to the understanding. It is the Mamamdo- Half Triangle story that really cemented my own understanding about the value of making mistakes and how it contributes to everyone's learning. Click on the picture below to watch the video. In the video, Mamamdo is asked to explain his thinking of a one half fraction of a rectangle. The teacher calls Mamamdo to the front of the class and asks his peers to track his thinking and identify other possible ways of answering the question. The teaching strategy she used allows for the student not to feel as though they were wrong, but to allow them, through the help of peers, to identify the 'mistake' so that he could solve the question. This helps the student because he is better able to understand the concept.

Mathematics Teaching and Learning to Teach, University of Michigan. (2010). In Mamadou-Half-Rectangle [Online]. Available: http://hdl.handle.net/2027.42/78024

Another teaching strategy that contributes to gaining this mathematical understanding is the Math Daily 3 activity. It involves the teacher allowing time for the student to first, try out the question on their own. Second, consult a neighbour. And finally, write a mathematical sentence about the answer. This is a great strategy because it allows students to communicate their approach in different ways which allows them to further reflect on the problem.

Finally, in order to provide a rich mathematical experience for the learner, I think it is important for the teacher to think about the different ways of delivering Math questions. This week we looked at Math problems from an Indigenous lens through the story, Small Number Counts to 100. Please watch video below.  This is a story about a boy named Small Number who tries to count tipis. Through the story, students are asked how Small Numbers was able to determine which was the 100th tipi without actually counting all the tipis. This inquiry based question can potentially have students draw the scenario or actually create the scenario in order to figure out different methods of finding out the answer. These are very different approaches to Math because it gives students real-life problems to solve and allows them to use their imagination and ask questions in order to solve the question. Additionally, it allows them to understand ways that Math is taught across cultures. What is particularly interesting about this video is that it is offered in both Cree and Blackfoot languages. This way the video also offers the student an opportunity to learn about Indigenous traditions, culture and language in a more meaningful way.

Sinclair, R. “Small Number Counts to 100” (2009). Available: https://vimeo.com/29064016

Overall, I think that this week has been an eye-opener for me in terms of the different directions to take teaching and learning Math. I hope in the coming weeks; I can add more tools in my Math tool box.