Wow. From grade seven. I wonder what she will have to say as the mathematics she does at school becomes more abstract and seemingly disconnected from "real life". Good for her to say how she feels and ask the tough questions. Although I wasn't expecting this today, I was prepared, am always prepared for how I might respond to this question.
Let me provide the context of this interaction...
I was at Quilchena Elementary for my monthly visit with the intermediate teachers. Today we focused on the role math materials/manipulatives can play in students' communication of their mathematical understanding and thinking.
We began our day in Una's grades 4 & 5 classroom working on using arrays to model multiplication and moving to using base ten blocks to model two-digit by two-digit multiplication with a focus on the place value language that "matched" the materials. This was hard work for these students. Many students were able to calculate the answers to the questions mentally and then modelled the answer with the base ten blocks. When re-directed to explain how this model showed the process of multiplication (which was the intention of the lesson), they were befuddled. The students needed some modelling and we used an approach to multiplication that could be described as distributed or parts-based and then connected this to the models that could be created with base ten blocks. There were some aha moments from students for sure but also, more work still to be done. Here are some examples of how the students worked through 12X23 and how some of the students represented the process in their math journals using pictures, numbers and words.
I moved on to Andrew's grade 7 class and worked through a similar process with the intention of moving to multiplication with decimal numbers. This is where the student's question came up as I moved from table to table. I took a few seconds to pause and calmly answered.
You probably won't use base ten blocks in any future job you have. You probably won't have to show your boss how you can multiply large numbers but...you will probably be asked to think, to problem-solve, to reason, to make sense of data and information. When we do things like this, it is to help you make meaning and create connections, to help you understand the mathematics more deeply, to be a thinker.
The principal takes all the intermediate classes for choir on the days that I visit so the teachers and I can meet together and discuss emerging issues in our collaborative inquiry. Today, we discussed students' notions of what math is, brain development, and why we teach math. Math isn't just for our students' future jobs. Being numerate is part of being an educated citizen who will make meaning of the world, ask questions and think critically. We talked about what mathematicians do...math is not about doing things quickly. Mathematicians spend long periods of time on one problem or proof, thinking, analyzing, synthesizing, generalizing, making conjectures, reasoning, creating models, etc. I think that sometimes we forget this in school mathematics which can often seem rushed and hurried to students.
After our collaborative time, I visited Tanya's grades 5 & 6 class that has been working on area and perimeter. With the resource teacher, I worked with a group of students on connecting arrays, area, perimeter, multiplication and division using colour tiles. Lots of oral explanations and mathematical vocabulary were used during our discussions.
For a performance-based task, the students in this class were designing their own apartments having to consider the total area and the area and perimeter of the rooms within. As I chatted with one student who had grandiose design ideas for her apartment, she said she liked doing this because it was real math, that she would use when she was grown-up.
Made me think...sometimes the contexts and applications we provide in math classrooms help students to see the relevance of the math they are learning. Sometimes, it's not so clear and that's okay. We learn and think about math because it is developing us as thinkers and problem-solvers and nurtures the habits of mind that are going to help us in "real life" regardless of what job we might have.
~Janice
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