Building on Student Ideas - The Border Problem
The article is the begining of a case study in Cathy Hunphrey's class.
Her interest is in "trying to make algebra more accessible" and to address the fact that "equality and variable are particularly thorny obstacles".
The case study centres around presenting the students with an image of a ten by ten grid with the perimeter squares shaded and they are asked to find a method for determining the number of squares in the perimeter without counting them.
The students undertake the first part of the problem to "figure out without talking, without writing and without counting one by one" how many squares are coloured. There are six methods.
The objective is for students to achieve insight over why the equation is formed. Working through worksheets solving algebraic problems does not provide that insight.
According to Boaler, students "...should receive many opportunities to explore the relationships between geometric and algebraic forms".
This problem undertaking is to help students to see that "algebra is a tool for representing a methmatical relationship, rather than a result". It's not about solving algebraic equations, it's about being able to create the algebraic equation to represent a problem which can then be solved.