Turning a Teacher-Centered Math Class into a Student-Centered One

If you read my earlier posts, you’ll recall that I approached the instruction of my Math 8 algebra unit in a very different way this term. The students had not had experience in solving algebraic expressions prior to this and it was not “instructed” as I traditionally do. In many cases they were given questions and corresponding answers, and were asked to figure out how to get from one to the other on their own. They had to come up with algorithms and illustrations to demonstrate understanding of the foreign concepts, in addition to creating new examples and solutions for their peers to solve. In most cases, they were paired up and worked through problems together, re-enforcing their comprehension and fine tuning problem-solving strategies. The process was frustrating for students who were used to being told how to do the math, and often learned by example. You could take a poll in my math class (and I’m sure that of most Math teachers) of how many students hate problem-solving questions, and I would almost guarantee the percentage to be in the high 90’s. There’s always a collective groan when word problems are thrown into assignments and tests. The concern for me as a mathematics educator is that life is not a series of computations and numbered questions – the types of problems that arise in the “real world” will require students to make inferences, draw on past knowledge, and make connections. So, my inquiry was to approach algebra in a way that fostered the problem-solving process in a way that was meaningful for each student individually, and have the learning be centered around them.

This was achieved through various learning activities I tried throughout the 2 month field study, note-worthy ones being:

• Learning how to collect like terms: Each pair of students was given a mini whiteboard and markers, and were given a question and corresponding answer, based on their ability level. The ability to differentiate the instruction based on mathematical strength attributed to the success of this activity. An example would be: Given 4x – 3y + 2x + y, show how we get the simplified form 6x – 2y. Be able to describe your method in words and come up with a new example with the correct solution. Students were then required to “teach” their peers how they came to their conclusions. As the teacher, I made myself available to scaffold and support the students as questions arose or to challenge their thinking.

• Learning how to solve linear algebraic expressions: Each pair of students was given an iPod Touch and worked through an app called “Algebra Touch”. This app started with a question (an example would be: 2x + 4 = 10) and the goal was to isolate x. Students could “drag” terms around and noted what happened to them when they crossed the equals sign. “Tapping” a term would factor it, and “striking out” a term would cancel like terms in a fraction. The app would complete the calculations, but the goal was for the students to predict what would happen before they dragged/tapped/struck out each term, and most importantly, be able to explain WHY that was happening.

• Learning how to solving more difficult linear algebraic expressions: Each pair of students was given a Macbook and used a program from the National Library of Virtual Manipulatives that illustrated balancing equations where the variable was on both sides of the equals sign, and then solving it. This program was easy to differentiate as there were varying levels for the varying abilities that exist in each class. Like the iPod, the computer program performed the calculations and students were left to answer how and why, rather than what.