Technology is great and all … but sometimes good old fashioned concrete manipulatives are the best way to help students grasp abstract concepts. While reviewing the process of solving for variables in math class, I realized that my students were having trouble recalling and carrying out the necessary problem solving steps, especially when more than one step was required. Capitalizing on a fantastic suggestion by my building’s math coach, I taught students how to use algebra tiles to make the concept visual, and it helped a great deal.
Now I’m allowing students the option of using the tiles (or colored highlighters to draw representations of the tiles) any time they feel it would be beneficial. However, as the size of the numbers being used increases, this can become a lot of work and take up a lot of paper space! So, when moving on to larger amounts, I’ve found it helpful to just verbally remind students to visualize the tiles when they get stuck and aren’t sure what to do next.
With a problem like 46 = -10n + 76, for instance, I might provide a prompt by asking, “If my goal is to isolate the variable, how could I first cancel out the positive 76 (picture 76 yellow squares)?” Usually, that would be enough to get a student to realize that he or she would first need to add negative 76 (picture 76 orange squares) in order to make zero pairs on one side of the equation before then doing the same thing on the other side of the equation.
In addition to making abstract concepts visual, it’s also important for students to see the real life relevance of concepts studied. So, we have focused quite a bot on using algebraic expressions and equations to represent authentic situations.
Finally, since teaching someone else is the best way to demonstrate mastery, I’ve had students wrap up the unit and prepare for an assessment by creating their own tutorials … saving technology integration until the very end. (And since my students were shy about sharing their final products with the larger world this time around, I’ve posted my own as an example.)