The class of 2021 is embarking on an exciting new journey in math with the introduction of Integrated Mathematics to the Freshman curriculum. Integrated Math breaks from traditional high school math courses in that it no longer divides content into subject-specific areas of math like Algebra and Geometry, but rather approaches the subject as it is encountered in the real world, where multiple areas of math may be needed to solve problems. It also looks to the outside world to provide problem-solving strategies to apply to traditional math problems. This approach was used in the Freshmen’s most recent task of solving single variable equations.
The students were given maps of Humboldt Park and asked to write out directions to go from our school to the soccer field in the park. Classes were pressed to give detailed directions including direction and distance and to lay out each step as a separate line. Upon completion, the maps were taken away and the students then needed to write out directions to get back to school from the park. After some deliberation, a consensus was reached and students wrote out their directions. They were then asked to compare the two sets of directions looking for any similarities and differences. The students discovered that while they used all of the same streets, each direction was opposite. Moreover, each step seemed to go in reverse. After more discussion, the practice was formalized as backtracking. This process was then applied to single variable equations. Much like the map activity, each student would have a starting position (the variable) and then would write down what happened next to the variable, until every operation had been completed. They would then, just as they had done with the map directions, backtrack to the answer:
Students who had been previously mystified by algebraic expressions found this approach much easier to understand and became proficient at solving problems of this type. The practice was then extended to writing out steps in the traditional manner, but students would still call on the problem-solving skills they developed by backtracking to find new solutions.