Dear Academic Approach Families and Colleagues:
Next, we come to math. Many students first come to us with a learned dislike for math after years of struggling in school. The questions they then encounter on the SAT and ACT seem at first only to reinforce that predisposition. Take these algebra questions:
Students might at first look at these questions in horror—they may seem far from the work they have done in any of their classes in school, and they don’t look too much like the algebra equations they’ve seen in class. Algebra is a core math skill that many students first encounter in middle school—but often, the questions on the SAT or ACT are much more challenging versions of those early skills.
In the first of these two items (among the easiest on an SAT), you can see that students aren’t just required to do algebra manipulation or identify the elements of an equation in slope-intercept form—they are required to really understand the structure of a linear equation and what each value means in a “real world” setting. In this case, they need to understand that the y-intercept ($6.50) represents the “flat fee” cost of the mug, whereas the slope ($2.30) represents the cost of each refill.
In the second (more challenging) question, these same skills are applied to a system of inequalities. Students must understand the functions of each variable and element and then convert what they read in the (quite long!) question into math language.
We often work with students who do quite well in Algebra, Algebra II, even Calculus courses in their school but still struggle with questions like these. To solve problems like these efficiently and accurately, our approach is to incorporate in-depth understanding of the skills with relational thinking between mathematical concepts and creative methodology. With a strong basis in relational thinking, students often return to their high school and college-level math courses more confident as adept problem solvers with a flexible skill set.
Matthew Pietrafetta, Ph.D., Founder & CEO