Algebra 1: Not just how but why
“Just show us the steps!”
This is a common plea in my high school math class. Many of my students don’t want me to explain why or how . . . and they definitely don’t want to have to deal with a word problem! Instead they want me to just show them what to do.
But is this the best way to learn math? Is it better to just learn one skill at a time then move on to something new? Or should students focus on conceptual understanding and spend time on projects and multi-step word problems? I did a mix of both when I was homeschooled and I benefitted from both approaches.
In elementary school I worked on problems in a book called Figure Out which was a collection of word problems written by other home educated students. The word problems were all mixed together so I had to learn to apply different skills at different times. In middle school I joined a math club where we read biographies of famous mathematicians and traced the development of mathematics throughout history. Additionally, we formed a MathCounts team and competed regionally against other schools. We learned to solve word problems quickly using any method we preferred as long as we could find the answer. Guess and check quickly became my favorite strategy. Afterwards we would all compare answers and I’d learn from my teammates. In high school I used textbooks published by University of Chicago School Mathematics Project (UCSMP) that incorporated projects and challenge problems that encouraged me to continue using creative thinking as I mastered new skills.
However, math wasn’t solely devoted to projects and clubs. There is always a set of skills that have to be mastered and there is no replacement for textbooks, clear examples, and lots and lots of practice problems. In elementary school I worked on “mad math minute” worksheets until I had memorized my basic math facts. In high school there was no alternative to memorizing trig identities with flashcards—there isn’t really a way to make that more exciting. And the vast majority of time I spent doing math was devoted to completing a long list of exercises in a textbook. Without this foundation I never could have studied calculus or succeeded on the SATs– procedural errors would have bogged me down.
When I designed the Aim Academy Algebra 1 course, I took all of these experiences into account. We will be completing lots of practice problems, memorizing certain properties, and even taking time to review basic skills if necessary. But students will also complete projects, discuss different methods for solving the same problem, and connect the content to their lives. This combination of procedural and conceptual learning establishes long-term retention. And success in math is the first step to a love for math! That’s my ultimate goal for all my students.
Update: Kristen Lauria has taken over teaching Algebra 1 for Aim Academy, using the same approach and textbook. Kathryn still teaches SAT Math Prep throughout the year for Aim–a course that reinforces conceptual and procedural understanding across algebra, geometry, and trigonometry.