I am sitting on an airplane with the movie Footloose playing in the background. True to my nature, watching the movie makes me think about math education. In the film, teens are unhappy about rules and expectations imposed on them. In the math classroom, students are similarly unhappy with the requirements. Are there any real parallels here? Let’s see.
Let’s start with the movie. Dennis Quaid plays a preacher who encourages his small town to outlaw dancing in public as a response to his son’s night-life induced, deadly auto accident. A battle ensues between arcane laws designed to quell youthful passion and a teen’s right to cut a rug in public. The film is one part morality play and three parts “dirty dancing”. One thing is for sure; these kids can boogie! So the drama is this: can the town elders and teenagers co-exist in a way that fosters joie de vivre? For the answer, watch the film.
Let’s move to math. Educators and policy makers play the role of delivering the compulsory curriculum that students must master. Students get to middle school and the math curriculum does not resonate for them. They regard math as irrelevant and too difficult, and many students rebel. They shut down and let themselves fail, or they find workarounds to simply pass the class in a relatively mindless manner. They decry math as stupid and their parents have little retort to change that tune. So the drama is this: can educators deliver curriculum that fosters joi de math? For the answer, keep reading!
The good news: middle school math is fundamentally relevant to students’ lives. Statistical analysis, ratios, rates, and the whole domain of proportional reasoning are skills central to success in business, money management, political and social movements, personal and public health, sports analysis – almost every personal and professional endeavor. If these are taught visually and conceptually, with an aim towards deep understanding, students will be motivated and connected. We should take great care and time to build these skills and foster these understandings, and we should reward students as successful mathematicians once these skills are attained.
The bad news: we, the elders, have taught middle school math poorly, using arcane methods. Much of middle school math has been taught on a procedural basis, with little attention paid to real life context or conceptual modeling. For example, the division of fractions is typically taught with an “invert and multiply” solution that involves virtually no true understanding. Liping Ma made this abundantly clear in her breakthrough book, Knowing and Teaching Elementary Mathematics (Ma, 1999), where she devoted a remarkable chapter to the failure of American educators to teach the division of fractions effectively. As students have moved beyond fractions into the vast domains of proportional reasoning, they have been ungrounded and often confronted with number-heavy, context-light curricula that turn off their passion, and turn on their fears.
More bad news: we, the elders, have positioned proportional reasoning, statistical analysis, and related topics as a gateway to algebra, with little intrinsic value or tangible reward. We have delivered a clear mandate: “You must pass algebra. Fail that class, and you fail in school . . . and you fail in life.” This is an unhelpful message, and disconnected from reality. Those students who master middle school math can tackle most any career, and should be celebrated!
Well, guess what? In our math movie, the elders are coming through! The next generation standards, whether called “Common Core” or tagged with another title, place deep emphasis on appropriate content areas, emphasize algebra in high school where it belongs for most students, and articulate Standards of Mathematical Practice that describe good teaching and learning. Visual learning, math discussions where students articulate their thinking, modeling with mathematics; these trends are transforming adolescent math into a much better dance! Students will better understand fractions and other challenging topics, teachers will ultimately be more relaxed with a workable curriculum, and everyone will have more time to focus on the dance-steps of mathematics applications in the real world. I really believe that we have a chance to make a big change and put many more smiles on the faces of both teachers and students.
Let the kids dance! Oh, and one more thing, be sure to check out the moves they make. Middle school math is not a stepping stone to “better math,” it’s hot stuff that most of us need every day to fulfill all of our daily needs.
[includes edits made in 2015]