The Problem with Problems
In mathematics, problems are opportunities.
Read MoreLearning from the Math Wars
Educators have debated about the best ways to teach math for the last fifty years, if not longer. Is it better to tell students the rules and have them practice to perfection?
Or to ask them questions and let them puzzle things out? Is it more important to understand concepts or to perfect skills?
This argument became so heated 20 or 30 years ago that it was dubbed the “Math Wars.” In response, research was designed to compare the results of traditional teaching (explain and then make students practice), inquiry-based teaching (let students puzzle things out), and teaching that combined both approaches. The results were shocking. Inquiry-based and traditional teaching were comparable, though in different areas each was superior to the other. But the combined approach was found to be much worse than either.
But these results can be explained if we remember that students spend roughly the same amount of time on math in each classroom, regardless of the teaching method. So it’s likely that in the combined method classrooms, components of each approach were implemented incompletely and combined randomly. Exploration of a concept can take a long time, and a teacher might stop it prematurely to have students practice for a test. But if the process of exploration ends before students reach interesting results and analyze them, and drills begin before students develop an understanding of the concepts, of course the result of the learning process will be disappointment and confusion!
So how can we teach students to become capable math “researchers” and thinkers, and to gain solid skills that they can use whenever needed? Is it necessary to lengthen the class time to accomplish this?
The answer lies in being wise about combining both methodologies. The exploration of a new concept cannot be left to the hands of students alone. A teacher must work to motivate the students and gently guide them to avoid dead ends. A teacher is also there to ensure that the process of exploration continues at a decent pace and gives students the satisfaction and joy of an interesting result.
Practicing skills can’t begin before the underlying concepts are understood completely. And it must be introduced in time for students to use their newfound skills as a tool for another exploration process.
Only with this careful integration can students learn math in a smooth, logical, efficient, and satisfying way.
