“Fuzzy math!” says one group.
Those two nifty little catch phrases seem to neatly encapsulate the discussion around math books these days.
On one hand, you have groups that despise the conceptual math books as an edu-fad. They feel (generalizing broadly here) that these types of books/curricular materials only expose kids to a bunch of different methods of solving the problem to find their own best way but don’t invite mastery of a concept or even an algorithm. For the folks who find these books fuzzy (not in a good way), proficiency and learning an operation or process until it becomes automatic is sacrificed to “feel good” notions of collaborative work.
Then on the other hand, you have those who tout conceptual math books as the only real way for kids to truly understand not only the what of math, but also the why. This group finds (again, broadly generalizing) that kids being able to explain the why of how they got to an answer as more important, often, than the answer itself. They point to what is derisively known as “drill and kill,” (likely the type of math instruction that most of us over the age of 30 has experienced) where a concept is presented with The One Right Way to solve the problem. Then students are given thirty or so problems to practice the algorithm, over and over. Sure, kids are doing algorithms like little robots, but this group believes that the kids don’t often understand why they are doing it.
And between those two poles is where the rest of us lay, right? And the bickering can be dizzying, inducing a kind of math whiplash in those trying to sift through the information. So, what are the best books to teach math to kids? How can we know if they truly understand concepts and even then, how would we measure it properly?
At Zeno, we’re truly curious to hear what you think about this.