Math Is Hard!

5 Replies to “Math Is Hard!”

1. The exact opposite of this is happening in my school here in California as I type this. As science department chair I am watching one of my best teachers lose her job because she is the “last hired-first fired” She has only been teaching AP classes and chemistry for eight years in our school.

   Another teacher has been moved from his normal class because too many students fail his science class because his standards are too high for “our kids.”

   I hope this report resonates with the public but I am afraid we are past the point of people understanding their pampered lifestyle of iPhones and fast food requires an educated citizenry to survive.
   /rant (Sorry but as my year is ending and these national reports pile up the system is moving the opposite way, its killing my optimism)

2. The biggest problem we have with regard to math in this country is that no one can decide whether our kids should learn math or do math. I sense in the curricula and textbooks I see in classrooms, that “learning” math in a passive sense is what we’ve decided on. Unfortunately, this produces poor results.

   In my own math teaching, I have always favored treating kids like mathematicians and designing units and lessons that use the math they find in their own real lives. We do “real life math” all the time. First we identify the categories of life experience where math occurs, then we develop our own problems based on those real life situations. Kids inevitably craft tougher problems for themselves than I would. And they get real life experience solving them.

   The other ridiculous discussion we’ve had over the years has to do with rote learning. Rote learning in math is perfectly acceptable for those things that don’t change. For example, basic math facts, certain measurements and conversions, etc. “Discovery” approaches or pure “Constructivist” methods are great for problem solving and unusual concepts. But they are inefficient when it comes to the simple stuff. And, surprisingly, that’s where most of our kids break down. Algebra is too hard when you can’t multiply 5 x 6 in your head.

   Finally, there’s good brain research (see Stanislas DeHaene’s “The Number Sense”) which shows that mental processing of math is very important to long term success. I do all kinds of “head” games with kids and they really seem to work well in terms of raising their capacity to process mathematical challenges. For example, how many numbers can you hold in your head at one time? Or jumping around on a mental number line.

   So, once again, I fear we’ll get a big bunch of standards but no techniques by which they might be effectively taught. Our “leaders” in the field seem to be a tad sheepish when it comes to the thorny subject of actually how to teach to a particular standard. (For the most part, I wonder if these people ever teach at all.) It’s sorta like a cook who won’t taste his own food because he knows it isn’t healthy. Or the CEO of a car manufacturer who won’t drive his own models because he knows they’re not safe. Some day, some smart policy wonk will see the value not in aligning standards with tests but in aligning curriculum with instruction that really works.

3. The Carnegie report appears to be another 30,000-feet view of what needs to be done. It’s surprisingly vague and absurdly overreaching (sure, we’ll change every school and peer group culture to be completely, thoroughly interested in and dedicated to learning math and science).

   It seems like Carnegie could do better. As in suggest that high school graduates be required to take (gasp) 4 years of math and 4 years of science! Or that it’s our middle schools where tons of students start to fall behind and lose interest.

4. Not all kids will be interested in these things at the time that they are scheduled. Should we just make them take the classes so that we can check a box? Kids won’t really get much out of a class they are taking because they have to. Make science and math interesting (could go all the way to “fascinating”) and many students will WANT to take the classes.

   Kids in elementary school are generally excited about science. It kind of dies after that — take a look at a few textbooks and you’ll see why.

5. ““Discovery” approaches or pure “Constructivist” methods are great for problem solving and unusual concepts. But they are inefficient when it comes to the simple stuff.”

   If the discovery approach is properly scaffolded, that is generally true. Not sure wha tyou mean by “pure constructivist”. If you mean minimally guided discovery, I disagree. Maybe so for students with large domain knowledge, and even then it can be inefficient — and ineffective.