Whose fault is it that you aren't good at math?

Yesterday, Seth Godin posted Good at math on his blog. There was a lot that I agree with in this short piece. For example, the second paragraph begins with:

I'll grant you that it might take a gift to be great at math, but if you're not good at math, it's not because of your genes.

Unfortunately, this is followed up with:

It's because you haven't had a math teacher who cared enough to teach you math. They've probably been teaching you to memorize formulas and to be good at math tests instead.

I am not surprised that Godin employs the "blame the teacher" canard. Our nation loves finding easy explanations to complex problems and, therefore, falls back on the "bad teacher" narrative on a regular basis whenever it comes to problems in education. However, this explanation of why you aren't good at math misses an important point. A point Richard Skemp makes in Relational Understanding and Instrumental Understanding.

I used to think that maths teachers were all teaching the same subject, some doing it better than others. 

I now believe that there are two effectively different subjects being taught under the same name, ‘mathematics’.

Skemp's realization can help us to make an important distinction. It isn't that your teachers didn't care. In fact, probably the problem was that your teachers, like the rest of our society, cared too much - cared too much about you being good at math tests. And this is the crux of the problem (and another place where Godin and I can find some agreement). In the third paragraph, he writes:

Being good at standardized math tests is useless. These tests measure nothing of real value, and they amplify a broken system.

So here is what I wish Godin had written in those two paragraphs (my edits in blue):

I'll grant you that it might take a gift to be great at math, but if you're not good at math, it's no because of your genes. It's because of your experiences. You did not encounter in math class the experiences you needed to be good at math. What you received, because of our broken system's obsession with test scores, were experiences meant to prepare you to be successful in schoolmath - memorization of facts and formulas that can be easily assessed using standardized-tests.

What can we do about this disconnect between math and schoolmath? We can begin by recognizing that being good at standardized math tests is useless. These tests measure nothing of real value, and they amplify a broken system.

What do you wish Godin had written? Because until we can understand the problem, to be able to put it into our own words, it will be nearly impossible to solve it. 

Lesson Planning in Tanzania - Poa

Collaborating at the Outpost Lodge

For the last post in this series on what I learned from my Study Abroad experience in Tanzania, I try to combine the themes from the previous three posts - resourcefulness, patience, and acceptance. In order to do this, I want to tell you a story about lesson planning in Africa. Each night, Sunday through Thursday, the teachers gathered to plan for the following day's lesson. The teachers were encouraged to collaborate, and the professors were available for consulting, if needed.

One night, a teacher came to me with a question about a log table.

She was teaching the Tanzanian students how to use the table in an upcoming lesson but she was unfamiliar with how to use this particular version. This made sense, since she had no experience with this type of log table. To be honest it took me a few minutes to understand how the table worked; it has been awhile since I did logs without using a calculator.

It would have been tempting to dismiss the table as ancient history and focus on applying logs in some real-life situation using available technology. I certainly have argued this before - making a point that "there's an app for that." In this situation, however, the teacher accepted that this was not ancient history for her students. They would be expected to know how to use tables like this for the national exam. And since the textbook was the available technology, she said "no thank you" (hapana asante in Swahili) to simply relying on our method of mindlessly plugging numbers into a calculator.

Another thing you should know is that there was only the single textbook for the entire class. Copies were difficult to make, so the teacher had to be resourceful. She took her hamna shida attitude (Swahili for "no problem) and began thinking about how we had come to understand the table. A breakthrough had occurred when we noticed the relationship between the log (2) and log (4). The teacher could write those values on the board and ask the students to consider how the table might be used given what they knew about the laws of logarithms. Then the students could share and critique the different ideas.

MO Snow Plow Convoy

Sure, the teacher could have sped up the lesson by focusing on the process (Skemp's Instrumental Mathematics), but we wanted to take it slow (pole pole). Making time for students to struggle and persevere with a problem is worth it. Recently, I heard someone share the term "snow plow parents" - people who make sure that no obstacles get in the way of their kids. In my opinion, teachers who focus on teaching Instrumental Mathematics are practicing the same principle and do students a disservice.

In this situation, focusing on what Skemp calls Relational Mathematics put logarithms into a context: reading a table. Sure it might be an out-of-date skill for us, but it was real for these students. Also, the students could use this experience of decoding the next time they had to understand something difficult in a mathematics textbook. We hoped that by combining all of these elements the students would experience a cool (Tanzanians might say, "Poa!") way to think about understanding the table and what it means to do mathematics.