Duh.

However, the article goes on to prescribe the cure: "focus on the process of learning math instead of simply trying to get students to churn out the right answer... A classroom culture where students aren't afraid to fail and are encouraged to learn by talking through wrong answers is optimal."

As someone that's actually in the classroom, these sorts of answers just piss me off. It's not that there isn't a

*lot*to be gained when students are willing to fiddle with an equation for a bit, or look over incorrect answers to learn to spot mistakes and learn from them. There absolutely is.

The problem comes in that students aren't willing to. All too often, students feel they've spent far too much time on a problem already, and having to look it over a second time is asking far too much. They're done. Time to move on. I've always offered students the option to take their homework, identify mistakes, correct them, and resubmit it for a good portion of the lost credit back. But even with this generous incentive, student's don't participate.

As far as process based learning, this too is a fantastic idea... but again overlooks the reality of the situation. Memorizing a set of steps to solve a quadratic equation by completing the square isn't nearly as good as teaching a student why completing the square works and having them work out the process behind the steps. But the reality is that this is a far deeper level of learning. Memorization of a few steps is the foundational level of Bloom's Taxonomy. Applying them is only the third. But a full understanding such that a student could fully understand the methodology is near the very top. And unsurprisingly, that deeper learning takes more explaining, more examples, and more

*time*, which is often at a premium in the classroom.

And even if I had that time, students again, don't want it. It doesn't feel solid enough for them. As a recent example, I concentrated heavily on the concepts of solving quadratic equations in my algebra II class. Explaining, the zero product property with factoring, and why when you complete the square, you need to take half of the coefficient on the linear term and square it, going through the derivation of the quadratic formula. The steps were, of course, all there, but it got so lost with all the rest, the student failed the test with a 40%.

I let her have another week to study and again, concentrated, initially heavily on the theory behind the machinations, but again, she made it clear she was utterly confused. So on the last day, I had her write out a list of the steps for each method, use them as a guide on a few practice problems, and suddenly, she was immensely confident. On her retake she scored a 96%.

So what's the lesson here? Distilling math into rote memorization of simple processes lead to significantly decreased anxiety and subsequently, higher test scores. Of course, I fully realize that if tested on these methods in a year, this knowledge will be nearly completely gone. It's not an ideal situation, but given the alternative, frustration and failure, I'll take the battles I can win and hope that even if the process isn't fully remembered, it's easier to learn a second time around and crystallization comes then when the knowledge and experience base has been expanded.

It's not the best solution, but it's reality.

## 2 comments:

I'm with you on this.

Fear of Math is real. If one adds 2 + 3 and gets 6, it's not close, but wrong. All math requires careful approach, careful execution, and careful cross checking. For example, in 2 + 3, start with two fingers, and add three more. The answer is 6. But 2 is even and 3 is odd, and an even plus an odd is always odd, and 6 isn't odd. All this careful stuff requires a huge investment, and if there is a percpetion of likely failure, the return on investment calculation (which for some reason is easy for everyone as it is a right brain function though apparently with output directly to the amygdala) comes up negative. It's no wonder that no one wants to do it. Just for fun, anxiety shuts down short term memory. Proof positive that God isn't very smart - though i can sort of see the evolutionary advantages.

My approach has been mostly to make the work more reliable. For example, when my son was adding 2 +3, he got 4, 1/3rd of the time, 5, 1/3rd of the time and 6, 1/3rd of the time. I had to watch him do this quite a bit before i figured out that he somehow was taught counting on his fingers in an unreliable manner. I introduced him to the japanese abacus, and in twelve weeks his addition and subtraction was reliable. I then showed him that he could use his fingers like an abacus (for two digits), and his math scores went from behind the class to ahead. Also, every time we were in the car, i drilled him mercilessly on "what is seven plus eight", "what is eight plus seven", "what is fifteen minus seven", and "what is fifteen minus eight". He eventually relented and memorized the answers. He was, however, incredibly stubborn. For the record, his memory is astonishingly good. He can normally repeat anything i've said just once in the past year verbatim with minimal prompting.

But in 7th grade, i'd spend all weekend getting him caught up with his homework, and he refused to turn it in. The next weekend, i'd spend all weekend making him do it over. Old homework that was finished started appearing out of nowhere, but i still couldn't get him to turn it in.

I've just reviewed my own K-8 report cards. While i was always at least a little above average in math, in 8th grade all my grades jumped up permanantly. I recall nothing of the sort. My son seems to have had a maturity growth spurt at the end of 7th grade. I hope so.

Just out of curiosity, have you tried khan's academy? I'm over 30 and was able to use their exercise dashboard to relearn most of the math I'd forgotten in school. Setting up math as a tree and making a game out of it (complete with achievements) makes it addictive as hell for those with OCD.

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