math mumblings

Last night we had a barbecue and had some of our good friends over. Alfredo did an awesome job barbecuing and we had a lot of fun. (Thanks Alfredo!!! You worked hard.)

While we were all visiting, talk turned to school and even to the math program used by the local elementary school. Teaching math has changed a lot since any of us were in school and I know that many parents are surprised and even sometimes upset by some of the changes. I tried to explain the reasoning behind some of the changes. Even after the barbecue, thoughts kept tumbling in my head about teaching math (as I've mentioned before, I am passionate about teaching and bringing up education is one way to get me going... I try to shut up before I drive everyone crazy, but don't always succeed). So here are a few random thoughts about teaching math.

First, since our nation is so caught up in multiple choice testing right now, here's a little multiple choice test for each of you readers to take.

1. How did you feel about math as a kid?
a. I hated it.
b. I tolerated it.
c. I loved it!

2. How well did you do in math as a kid?
a. It was my worst subject. I was terrible at math.
b. I did pretty well, but I didn't REALLY understand it or like it.
c. I was a straight A student in math and I totally got it.

3. When you got to high school or college, how many math classes did you take?
a. I couldn't even pass basic algebra or geometry.
b. I took the bare minimum to graduate/get my degree.
c. I took as many math classes as I could.

4. When you reached higher level math classes (advanced algebra, trig, calculus), how did you feel/do?
a. It felt like I had accidentally walked into a third year Russian class, and had never taken Russian before.
b. I did okay, but I had to spend hours and hours studying and get some extra help.
c. I loved the challenge and did well.

So, I would guess that most people picked A's and B's. My mom was a math major in college and taught high school math for several years. I always did well in math because I was good at plugging in the formula or memorizing and using the algorithm. But honestly, despite my mom's background and my good grades, I really didn't understand math. I was just good at following the rules. Then I took AP Calculus and it felt like a foreign language. I didn't have a good enough understanding in why math worked to do well in calculus.

Today, the emphasis in teaching math has changed from learning one algorithm and solving a thousand problems using that algorithm to understanding how math works and finding a way to solve problems that works/makes sense to you. Most of my students end up loving math.

NCTM (National Council of Teachers of Mathematics) has done a ton of research on what works and have developed a five strand approach to teaching math: Understanding, Computation, Application, Reasoning, and Engagement. Good teaching does all of these things. It DOES teach computation and kids should learn their facts. But it ALSO helps kids (adults) to understand how and why math works, to be engaged in difficult math problems, to be able to articulate their thinking and apply math to real life. Someone said that their child's teacher said "It isn't about getting the right answer." I would amend that to "It isn't JUST about getting the right answer."

A few more thoughts:
1. Of course, kids need to be able to do basic (and advanced) computation... +, -, x, and division. But if a child can do 15 problems correctly, is it really a good use of time to make them do another 45? And if a child CAN'T do 15 problems correctly, are they suddenly going to if you give them 45 more? (NO! If they get it, they get it. If not, they need to be retaught.) So today you'll usually see less problems on worksheets.
2. There is a stronger emphasis on rounding and estimating. I think this is good. How often do you REALLY, in real life, have to do long division or add up a bunch of multi-digit numbers without a calculator? Yet, I"m always estimating. As I grocery shop, I estimate how much I'm spending. As I get ready, I'm estimating how long it will take me to get to a certain place and what time I need to leave. I sometimes even estimate when I cook (although usually i follow recipes carefully). If I need to figure out an exact answer, I usually use a calculator. I can Add or divide but I rarely do. If I need to know what 472 x 31 is, I'll either grab a calculator or I'll think well, 500 x 30 =15,000 and 450 x 30= 13,500. So it's between there, about 14, 250.
3. If kids love math as young kids (or science or reading or whatever) they are more likely to be willing to put in hard work and keep trying when problems are difficult. Engagement (in any activity) is a huge part of people's willingness to put in an effort to succeed.
4. Most of us were taught one standard algorithm how to add or subtract. That is just the algorithm that someone decided should be taught. It is not always the easiest, fastest, or most accurate. In fact, other algorithms are taught and have been for years in other countries. Teaching kids more than one way to solve a problem helps more kids to find success. I shared this last night, but the standard way we were taught to subtract with regrouping has 52 ways you can make an error. But there are other ways that are less error prone and work just as well.
5. Programs are only as good as the teachers who use them. NOOO program out there is fail proof or can make up for poor teachers. But poor programs and some school's/district's insistence on using them can seriously hinder good teachers.
6. Again, facts are important, but they are less important, in my opinion than critical thinking skills, reasoning skills, etc. I would rather have a child be able to explain why his way of solving a problem works or be able to see how a skill learned in school is applicable to his life at home than have him be able to do 100 multiplication facts in 5 minutes, but not really understand what it means. (That was me as a child!)

I hope and believe that if math is taught well using these newer methods, then most kids would answer my multiple choice test with C's and B's, not A's and B's. That has been my experience.


SORRY... probably most of you could care less about all these ramblings about math. :) But at least getting them down, gets them out of my head so I can think about other things.