"given an existing problem, it may be better not to do something, or even to do nothing, than to risk causing more harm than good".I've been contemplating the phrase in relation to math--specifically the teaching of math. In my job I am privileged to work with a wide variety of ages, abilities, grade levels, and teaching situations. I'm alternately awestruck by some students' mathematical thinking and downhearted to see some students--still quite young--who have already had their little mathematical minds messed up. Some of these kiddos, only a few years into their school careers, have decided that

*math isn't supposed to make sense*. Math is just a confusing, random, jumble of rules that they cannot remember...or rules that they can't apply to situations outside the 25 identical problems given on the daily assignment in their textbook. It's painful to watch a child pull numbers out of the air, as he assumes that a random guess has as much likelihood of being correct as anything else he might figure out. As an esteemed colleague said, "Nothing makes sense after you've had your thinking taken away." I worry about these kiddos. A lot. And they're found everywhere. In every grade. And in every school situation: home, private, and public.

Here we read:

A related section from the Hippocratic Oath has been translated asWhat if we applied it to the teaching of math?

I will follow that system of regimen which, according to my ability and judgment, I consider for the benefit of my patients, and abstain from whatever is deleterious and mischievous. I will give no deadly medicine to any one if asked, nor suggest any such counsel...

In the homeschool world we hear a lot of debate about the practice of "unschooling"; I hesitate to even mention it because the concept means such different things to different people. But I will say this. It is far easier to introduce mathematics to a child who has never been taught formal math than it is to try to reintroduce a concept to a child who has had his thinking taken away.I will teach in a way which, according to all that is currently know about learning mathematics, I consider for the benefit of my students, and abstain from whatever will prevent them from becoming the best mathematicians they can be. I will do nothing to mess up any mathematical minds (even if a fellow teacher, homeschooler, administrator, or standardized test points me toward unhealthy teaching practices), nor will I suggest any mathematical teaching strategies that may harm someone else's child.

First do no harm.

Blessed be.

ReplyDeleteThank you, Sue! And thank you for working so hard to undo the harm that has come to your students long before you ever started teaching them!

DeleteYou're a sweetie, Cindy, but I'm afraid I sometimes add to the harm. I wish we could let students learn at their own pace in college.

ReplyDeleteWe all add to the harm at one time or another. Me included. BUT I don't think that we'd have nearly the ramifications to deal with in the upper levels if things hadn't been so undone in the lower levels. Some of your struggling college students are struggling BECAUSE their mathematical thinking was taken away a long, long time ago. I see kids struggling because of what happened in their math classes only a year or two before. And I know it happened to me as a student. Probably why I'm passionate about the topic! :)

DeleteCindy,

ReplyDeleteI love this post! It is making me ponder my practices. I teach a K/1 combo and there are times when I feel the time crunch that I want to say, "Just do it this way." I confess sometimes I actually do say that. Your post is a great reminder that our goal is not to turn out children who score well on end of year tests to show mastery of skills, but to light the fire in children so they are mathematical thinkers (AND LOVERS OF MATH). Thank you again for making me think AND for raising the bar for my own teaching!

Camille

An Open Door

I have sooooo felt that time crunch. But the crazy thing is that if we let the kids think, we will turn out kids who score well on tests...AND light the fire to be mathematical thinkers and lovers of math. But we have to trust kids. Which is so, so hard to do in the current climate. Keep up the hard work...and the great reflecting!!

DeleteI decided to unschool because I was doing harm to my very bright oldest daughter.She is 9 y.o. and has a very logical and mathematical mind, EXCEPT when I try to make her do worksheets, then she bucks and won't work. I believe it's simply because she does not like the methodology but because I insisted for so long now she thinks math is hard and confusing. However if I need fast mental calculations she is the first to give me the correct answer. If we play word problems game, she always answers them correctly. She is very competitive, so she enjoys the games. If we are cooking she can figure out how to double or triple a recipe. She has no trouble with math unless I want her to memorize the multiplication tables or do a set of 20 repetitive problems. She loves to watch programs geared to teach math like Ruff Ruff man or Cyberchase. I got some logical thinking books and she loves to "play" and use them. So I am learning to relax and let her learn as she goes. I sometimes worry about higher math. Do you have any suggestions??? Do you think I can undo the damage and maybe one day she will like textbook math?? (who does anyway??)

ReplyDeleteIt sounds like you're on a great path. On higher math, one question to think about is how high do you think she'll want to go and what's the best path to achieve that level? I know that you can undo the damage, mostly because I'm constantly undoing of the damage that was done to me. I have learned more about math by teaching it (with amazing math mentor teachers to help me along the way!) than I ever did by having textbooks and massive amounts of rote practice. That said, I look forward to the day when more upper level math teachers are able to present math in a way that makes more sense. Look at the work of Dan Meyer (see his blog, dy/dan in my blogroll) and Jo Boaler (What's Math Got to Do with It?) While upper level math often equates "textbook math," it certainly doesn't need to. Upper level math should equate rich mathematical thinking...an extension of the rich mathematical thinking that should be occurring in the lower grades. Keep thinking and reflecting. You sound like an awesome mom/teacher.

DeleteInteresting higher level math abounds:

DeleteMathematics: A Human Endeavor, by Harold Jacobs is an alternative textbook, at about the level of pre-algebra. TheNumber Theorytextbook from Art of Problem Solving (artofproblemsolving.com) looks pretty conventional, but the thinking involved makes it very interesting for someone who likes math. The student I tutor is working through Euclid'sElements. I didn't think it would happen, because I found the text too hard to read myself. But he's getting a lot out of it on his own. There's a book titledMath Girlsthat's both a teen romance (anime style) and some very deep mathematics - I still want to work through one chapter again.At higher levels it becomes more important to find just the right match, though, between student and text. I'm open to those questions.

Thank you so much, Sue!! Great information for those searching at the higher levels...

DeleteThis is interesting to me. I joined this group to help me to do better with teaching Math. It was always my weakest subject. I never wanted anybody here to know that. But anyway, I wanted ideas, accountability and help, and I have gotten it here. Thank you! I kind of unschool, sort of, in a way. When it comes to Math, we have used workbooks of all sorts and tried many different curricula. I try not to convey my own negative feelings toward Math to my kids, but some of them seem to have developed their own feelings of not being good at Math. I actually took advanced Math in high school but had to work VERY hard at it. After graduating, I actually tutored Algebra and loved it! But I don't enjoy teaching Math. I usually just get my kids books that explain it really well, so they can pretty much do it on their own. I have 10 kids, so I have lots of things I have to teach, so I do the things I like the most. I have found out that I have a few who really enjoy Math and are good at it. My 11 year old son likes it, so I got him a book of word problems and balance math and a rubiks cube and some Math dice. I try to get Math type stuff for him as gifts. Most of my older kids enjoyed Cyberchase, but we don't really have any television anymore, not even PBS. I think I'm doing my kids more good than harm by not trying too hard to force a certain Math curriculum or way of doing Math on them. My 21 year old was kind of stuck on Geometry for a couple of years. He hated the proofs. I consulted a former homeschooler who has written some books about teaching Math from a biblical perspective, Katherine Loop. She told me about Geodaesia, and my son looked at it on Google books, and one day for several hours he studied how to figure out square roots of numbers. He did this just because he wanted to. The approach was more of an application type of approach, which he likes, and it uses geometry to teach how to survey land. He always hated memorization. I have had problems with several of my kids memorizing the multiplication facts even though I've tried Wrap-ups, Calculadders, Times Tales, Timez Attack, Math Blaster, etc. Most of my older ones have almost all of the facts memorized now. But the reason I'm commenting is to thank you for encouraging me by saying that it's better to do no harm. I think I could do a lot of harm by pushing and getting impatient and maybe even yelling and saying things I shouldn't to my kids. Let alone teaching them wrong! I actually pray a lot about how to teach my kids. As they need to learn the higher math, I believe they will be given the opportunities and methods they need. In the meantime, I will continue to teach them the basics and provide books and activities to help them think mathematically and encourage them to learn what they want to know. Thanks for this post. It encouraged and reassured me.

ReplyDeleteIt's interesting to read that you enjoyed tutoring algebra but don't enjoy teaching math. I wonder what makes the difference?

DeleteThe great thing with your kids is that there are enough to have rich mathematical discussions. Math is such a social activity that is too often make solitary. You could have amazing discussions with your group. Play games with a healthy amount of discussion about strategies.

On memorizing facts... It's certainly helpful. I like to be able to come up with a quick answer when I'm shopping, etc. But some of the math teachers that I most respect cannot memorize. They don't know their "facts." But they have an incredible number of math strategies to draw from...and can strategize about as fast as I can pull a fact from memory. Talk with your kids about different ways to solve problems. Ask them to show you another way to solve a problem. Have 3 kids show three different ways and discuss it together. And continue to provide that rich mathematical environment with books and activities and lots of "math strewing." You are doing some great thinking here. Keep it up! :)