By Mark
I'm lucky that my 5-year-old son comes to work with me each day. His preschool is housed in the high school where I teach 9th and 10th grade. In fact, his classroom is literally across the hall from my 6th period and just around the corner from the room where I teach the rest of the day.
Not long ago, I went in to visit him and his peers during my plan period. He and his little buddies were sitting around a table doing a math worksheet. Two frogs on lily pads plus five frogs on lily pads makes a total of seven. Three frogs jump off and you're left with four. Good stuff for pre-K. Sure, an occasional finger was employed in these basic mathematical operations, but for the most part this computation was quick, confident, and alarmingly accurate for a bunch of pre-K-ers.
I listened as the little folks' conversations about math escalated until those little five-year-olds were adding and subtracting frogs accurately up in to double digits, and I kid you not, I heard one boy talk to another about the "pattern" he saw that the numbers repeated, and yes, he used the word "pattern." He pointed out that if he added three to nine it made 12, and if he added three to NINEteen, it made 22, and if he added three to twenty-NINE if made 32. Good stuff…not every 5-year-old will get that, but it doesn't seem unreasonable that every 15-year-old should.
I work with 9th graders daily, assisting them with their science, math and English homework. These are mainstream, good kids enrolled in "college track" coursework. So often, when I assist them with their math, I see a common problem–the inability to do basic addition and subtraction computation, even of one- and two-digit numbers. I find it astonishing that in the near decade of education between pre-K and 9th grade that such fundamental skills do not get mastered. Where is the disconnect? Why do I have 9th graders who still use their fingers to add numbers under 20 and cannot confidently, immediately state that nine plus three is twelve without stating the answer with the inflection of a question? I've had kids who are combining like terms to find an unknown in Algebra I, such as 3x+7x= 40, and they either pull out a calculator to compute the sum of 3 and 7, use their fingers, or simply guess (eleven?). I hear from my math counterparts that kids actually do well with the overarching concepts of Algebra, but where they fail is in computational fluency. How does this get missed?
I think we need to make our students play Yahtzee from a young age. It should be required curriculum.
I'm not a math teacher and I'm not intending to criticize math teachers. And I'm sure that there are plenty of language arts concepts that other teachers cannot understand why kids haven't mastered ("Why don't they just capitalize the first letter of the sentence! This is AP Bio, for crying out loud!"). How is it, then, that these kinds of basic skills which are masterable by the youngest of our ranks are still the focus of so much energy by the time kids get to high school?
I don’t know, Mark. It’s kind of fun having my students think I’m a genius because I can multiply 23×12 in my head and get 276.
But seriously, you’re right. I can’t teach Algebra to a student who doesn’t know the perfect square numbers, or what factors of 12 add up to 7. Or what factors of -20 add up to 1.
And I agree with Tom, at one point they knew. I think teachers at each grade level are doing what they need to do, we just need to constantly reinforce computational skills.
I think it’s a matter of using it. Remember in the seventies, when adults swore that calculators would ruin our ability to add? They discussed the effects of the slide rule and other crutches.
As a language arts teacher, I see the same weaknesses with spelling that you see with computation, because kids rely on Spellcheck.
I think the solution is to be explicit with the usefulness of the skill, and then drill, drill, drill, like basketball players do with free throws. It wouldn’t take much time out of the day to have them partner up and run through a pack of flashcards, even as tenth graders.
When I was a sub in a math class, the eighth graders were crazy about a contest that was running between the periods. The game was a series of cards, passed out to the kids. One card said, “5+1” and the kid who had “6-3” had to jump up and read his card, his first number being the answer to the previous card. Then the kid with “3-4” had to jump up, then “-1+8” and so forth. They were timed, and the scores recorded on the board. They LOVED it.
Actually, I should do that with my 10th grade LA classes. It would be a good sponge activity.
I’m not trying to indict the elementary teachers or the math teachers—many fundamental skills of elementary school language arts consume much of our time and energy at the high school as well.
If they lose it when they don’t use it, it worries me that they go through some period of life where they aren’t using it therefore can lose it…
As an elementary teacher, I watched this happen. We’re only just now starting to transition out of it. There was a movement in math that sought to get kids to reason about math. The curriculum we all adopted withheld algorithms and formulas and made kids “discover” how to solve problems. The kids played games that were fun, but didn’t always make obvious connections for them.
We spent far too much time sharing how each student solved the same problem, celebrating the differences. It was like a diversity fair in math class. We had to honor the different ways that everyone found to solve a simple math problem and emphasize that there’s not just one way. The algorithm may be one way, but all the others were equally valid.
Teaching algorithms became frowned upon. I know teachers who hid computation worksheets when they saw their principals coming. And I still remember the awkwardness I felt the day the surprise walk-through came into my classroom when I broke down and decided my kids were learning long-division. So along with that, memorizing facts became something teachers were discouraged from teaching.
It’s not the kids’ fault. It’s the lack of balance between math reasoning and giving students fool-proof strategies for solving math problems. When kids fell way far behind, we left them in their math class and pulled them out of science or social studies to teach them the same thing they didn’t understand in class with a smaller group of students. We even made parents feel like idiots, because they could no longer help their kids in math.
Sorry, Mark. Whose idea was this and how did they convince us all to get rid of all our books on computation? I don’t know. But, the publishing companies made a killing.
We’re doing our best, Mark; believe me. I spend at least ninety minutes a day on math, plus homework.
One of the unique features of math is that if you don’t use it, you soon lose it. I can’t tell you how many times I see one of my former third graders two or three years later and just out of curiosity I’ll ask them something like 6 times 8? They’ll hem and haw and make a wild and incorrect guess. And these were kids who knew their times tables fluently when they were eight.
Mrs. Bluebird recently had a blog entry on this subject. http://bluebirdsclassroom.blogspot.com/