Are your kids good at math? How do you know?.....How I learned to Stop Worrying and Love Homeschool Math
Last year, the Atlantic featured a great article called The Math Revolution about how more American kids are doing math competitions and are doing well. It’s long, but an interesting read.
Though not the only point in the article, it touches on how bad we are at identifying kids who are good at math.
A few passages stood out to me:
The roots of [poor preparation in math] can usually be traced back to second or third grade, says Inessa Rifkin, a co-founder of the Russian School of Mathematics, which this year enrolled 17,500 students in after-school and weekend math academies in 31 locations around the United States. In those grades, many education experts lament, instruction—even at the best schools—is provided by poorly trained teachers who are themselves uncomfortable with math.
This past year I have had two of my children “hate math.” They came home from school complaining that math was boring and repetitious.
The new outside-of-school math programs like the Russian School vary in their curricula and teaching methods, but they have key elements in common. Perhaps the most salient is the emphasis on teaching students to think about math conceptually and then use that conceptual knowledge as a tool to predict, explore, and explain the world around them. There is a dearth of rote learning and not much time spent applying a list of memorized formulas. Computational speed is not a virtue.
Also, the children had both decided that they were bad at math - because they were not succeeding in timed tests (addition under 10 for one, multiplication tables for another). For unrelated reasons, my children have had IQ testing. They score quite high on quantitative ability. I don’t say that to brag - but to note that I was ready to reject the claim that they were “bad at math” because I knew they had intrinsic ability. If I didn’t have that information, I might have believed that they were struggling. The teacher told me that the 7 year old had trouble counting to 120 because she had missed a problem on an assessment (at the same time that child was easily adding 2 digit numbers in her head).
It was at this point that I decided to homeschool math (and a few weeks later, I broke with the school altogether and pulled my children out). When I saw how badly things were going, I thought I couldn't do worse at home. With some mostly empty workbooks from the local thrift store, we started doing problems at the kitchen table.
While I agree that kids need to learn fluency with numbers (first addition, then times tables) and that speed and accuracy are important goals, I found that the school system was imparting the following things to my children:
-speed is success
-math is memorization
-math work means repetition
-there is no creativity in math
If I was a parent with less resources, more demands on my time or less inclination to get involved, I might have simply said, “I know, math is hard for some people. It’s okay!” and allowed them to continue on the path to math illiteracy. I was fortunate enough to be armed with standardized test information and my own joie de numbers to reject the narrative they were constructing.
While I have been pondering all of this, I cam across this profile of Barbara Oakley called How a Polymath Mastered Math—and So Can You
about a woman who wasn’t successful at math until she left the army and returned to school, only to now be considered a math superstar. It furthered my belief that we turn children off to math quite early and often lose them forever.
All of this has me wondering, other than standardized ability (not achievement) testing, how do we identify kids with good ability in math? I was fast at math, and that’s how I knew I was good. How did you know you were good at math?
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As a 5th grade teacher, the one thing that peeves me the most is when I find that the teachers below me are doing timed tests. They are a complete waste of time and do not measure math ability. I have primarily worked with the math curriculum "Bridges" which is a conceptual based curriculum. I have provided a lot of professional development to teachers using the curriculum and one of the things that we often discuss is the mismatch between computational fluency (what is taught through Bridges) and fluency as it is presented through timed tests. Computational fluency is not about how long it takes to figure out a problem, but whether students understand how the numbers work and can decompose and sort numbers in an efficient manner to get to the answer. For example, do they understand that 2 X 3 is 2 groups of 3 and can they visually represent this either in their head or with physical/visual models to get to an answer. We typically start by building a model, move to a color-coded visual, until students are able to do visualize in their head. A student wanting to solve 2 X 8 demonstrates computational fluency if they are able to use a strategy that is efficient, but not necessarily under time constraints. For example, can they decompose the number into 2 X 4 = 8 and 2 groups of 8 = 16. When it comes to other traditional algorithms, Bridges and many other conceptual math programs focus on building the the concept and letting the students discover traditional algorithms after playing with their own constructed algorithms and other scaffolded algorithms that are built around visual models. When students understand the concept thoroughly, the standard algorithms begin to make sense, rather than being a memorized process.
The bolded phrase somewhat concerns me. If the teachers are uncomfortable with math themselves then it could show when they teach students. It may pass on to the students and make them feel uncomfortable too.
There is more to math than memorizing the time tables and algebra. I'm more of an applied math/stats type person who likes to see math applications and motivating examples. Showing the students what math is used for can inspire and motivate.
I do agree with the statement
there is no creativity in mathfor early math learning where there is a large emphasis on algebra rules and memorization. Math is like a language where you got to understand rules and then later you can apply it later in different ways. This application part takes a long time unfortunately.I disagree, but I appreciate you commenting. I think there is room for "hard math" in those ages. You should check out my sprocket problem or kangaroo math - both examples of challenging math for early elementary.
I may have been unclear in my last section of the post where I refer to the algebra rules in preparing students for calculus.
I think the term "hard math" can vary depending on the person. We may have different views on "hard math". I view it as the theoretical and abstract type at the university level. Regardless of math level, math is a challenging and time consuming subject for many.
I did see one of your other posts where there is a question on the number of paths from one point to another. That is a good question in the sense that it promotes problem solving and not so much on memory.
Oh! I strongly suspect we have very different views on "hard math" - I think that I am in the running for "Most Frequent Math Commenter and Poster With Very Little Math Training." What is hard for me is probably not hard for most of the math-y people here. What I mean by "hard math" I should have defined better. For my kid who can mutliply two digit numbers, finding 25x25 is not hard. However, identifying a pattern of how to quickly calculate 35x35 or 24x24 etc. is "Hard Math". In my mind "hard math" is something that can't be solved with a calculator - something you need to think about and be creative to solve - no matter what basic skills you are starting with.
I've written about this elsewhere - but for anyone reading this and thinking about homeschool math - I think that Beast Academy introduces "hard" concepts at a much earlier stage and I love that.
I loathe standardized testing and Common Core for this reason. Both my kids have attention deficits and lower than average working memory, my son especially. Which means neither does well on rote memorization and regurgitation. I find that applied math, however, has been excellent for us to reinforce concepts I am trying to teach. We're not just learning these concepts, we're immediately using them. Fractions are inherently more interesting when being baked into cookies.