I recently read an article (Math Meltdown by Patrick Welsh) sent to me by my superintendent about math instruction in the US. The basic premise of the article is whether or not math instruction tries to cover too much material at the risk of not allowing students time to learn all the basic facts really well. The author asserts that across all subject areas, instruction now focuses on conceptual thinking rather than some basic memorization. So students are being "trained" to think about big pictures and problem solving at the risk of not having basic skills. Welsh believes that it is necessary to put more emphasis on teaching kids basic skills - addition, subtraction, fractions, whole numbers, etc. - in the early grades and leave the conceptual thinking until kids are teenagers and have a better ability to think abstractly.
This has been a great dilemna recently. I felt the pull as a classroom teacher myself. I had so many standards to cover to prepare my kids for the state test (PACT) that I felt like I had to cover every standard to make sure that kids would be able to attempt every question on the test. What I didn't realize is that by covering the surface of everything, that I probably didn't do a great job of teaching most things. I was going an inch deep with most math skills, enough for students to give it back to me successfully on an assessment, and covering a million areas.
I look at it now and see that it is probably more important to cover less topics (an inch wide) and go deeper to make sure that kids truly understand the skill that is to be learned.
This approach to teaching takes great skill, because with a heterogeneous classroom, some students will be ready to move on well before others. This requires a teacher to differentiate the curriculum to make sure that all students' needs are being met.
However, in SC, we still test students at the end of the year on a "million" topics covering all of the standards. Maybe we will get to the point where we decide to have fewer standards in order to cover them more deeply. Our district has adopted a math program (Everyday Counts Math) that promises to strike a balance between conceptual thinking and basic skills (memorization). I don't know if we will ever get to the point where we can cover math skills a mile deep until math standards are rewritten to include fewer skills and are more age appropriate.
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