In Pensylvania, homeshool kids have to take standardized tests every few years (at grades 3, 5, and 8). When he took the grade 5 exams last year, Peter did very well in all subjects, including math, though he 1) often says he hates math and 2) wastes a lot of time not doing math (staring into space and finding excuses to get up from the kitchen table) that he could spend more productively. He gets very discouraged/overwhelmed when he sees a blank page of math problems, particularly when he knows the process involved and doesn’t see the value of performing it that many times.
I’ve been working with him on that, with the help of the book The Ten Things All Future Mathematicians and Scientists Must Know (But are Rarely Taught) Each chapter first explains the scientific concepts (Occam’s Razor, correlation vs. causation, etc.) and then offers a couple pages of scenarios that require lots of numerical problem-solving. The extra time we spend front-loading the science concept, rather than jumping right to the drill, helps him to integrate the math (which he can tolerate, but otherwise does not enjoy) with the science concepts he loves.
We have a long tradition of reading science books at bedtime, and to Peter, this math textbook is just another science textbook. (Education win! But writing this reminds me that we’re not very far along in that book — I’ve got to step it up in order to take advantage of its usefulness.)
The heart of the disagreement between progressive math educators and mathematicians is whether students are acquiring a foundation in arithmetic and other aspects of mathematics in the early grades that prepares them for authentic algebra coursework in grades 7, 8, and 9. If not, they then cannot successfully complete the advanced math courses in high school that will prepare them adequately for freshman college courses using mathematics. To address these concerns, the president issued an executive order in 2006 forming the National Mathematics Advisory Panel, of which I was a member. The panel, composed of mathematicians, cognitive psychologists, mathematics educators, and education researchers (my expertise is in reading research, K-12 standards, and teacher education), and appointed by then-secretary of education Margaret Spellings, would examine how best to prepare students for Algebra 1, the gateway course to higher mathematics and advanced science, based on the “best evidence available.” For the panel, educational
equity meant not dumbing down content but enabling most U.S. students to travel the same road together to Algebra 1–before ninth grade–just as students do in top-achieving countries. The panel also spelled out the 27 major topics of school algebra that should be taught in every American high school to make us internationally competitive.The panel found little if any credible evidence supporting the teaching philosophy and practices that math educators have promoted in their ed-school courses and embedded in textbooks for almost two decades. It did find evidence for the effectiveness of a highly structured approach to teaching computational skills, called Team Assisted Individualization; of formative assessment, which entails ongoing monitoring of student learning to inform instruction; of the use of high-quality technology for drilling and practicing; and of explicit systematic instruction for students with learning disabilities and other learning problems. Despite the proven effectiveness of these strategies, many math educators view most of them with disdain–most likely because they entail more traditional, structured teaching. –Sandra Stotsky, City Journal