We overtalk the matter of education reform and the achievement gap, and we do too little. I increasingly observe that what we need to do is very clear, that we need to cut way back on the verbal exchanges about the key issues with regard to educational advancement in our K-12 schools, and that we need to start applying the elbow grease in much greater quantities. But that is an implicit problem. Adults tend to want to make themselves feel very smart by intellectualizing about matters of educational philosophy, rather than simply to sit down beside a child and teach her or him what that student needs to know at the relevant grade level.
Take math, for example. Math education professors and others tend to discuss approaches to math instruction as if such discussion involves some really perplexing issues. Often such discussion assumes that students need to be drawn to math through games and projects and activities that make math fun and engaging. Of course, this is one of many matters in which adults have vested interests in the education of K-12 young people, because math education professors (as opposed to professors of math as a legitimate discipline)would have no jobs if enough people realized what actually needs to be done rather than discussed.
At the kindergarten through Grade 2 level, students need to learn how to add and subtract, including eventually the knowledge of how to "regroup" (carry and borrow). Along the way they also should acquire knowledge of such things as calendars and time recognition (clocks and watches), but these latter things tend to fall into place when the strong number sense implied by addition and subtraction is acquired.
Most of my students in the New Salem Educational Initiative who begin studying with me as kindergarten or Grade 1 students tend to acquire all of the above skills by Grade 2 and to move on to multiplication. I have students as young as those at Grade 1 who have mastered their multiplication tables from 0 through 9, a skill that traditionally has been taught at Grade 3.
So my veteran students are ready at Grade 3 to move on to multi-digit multiplication and division. From there they progress as fast as time and care allow through a sequence of skills involving fractions, decimals, percents, proportions, ratios, and probability. They learn how to deal with increasingly sophisticated data, graphs, and tables. By Grade 6, my veteran students are ready for algebra and geometry of the sort that traditionally has been taught at Grades 9 and 10. So engaging in these subjects at such a young age, they gain the intellectual weight and ballast to thrive when they get to algebra and geometry in school, and they are laying the foundation for success in trigonometry and calculus.
Many employers would be thrilled if they had more applicants who know math at the level mastered by most of my students by Grade 6. How do I impart knowledge of math to my students? I just show them what to do. This is what would deeply disturb many math education professors and those who would like to discuss math instruction as if students do not like math and as if math instruction is some recondite matter for adult intellectualizing. It isn't. When I teach students addition and subtraction by sitting down beside them and sketching out problems on a yellow pad, they get it. They like it. Success builds on success, and they want more. No tricks or time-wastng projects are necessary. Well-selected word problems obviate the necessity for time-consuming projects, and my students get all the real-world application that they need. With addition and subtraction mastered, I proceed with multiplication along the lines detailed in another article. And so it goes on my yellow pad through division, fractions, decimals, percentages, proportions, ratios, probability, and tables and graphs; and from there to the skills relevant to algebra, geometry, trigonometry, and calculus.
Similarly, as my students in the New Salem Educational Initiative learn to become better readers, they read a wide variety of material from fiction, poetry, history, government, economics, and the natural sciences. These subjects lead to interesting discussions in the classroom and in transport to and from the academic sessions, involving additional topics from such fields as geography, psychology, and philosophy.
So this is what it takes to impart high quality education to students: a well-educated teacher willing to apply the elbow grease in time-efficient applications, and comfortable discussing a wide variety of subjects.
The next time you are tempted to overintellectualize about matters of pedagogy and educational philosophy, save your breath. Instead, go sit down beside a child and start explaining. You'll then find out how much young people yearn for substantive knowledge, how appreciative they are, and how they don't need your tricks: They just need your knowledge, your time, and your love.
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