Instruct for Mastery
To upgrade high school math, we first need to upgrade K-8 math, starting in grade 1.
Fifty-four percent of Singapore 8th graders reach the Advanced Level in an international math test (TIMSS), which is mostly problem-solving, compared to only 10% of U.S. 8th graders. While American students stumble over basic arithmetic and algebra, Singapore teachers introduce math and science far ahead of its national curriculum. Singapore teachers instruct students for content mastery, and they don't limit students to grade-level content.
Upgrade School Math Content
To upgrade content, schools should boot the Common Core (CC) grade levels and embrace the Core Knowledge (CK) math guidelines that prepare most students for Algebra-1 by the 8th grade. Start with CK K-8 math guidelines, which are world-class. The CK math guidelines embrace the teaching of standard arithmetic for mastery with memorization and practice-practice-practice.
Make the Right Move: Upgrade to Core Knowledge!
Forget Common Core!
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| We can change the outcome for many children if we switch from Common Core grade levels, state standards, and annual testing to the Core Knowledge Math Guidelines for K-8 and adopt a mastery instructional approach for essential content (i.e., factual and procedural knowledge). Changing to Core Knowledge math would be a step in the right direction, but we must also acknowledge that school achievement is 60% DNA. Indeed, academic achievement is tied to academic ability. Note. Read DNA! |
Whole number operations and their standard algorithms should be taught no later than the 3rd grade, so that 4th-grade students can concentrate on fractions-decimals-percentages and begin prealgebra arithmetic such as exponents, order operations, negative and positive integers, square roots, graphing in the coordinate plane, solving linear equations and proportions, etc. But, students can't do this without learning basic arithmetic in the early grades. We need to prepare students much better and not restrict instruction to grade-level content. In short, students are not ready for future grade levels if the instruction is confined to the current grade level as is the case with Common Core and state standards.
Starting in the 1st grade, educators should focus on the mastery of basics, not learning for the state or district test.
Our elementary school math curriculum needs to upgrade content and change to a mastery instructional approach. Children should learn math content, which includes calculating on paper, to solve math problems. But, today, we have a [thinking] skill approach, not a content approach. Reformers say that students should learn to observe, reflect, and analyze independently of content. Well, it doesn't work that way, retorts Mark Bauerlein. It is a radical view.
“The skills-not-content approach doesn’t produce the learning that its advocates promise,” writes Bauerlein. “Without a body of material which students have first studied and retained and to which they may apply their aptitudes, the exercise of thinking skills is empty and erratic.” (Bauerlein's Quote from Joanne Jacobs blog)
Educators have been led to believe that skills--such as training the mind to observe, reflect, analyze--are more important than content knowledge. In fact, the 21st-Century crusaders boast that knowledge isn't needed. This radical approach is dead wrong. Immanuel Kant (1724–1804) made clear that thinking without content is empty. Kids learn higher-level thinking skills when they learn math and science content. Thinking in math (logic from true statements) is different from thinking in science (observation/inference). Math is not a matter of opinion; it is a matter of fact. Math is absolute; science is uncertain. Also, as E. D. Hirsch Jr. (Why Knowledge Matters) points out, a generalized "thinking skill" doesn't exist.
Thinking in math requires knowing factual and procedural knowledge. You just can't "google" your way into critical thinking. You must know stuff in long-term memory. Critical thinking in math is called problem-solving. Students should start with routine problems first and build on them.
Thought is domain-specific.
You can't solve a trig problem unless you know trig. You can translate Latin unless you know Latin. Thinking comes from knowledge, not thin air. And, as Joanne Jacobs says in her blog, "You have to know something before you can think about it."
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