7 Lessons (From 2-20-19 to 4-17-19)
Teach Kids Algebra, TKA
Here are some thoughts on teaching 2nd-grade students algebra lessons. There is a lot of calculating involved (i.e., standard arithmetic). This is not a curriculum.
In regular math class, kids need strong teacher guidance, a world-class math curriculum, a grouping that matches their achievement level, lots of practice to master math, and persistence. In short, they need to master standard arithmetic. Yet, many of these are absent in progressive, reform math classrooms.
In arithmetic, kids must memorize basic stuff and practice the retrieval of facts, so they stick in long-term memory for immediate use in problem-solving (critical thinking).
The 2nd-grade students were taught the idea of equality (=) and equation structure (expression = expression). Students determined whether a numerical equation was true or false. Both sides of the equation must balance to make a true statement, which is a critical idea. For example, the equation 4 + 5 = 12 - 2 is false because 9 ≠ 10, while the equation 3 + 4 = 10 - 3 is true because 7 = 7.
x - 34 = 62 is an open equation (x is a variable that represents a number, an unknown). Stress, x is a number. We don't know if the equation is true or false until we substitute a number for x and test the left side = right side. Students should think like a balance.
Moreover, students applied the algebraic rule for substitution (x + x), solved equations with one unknown [e.g., (x + x) - 3 = 9] using guess and check {x = 6}, calculated expressions with parentheses, added and subtracted left to right (order of operations), inserted parenthesis to make a statement true, and used "guess and check" as a beginner strategy. Also, they wrote and solved equations in one variable. They developed a method for calculating the perimeters of rectangles.
Note. x + x is a double like 3 + 3. Also, x + x is the same as 2x in algebra. Letters, such as x or y, are used as symbols for unknown numbers, such as x + 5 = 11, a missing addend equation. If the right side is 11, then the left side must make 11, too, for the equation to be true. Thus, x = 6. Math, unlike science, is built on true statements, such as x + 0 = x. Algebra can be thought of as symbolic arithmetic. I fuse algebra ideas to standard arithmetic, which makes some fundamentals of algebra accessible to very young minds.
Furthermore, students calculated integers (e.g., -4 + 7 = 3), often using a number line, and evaluated expressions such as 30 - (9 - 8) by following the order of operations. Debt was a negative number. Also, students built a table of values using a rule (i.e., an equation such as y = x + -4) and plotted (x, y) number pairs, linking equations, tables, and graphs--the three representations of a function. Kids can learn so much more than the current curriculum. Preparation for algebra begins in the lower elementary school grades. It can start in grade 1.
In elementary school, some concepts are easy to learn. But, students can't live on concepts alone. What's missing in U.S. math programs is the mastery of calculation skills--through practice-practice-practice--that are associated with and supportive of the ideas. Singapore kids, for example, memorize sums (math facts) and start multiplication sums in the 1st grade. In contrast, U.S. 1st-grade students learn substantially less because the focus in reform math has not been the mastery of essential content. Also, the math curriculum in most American schools is not world-class, another limiting factor. The problem in the early grades has been that the fundamentals of math are not taught for mastery. Unlike East Asian parents and teachers, Americans do not focus on early math at home or school, even though early math is probably more important than early literacy.
TKA works for many students, but not all. Kids need feedback and more repetition.
Some of the content of this post was from "Contrarian Math Page" at ThinkAlgebra.org.
https://thinkalgebra.org/contrarian-math-page.html
Comments: ThinkAlgebra@cox.net
My main page is: https://thinkalgebra.org/index.html
To Be Revised
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