Sunday, January 6, 2013

First Grade

Our kids lack mathematical knowledge (factual, which includes conceptual, and procedural) because they are not exposed to math skills and ideas that kids in other nations master early on. Our first-grade students should master math skills on par with Asian children. They don't. The NCTM reform math standards and the new math standards (Common Core and state standards) do not require such mastery. 

Rational number fluency (fractions, decimals, and percentages) is a critical foundation of algebra (National Mathematics Advisory Panel, 2008). The meaning of fractions, which should start in 1stgrade, and fraction operations are poorly taught in the US classrooms. FYI: The international benchmark for fractions (fraction equivalency and the four fraction operations) is focused in the 4th grade.

In exploratory research, Pamela M. Seethaler, et al., found that the “incoming computation skill [whole numbers]” of students coming into the 3rd grade is the “greatest predictor of computation fluency three academic years later (3rd, 4th, and 5th grades),” not only in whole numbers but also in rational numbers (fractions). Intensive intervention programs should be in both 1st and 2nd grade, which is exactly what Singapore does. Seethaler writes, “This finding [incoming computation skills] underscores the importance of intervening early to address students’ deficits with foundational mathematics skills to offset future and more pervasive difficulty.” 

First Grade Addition
Mastering the basics (facts and procedures) early on sets Singaporean students up for fractions and for algebra. An emphasis in Singapore math is on computation skill, which starts in 1st grade. First grade students practice number facts for auto recall and procedures (standard algorithms) for fluency in addition and subtraction. Furthermore, in Singapore, 1st-grade students apply operations (+, —, and x) to word problems, write equations in one variable that model word problems (symbolics), and work with multiplication as repeated addition (3 x 4 = 4 + 4 + 4 = 12). In second grade, students memorize half the multiplication table. Thus, Asian kids move forward while our kids lag significantly behind. 

Starting in 1st grade, the primary focus for doing arithmetic and solving word problems should be "memorized arithmetic facts" and "standard algorithms." Still, most US students in 1st grade are taught to use strategies to add and subtract, not math facts and algorithms. Indeed, memorizing math facts and using standard algorithms are discouraged. In my view, the strategies are often a waste of instructional time and confusing to kids because the strategies are more complicated than simple addition. 

I think the US focuses too much on strategies for adding and subtracting. In contrast, the instruction should concentrate on gaining factual and procedural knowledge in long-term memory, which requires memorization and practice. This process starts in the 1st grade. 

First Grade Student in Teach Kids Algebra
Thus, it is critically important that 1st-grade teachers concentrate on competency; i. e., the auto recall of number facts and fluency with standard algorithms. I also think fundamental algebra ideas, which grow out of arithmetic, along with parts of geometry and measurement should be part of the first-grade curriculum. 

Furthermore, 1st-grade students who are weak in number skills should be pulled out for math class (which is what Singapore does) with the understanding that low kids should learn the same core curriculum as the regular kids. Also, 1st-grade students who are advanced should be pulled out for math class (See Math Grouping). 

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Last updates: 1-6-13, 1-21-13