Sunday, February 10, 2013

not catching up

Internationally, fractions are focused in 4th grade.
Equal coverage of core academic content. 

Equality of Educational Opportunity by Schmidt, Cogan, McKnight

Reform Math And Common Core: Not Catching Up!
Reform math programs have dominated our schools for decades and have shortchanged our kids. Memorization and practice have been marginalized. Fractions and long-division have been ignored, etc. Our kids do not have a firm grasp of basic arithmetic needed to do algebra by middle school. Kids lack number sense and are deficient in mental arithmetic,  operations, fractions, etc. Some have become calculator dependent, even in elementary school. Fractions are focused in 4th grade internationally, but not in the US. Furthermore, college professors lament that incoming students can't do simple arithmetic without a calculator (e.g., 10% of 25). Community colleges are swamped with students who place in remedial math. Indeed, the K-12 [NCTM] reform math often leads to remedial math in community college.

The new math standards (Common Core) won't help much. Even though they offer the promise of uniformity, the core, itself, is not world class, according to my analysis. Algorithms for whole number arithmetic are delayed, and algebra standards are pushed to 9th grade. The new math standards may be better than we had before, but they are weaker than many benchmarks established in other nations (and even in some states), so, in my view, common core is unacceptable as a starting document to rebuild American math education.

Schmidt, Cogan & McKnight define educational equality as "equal coverage of core academic content." Is this realistic? When does this happen, even in the same school?  Core math must match or exceed the core math taught in top-performing nations. Common Core is not up to the task. Teachers are not ready. Indeed, even though I think our kids are learning more mathematics and scoring better on tests, they are not catching up. Like Alice in Wonderland, we seem to be running faster and faster but not advancing much, at least not like other nations. We are not leapfrogging! "Now, here you see, it takes all the running you can do, to keep in the same place. If you want to get somehere else, you must run at least twice as fast as that!" said the Queen. Hanushek, Peterson, & Woessmann write in Education Next, "The failure of the US to close the international test-score gap raises questions about the nation's overall reform strategy."  2-6-13


"Americans are undereducated." Many US math programs tend to marginalize the early development of key arithmetic skills, starting in 1st grade. Other nations do not. US students are not asked to practice enough to master key content (facts, procedures, concepts). Teachers are taught in schools of education that drill is bad for kids. It's not! It's essential for building essential knowledge (facts, procedures, concepts) in long-term memory. To get good at arithmetic or algebra, kids need to practice in school and at home. Some kids need more practice than others. 
Moreover, the new Common Core reform math standards state that students do not need to be fluent in the standard algorithms for whole number addition or subtraction until the end of 4th grade. Really? [See chart at end of post.]

Mastery (auto recall) of single digit arithmetic facts is required for standard algorithms. In fact, practicing the standard algorithm is an excellent way to practice and retrieve single digit number facts, starting in 1st grade. "Economic growth is linked with educational attainment." Quotes: The Undereducated American, pdf)

A study by Price, Mazzocco, & Ansari (The Journal of Neuroscience, January 2, 2013) points out that the lack of mastery [rote memory] of single digit arithmetic facts in early elementary school, starting in 1st grade, affects achievement in high school. Indeed, memorizing anything has been out of favor in our schools for decades―from math facts to poetry, capitals of states, etc. 

Thomas L. Friedman (The World Is Flat) writes, "When I asked Bill Gates about the supposed American education advantage--an education that stresses creativity, not rote learning--he was utterly dismissive. In his view [Gates], the people who think that the more rote-orientated learning systems of China and Japan can't turn out innovators who can compete with Americans are sadly mistaken." Indeed, like Asian students, our students should learn skills to automaticity. The automation of fundamentals in arithmetic and algebra through practice is rote learning. I am saddened when I ask 3rd grade students to add 2 to 17, and some cannot without calculating. The lack of simple mental arithmetic, such as adding 2 to a number, predicts poor math achievement in high school where the content is more complex. 

Our students underperform in mathematics, grade by grade, compared to peers in many other nations, especially Asian nations. In my view, NCTM reform math and its replacement (common core reform math) are a lot alike; students will continue to underperform. Professor W. Stephen Wilson points out that the lack of instant [rote] recall of multiplication facts in 3rd grade "permanently slows students down." The mastery of single digit facts and standard algorithms go together. 

We are in a test culture rather than in an achievement culture. Furthermore, often, teachers are pressured to spend more time on test prep, which leaves less time for solid arithmetic  instruction and practice. 

Alternatives to the "status quo" in math education include grouping students by achievement levels for math class, using fully-guided [explicit] teaching of content (pdf), teaching world class content grade by grade for mastery (i.e., content that matches or exceeds that of top-performing nations and prepares more students for Algebra 1 in middle school), implementing intervention programs that work for incoming 1st grade students with weak number skills, which is what Singapore does, and upgrading the academic training of elementary and middle school teachers in math and science. 

Common Core delays the fluency in standard whole number algorithms. It makes no sense. 
Delay Chart by LT 2010

©2013 LT/ThinkAlgebra/Math Notes

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). 

©2013 LT/ThinkAlgebra/Math Notes by ThinkAlgebra
Last updates: 1-6-13, 1-21-13