The Failure of a Reform Math Curriculum and its Pedagogy
Content standards are not the same as curriculum standards.
The curriculum is someone's interpretation or translation of content and how it should be taught. Common Core state standards have been understood as reform math that flunked in the past. Therefore, instead of learning one way to multiply (i.e., the standard algorithm), reform math students are fed a multitude of alternatives or unconventional methods; e.g., arrays, lattice model, area model, partial products, etc. The standard algorithm that is needed for algebra is pushed aside, a big mistake.
No one uses the area model, the lattice model, and so on to multiply numbers, yet these alternatives are the priority in most elementary schools. In contrast to reform math, students should use the standard algorithm from the get-go (3rd grade) and start long-division in the 2nd semester or 3rd grade (1997 California State Math Standards). The standard algorithm for multiplication is built on a place value system, the distributive property, and the instant recall of single-digit number facts (the multiplication table). Yes, students need to memorize, drill-to-improve-skill, and regularly review the math facts, but they should also practice the standard multiplication algorithm until it is automatic.
Notes:
(1) A typical 3rd-grade multiplication is 3476 x 8. A typical 3rd-grade long division is 768 ÷ 8. The standard algorithms are used, of course.
(2) First-grade students in Singapore start multiplication as repeated addition. Thus, 3 x 4 means 3 groups of 4: 4 + 4 + 4 = 12. Half the times table is memorized in 2nd grade, the rest in 3rd grade. The formal algorithm is 3rd-grade content.
The content standards are different from the curriculum standards, explain Marzano and Kendall (1998). The curriculum reflects how kids are taught to achieve the standards (e.g., linking specific content to specific methods of instruction). In my view, the problem is that the Common Core curriculum stresses the alternative strategies of reform math (low value) and downplays the critical importance of mastering the standard algorithms needed for algebra in middle school (high value).
One result has been that American students stumble over basic arithmetic, even in middle school, which has led to a massive influx of students in remedial math at community colleges. In short, our math instruction has been ineffective for decades upon decades. It seems clear, at least to me, that the American "reform math" curriculum, progressive methods of teaching and ideology have not been the best way to teach students standard arithmetic. Beginners don't need a bunch of alternative strategies; they need one efficient method (standard algorithm) to do each operation, which requires the memorization of single-digit number facts starting in 1st grade.
In 1938 William Bagley (Columbia University) pointed out that "American elementary and secondary students fail to meet standards of achievement set by students in other countries," even though "more money has been spent on education than ever before." (Quote from Ellis and Bond, Research on Educational Innovations, 2016) Sound familiar?
In the real world, the Common Core content standards are not world-class. For example, Singapore 1st-grade students learn significantly more standard arithmetic than American students, according to my analysis. Singapore content standards are straightforward, and the instructional methods are largely supported by the cognitive science of learning. Starting in the 1st grade, Singapore students memorize, drill to improve skill, and regularly review arithmetic basics to cement them to long-term memory for mathematical thinking, learning new content, and problem-solving.
Ellis and Bond question the "linking the achievement of certain content goals with certain methods of instruction in the absence of clear and convincing evidence." American students are not meeting the standards set by students in other countries because of the reform math curriculum and methods of instruction along with progressive ideology. “The more things change, the more things stay the same.”
Al Manne (Stanford) admonishes, "To get a large model to work, you must start with a small model that works, not a large model that doesn't work." In American schools, shoddy models abound. Note: Teachers don't have much choice in a top-down bureaucratic education system. They are required to teach a substandard curriculum with inferior instructional methods.
It is 2017, and our goal of being the best in the world in math and science has failed repeatedly. American students are not meeting the achievement levels set by students in the East Asian nations, such as the Advanced Levels (TIMSS). Unfortunately, some education leaders rationalize the lackluster performance in math by saying American students have never done well on international tests. It's no big deal; after all, there are incremental improvements. No, it is a big deal!
February 9, 2017
©2017 LT/ThinkAlgebra
