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| Lost in Math. You are not alone. 66% of 8th-grade students are not proficient in math. 66% of 8th-grade students are not proficient in reading. |
Notes.
NCTM: National Council of Teachers of Mathematics
OECD: Organization for Economic Cooperation and Development
NAEP: National Assessment of Education Progress
WM: Working Memory
CC: Common Core
Only 35% of 4th graders are proficient or above in reading. Also, a child rated as proficient in reading does not mean the child is reading on grade level, warns the NAEP. It is the same story in math--only 41% of 4th graders reach the proficiency cut scores. Again, a student who is rated as proficient does not mean the student is doing the math on grade-level. Indeed, kids are poorly trained for college-level work. And many blame Common Core and state standards that are primarily based on CC. Betsy DeVos slammed the K-12 education establishment for allowing students to fall behind in math and reading (Newsweek). I blame the reform math curriculum, along with faulty or inefficient math instruction (the teaching) that often conflicts with cognitive science. Teachers are not teaching conventional arithmetic; they are teaching reform math leftover from the failed 1989 NCTM math standards, which, unfortunately, were resurrected via CC.
Elementary school teachers tell me that they have to teach many of the strategies because they are on the state test and in materials they are told to use. Where are the standard algorithms?
Strategies Crowd the Curriculum
Standard Algorithms Are Not a Priority
Memorization and Drill Are Downgraded
Standard Algorithms Are Not a Priority
Memorization and Drill Are Downgraded
"For each of the four multi-digit operations, the Common Core standards ask students to practice multiple strategies for one year or two before learning the standard algorithm," writes Eric A. Nelson ("Cognitive Science and the Common Core Mathematics Standards"). The strategies crowd the curriculum, along with a bunch of other stuff, such as the eight standards for mathematical practice, social-emotional learning, self-esteem and mindfulness activities, and lots of group work (e.g., discovery learning, project-based learning, and so on). The consequence has been to downgrade the importance of the standard algorithms. "Students are taught under math standards that discouraged initial memorization for math topics ... [thus, they] will have significant difficulty solving numeric problems in mathematics, science, and engineering." Nelson points out that U.S. 16-24-year-olds ranked dead last on a recent OECD assessment of numeracy skills among 22 developed-world nations. Nelson writes, "The CC standards do not ask students to memorize facts and procedures for some key topics and delay work with memorized fundamentals in others."
The CC math standards do not ask students to memorize the subtraction and division facts. Furthermore, many students coming into the 4th grade and 5th grades have not mastered the multiplication facts. Teachers have been taught to decrease memorization and drill (aka practice). Doing this is contrary to the cognitive science of learning.
The multiplication table and the standard algorithms for both multiplication and long division should have been learned no later than the 3rd grade so that students can engage in problem-solving.
"When solving math problems of any complexity, due to Working Memory limits, students must rely almost entirely on well-memorized facts and algorithms," writes Nelson. CC does not require students to memorize half of the math facts. Subtraction and division facts are not remembered and are calculated as needed using strategies, which is a backward approach.
Nelson writes, The 1989 NCTM standards called for "increased attention" to "reasoning" and decreased attention" to "memorizing rules and algorithms," "manipulating symbols," and "rote practice." He points out that there has been a sharp decline in student test scores in math computation.
In short, to improve student problem solving (avoiding the limits of the Working Memory), students should automate (memorize) the math facts and learn the standard procedures first, not a bunch of strategies that interfere with and downplay the standard algorithms and math facts. Why waste a couple of years of instructional time teaching strategies instead of what students must know for problem-solving: math facts and standard algorithms? Who uses the array, lattice, or area strategies to multiply numbers? Is it any wonder that American students are behind international math benchmarks?
FYI: Incidentally, the student at the top of the page (Kailey), when she was in 7th grade, solved quadratic equations by completing the square. All 7th graders took Saxon Algebra One. Most of the children who model for my illustrations are excellent math students.
In short, to improve student problem solving (avoiding the limits of the Working Memory), students should automate (memorize) the math facts and learn the standard procedures first, not a bunch of strategies that interfere with and downplay the standard algorithms and math facts. Why waste a couple of years of instructional time teaching strategies instead of what students must know for problem-solving: math facts and standard algorithms? Who uses the array, lattice, or area strategies to multiply numbers? Is it any wonder that American students are behind international math benchmarks?
FYI: Incidentally, the student at the top of the page (Kailey), when she was in 7th grade, solved quadratic equations by completing the square. All 7th graders took Saxon Algebra One. Most of the children who model for my illustrations are excellent math students.
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