According to Price, Mazzocco,& Ansari (The Journal of Neuroscience), students who memorize by rote single-digit math facts starting in 1st grade, rather than always calculating them, become good math students, and the benefits reach far into high school with much higher PSAT scores. Being able to retrieve 5 + 6 = 11 automatically from long-term memory is different from [and better than] calculating it using a strategy (e.g., 5 + 6 = 5 + 5 + 1 = 10 + 1 = 11), which is a different mental process that clutters working memory, leaving less space for problem solving. Even though mathematicians repeatedly have stated that kids must learn facts by rote, which requires a lot of memorization, practice, and constant use, many US educators have gone a different road, that of calculating by using strategies (e.g., NCTM reform math, now Common Core reform math).
Why are Asisan students superior in math?
A January 2013 article in The Journal of Neuroscience by Price, Mazzocco, & Ansari confirms the rote learners. The reason that Asian kids excel in math, while US kids struggle, is that Asian kids memorize by rote the single digit math facts early on (1st grade, even earlier) and become proficient in using the standard algorithms at the same time. Strategies (US approach) and calculators (Finland's approach) should not replace or delay the instant recall of single-digit math facts. Instant recall of single-digit math facts is necessary for proficiency in standard algorithms.
What about problem solving?
In TIMSS (4th & 8th grade students), students who scored at the Advanced Level are good problem solvers. Asian nations consistently have 40 to 50% of their 4th and 8th grade students scoring at the Advanced Level in TIMSS compared to only 7% of US students and 4% of Finland students. In fact, in TIMSS math, the US and Finnish students scored about the same [1].
The "rote-learners" from Asian nations are not only tops in international math tests (TIMSS, PISA-15 year olds), but also tops in "creative problem solving," a new test from PISA. (The results were released earlier in 2014.)
Children who have auto recall will not be inclined to calculate basic facts; they will automatically retrieve them as needed. No matter, the strategy shown above (reasoning from doubles) won't work well without instant recall of 5 + 5. Kids often use strategies to remember 3 or 4 demon facts, which, at first, is okay.
Too often, in US math programs the cart (Whys) is put ahead of the horse (Hows). US students are weak in procedures, such as standard algorithms, while Asian kids excel in them and in problem solving.
Standard Algorithms are Key
Dr. H. Wu states, "The multiplication algorithm reduces the multiplication of all numbers to the multiplication of single-digit numbers, which is part of a general pattern. If you can add, subtract, multiply, and divide using single-digit numbers, then you can add, subtract, multiply, and divide all numbers no matter how big." This is the importance of standard algorithms: They are powerful and fast, and they are based on auto recall of math facts. Unfortunately, Common Core tends to ignore or delay standard algorithms, which is another way of saying that in Common Core reform math the memorization and practice of single-digit math facts early on are not that important.
[1] If you analyze the TIMSS results (2011), the Finnish and US 4th and 8th grade students, on average, are almost the same with Finland having a very slight edge. However, 7% of US 8th grade students reach the TIMSS Advanced Benchmarks in math, compared to only 4% of Finland's 8th graders. [Problem solving is thought to be one of Finland's strengths, but this may not be the case.] In 4th grade, the percentages for the TIMSS Advanced Benchmarks are about the same: US 13%, Finland 12%. For perspective, 40% to 50% of 4th and 8th grade students in the top performing Asian nations reach the Advanced Benchmarks. See Finland.
Recently, Pasi Sahlberg (How American Innovation Improved Finnish Education) wrote that Finland turned around its education system based on innovations in the US, which include progressive ideas (Deweyism: social interaction and group work), cooperative learning (group work), multiple intelligences, alternative assessments, and peer coaching. What turn around? Finnish 15-year-olds dropped from 1st to 12th in the matter of a decade (PISA). Their 4h and 8th graders are not any better than US kids (TIMSS). And, the innovations Dr. Sahlberg talks about were failures in US classrooms, which is a reason that our 4th and 8th graders are about the same in math achievement and problem solving.
1. See Multiple Models (Different Strategies)
Students are taught inefficient, alternative strategies (reform math) instead of tried and true standard algorithms to do arithmetic.
2. See PiagetianMyth
Constructivism does not work in the classroom.
3. See Memorization & Practice
Very young children can learn a lot more than we think or are prepared to teach. American children underperform in math! Parents should drill math facts at home before kids are school age. It is easy to show 4-year-olds addition using a number line. Early on, parents should provide the environment for achievement and teach their kids how to be successful in school. Early arithmetic at home pays off.
4. See CommonCore
Common Core is part of the progressive agenda to downgrade American education. Every student gets the same. The government has taken over and controls education. Teachers are no longer in charge of education.
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To Be Revised
7-30-14, 8-1-14
© 2004 LT/ThinkAlgebra
