Garelick gets it right

Barry Garelick Gets It Right! 

To Parents & Teachers

Barry Garelick (Teaching Math in the 21^st Century), who embarked on a second career as a secondary math teacher in California, disagrees with the way math is taught in our schools. Mediocre math achievement comes from bad policies and bad teaching starting in early elementary school. Garelick writes, “I believe strongly in how math should be taught and even more strongly in how math should not be taught" (p. 21). He points out that practice is the key to learning math well. He writes, "I believe practice is essential in mathematics; it results in automaticity which ultimately allows students to take on increasingly complex tasks” (p. 27). He disputes the value of block scheduling, group work and collaboration, inquiry/discovery activities, teachers as facilitators, far-fetched/nonstandard word problems, and much more.

Garelick observes that the “education establishment mischaracterizes traditionally taught math as being devoid of thinking and solving problems.” For multiple decades, traditionally taught math has been attacked by reformers, calling it obsolete and old school and branding it as poor teaching. Garelick, who has a degree in mathematics, says the reformers are dead wrong! He explains that the traditional teaching of math is not poor teaching. Indeed, traditional instruction demands mathematical reasoning, memorization, and practice to automate essential factual and efficient procedural knowledge in long-term memory for instant use in problem solving. Furthermore, traditional instruction is supported by the fundamental ideas of cognitive science and works well when taught well.

Garelick also finds fault with the eight Standards for Mathematical Practices (SMPs), which are the core of Common Core. He says they are unrealistic and have been strongly criticized by several mathematicians. The SMPs describe “expertise,” but kids are novices, not experts or little mathematicians. 

The reason some kids are below grade level by middle school is that they weren’t taught to "think" or "understand" in elementary school, which is the typical narrative among Common Core and 21st century reformers. But Garelick argues that kids are below grade level mainly because they weren’t required to master the basics. Mastering math requires memorization and practice. 

At a meeting discussing a struggling algebra student, the team contended that under Common Core, which is "more about understanding," the student "wouldn't be burdened with memorization of procedures," such as the quadratic formula. But, this line of thinking baffles Garelick: “How a student could be deemed to understand the quadratic formula without knowing it was puzzling” (p. 146).  Indeed, how can a student understand mathematics that he or she does not know well (i.e., able to do and apply successfully)? The idea that understanding is all students need is misguided! Understanding does not produce mastery; practice does!

Apparently, under Common Core, being able to do and apply the mathematics and get the right answer are not that important. But, they are important, critically important! Those who say they know or understand the math, but can’t do it or apply it, don’t know the math at all. Nobel Prize physicist Richard Feynman wrote, “You do not know anything until you have practiced.” Math is hard to learn compared to other academic subjects because it is abstract, cumulative, and requires focus, effort, perseverance, and practice to learn well. Barry Garelick thinks there is no substitute for practice. Without a solid background in basics, higher math becomes a struggle. Practicing math should be a daily habit.

There is much more to his experiences teaching math as a semester-long substitute teacher at a California middle school. Parents will be astounded at what he was told about Common Core at teacher meetings.

LarryT, ThinkAlgebra.org
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