In researching the best way to tutor my daughter at home, I ran across an article that provided a clear path, as well as an interesting structure for understanding what is wrong with Everyday Mathematics.
Dr. Daniel Willingham is a professor of cognitive psychology at the University of Virginia (My nephew, who graduated from UVa as a Mechanical Engineer, assures me it is an excellent school. His brother, who graduated from Virginia Tech as a Chemical Engineer, respectfully disagrees). The article asks and answers the question, “Is it true that some people just can’t do math?”
Referring to the National Mathematics Advisory Panel report that argues that factual, procedural, and conceptual knowledge are required to learn mathematics, Dr. Willingham develops the linkages between the three knowledge types. “Factual knowledge refers to having ready in memory the answers to a relatively small set of problems of addition, subtraction, multiplication and division.” Procedural knowledge is the knowledge of “a sequence of steps by which a frequently encountered problem may be solved.” “Conceptual knowledge refers to an understanding of meaning; knowing that multiplying two negative numbers yields a positive result [the procedure] is not the same thing as understanding why it is true” [the concept] (brackets added). Dr. Willingham goes on to discuss the math wars, where the conceptual versus procedural question is at the battle front. He reasons that both types of knowledge should be taught together.
Which brings us to Everyday Math. When I read the article, most of the shortcomings of EDM came sharply into focus. We just have to look at the draft Math Monitoring Report to learn that our Middle School Math teachers are concerned about their sixth graders “Basic fact fluency,” also know as factual knowledge. Ask any parent who works with their child on their math whether their students know their multiplication tables cold, or their division facts well. I would wager the answer would be a resounding “No!” And these are kids where the parent works with them. Everyday Math doesn’t even pretend to take students to the required level of automaticity for these facts, despite the recognition that “Automatically knowing basic number facts is as important to learning mathematics as knowing words by sight is to reading” (EDM Teacher Manual). Strike one.
Two other concerns the Middle School teachers have are “Operations with fractions” and “Long division competency,” which point to issues with procedural knowledge. The standard algorithms are given limited attention in Everyday Math, but a variety of other algorithms (e.g., lattice multiplication, partial-sums addition) which have limited application in more advanced math are given time. And the practice to ingrain any of these procedures, much less the standard procedures, is limited. Strike two.
So at least Everyday Math is teaching the concepts, the whys (ever wonder why that word is not spelled “whies?”), right? Dr. Willingham discusses the conceptual problem with understanding that an equal sign refers to equality (mathematical equivalence). “Students often think it signifies ‘put the answer here.’” Could it be because they are more commonly referred to as “number sentences” so as to include inequalities? Ask your child what an equal sign means. If they are above sixth grade, let’s hope they understand. If so, according to one study, they would be better off than 72% of their classmates, meaning only 28% understood. If they were in China, 98% of their fellow students would understand.
Everyday Math or teacher preparation? I’ll give half a strike to EDM.
All-in-all, a reasonable explanation why Everyday Math is failing our children.
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