Dr. James Milgram who has become an outspoken opponent of the common core standards spoke to Breitbart News yesterday adding some additional insight to Dr. Martina Ratner’s comments in the Wall Street Journal.

“It is believed by most U.S. math education Ed.D.’s that at-risk students learn better using manipulatives and that the focus of U.S. standards should always be these students,” Milgram said. “So they choose pedagogy that effectively turns off the average and even more so the above-average students in a desire to focus on the weakest students.”

Milgram observes, however, “The research on how at-risk students learn most effectively is absolutely clear on the fact that this is the worst possible method for teaching these students this material.”

What Milgram is pointing out that the public needs to understand about these standards (and Missouri’s previous math standards) is the difference in approach to standards development between math educators and actual mathematicians. Math educators, who go through our schools of education, focus on pedagogy, or the process of teaching. This allows teachers to take students with numerous different learning styles and adjust their teaching methods to try to accommodate all the different students. Unfortunately what often happens, like in the Everyday Math program which uses the tactic of “spiraling” or returning again and again to a small element of the math concept, is that lessons are designed for the ease of the teacher’s pedagogy, not the best understanding of the topic.

Many teachers like programs like Everyday Math because it only requires them to get the students to understand a small portion of the math process at any one time, say for instance numerators. They can spend a couple days just talking about numerators, getting kids to recognize them and name them without teaching the full concept of a fraction. They get to that later, sometimes months later. Throughout the lessons, however, the children appear to be learning math because they can provide the correct limited responses. My own district’s curriculum director told me the teachers loved the Everyday math program because it never required them to teach to the level of “mastery.” How I was supposed to think that was a positive I cannot say.

Teachers, especially teachers who lack a serious grounding in the content area, will happily use these kinds of programs and “love” standards that support their use. That should be telling us something about the teachers who say they love the CC standards.

Unfortunately, as Milgram stated, research into using methods other than direct instruction of mathematics shows that focusing on real world applications actually makes it harder for children to learn math.

Dr. Jennifer Kaminski, a research scientist at the Center for Cognitive Science at Ohio State, examined the belief that children learn best by relating concepts to the real world. She and Dr. Valdamir Sloutsky conducted randomized, controlled experiments and concluded that the findings did not support the belief.

“The motivation behind this research was to examine a very widespread belief about the teaching of mathematics, namely that teaching students multiple concrete examples will benefit learning,” said Dr.  Kaminsk told the New York Times. They found that “It was really just that, a belief.” Their research, which included 11 year old students as well as college students, concluded that real-world examples “obscured the underlying math, and students were not able to transfer their knowledge to new problems.”

From the New York Times

“In the experiment, the college students learned a simple but unfamiliar mathematical system, essentially a set of rules. Some learned the system through purely abstract symbols, and others learned it through concrete examples like combining liquids in measuring cups and tennis balls in a container.”

“Then the students were tested on a different situation — what they were told was a children’s game — that used the same math. “We told students you can use the knowledge you just acquired to figure out these rules of the game,” Dr. Kaminski said.

“The students who learned the math abstractly did well with figuring out the rules of the game. Those who had learned through examples using measuring cups or tennis balls performed little better than might be expected if they were simply guessing. Students who were presented the abstract symbols after the concrete examples did better than those who learned only through cups or balls, but not as well as those who learned only the abstract symbols.”

The research that David Coleman et al were focusing so arduously on when drafting the common core math standards clearly did not include Dr. Kaminski’s studies. Instead they seem to rely on the common belief of education masters that illustrations, manipulatives and constantly relating school work to the real world was going to make our students understand math concepts much better. The result is the confusing or boring lessons being developed for common core. The result is school districts spending thousands of dollars on new curriculum based on a false belief about how students learn.


August 7, 2014

Anne Gassel

Anne has been writing on MEW since 2012 and has been a citizen lobbyist on Common Core since 2013. Some day she would like to see a national Hippocratic oath for educators “I will remember that there is an art to teaching as well as science, and that warmth, sympathy and understanding are sometimes more important than policy or what the data say. My first priority is to do no harm to the children entrusted to my temporary care.”

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