The philosophy of mathematics
Board members, task force discuss the pluses and minuses of 'conceptual'- and 'procedural'-based teaching
The Moffat County School District math task force, formed last fall to investigate the school district’s math curriculum and come up with recommendations to improve it, presented its suggestions to the board of education Monday.
One of the main recommendations outlined in the 13-page report was that the district shift to a more conceptual-based mode of teaching, supplemented by procedural-based teaching.
Curriculum Director Janet Bohart, who served on the math task force, said conceptual-based teaching involves asking students to explain how they came to their answers, instead of just drilling the process of how to get to an answer.
“A teacher should say ‘today I’m going to explain what it means to find the square root,'” Bohart said. “Next they should say ‘this is the procedure on how you find the square root.'”
Currently math instruction in Moffat County is mostly procedural, she said.
According to a report handed out to the board Monday, 33 of 48 math teachers surveyed in the district reported that they did conceptual teaching “sometimes,” “rarely”
When asked how often they asked students to explain their answers, 28 of the 48 teachers said “sometimes,” “rarely” and “never.”
“It is the judgment of the task force that a majority response of ‘sometimes,’ ‘rarely’ or ‘never’ indicates an inconsistent use of research-based teaching strategies to improve student achievement,” the report stated.
The report also mentioned that the Colorado Student Assessment Program (CSAP) test asks conceptual based questions and asks students to explain their answers.
At the fifth-grade level there were 69 math questions on the CSAP, the report said. Of those 69, only nine asked for computation without explanations of answers.
“CSAP is in the conceptual zone,” Superintendent Pete Bergmann said. “There’s very little computation on CSAP. It is 80 percent conceptual.”
The lack of conceptual teaching has reflected on low CSAP math scores in the Moffat County School District, which is why the math task force was formed in September to study the district math curriculum.
“With math you’re seeing what reading was six or seven years ago,” Bohart said. “Then along came the CSAP and the district started to seriously study reading. CSAP has forced our attention to getting some consistency in the curriculum.”
Bohart gave a higher estimate than Bergmann on how much focus is currently put on procedural math teaching.
“I would say right now we’re 90 percent computation, drill driven in our district,” Bohart said.
Board member John Kinkaid, who has taken significant interest in math teaching methods, disagreed with the new math teaching philosophy presented by the task force Monday night.
He referred to conceptual math teaching as “fuzzy math practices.”
“If we don’t dump ‘fuzzy math’ practices we cannot improve math achievement,” Kinkaid said. “‘Fuzzy math’ emphasizes process over content. You have to know it before you can apply it.”
Kinkaid said he thinks the new trend in teaching math is hindering math education.
“Lately there’s been so much concern over how they can apply it,” Kinkaid said. “You have to have the basics down first. We’re asking teachers to ask kids to write to explain their thinking. It’s going in the wrong direction in my opinion. At some grade level I think you would begin to phase that out.”
Board member Steve Hafey, who said he was skeptical about a shift in math instruction at first, said Monday night that he realized a district could get itself in trouble if it did not change to meet the standards set forth by state assessments.
But he did have one direct question for task force members.
“Are you confident a person that learned conceptually can go straight into a job in which they need to use fractions?” Hafey asked.
High School math teacher Cassia McDiffet, who was a member of the math task force, said she believed students who learn conceptually are better prepared.
“A student that didn’t even speak English could understand fractions when I used egg cartons to explain it,” she said. “I think that’s what is important about conceptual teaching. Students can remember it further on down the road. Some students remember it better when there is something to tie it to.”
Nothing was adopted Monday night regarding math curriculum, but Bohart said the task force findings would be used in making adjustments to teaching practices in Moffat County this year.
“The goal tonight was to raise your awareness of what the task force has been doing,” Bergmann told the board.
“We’re not here to make a decision tonight.”
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