Inviting Students to Think

When The Nation’s Report Card: Mathematics 2009 was issued in the fall of 2009, U.S. Secretary of Education Arne Duncan was clearly disappointed. “None of us should be satisfied. We need reforms that will accelerate student achievement,”he said.

His response was not unexpected. According to the report card, there had been no significant change in the performance of America’s fourth graders in mathematics from 2007 to 2009. Worse, the United States continued to lose ground to its counterparts in the international community, falling to the bottom quarter of industrialized nations in math testing.

“We may need to look to our past to come up with fresh, innovative solutions to mathematics education,” says Lynn Columba, associate professor of teaching, learning and technology. “We need to find better ways to challenge our young students, to invite them to think.”

Many different philosophical orientations and instructional theories offer quality mathematics preparation, but Columba supports an old favorite: Bloom’s taxonomy of the Cognitive Domain.

The theory allows teachers to differentiate their lessons among classrooms that are becoming more and more academically diverse, but also highly integrated.

Effective questions in the math classroom challenge students to think critically and engage the material. Bloom’s taxonomy accomplishes this by creating a series of questions that get progressively challenging, encouraging students to think at a higher cognitive level.

All educators learn about Bloom’s taxonomy in their college courses, but often need a reminder to put it into practice, says Columba.

“We’re getting insight into our students’ mental processes simply by having a conversation about mathematics,” says Columba.

“The goal of our questions should be to deepen student understanding of mathematical concepts,so preparing questions effectively is critical. Think about it: for a student to explain ‘Why,’ it requires reflective thinking and diminishes guesses or responses based on rote memorization.”

“At a time when differentiation is becoming more important in the classroom, we should all aspire to help out students become critical thinkers,” she adds. “Bloom’s taxonomy does just that.”