We can agree on pedagogy and theoretical constructs but what happens in the classroom when instruction begins is the real test of buy-in and willingness to struggle with change. The question continually on my minds is how, as an administrator, I can support, empower, and encourage the tenacity necessary to change old habits.
Recently I have been thinking and reading about math instruction and ran across an article that is an excerpt from the book Treating Children as Mathemiticians by E. Geist. Based on the understanding that Japan and other countries have outpaced the United States in mathematical competencies a study was conducted of eighth grade classrooms to compare “the process of classroom instruction in different cultures to improve student learning in our schools” (Third International Mathematics and Science Study, 2004a, 2004b; Greene, Herman, Haury, & ERIC Clearinghouse for Science, 2000). The book reports on the findings, contrasts the common instructional pattern in the United States and Japan, and outlines what they have identified as the key components of effective mathematical instruction. The book title in some way says it all- Are we teaching students to think as mathematicians? (Or simply to be accurate number crunchers?)
The primary difference between the instructional methods observed focused on thinking about concepts versus memorizing formulas to get the right answer. Do not misunderstand, the right answer is important in math. However if we are to apply our mathematical learning to new problems and situations, we have to understand the concepts behind the computation. The problem here is not that we do not understand this idea but rather that our actions speak louder than our words. If you were to do a walkthrough of the math classes in your school this week what would you observe?
According to the studies referenced in the book, the primary focus of math instruction in the United States from elementary school through high school is on memorization and practice. Some of the key pieces of instruction in the U.S. classrooms were: call and response ( problem/answer) , math as a solitary activity, practice of large groups of problems both in the classroom and for homework, there was one chance to get it right, and students learn to rely on the teacher for the right answer. By contrast the Japanese classrooms focused on: conceptual think ( less memorizing), time to think and experiment with different approaches (many fewer problems -3 in a fifty minute period), collaboration, students were required to reason and prove answers, they worked on complex problems ( but not contrived problems), and “unsuccessful attempts were stepping stones to a solution” (Please do take the time to read the whole article)
I think most people will agree with the article in theory,and on one level or another we have probably discussed similar ideas in our math departments but the correct answer is still king. Why does our math instruction stop there? It would be easy to give a litany of excuses from standardized testing or time constraints to inadequate training/professional development but if we do acknowledge the efficacy of these pedagogues then as administrators how can we effect change? Collaborative honest and open discussion of our current programs, realignment of our goals and permission for the faculty to be risk takers as well as support and encouragement are perhaps the key components.
In the end though, it is not about knowing that there are better ways, it is about a willingness to be transparent in our classrooms and open about our instructional practices. To my way of thinking, this is the culture we need to cultivate and is the culture that supports on going school improvement.
by Barbara Barreda
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