Dr. James Stigler (Professor of Psychology at UCLA, Director of the TIMSS Video Studies) made a presentation to the California Board of Education entitled: Reflections on Mathematics Teaching and How to Improve It.

Dr. Stigler states that the most important things we have learned from this research and the implications that the research has for teaching (mathematics teaching in particular) are the following:

1. Teaching is a cultural activity. In Japan, teachers will give students problems to solve that they have never seen before. We actually don't do that in our country. In Japan, they have a high tolerance for what I would say is "confusion" in the classroom. They'll give a math problem and no one knows what to do. They sit there and they sweat and they look confused and they pull their hair out and they try to figure out what to do. In the U.S., if you give a math problem and everyone looks confused, the teacher steps in right away to stop the confusion--clear it up, give a hint, tell them what to do-anything to stop the confusion. Cultural activities are very hard to change. And one of the reasons for this is that there are all sorts of forces that work against changing cultural norms. We have to recognize that fact as we try to figure out how to improve teaching.

2. The second thing we've learned is that there are many ways to teach effectively…Teaching is contextual. There is no one best way.

3. Teaching quality needs to be defined not by what teachers DO but by the learning opportunities they create for students…. One finding: we marked every time a math problem started and stopped. And then we categorized the problems into one of three types: (a) Stating Concepts (recall a fact), (b) Using Procedures (e.g., do a worksheet practicing a taught procedure), or (c) Making Connections (very rich problems that connect students with core mathematical concepts). Teachers in every TIMSS country used some of all of these types. However, when looking at the videos, a pattern emerged. In the higher performing TIMSS countries such as Japan or Hong Kong, "Making Connections" problems remained as "Making Connections" problems. However, when these types of problems were given in the U.S., the problems were translated into "Using Procedures" problems by every teacher, which was related to the observation above about a cultural proclivity toward alleviating student confusion in the classroom.

He also stated that a review of research by Hiebert and Grouws identifies two features of classroom instruction that are associated with students' understanding of mathematics:

- Connections: Making mathematical relationships-among concepts, procedures, ideas-explicit in the lesson

- Struggle: Students spend at least some time struggling with important mathematics.

Implications:

1. We need to shift the emphasis from "teachers" to "teaching" (need to change cultural routines to make them better over time)

2. We need to redefine "quality teaching." It's not a set of skills and strategies (e.g., lecturing vs. using small groups) but making informed judgments in the classrooms--how what teachers do creates opportunities for students to achieve important learning goals (i.e., for math, explicit ideas and struggle).a. Clearly define learning goals and understandings needed to achieve them (subject matter knowledge essential)

b. Design lessons that use strategies shown effective for achieving the goals and judged appropriate for specific content.

c. Study effectiveness based on students' learning from instruction, and analyze teaching/learning as cause/effect (so teacher can learn from experience). Teachers need to analyze their students' thinking and reasoning.

d. Provide teachers with opportunities to learn the knowledge, skills, and judgment they will need for continuous improvement: stable settings to work with colleagues to learn what works better and share what is learned with the profession.

Moreover, Stigler, in a response to a question from Commissioner David Pearson, stated:

. It takes patience and fortitude to implement new teaching strategies, but it's possible to create a new classroom culture… Too many people think that mathematics isn't about thinking-it's about remembering. Once you get to algebra, you have a lot of steps to remember. However, if you can reason about what the steps are, it gives you a lot more power. In science, there's some real parallel findings. A lot of time is spent in lab activities, but not much time is being spent in the U.S. connecting the lab to science concepts.The goals of mathematics learning in the United States are very procedural, and teachers don't know how to talk about what it is that they want students to understand (apart from how to do procedures)

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