MP 8: Look for and Express Regularity in Repeated Reasoning
The habits of mind embodied in this practice should enrich the problem solving experiences of math learners. Some of those habits can be described as looking for patterns, generalizing results, monitoring the solving process, checking the reasonableness of answers, making discoveries, and devising new avenues to explore.
Research has shown that early work on these habits, such as looking for patterns, can have a positive impact on later mathematical and language ability. Pedagogical methods that put these habits into practice are illustrated in the “Designing Math Curricula” webinar, in the video “Cluster Problems,” and in the discussion of extending several problems in the resource called “Opening Out.”
Strategies for Implementing Practice Standard 8
The raw material for implementation comes from the cultivation of good questioning about good problems. The videos from Inside Mathematics demonstrate practice standard 8 in action in classrooms. The slide presentation called “Making Bags of Apples” shows both the teacher-student interaction as well as the explanations about the ways students are looking for and expressing regularity in repeated reasoning.
Sources of Problems
You will find resources that contain rich problems including “Grade 1 Practice Problems” (part of a vast problem bank from Port Angeles, WA); “Calling All Students” (from Exemplars); the extensive Noyce collection of “Problems of the Month;” and the problems in “Guess-Check-Improve Strategy” from Victoria, NSW. These resources will assist teachers as they search for problems for a variety of grade levels and covering many content standards.
Kindergartners and first-grade students listen excitedly to a modified storybook to guide their geometry activities. Using pattern blocks to create first simple patterns based on the story, they go on to create more complex patterns and ultimately to look for numeric patterns related to the geometric patterns.
This article describes the teacher's role in promoting mathematical thinking and problem solving in the classroom—identifying critical teacher actions and decisions; considering how beliefs influence the teacher’s actions and decisions; and suggesting implications for teachers and students. The author contrasts two different approaches to the presentation of a problem and points out strategies that foster understanding, perseverance, and confidence in students.
This article presents the use of a problem-based instructional task in an elementary classroom. After estimating the number of blades of grass on a football field, students write letters to explain the results of their research. Teachers will learn how to implement this task and similar problem-solving tasks in the elementary mathematics classroom.