Iowa's mathematics educators are taking what we know from research and putting it into practice to improve K-12 student achievement. Iowa's ESC project has three fundamental research-based components:
• Teaching for Understanding
• Problem-Based Instructional Tasks
• Meaningful Distributed Practice
The ESC goals are to 1) Improve achievement of K-12 students in mathematics and 2) Build learning communities engaged in the study of mathematics, mathematics instruction, and student achievement in mathematics through effective implementation of Iowa's Professional Development Model.
The Every Student Counts initiative states clearly that Teaching for Understanding emphasizes Problem-Based Instructional Tasks and Meaningful Distributed Practice, which are briefly described here.
“Learning for understanding is essential to enable students to solve the new kinds of problems they will inevitably face in the future.” (NCTM, 2000, p.21)
“Students who memorize facts or procedures without understanding often are not sure when and how to use what they know, and such learning is often quite fragile.” (NCTM, 2000, p.20; referencing Bransford, Brown, and Cocking, 1999) |
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Teaching for Understanding (T4U)
- Developing deep conceptual and procedural knowledge of mathematics
- Posing problem-based instructional tasks
- Engaging students in the tasks and providing guidance and support as they develop their own representations and solution strategies
- Promoting discourse among students to share their solution strategies and justify their reasoning
- Summarizing the mathematics and highlighting effective representations and strategies
- Extending students' thinking by challenging them to apply their knowledge in new situations, especially in real world situations
- Listening to students and basing the instructional decisions on their understanding
Problem-Based Instructional Tasks (PBIT)
“Instructional programs that emphasize conceptual development, with the goal of understanding, can facilitate significant mathematics learning without sacrificing skill proficiency.” (Heibert, 2003, p.16) |
- Help students develop a deep understanding of important mathematics
- Emphasize connections, especially to the real world
- Are accessible yet challenging to all
- Can be solved in several ways
- Encourage student engagement and communication
- Encourage the use of connected multiple representations
- Encourage appropriate use of intellectual, physical, and technological tools
Meaningful Distributed Practice
“Problem solving should be the site in which all of the strands of mathematics proficiency converge.” (Kilpatrick, Swafford, & Findell, 2001, p.421) |
- Builds on and extends understanding of important mathematics
- Distributes short periods of systematic practice over a long period of time
- Links to curriculum goals and targets an identified need based on multiple data sources
- Helps students develop flexibility and fluency with skills, concepts, problem solving and reasoning
- Uses problems and activities that help students learn to use multiple representations and learn to use multiple reasoning strategies
- Uses problems and activities from a variety of contexts so students learn to recognize, make, and use connections
- Provides opportunities for formative assessment (assessment for learning)
- Classroom implementation
“Practice should be used with feedback to support all strands of mathematical proficiency and not just procedural fluency…practice on computational procedures should be designed to build on and extend understanding.” (Kilpatrick, Swafford, & Findell, 2001, p.423) |
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