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“There is a long history of research on the effects of teaching for meaning and understanding in mathematics. Investigations have consistently shown that an emphasis on teaching for meaning has positive effects on student learning, including better initial learning, greater retention, and an increased likelihood that the ideas will be used in new situations. These results have also been found in studies conducted in high-poverty areas.”
(Grouws & Cebulla, 2000, p. 13).

Components of Every Student Counts (ESC)

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)

ESC is based on
NCTM standards:
•Numbers & Operations
•Algebra
•Geometry
•Measurement
•Data Analysis/Probability
•Problem Solving
•Reasoning & Proof
•Communication
•Connections
•Representation

Go to:
Overview packet (doc)

•TU slide

•PBIT slide
•PBIT planning guide
•PBIT template

•MDP slide
•MDP template

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 of Skills, Concepts, Problem-Solving, and Reasoning (MDP)

“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
  –meaningful practice to support and provide scaffolding for PBITs (preview and review)
  –meaningful practice for a big idea
  –meaningful practice on a concept or skill to improve results on high-stakes tests
  –meaningful practice on notation and terminology
  –meaningful practice on important out-of-context procedures, algorithms, skills
• 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
   –5 minutes or less
   –Whole class
   –Students work and report
   –Manipulatives and technological tools typically only used by teachers
   –Preview or review

“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)

We are taking what we know from research and putting it into practice to improve student achievement because
Every Student Counts.