example-based math assignments for 4th and 5th graders

COMING SOON

About Learning with Examples

Why this approach?

Research shows that students often enter a math class holding misconceptions that could derail new learning. Teachers, then, need to identify and target misconceptions and build up accurate conceptual knowledge, all while providing students with instruction on the procedural skills that are required by the standards and by standardized testing.

Studies show that when students engage with both correct and incorrect worked examples and explain the associated mathematics, real progress occurs to help dislodge sometimes stubborn misconceptions.

Learning via Self-Explanation.

Self-explanation means explaining information to oneself as one reads, solves problems, or attempts to learn. When individuals self-explain, they integrate knowledge (from prior knowledge and/or instruction), infer to fill their knowledge gaps, and make explicit new knowledge and connections. This is all beneficial for learning.

Explaining Correct Solutions.

In some exercises, students are told that the solution is correct and are asked to explain why it is correct. Research suggests it is important to require students to explain not only what was done in the example but also why it was correct. This encourages students to go beyond procedural explanations (e.g., "It's right because he divided both sides by 3") to produce more principle-based, conceptual explanations leading to improved conceptual understanding.

Learning via Explanation of Incorrect Solutions.

In half of the exercises, students receive an incorrect problem solution and are asked to explain why it is incorrect. This type of activity is believed to improve learning because it helps students to reject their own similar, incorrect procedures. The idea that errors can be effective learning tools is not new: Studies show that asking students to explain both incorrect and correct solutions leads to greater learning. Worked examples can also help motivate students, especially those who are underrepresented in the mathematically proficient.

Extending the “ByExample” Approach to Grades 4 & 5.

Analysis of SERP's AlgebraByExample materials revealed that many misconceptions have their roots in earlier grades. Addressing elementary math misconceptions before middle school is doubly important because failure-related declines in motivation can hinder success even further. Traditional practice activities do not address common misconceptions about the problems to solve, allowing misconceptions to linger long after elementary school. Addressing this early is even more important as standards for rigor rise. Better-prepared students will free teachers in higher-level math courses to focus on grade-level content, making it more likely that students succeed in higher level math.

 

Development of MathByExample was led by Julie Booth (Temple University) through a SERP collaboration with several school districts. The collaboration has been supported to conduct this work by the Institute of Education Sciences, U.S. Department of Education, through Grant R305A150456 to Strategic Education Research Partnership Institute. The information provided does not represent views of the funders

 

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