Poster #81 - Reducing Fraction Errors with Worked Examples

• In Event: 2-163 - Poster Session 08
  In Poster Session: PS 08 Section - Education, Schooling

Integrative Statement

Algebra is a gatekeeper to later mathematics opportunities and careers associated with higher level mathematics; however, many students struggle to master algebra. One potential cause of students’ difficulties in Algebra lies in their early mathematics knowledge and experiences. A lack of understanding basic mathematics principles can cause later errors and misconceptions. Specifically, students’ fraction knowledge is predictive of their readiness to enter algebra (Booth & Newton, 2012) and is predictive of algebra learning (Booth, Newton, & Twiss-Garrity, 2104).
The Common Core State Standards Initiative (2010) calls for mathematics lessons to reflect both conceptual and procedural content, yet traditional instruction often devotes more time to procedural practice. A traditional mathematics lesson often starts with direct instruction about a topic; next students and the teacher solve a few problems together, and finally the student completes a string of procedural practice problems alone or in a group. An alternative way to practice and engage with mathematical content is with worked examples. The Worked Example Principle states that having students study and engage with already completed problems is better than having students solve all of the practice problems themselves (see Booth, McGinn, Young, & Barbieri, 2015 for review). It is believed that worked examples are effective because they reduce students’ cognitive load, allowing them to focus their working memory on understanding the mathematical concept in the example rather than solely on the procedures used to solve the problem.
Prior studies have shown that infusing worked examples into Algebra classrooms reduce student misconceptions and improves learning (e.g., Booth, Cooper et al., 2015). While this work is promising, often students enter Algebra with misconceptions from earlier math concepts, like those introduced in elementary school. The current study tested whether worked examples would benefit a younger population, 5th grade students, and whether they could reduce the prevalence of three specific fraction errors.
The current study had a quasi-experimental design, where 5th grade students (from 10 classrooms; n=188) were assigned to experimental and control groups according to their classroom. Experimental classroom teachers were given booklets of worked examples, which covered the breadth of all 5th grade Common Core State Standards. Control teachers were given booklets that contained traditional practice problems for students to complete. All teachers chose when and which pages to use depending on their curriculum. At both the beginning and end of the school year students were given three problems that were designed to measure three specific fraction errors. These problems dealt with subtracting and dividing two fractions, and multiplying a whole and mixed number.
Our results revealed a significant time by condition interaction. As illustrated in Figure 1, while all students reduced the prevalence of errors from the beginning of the school year to the end of the school year, experimental students reduced the prevalence of errors more than control students. These results also show that the Worked Examples Principle can be applied to young students who are learning foundational mathematics concepts.

Authors

• Laura K Young, Temple University
  Presenting Author

• Julie Booth, Temple University
  Non-Presenting Author