Poster #75 - Examining Common Student Arithmetic Errors in Response to a Fraction Sense Intervention

• In Event: 3-106 - Poster Session 11
  In Poster Session: PS 11 Section - Education, Schooling

Integrative Statement

Fraction understanding is a difficult area of mathematics for many students (NMAP, 2008). Children who leave sixth grade with poor fraction knowledge may never catch up and are almost certain to encounter difficulties with algebra (Mazzocco & Devlin, 2008). Current research suggests that understanding fraction magnitudes on the number line is a critical linking mechanism to learn fraction concepts and skills (e.g., Saxe, Diakow, & Gearhart, 2013). Unfortunately, this instructional approach is underutilized in many programs for struggling learners.

We examined potential learning benefits of a fraction intervention centered on a number line in a randomized study of sixth graders with poor fraction proficiency. Participants (N = 81) were randomly assigned at the individual level to an intervention or a control group that received their school’s math intervention. The intervention was conducted in schools serving low SES communities. Students in the intervention made significant gains compared to the control group at posttest in all conceptual areas of fractions (e.g., magnitude knowledge) but not in fraction arithmetic accuracy. The focus of the current study was to explore why fraction arithmetic problem solving accuracy seems change resistant, despite an intensive intervention that provided conceptually-based practice in this area. The fraction arithmetic task included 26 problems involving addition, subtraction, and multiplication.

Table 1 presents percent correct on different problem types as well as type and frequency of errors for addition/subtraction; examples of errors are shown in Figure 1. Most students were accurate on addition/subtraction fractions with like denominators. For unlike denominators, we explored common errors types. Interestingly, the most common error type at pre/posttest for both groups of low achievers was adding across the denominators, suggesting persistent application of an inappropriate whole number strategy. However, both intervention and control groups demonstrated a sizable decrease in the use of this strategy at posttest. A possible reason for the decrease by both groups is the emphasis on arithmetic in the regular classroom. Notably, when some intervention children used the correct common denominator procedure, their accuracy was compromised by calculation errors. In multiplication, children’s accuracy decreased when asked to multiply a fraction by a fraction, or fraction by a whole number, with both groups misapplying addition/subtraction strategies (e.g., find a common denominator; or multiplying a whole number by the numerator and denominator of a fraction). However, increase in the misapplication of addition/subtraction strategies was noticeably greater for the control group (intervention: +3.28%; control: +15.33%).

The mix of conceptually inappropriate procedures used by struggling sixth grade students highlights the difficulty of helping them base their arithmetic on understanding of fractions. Although our intervention children made significant gains in a range of fraction concepts, they did not easily apply them to arithmetic problems. Additionally, learning procedures for fraction addition/subtraction seems to interfere with multiplication (Newton et al, 2014). Moreover, their accuracy is hindered by poor whole number fluency. Additional work, therefore, should explicitly address how to help students leverage their knowledge of fraction concepts to solve fraction arithmetic problems and to encourage them to abandon inappropriate procedures.

Authors

• Kelly-Ann Gesuelli, University of Delaware
  Presenting Author

• Nancy Dyson, University of Delaware
  Non-Presenting Author

• Brianna Devlin, University of Delaware
  Non-Presenting Author

• Nancy Jordan, University of Delaware
  Non-Presenting Author