Analyzing Misconceptions and Exploring Student Explanation Using the Early Grade Mathematics Assessment (EGMA)

• In Event: Beyond Student Outcomes in Early Grade Mathematics: Expanding Opportunities for Measurement

Proposal

The purpose of this presentation is to illustrate how student response data can be used to better understand student errors, misconceptions, and reasoning, which may lead to more targeted interventions and strategic instructional decisions. Typically, student scores on mathematics assessments indicate the number of correct responses, which is often used to gauge overall mathematics proficiency with a tested construct. However, these numeric scores are limited and do not reveal any information about the ways students solve problems and why students may be answering incorrectly.

For this study, we draw on two sources of data. First, we piloted the EGMA Relational Reasoning and Spatial Reasoning subtasks in a Central Asian country. The EGMA Relational Reasoning and Spatial Reasoning subtasks were modified based on the original pilot study data from Jordan (Perry, 2016; Perry, 2019). The Relational Reasoning subtask included items to test students’ knowledge of symbolic equivalence and focused on non-standard equations (e.g., 8 + 4 = 7 + __). The Spatial Reasoning subtask included items to test students’ two-dimensional and three-dimensional spatial structuring skills. In this study, Instead of having enumerators mark correctness during the data collection exercises, they were asked ti record the actual numeric response given by each student. These responses were analyzed to determine possible misconceptions, using existing literature as an initial guide (e.g., Carpenter et al. (2003) or McNeil & Alibali (2005) for misconceptions stemming from knowledge of the equal sign; Battista et al. (1998) for spatial structuring). These misconceptions were also compared to the previous EGMA Relational Reasoning and Spatial Reasoning pilot test in Jordan (e.g., Eichorn et al., 2018).

Results from these analyses indicate that students exhibited many misconceptions in relational reasoning and spatial reasoning. For example, when responding to 9 + 6 = ___ + 10, 34% of students determined the correct answer of 5. The next 3 most common responses all represent common misconceptions or errors: 15, which is the “do something” misconception; 25, which is “the total” misconception; and 6, which is based on the proximity of the numbers to the equal sign. Each of these incorrect responses indicates these students do not have a relational understanding of the equal sign. Knowing that the most common incorrect answers were not due to slips or incorrect counting is critical and can be important for intervention development and evaluation.

Second, from another Central Asian country, we piloted asking students to explain how they solved chosen problem to better understand the student strategy and ability to explain. We conducted field tests to gather possible student answers, and then trained enumerators to be able to choose the closest response for student explanation. Student explanation is especially important for problems such as relation reasoning above, where understanding the process by which students solved the problem provides insight into their relational reasoning skills.

Data, such as these, that go beyond correct/incorrect responses, allow users to better understand students’ reasoning and to dig deeper into the “why” behind incorrect responses.

Authors

• Lindsey Perry, Compassion International

• Adema Zholdoshbekova, RTI International

• Yasmin Sitabkhan, RTI International