Eliciting All Students' Conceptual Knowledge to Inform Instruction and Take Action

• In Event: 66.022 - Formative Assessments as a Response to the Standards Reform Movement

Abstract

Most American math classes today tend to focus on procedural learning to the expense of conceptual understanding and complex reasoning (e.g., Hiebert and Stigler, 2004). While demographic and societal shifts have altered the face of school and educational expectations have greatly increased, particularly with the recent introduction of Common Core State Standards (CCSS), math instruction has proven stubbornly resistant to change (Hiebert, 2013).
A common challenge that K-12 math educators face in transitioning to the CCSS relates to incorporating complex problems that elicit mathematical reasoning into their instruction. Such reasoning provides a gateway to more abstract content in later coursework. This poster explores a component of a larger exploratory, intervention study focused on the development of formative tasks that confront these issues with math instruction by promoting complex thinking, peer feedback, student self-reflection, and teacher analysis of data. This study was conducted in two small to medium sized school districts in California. Participants included students in 36 classes (n = 638), spanning 11 teachers, and six schools. Teachers and students were nested in schools, with each school assigned to treatment or control groups. Pre/post-tests and attitudes surveys were administered to all students before and after the intervention period. In addition, in the treatment schools student artifacts from the tasks were collected as were teacher reflections.

The tasks are structured like an exercise routine; students are given progressively more challenging materials through a series of independent, pair and whole group activities. Powerpoint slides that include exemplar student work accompany the task allowing students to self-assess their understanding midway. Aligned to foundational Algebra concepts related to CCSS 8EE5-6, students are scaffolded in making connections between proportional reasoning, lines, and linear equations. In addition, the tasks emphasize Math Practice 3 through open-ended items that require students to explain their thinking. Multiple representations are also used as a means for students to, as the task encourages, think through a problem and share their thinking with others.

Artifacts from the tasks will be shared to reveal how understanding of key content and student self-perceptions of performance may lead to actionable next steps for both teachers and students. In addition, we will use student artifacts to provoke discussion among participants regarding 1) the accessibility of task activities for diverse students, 2) evidence of students’ understanding of key content, and 3) possibilities for ongoing task enhancement to provide improved opportunities for students to develop mathematical reasoning and master key concepts.
While analyses revealed that the tasks were generally difficult for students, teacher reflections demonstrated that they provided diagnostic information. In contrast, students’ self-reflections were less aligned with performance, especially for those who weren’t as successful. Furthermore, ANCOVA analyses revealed significant differences with treatment students scoring higher in relation to control students on the post-test (F = 7.30, p = .00) as well as the post-survey (F = 5.70, p = .02). In both cases the effect sizes are small in nature (_p^2 = .01).

Authors

• Christine Ong, University of California - Los Angeles

• Deborah M. La Torre, University of California - Los Angeles

• Kevin Schaaf, University of California - Los Angeles