Considering the Whole Child in Mathematics: Blending Cognitive and Non-Cognitive Indicators to Guide Placement in Middle School Mathematics

Public Deposited

Cognitive measures, such as ability tests, placement tests, and final grade point averages, have been the metrics traditionally used to determine students’ placement and to predict success in mathematics ability-level courses. However, there is growing evidence that non-cognitive traits, such as grit (2016) and a mindset (2006), challenge educators to consider the validity of adding measures of students’ attitudes toward learning as non-cognitive predictors of their success in mathematics. The purpose of this mixed-methods study was to explore the relationships between cognitive and non-cognitive predictive measures of fifth-grade students in order to create an alternate formula for refining the placement process, enhance their academic success in sixth-grade mathematics, and capture the students’ voices to better understand their struggles and successes in mathematics. For this mixed methods study, data were collected quantitatively and qualitatively. Specifically, the fifth-grade students completed two surveys, the Grit-S survey and a Mindset survey, to measure two non-cognitive domains. Three cognitive measures were considered for the fifth-grade students: their Math 6 Placement Test scores, their Math 5 GPAs, and their grade 4 CogAT 7 scores. To collect students’ definitions of success in mathematics, the study concluded with interviews prompted by open-ended questions designed to solicit greater insight into students’ understandings of their own successes and challenges in mathematics. These quantitative and qualitative data revealed that developing formulas that included all five independent variables’ non-cognitive and cognitive measures would be more effective than the district’s present “cognitive only” approach for determining students’ placement into sixth grade mathematics. The researcher identified the non-cognitive skill of grit as an important factor when predicting Math 6 Accelerated results. Students’ responses indicated that they dedicated over three and a half years to their favorite activity, a finding that confirms Duckworth’s (2016) research on strategies for developing an individual’s passion, persistence, and resilience. In the interviews, students revealed an emphasis placed on speed in mathematics. If the students were fast, then they believed they were good at math. However, if they were not fast, they believed that they were not good at math, which could lead to math anxiety (Boaler, 2015). The students’ beliefs in their abilities to learn and understand mathematics was supported by their interview responses. Their positive attitudinal responses suggested a growth mindset, and negative attitudinal responses echoed a fixed mindset (Dweck, 2006). The students shared that, when they faced a challenge in math, they used positive behavioral learning strategies, both individual and interpersonal, that allowed them to persevere while struggling with math concepts. Together, these strategies confirmed the research of Dweck (2006), Boaler (2015), and Duckworth (2016). The students articulated that they enjoyed learning mathematics when the lessons were active and hands-on, and when they searched for patterns through problem solving, which confirms Boaler’s (2015) argument that a constructivist pedagogical approach to teaching mathematics engages and deepens students’ learning and conceptual understanding.

Last modified
  • 02/01/2024
Date created
Resource type
Rights statement


In Collection: