Exploring Students' Calibration in High School Mathematics: A Classroom Intervention

• Author / Creator

  Herbst, Behnaz

• Through this study, I sought to explore the change in students’ calibration in a Grade 11 mathematics classroom. The intention was to inquire about the extent to which students’ self-estimations of task performance aligned with their actual task performance on classroom tests. Such alignment is generally referred to as metacognitive calibration, or calibration for brief. Calibration indicates how closely students’ self-estimations of their task performance outcomes match their actual task performance outcomes in any field of study. Improving students’ task performance outcomes (i.e., their grades)—although often a by-product of improved calibration—was not the intention of this study. To explain, in my attempt to study students’ calibration and to gain insights into the potential change and development in students’ calibration, I designed and used a pedagogical intervention in a Grade 11 mathematics classroom. However, influencing students’ task performance outcomes was not a pursued goal of my study.
  To conduct this research, I used a mixed methods methodology in three phases of pre-intervention, intervention, and post-intervention. The pre- and post-intervention phases involved the collection of only qualitative data, whereas the intervention phase involved the collection of both qualitative and quantitative data. My intervention consisted of four components: monitoring strategy training, curriculum-based classroom tests, students’ calibration graphs, and students’ reflection notecards. As such, I incorporated the elements of these four components into a classroom intervention that I merged with students’ daily learning activities. Except for the final exam and the follow-up interviews, all my intervention activities were completed between February 3, 2016 and May 13, 2016 (see Appendix J). However, with ethics permission, the students made one last performance estimation on their final exam and the follow-up interviews were conducted after the end of the school year, in the first two weeks of July 2016.
  My qualitative data sources consisted of student questionnaires, reflection notecards, and follow-up interviews, while the quantitative data sources consisted of students’ task performance outcomes, task performance estimations, and students’ individually prepared calibration graphs. I performed one round of statistical data analysis followed by three rounds of blended data analyses in which I combined qualitative and quantitative data to facilitate an in-depth analysis of the collected research data.
  The findings revealed an optimistic view in which calibration was perceived to be malleable, improving incrementally in the context of the employed classroom intervention, while also challenging the prevalent assumption that calibration can only be understood and explained numerically. The findings have potential implications for mathematics education, particularly for high school mathematics teachers. The results demonstrated that although cognitive skills are clearly necessary for learning mathematics, being metacognitively calibrated provides mathematics students with an understanding and awareness of their subject-related strengths and weaknesses so they can allocate their time, attention, and study efforts accordingly. The findings also underscore the key role of students’ self-perceptions in guiding their calibration and provide insights for future research on calibration.

• Subjects / Keywords

  • Metacognition

• Graduation date

  Fall 2020

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/r3-ksv3-7p93

• License

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