High school STEM students' development of definite integral model through a local instruction theory

Date of Publication

8-2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Science Education Major in Mathematics

Subject Categories

Science and Mathematics Education

College

Br. Andrew Gonzalez FSC College of Education

Department/Unit

Science Education

Thesis Adviser

Auxencia A. Limjap

Defense Panel Chair

Minie Rose C. Lapinid

Defense Panel Member

Arlene A. Pascasio
Celina P. Sarmiento
Levi E. Elipane
Voltaire M. Mistades

Abstract/Summary

The study aimed to develop a local instruction theory (LIT) in definite integral. The LIT can be used by teachers as a framework of reference in designing learning trajectories for their own classroom. After three cycles of teaching experiments and retrospective analyses an emergent LIT was developed. The cycles involved mathematics teachers, mathematics student teachers and grade 11 STEM students. The LIT aimed for students’ development of definite integral models to solve STEM related problems. It also considered students’ understanding of functions and antiderivatives as starting points. The elements of the LIT include the description of the learning route and its rationale, the social and sociomathematical norms, and the proactive role of the teacher. The learning route is conceptualized as an evolution of students’ informal solutions of area related problems to the mathematical practice of calculating area using definite integral models. A bridging activity of estimating area through a controlled strip was introduced and used as an enabling prompt. The main purpose of the controlled strip activity was for students to develop a Multiplicatively-based sum conceptualization of definite integral. The activity engendered normative ways of reasoning to emerge and be established.These norms together with a historical interpretation of the definite integral symbol ∫ facilitated students’ development of the definite integral model. Also, these normative ways of reasoning facilitated students’ productive sense making of STEM related problems. Norms related to the MBS conceptualization enabled students to productively make sense of the STEM related problems than those with function matching and perimeter-area conceptions only. Moreover, the classroom culture of explaining reasoning by stating explicitly assumptions and reasoning and making sense of the explanation of others were also significant in the attainment of the LIT’s envisioned goal.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTG008226

Keywords

Mathematics—Study and teaching (Secondary); High school students

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3-26-2025

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