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Research

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Gainsburg, J. (2011). Book Review: Hoyles, C., Noss, R., Kent, P., & Bakker. A. (2010). Improving mathematics at work: The need for techno-mathematical literacies. Educational Studies in Mathematics, 76(1), 117-122.

Abstract

"As mathematics educators, we constantly read about the failure of our schools to prepare graduates for the mathematical requirements of the modern workplace. Most of us accept this idea without question, perhaps because calls for more mathematics education keep us employed. Yet it is surprising that more of us don’t question this “failure,” given the conventional wisdom that adults rarely use the mathematics they learned in school and that, when mathematics is needed in the workplace, computers handle it. In this era of national standard setting and high-stakes mathematics examinations for school students, it seems to behoove us to understand what are the mathematical requirements of today’s jobs and how well today’s workers meet them. Celia Hoyles, Richard Noss, Phillip Kent, Arthur Bakker, and other colleagues have led this area of research for years through major projects exploring the mathematics used by entry-level, intermediate, and professional employees in a range of fields. Improving Mathematics at Work is the most recent and possibly most extensive report on their ethnographic and design-based workplace studies."

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Gainsburg, J. (2015). Engineering students’ epistemological views on mathematical methods in engineering. Journal of Engineering Education, 104(2), 139-166.    

Abstract

Background This study was motivated by the ubiquity and apparent usefulness of general epistemological development schemes, notably that of William J. Perry, Jr., in engineering education, but also by limitations that derive from their generality. Purpose/Hypothesis Empirical data were used to articulate engineering students’ epistemological views on the role of mathematical methods in engineering and to explore the fit of a stage-based developmental model to those data. Design/Method Data included interviews, think-aloud protocols, and classroom observations over a one-year period. Ten undergraduates and four instructors in a civil engineering program participated. A grounded-theory approach was used to identify levels of epistemological views. Perry’s scheme provided a starting framework. Skeptical reverence, the view veteran engineers hold regarding mathematics in engineering, which was previously identified by the author, was taken as a normative endpoint. All data were coded by view level and various contexts to detect students’ epistemological developmental patterns. Results This article proposes three categories of engineering students’ views on the role of mathematical methods in engineering: dualism, integrating, and relativism. Dualism and relativism reflect elements of Perry’s general categories, but integrating, a new category, diverges significantly from Perry’s middle category of multiplicity. No evidence supported a stage-based developmental model. Conclusions This empirically based scheme, while exploratory, provides further evidence that epistemological development differs across disciplines, and offers four levels of epistemological views held by engineering students on the role of mathematics in engineering. Conjectures about how to promote engineering students based on classroom observations, are also offered.

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Gaspard, C. & Gainsburg, J. J Math Teacher Educ (2019). https://doi.org/10.1007/s10857-019-09440-5

Abstract


This study investigated the types of questions that student teachers of mathematics asked their students during whole-class discussions, how these questions changed over time, and why. Four student teachers were interviewed at the beginning and end of a ten-week period of student teaching to elicit their views about the kinds of questions mathematics teachers should ask. One lesson per week, for eight lessons, was video recorded for each student teacher. These videos were analyzed for the kinds of questions the student teachers asked and the nature of the responses from their high-school students. We found that the student teachers initially expressed the view that it was important to ask questions that required students to explain their thinking—a view that aligned with what was promoted in their teacher-preparation program—and that they attempted to ask questions with unpredictable answers in the early weeks. Over time, however, they asked fewer questions overall, with an even greater reduction in the number of questions with unpredictable answers. Interviews revealed that the student teachers’ views about what kinds of questions to ask were influenced, over time, by the responses of their students. The videos offered additional insights into the nature of the students’ responses.videos offered additional insights into the nature of the students’ responses.

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English, L., & Gainsburg, J. (2015). Problem solving in a 21st-century mathematics curriculum. In L. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd edition) (pp. 313-335). New York: Routledge.