Mathematical modeling of tech-related real-world problems for secondary school-level mathematics

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Abstract

The use of authentic real-world problems that reflect the applied nature of mathematics is not prevalent in formal secondary school settings. In this study, we explore the interface between workplace mathematics, particularly tech-related real-world (TRW) problems, and school mathematics, through the explication of mathematical modeling. The research questions are (1) in which tech domains can real-world problems be identified that can be addressed using mathematical modeling for the secondary school level? (2) Which methods do engineers use to simplify tech-related problems for non-experts in their field? (3) In which areas in the secondary mathematics curriculum can TRW problems be mapped? We present a three-phase model which yielded the creation of a pool of 169 TRW problems. The first two phases of the model included extracting authentic problems from the work of tech engineers and simplifying them to be meaningful or perceivable to students. These were explored by conducting task-oriented interviews with senior tech engineers and scientists from leading companies and universities. The third phase was accomplished by interviewing mathematics education experts, and included verifying the compatibility of the problems with the formal, secondary-level mathematics curriculum. The study has methodological, theoretical, and practical contributions. These include methodology that enables identifying TRW problems that are compliant with the secondary mathematics curriculum; adding to the literature about mathematical modeling by demonstrating the interface between workplace mathematics and school mathematics; and creating a large pool of TRW problems that can be used in secondary school math lessons.

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Three approaches to qualitative content analysis.

Hsiu-Fang Hsieh, Sarah Shannon (2016)

Content analysis is a widely used qualitative research technique. Rather than being a single method, current applications of content analysis show three distinct approaches: conventional, directed, or summative. All three approaches are used to interpret meaning from the content of text data and, hence, adhere to the naturalistic paradigm. The major differences among the approaches are coding schemes, origins of codes, and threats to trustworthiness. In conventional content analysis, coding categories are derived directly from the text data. With a directed approach, analysis starts with a theory or relevant research findings as guidance for initial codes. A summative content analysis involves counting and comparisons, usually of keywords or content, followed by the interpretation of the underlying context. The authors delineate analytic procedures specific to each approach and techniques addressing trustworthiness with hypothetical examples drawn from the area of end-of-life care.

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Reducing Confusion about Grounded Theory and Qualitative Content Analysis: Similarities and Differences

Ji Hong Cho, Eun-Hee Lee (2014)

Although grounded theory and qualitative content analysis are similar in some respects, they differ as well; yet the differences between the two have rarely been made clear in the literature. The purpose of this article was to clarify ambiguities and reduce confusion about grounded theory and qualitative content analysis by identifying similarities and differences in the two based on a literature review and critical reflection on the authors’ own research. Six areas of difference emerged: (a) background and philosophical base, (b) unique characteristics of each method, (c) goals and rationale of each method, (d) data analysis process, (e) outcomes of the research, and (f) evaluation of trustworthiness. This article provides knowledge that can assist researchers and students in the selection of appropriate research methods for their inquiries.