The Development of Teachers’ Knowledge of the Nature of Mathematical Modeling Scale

Abstract

This study addresses a gap in the literature on mathematical modeling education by developing the mathematical modeling knowledge scale (MMKS). The MMKS is a quantitative tool created to assess teachers' knowledge of the nature of mathematical modeling. Quantitative instruments to measure modeling knowledge is scare in the literature partially due to the lack of appropriate instruments developed to assess such knowledge among teachers. The MMKS was developed and validated with a total sample of 364 K-12 teachers from several public-schools using three phases. Phase 1 addresses content validity of the scale using reviews from experts and interviews with knowledgable teachers. Initial psychometric properties and piloting results are presented in phase 2 of the study, and phase 3 reports on the findings during the field test, factor structure, and factor analyses. The results of the factor analyses and other psychometric measures supported a 12-item, one-factor scale for assessing teachers' knowledge of the nature of mathematical modeling. The reliability of the MMKS was moderately high and acceptable (α = .84). The findings suggest the MMKS is a reliable, valid, and useful tool to measure teachers' knowledge of the nature of mathematical modeling. Potential uses and applications of the MMKS by researchers and educators are discussed, and implications for further research are provided.

Teaching math modeling through 3D‐printing: Examining the influence of an integrative professional development

“…The first part included items adapted from the mathematical modeling knowledge scale (MMKS). The MMKS (Asempapa, 2020) is a validated 13‐item questionnaire that measures practicing teachers’ knowledge of mathematical modeling. The scale comprised of 12 true or false items and one open‐ended item that explored how teachers conceptualize mathematical modeling.…”

“…The scale comprised of 12 true or false items and one open-ended item that explored how teachers conceptualize mathematical modeling. The reliability measure of the MMKS's internal consistency is reflected in the Cronbach's alpha of 0.84 for the 12 items (Asempapa, 2020). The MMKS has been used in other PD programs including advanced teacher capacity "modeling with algebra and geometry" organized by the Ohio University, and teaching "modeling across the curriculum" organized by Penn State Harrisburg and found to be useful.…”

Examining Practicing Teachers’ Knowledge and Attitudes toward Mathematical Modeling

“…[MMKS] instrument (Asempapa, 2016(Asempapa, , 2018(Asempapa, , 2020. Similarly, teachers' attitude was defined in this study as the feeling of practicing teachers toward modeling and the teaching of modeling standards and practices as measured by the Mathematical Modeling Attitude Scale [MMAS] (Asempapa, 2016(Asempapa, , 2019Asempapa & Brooks, 2020).…”

“…The survey used to collect information on teachers' knowledge and attitudes toward mathematical modeling consisted of two validated scales. The two validated scales used to collect data were the MMKS (Asempapa, 2016(Asempapa, , 2018(Asempapa, , 2020 and MMAS (Asempapa, 2016(Asempapa, , 2019Asempapa & Brooks, 2020). The MMKS is a 12-item unidimensional Likert survey that measures practicing teachers' knowledge of mathematical modeling.…”

“…The items on the MMKS were derived from current and relevant literature including the CCSSM modeling standards, the GAIMME report, and the NCTM's annual perspectives in 2016 on mathematical modeling (COMAP & SIAM, 2016;Hirsch & Roth McDuffie, 2016;NGA Center & CCSSO, 2010). The MMKS is single-factor scale and was supported in its development and validation by a scree plot, factor structure, exploratory factor analysis (EFA) (Asempapa 2018(Asempapa , 2020 and confirmatory factor analysis (CFA) (Asempapa & Brooks, 2020). The reliability measure of the scale's internal consistency for the 12 items (without the demographic information) is reflected in the Cronbach's alpha of .84 (Asempapa, 2016(Asempapa, , 2018(Asempapa, , 2020 by a scree plot, factor structure, and exploratory factor analysis (EFA) (Asempapa 2019, Asempapa & Brooks, 2020 and confirmatory factor analysis (CFA) (Asempapa & Brooks, 2020).…”