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Measuring Professional Competence for the Teaching of Mathematical Modelling

Raphael Wess, Heiner Klock, Hans-Stefan Siller, and Gilbert Greefrath
Publication Date: 
Number of Pages: 
[Reviewed by
Jasmine Sourwine
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Measuring Professional Competence for the Teaching of Mathematical Modelling is primarily a tool for assessing pre-service teachers’ knowledge about mathematical modeling as a practice. The book is part of a series titled International Perspectives on the Teaching and Learning of Mathematical Modelling. The primary audience includes mathematics methods instructors for pre-service teachers or even department heads or mentors for current math instructors trying to improve their modeling instruction. 
The book begins with a description of mathematical modeling and its purpose. It includes discussions about sub-competencies within mathematical modeling, justification for including it in mathematics instruction, current directions, and developments in the field, what it means to design authentic tasks, criteria for modeling tasks, anticipated student difficulties, and adaptive intervention strategies.
Continuing from a general overview of the subject, the book illustrates what it means to be competent in mathematical modeling related to teaching and teaching mathematics in particular. Some facets include knowledge about interventions, modeling, processes, modeling tasks, and aims and perspectives. For those looking for a tool to measure competence who already have a solid foundational understanding of mathematical modeling, the first two chapters are not crucial but a reinforcement of the idea.
Chapter 3 introduces the main purpose of the book, the test instrument. This chapter includes a thorough description of the test book and justification for selecting the questions and possible responses included. The test instrument contains seven sections, and all responses are in the form of a checkbox: true/false, Likert scale, multiple-choice, etc. The sections include topics around self-reporting on mathematical modeling experiences, preparation, assessment of “good” modeling task attributes, and follow-up actions to student responses. There are six vignettes in the test book containing a modeling problem, student dialogue, and follow-up questions for the teacher. The vignettes range from 6th to 12th-grade content. The entire test instrument is included, along with the correct answers. 
Following the test instrument is a discussion of its quality, including a description of ways to ensure implementation objectivity, evaluation objectivity, and interpretation objectivity. Calculations describing the correlations to test the validity of the instrument are also discussed. 
This tool is valuable for an initial assessment of pre-service teachers’ progress in understanding mathematical modeling as it relates to students. However, due to the checkbox nature of the assessment, there is little room to assess the teacher’s ability to effectively facilitate conversations to help students discover key concepts, connect multiple representations and ideas, or design effective mathematical modeling tasks themselves. The title states it will measure competence, and I don’t know if it can accurately do that with its binary nature.


Jasmine Sourwine is a Ph.D. student in mathematics education at Iowa State University. As a former secondary mathematics instructor, her research focuses on effective strategies to increase equity in mathematics classrooms.