The Influence of Textbooks on Mathematical Readiness for University Calculus - A Material Requirements Planning (MRP) Approach

Abstract

There is a troubling trend regarding the competency of first-year university students in the subject of mathematics. Literature reflects a perspicuous disappointment in secondary school graduates’ ability to perform simple mathematical tasks for employers or to succeed in upperlevel mathematics courses in colleges/universities. The profoundness of inability is revealed, in part, by the proliferation of remedial mathematical courses at colleges/universities and the increase in elementary training programs implemented by employers so that employees can function at a minimum requirements level. This research investigates, via survey data collection, descriptive statistics, initial factor models (using SPSS v20.0), and confirmatory factor analysis and Structured Equation Modelling (via Mplus v7.1) the interaction of possible contributing causes to ascertain whether the absence of mathematical maturity in secondary school graduates can be linked to the trend of mathematical textbooks having a content and presentation inconsistent with the entrance requirements of the college/university sectors. Specifically, this work focuses on the preparation of year-12 precalculus students to succeed in their first-year university calculus course by analysis of precalculus textbook content, trust, and use. This study uses a mixed methods approach to integrate and optimize the affirming value of qualitative and quantitative data analysis. It uses a Likert scale questionnaire and demographic survey questions that included identification of the textbooks in use so they could be acquired and qualitatively analyzed through a rigor measuring tool developed as part of this project. This study suggests the applicability of Material Requirements Planning (MRP) to the academic environment as a tool for restoring tertiary institutions as the proper drivers for secondary mathematical exit requirements and for guiding development of secondary mathematics curricula, syllabi, and textbook content. MRP has at its core a focus on customer requirements for a particular product; when applied to the mathematical education of inbound tertiary mathematics students, MRP can identify tertiary institutions’ minimum requirements of mathematical maturity as the customer requirements that secondary schools can then prioritize in their mathematics programs. This research demonstrates the solid connection between mathematical maturity and textbook content in that textbook completion influenced year-12 student and teacher confidence in student readiness for year-13 calculus. This finding prompted creation of a unique tool for measuring the rigor of precalculus textbooks designed to prepare secondary students for their university elementary calculus course. Rigor is defined as the extent to which a textbook facilitates student mastery of relevant mathematical concepts while simultaneously preparing them to master ever more complex concepts. Accordingly, the rigor tool described in this study assesses the extent to which a precalculus textbook presents core calculus prerequisite topics recursively, employing a cohesive continuum of topic introduction, topic relevance, topic theory, and topic practice while maintaining a maturing connection to previous topics. Using the rigor tool, year-12 precalculus textbook rigor was qualitatively analyzed into measurable quantitative data from which a rigor score was derived for selected textbooks. The level of misalignment between the year-13 calculus prerequisites and the year-12 targeted outcomes was made apparent through this process.