DRUMM: DIMENSION REDUCTION USING MIXED METHODS TO INVESTIGATE AFFECT AND ATTITUDES IN UNDERGRADUATE MATHEMATICS STUDENTS

Abstract

This project consists of two studies and pursues two goals: (1) to define and measure constructs associated with success in math courses among undergraduate students; and (2) to study the feasibility of the use of qualitative thematic analysis to complement the development of quantitative instruments to measure affective and attitudinal constructs. Study 1 consists of a quantitative phase followed by a qualitative phase. In the quantitative phase, n=53 students enrolled in undergraduate math courses complete a 52-item survey composed of items from existing inventories including the Attitudes Towards Mathematics Inventory (ATMI; Tapia & Marsh, 2004); Math Anxiety Scale – Revised (MAS-R; Bai, et al., 2008); Abbreviated Math Anxiety Scale (AMAS; Hopko, et al., 2003); Math Anxiety Rating Scale, Brief Version (MARS; Suinn & Winston, 2003) and Motivated Strategies for Learning Questionnaire (MSLQ; Pintrich, et al., 1991). A series of principal components analyses (PCAs) are conducted to determine that a five-component structure offers optimal fit and interpretability. Cluster analysis guides participant selection for a focus group and an interview, in which prompts are written loosely based on the five components which emerged in the quantitative phase and to further investigate some notable items. The qualitative data are analyzed using thematic analysis (TA) in which codes correspond to beliefs, behaviors, and experiences that participants discuss, but these codes cannot be placed in correspondence to the five constructs which emerged in the quantitative phase.Study 2 builds upon the qualitative phase of Study 1 by utilizing items developed based on participant quotes from the focus group and interview, while returning to quantitative data from Study 1 to eliminate some items and refine the goal of the inventory. An additional, emergent goal of Study 2 is the identification of clusters of behaviors which are associated with the constructs which emerged in Study 1. Study 2 includes n=139 participants recruited from undergraduate math courses and incoming math students taking an institutional math placement exam. This study fails to identify clusters of behaviors which became of interest after Study 1 but is notable in the three constructs identified using PCA and structural equation modeling (SEM): (1) math performance security (MPS); (2) productive disposition (PD); and (3) valuation of mathematics (VM). MPS and VM are similar to various previously-studied construct such as ATMI sense of security and MAS-R positive affect, respectively. There is less existing work on the measurement of PD, but this construct is described in a very similar form in Adding it Up (National Research Council, 2001) and has commonalities with notions of self-efficacy (Bandura, 1977), growth mindset (Dweck, 2009), and MSLQ task value. All subscales demonstrate adequate internal reliability, but MPS and PD are associated with subpar average variance extracted. I find a significant association between math performance security and achievement, but productive disposition is significantly associated with achievement only when the effect of valuation of math on achievement is restricted exclusively to an indirect effect through productive disposition. However, both productive disposition and valuation of math have a significant link with self-defined success and have a very strong correlation between each other, though two-component models do not offer optimal fit. Further work is needed to refine the measure of productive disposition and validate the measures for math performance security and valuation of mathematics on a broader scale. Educators can utilize these scales to inform the interpretation of student data, serve as outcomes in themselves, and make course recommendations to students.