Cognitive and Learning Style Predictors of Students' Achievement in Developmental Mathematics

1. Figure 1: Distribution of Regulatory Categories Among DM students. Table 1: Regulatory Categories Competent Regulators: Are consistently (2 or more trials) certain (score of 3 or higher) that only no preference is an analytic response option Conflicted Regulators: Are consistently certain that preferred gambles (e.g., 1/10 and/or 10/100 option) and no preference are both analytic responses. Flawed Regulators: Are consistently certain that a preferred gamble (e.g., 1/10 and/or 10/100) is the only analytic response option. Other Regulators: Are consistently certain that no response option (1/10, 10/100 and no preference) is analytic. Table 2: Students’ Judgments and Decisions by Regulatory Category. __________________________________________ Mean Frequency Regulatory Categoryof Trials … ______________________________________ Competent Conflicted Flawed Other _________________________________ Making No Preference2.00 1.70 .66 1.20 Judgments (Max=3) Making Large Gamble (10/100) .29 .50 1.44 .75 Judgments (Max=3) Paying for a Preferred .00 .25 .66 .16 Gamble (Max=3) Cognitive and Learning Style Predictors of Students' Achievement in Developmental Mathematics Krys Johnson, Eric Amsel, and Adam Johnston Weber State University Abstract College students (N=47) in developmental math classes were assessed for their cognitive regulatory skills and learning style. A stepwise multiple regression on anticipated final grade revealed a significant three-factor solution, which included student status, learning style, and cognitive regulatory skill as significant predictors. Method Participants A total of 47 students (10 Male, 37 Female) volunteered from college Developmental Math classes to serve as participants. Most were freshmen (54%) but some were sophomores (20%), juniors (17%) and seniors (9%). The average participant age was 26 years and self-reported ACT was 20. Procedure Participants completed an on-line questionnaire assessing demographic information (age, sex, student status, anticipated final grade) Ratio- Bias task performance, and Learning Style. Final anticipated grade was the Dependent Variable in the regression analyses. Such verbal reports have been shown to be reliable (Trice, 1990). Ratio-Bias Task. Three Ratio Bias task trials were constructed with each task having a Ratio Bias Judgment (RB-J) and Evaluation (RB-E) task. In the RB-J task, participants imagined being offered a choice between two equal gambles (e.g., 1/10 vs. 10/100). They were then told of their equality and asked which gamble they preferred (e.g., 1/10 or 10/100 gamble) or to express “no preference”. Participants were also assessed for whether they would be willing to pay for a preferred gamble. In the RB-E task, participants were given a definition of analytic-based processing (a “logical, thoughtful, and mathematically sound analysis of the situation”),then evaluated their certainty that choosing each response option (e.g., preferring 1/10, 10/100, and no preference) reflected the product of an analytic process on a 4-point scale (1 and 2 were coded as uncertain and 3 and 4 as certain). Participants were given three trials in which they completed a pair of RB-E and RB-E tasks. Each trial varied the ratios, but kept the equality between them (1/10 vs. 10/100; 9/10 vs. 90/100; 5/10 vs. 50/100).   Learning Style. Participants completed Biggs et al.’s (2001) Revised Study Process Questionnaire (R-SPQ-2F) which assesses Surface and Deep Learning motivation and strategies. An example of a Deep Learning strategy item is, “I find that I have to do enough work on a topic so that I can form my own conclusions before I am satisfied”. Each of the four subscales had five questions with each judged on a five-point scale, from never (1) to always (5) true of me. There was an acceptable Cronbach’s alpha for each scale (ranging from .57 to .72). Results Demographics Student’s anticipated grade distribution was high (averaging a B). No student anticipated failing, despite DM courses having among the highest non-completion rates of any course in the university. Learning Style The subtest scores of the Study Process Questionnaire were analyzed in a one-way repeated measures ANVOA. As a group, participants had higher Deep Learning motivation (DLM) scores (M=3.02) than other scores (DLS=2.87, SLS=2.37, and SLM=1.83). This pattern suggests a sample which, by DM instructor reports, may not be representative of the population.. Cognitive Regulation Participants were categorized into one of four regulatory statuses (see Table 1) based on their performance on the RB-E task. To be categorized, a participant had to give the same pattern of RB-E responses on at least two of three trials, the prior probability of which varies from .19 for Conflicted and Flawed to .02 for Other and Competent Regulators. Of the 45 students who completed all three RB tasks, 40 could be categorized (prior p =. 42, binomial p<.001). The distribution (Figure 1) of response categories replicates previous research on the same population (Amsel et al., in prep.) Moreover, as predicted, Competent and Conflicted Regulators made more no preference, fewer large gamble, and fewer willingness to pay judgments than Flawed Regulators, all t’s(36) 2.52 - 3.73 p < .05 - .001 1-tail) (see Table 2) . Predicting Anticipated Developmental Math Grade To assess the whether LS and CR predicts students’ DM performance, a stepwise multiple regression was run. The criterion variable was anticipated final grade (range: 1-3). The predictor variables included scores on all four LS subtests (range: 5-25), overall deep learning and surface learning scores (range: 10-50), the frequency of each regulatory status (range: 0-3), the frequency of each RB-J response type (range: 0-3), and the frequency of “willingness to pay” judgments (range: 0-3). Student age sex and status were also included as predictors. The regression analysis returned a three-factor solution, R=.63, F(3,41)=9.14, p<.001). The three factors predicting anticipated final grade were Deep Learning Strategy (Beta = -.41), Conflict Regulatory status (Beta = -.28) and Student Status, (Beta = .25). The model relates higher math achievement to students who more regularly use deep learning strategies, who more often confuse experiential with analytic processes (but not vise versa), and who are earlier than later in their college career. Discussion The regression analysis confirmed the hypothesis that extra-mathematical factors (Student Status, LS, and CR) contribute to students’ DM achievement. Lower student status (i.e., under- than upper-classmen) may have predicted higher DM grades because students who delay taking DM courses may have math anxiety (Ashcraft, 2002), perhaps failing to successfully complete the course previously. As expected, higher DM achievement was associated with students who more frequently use deep learning strategies. Biggs et al., (2001) note that students may spontaneously use such strategies, but they may also be elicited by skillful teachers. Surprisingly, higher DM achievement was predicted by more frequent cognitive regulatory Conflict (not Competent) responses on the RB-E task. Students who made Conflict responses more frequently, understand that mathematics requires analytic processing (unlike frequent Flawed and Other responders) but have yet to resolve the role of experiential processing (i.e., their intuitions). A confusion reconciling analytic- and experiential-processing in mathematics may compel students to more deeply engage the DM class material than Competent Regulators who, although having skills to perform well, may not find the course engaging. This account is consistent with other work citing a central role of student interest in math cognition, learning, and achievement (Renninger, et al., 2002). We are planning future work to explore these issues longitudinally, with a larger and more representative sample of DM students. Introduction Almost three quarters of Weber State University freshman in Fall 2003 at took a Developmental Math (DM) class (WSU, IR, 2004), which is the same rate as freshmen entering the California State system (McClory, 2002). Although the curriculum is drawn from middle- and high-school Pre-algebra and Algebra classes, the DM courses have the highest student non-completion rates in the university, hovering at 40% (WSU IR, 2004). WSU is not unusual in this regard (NCES, 1996). This study addresses the issue by exploring the influence of extra-mathematical factors on students’ success in college DM classes, including cognitive regulation (CR) skills and learning style (LS). Cognitive Regulation CR refers to an ability to distinguish between experiential-based (automatic and heuristic) and analytic-based (conscious and algorithmic) cognitive processing systems and to respond with the analytic system on a math task (Amsel et al, submitted, in preparation). Previous work has shown that DM students have more limited CR skills than students in more advanced classes (Amsel et al., submitted). Low CR skills was related to students' difficulty generalizing the same response on isomorphic math tasks, a tendency to make irrational gambling judgments, and to math underachievement (Amsel et al., in prep). CR skills are measured by performance on the Ratio-Bias task in which students choose between two equal gambles (Amsel et al, submitted, in preparation). Student Learning Style Students’ tendency to engage in DeepLearning may also contribute to their DM course success. Deep Learning refers to students’ motivation and strategies to reflect upon educational experiences (e.g., a solved algebra problem, etc.) in order to deliberately create new knowledge, connections or understandings. Such a tendency is measured by the Study Process Questionnaire (Biggs et al., 2001), which assesses deep and superficial learning strategies and motivations. It was hypothesized that DM achievement will be predicted by such extra-mathematical factors as students’ cognitive regulatory competence and a deep learning style. References Amsel, E., Close, J., Sadler, E., & Klaczynski, P. (in preparation). The development of dual process regulatory competence: The role of age and expertise. Amsel, E., Close, J., Sadler, E., & Klaczynski, P. (under review). Awareness and irrationality: College students' awareness of their irrational judgments on gambling tasks. Journal of Gambling Studies. Ashcraft, M. (2000). Math anxiety: Personal, educational, and cognitive consequences. 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