How do students deal with difficulties in mathematics?

We report on a study carried out by the Mathematics Department at the National University of Ireland Maynooth to determine why students do or do not engage with mathematics support. Initial interviews were conducted with students who had failed first year. This paper gives preliminary findings from interviews with a second group of students who had passed first year. Students were chosen who had similar mathematical backgrounds to the first group and who had all engaged with mathematics. The students’ mathematical backgrounds do not appear to be the only major factor in determining engagement. We found that both groups experienced similar difficulties and problems. However, the second group had several different strategies or coping mechanisms to enable them to get through. We compare the two groups and will discuss some of these coping mechanisms in detail

USING STIMULUS EQUIVALENCE TECHNOLOGY TO TEACH RESEARCH DESIGN CONDITIONAL RELATIONS FOR UNDERGRADUATE STUDENTS

The purpose of this study was to evaluate the effects of a stimulus equivalence instructional package on undergraduates' performance in conditional discrimination tasks that involved research design names, definitions, notations, and examples. Participants were four undergraduate students whose primary language was Portuguese. Participants remained in the study only if their percentage of correct responses in Probes 1, 2, and 3 was lower than 20%. Thirty-six experimental stimuli were used in the study. They were comprised of nine research design names, nine research design definitions, nine research design notations, and nine examples presented in a matching to sample format during teaching and emergent relations sessions. Probes consisted of nine open-ended questions on the taught conditional relations and new examples. All participants learned all conditional relations, showed emergence of symmetric and transitive relations, and generalized from the selection-based tasks (multiple-choice tasks) to the topography-based tasks (open-ended probes). Lessons learned from this study can help in programming effective instruction for higher education settings

Learning Stoichiometry: A Comparison of Text and Multimedia Formats

Background: The current mode of stoichiometry instruction employs a passive pedagogy that consists of students reading, listening, watching, and memorizing disembodied facts, procedures, and principles in preparation for future application. But chemistry students are often subsequently unable to apply this stoichiometry knowledge in equilibrium and acid-base chemistry problem solving. Cognitive research findings suggest that for learning to be meaningful, learners need to actively construct their own knowledge by integrating new information into, and reorganizing, their prior understandings. Scaffolded inquiry in which facts, procedures, and principles are introduced as needed within the context of authentic problem solving may provide the practice and encoding opportunities necessary for construction of a memorable and usable knowledge base. The dynamic and interactive capabilities of online technology may facilitate stoichiometry instruction that promotes this meaningful learning. Purpose: To compare students' performance after studying one of two cognitively informed sets of stoichiometry instructional materials in order to determine if the dynamic and interactive capabilities of online technology promote greater learning outcomes than studying from text-based materials alone. Setting: Requests for volunteers, collection of background data, treatment assignment, and a post-treatment assessment were all delivered online. A second parallel assessment one-week post-treatment was administered in a proctored classroom on the Carnegie Mellon University (CMU) campus. Participants: Volunteers of at least 18 years of age were solicited from incoming CMU freshman affiliated with either the Mellon College of Science (MCS) or the Carnegie Institute of Technology (CIT). Forty-five (out of 426 solicited) participants completed one of two sets of stoichiometry instructional materials within a six-week period in July and August, 2005. Intervention: Volunteers were randomly assigned to one of two treatments--a text-only or technology-rich, dynamic and interactive stoichiometry review course. Research Design: Randomized posttest-only controlled trial. Data Collection and Analysis: Background data included participants' SAT scores, number of chemistry courses taken, and gender. Parallel posttests of stoichiometry concepts and procedures were administered two times post-treatment--upon completion of study materials and one week later. Participants' interactions with the technology-rich treatment were recorded in log files. Exploratory data analysis was performed to look for patterns in the data. Modeling of the data was executed by single regressions of posttest scores on treatment, background characteristics, and log files to determine the contribution of each variable to learning. A multiple regression of posttest scores on the variables significantly correlated with them revealed what proportion of the variability in posttest scores could be attributed to specific variables or interactions among them. Findings: SAT scores and gender were stronger predictors of posttest performance than either treatment. Examination of the statistically significant correlation between SAT score and gender revealed a differential in the SAT scores of females and males admitted to MCS and CIT with males having higher scores overall. The mean SAT score for female volunteers was significantly lower than that for the female population. There was no such discrepancy between male volunteers and the male population. Within the technology-rich treatment group, participant interaction with the Virtual Lab simulation, but not SAT scores, is related to posttest performance. Whether this interactivity can offset possible gender effects is uncertain because of the small number of females in the technology-rich treatment group. Conclusions: Future users of the online course should be encouraged to engage with the problem-solving opportunities provided by the Virtual Lab simulation through either explicit instruction and/or implementation of some level of program control within the course's navigational features. The variability of students' prior knowledge levels in quantitative areas points to a need for rigorous support systems during first-year courses in order to curtail poor performance that could result in increased attrition rates. One type of support system could be supplemental instruction grounded in findings from the learning sciences and facilitated by the dynamic and interactive features of online technology