Steven Rosenfield

The puzzling reliability of the Force Concept Inventory

The Force Concept Inventory (FCI) has influenced the development of many research-based pedagogies. However, no data exists on the FCI’s internal consistency or test-retest reliability. The FCI was administered twice to one hundred students during the first week of classes in an electricity and magnetism course with no review of mechanics between test administrations. High Kuder–Richardson reliability coefficient values, which estimate the average correlation of scores obtained on all possible halves of the test, suggest strong internal consistency. However, 31% of the responses changed from test to retest, suggesting weak reliability for individual questions. A chi-square analysis shows that change in responses was neither consistent nor completely random. The puzzling conclusion is that although individual FCI responses are not reliable, the FCI total score is highly reliable.

Are All Wrong FCI Answers Equivalent

The Force Concept Inventory (FCI) has been efficiently used to assess conceptual learning in mechanics. Each FCI question has one Newtonian answer and four wrong answers (distracters). Researchers and practitioners most frequently use measures of total score to assess learning. Yet, are all wrong answers equivalent? We conducted Latent Markov Chain Modeling (LMCM) analyses of all choices (right and wrong) on a subset of four FCI questions. LMCM assesses whether there are groups of students sharing similar patterns of responses. We infer that students sharing similar patterns also share similar reasoning. Our results show seven reasoning‐groups. LMCM also computes probabilities of transition from one reasoning‐group to another after instruction. Examining transitions between groups, we note a clear hierarchy. Groups at the top of the hierarchy are comprised of students that use Newtonian thinking more consistently but also choose certain wrong answers more frequently; suggesting that not all wrong answers ...

Do I Really Hafta? WebCal, A Look at the Use of LiveMath Software in Web-based Materials That Provide Interactive Engagement in a Collaborative Learning Environment for Differential Calculus

This paper describes the use of a Web-based Computer Algebra System (CAS) called LiveMath in a computer supported collaborative learning environment for Differential Calculus. The instructional design incorporated a Reform Calculus notion of Calculus and a constructivist philosophy of learning. Based on interviews with students, independent observations in the classroom, and observations by the teacher, this paper provides insight for students, instructional designers and classroom educators into the issues raised in this environment. The study was exploratory in nature, concerning itself with testing and revising both the materials and the setting in which they were used. The intent was to discover interaction between characteristics of students and the environment which warrant future study. For example, the use of LiveMath seemed in some cases to cause cognitive overload. In addition, student epistemological beliefs, prior knowledge of symbolic representations of functions and propensity for self-directed learning interacted with the ability of students to use LiveMath inserts to attain conceptual understanding. While students appear to have learned some concepts more deeply, and others more rapidly than anticipated, they reported that they judged that they were working harder than friends in other sections. Further, being in a student centred learning environment was unsettling for both the students and the instructor.

Using Interactive Software to Teach Foundational Mathematical Skills.

The pilot research presented here explores the classroom use of Emerging Literacy in Mathematics (ELM) software, a research-based bilingual interactive multimedia instructional tool, and its potential to develop emerging numeracy skills. At the time of the study, a central theme of early mathematics curricula, Number Concept, was fully developed. It was broken down into five mathematical concepts including counting, comparing, adding, subtracting and decomposing. Each of these was further subdivided yielding 22 online activities, each building in a level of complexity and abstraction. In total, 234 grade one students from 12 classes participated in the two-group post-test study that lasted about seven weeks and for which students in the experimental group used ELM for about 30 minutes weekly. The results for the final sample of 186 students showed that ELM students scored higher on the standardized math test (Canadian Achievement Test, 2008) and reported less boredom and lower anxiety as measured on the Academic Emotions Questionnaire than their peers in the control group. This short duration pilot study of one ELM theme holds great promise for ELM’s continued development.

Roles that gender, systemizing and teacher support play in STEM education

This study examined the impact of several factors on the decision of 18-19 year old Canadian and Swedish students as to whether or not to enroll in STEM studies at university. Amongst the factors that were examined were: student perceptions of their learning environment in science and mathematics classes; cognitive style (systemizing); learning anxiety; and, intrinsic motivation. A theoretical model of relationships between these factors and the decision to pursue STEM studies was hypothesized. Structural Equation Modeling was used to test the model and its gender invariance. The model was determined to be gender invariant, and suggests that the “gender gap” may in fact in part be a “systemizing gap”. The root causes for any effectiveness of an interdisciplinary approach to STEM education are probably many, but it is likely that overcoming this systemizing gap may be one of them.

A calculator‐based computational approach. Part 4. On differences and graphs

This paper extends the ideas and themes on the computational approach discussed in Parts 1, 2 and 3 (Int. J. Math. Educ. Sci. Technol.,18, 393‐402; 19, 691‐703; 21, 645‐659) to the generalization of differences, the connection to graphs, and to linearly‐rational functions. First, using elements from Calculus, we show how to extend from forward difference to central differences in order to preserve the natural properties of quadratic and higher degree polynomial functions. Second, we use graphs to illustrate the connections between the central difference and quadratic functions. We also illustrate graphically the relationship between a function and the components of its decomposition. Third, we introduce the geometric difference to show how to classify and analyse functions with one singularity using linearly‐rational functions.