Diagnosing students’ misconceptions in algebra: Results from an experimental pilot study

Computer-based diagnostic assessment systems hold potential to help teachers identify sources of poor performance and to connect teachers and students to learning activities designed to help advance students’ conceptual understandings. The present article presents findings from a study that examined how students’ performance in algebra and their overcoming of common algebraic misconceptions were affected by the use of a diagnostic assessment system that focused on important algebra concepts. This study used a four-group randomized cluster trial design in which teachers were assigned randomly to one of four groups: a “business as usual” control group, a partial intervention group that was provided with access to diagnostic tests results, a partial intervention group that was provided with access to the learning activities, and a full intervention group that was given access to the test results and learning activities. Data were collected from 905 students (6th–12th grade) nested within 44 teachers. We used hierarchical linear modeling techniques to compare the effects of full, partial, and no (control) intervention on students’ algebraic ability and misconceptions. The analyses indicate that full intervention had a net positive effect on ability and misconception measures.     

Analysis of the Talmudic Argumentum A Fortiori Inference Rule (Kal Vachomer) using Matrix Abduction

We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix \({\mathbb {A}}\) with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a _i,j =?. The method allows us to decide whether to declare a _i,j = 0 or a _i,j = 1 or a _i,j =? undecided. This algorithmic method is then applied to modelling several legal and practical reasoning situations including the Talmudic rule of Kal-Vachomer. We add an Appendix showing that this new rule of Matrix Abduction, arising from the Talmud, can also be applied to the analysis of paradoxes in voting and judgement aggregation. In fact we have here a general method for executing non-deductive inferences.     

Emotive concept nouns and motor responses: Attraction or repulsion?

We carried out three experiments aimed at testing whether hand posture affects the compatibility effect that Chen and Bargh (1999) found between a word’s emotional connotation and arm movement direction. In the present study, participants responded by pressing two buttons: one placed near their body, the other far away. In Experiment 1, in which they pressed the response button with their hand open, RTs were shorter when participants pressed the far button for positive words and the near button for negative words, as if they simulated reaching for something good and avoiding something bad. However, in Experiments 2 and 3, in which participants pressed the response button with a tennis ball in their hand, RTs were shorter when participants pressed the near button for positive words and the far button for negative words, as if they simulated drawing a good thing closer and pushing a bad thing away. Results are discussed within the framework of theories on concept grounding in emotion and action systems.     

Bad company generalized

The paper is concerned with the bad company problem as an instance of a more general difficulty in the philosophy of mathematics. The paper focuses on the prospects of stability as a necessary condition on acceptability. However, the conclusion of the paper is largely negative. As a solution to the bad company problem, stability would undermine the prospects of a neo-Fregean foundation for set theory, and, as a solution to the more general difficulty, it would impose an unreasonable constraint on mathematical practice.     

HSP-type Characterization of Strong Equational Classes of Partial Algebras

This paper presents the first purely algebraic characterization of classes of partial algebras definable by a set of strong equations. This result was posible due to new tools such as invariant congruences, i.e. a generalization of the notion of a fully invariant congruence, and extension of algebras, specific for strong equations.     

Inhibition,Reinforcement Sensitivity and Temporal Information Processing in ADHD and ADHD+ODD: Evidence of a Separate Entity?

This study compared children with ADHD-only, ADHD+ODD and normal controls (age 8–12) on three key neurocognitive functions: response inhibition, reinforcement sensitivity, and temporal information processing. The goal was twofold: (a) to investigate neurocognitive impairments in children with ADHD-only and children with ADHD+ODD, and (b) to test whether ADHD+ODD is a more severe from of ADHD in terms of neurocognitive performance. In Experiment 1, inhibition abilities were measured using the Stop Task. In Experiment 2, reinforcement sensitivity and temporal information processing abilities were measured using a Timing Task with both a reward and penalty condition. Compared to controls, children with ADHD-only demonstrated impaired inhibitory control, showed more time underestimations, and showed performance deterioration in the face of reward and penalty. Children with ADHD+ODD performed in-between children with ADHD-only and controls in terms of inhibitory controls and the tendency to underestimate time, but were more impaired than controls and children with ADHD-only in terms of timing variability. In the face of reward and penalty children with ADHD+ODD improved their performance compared to a neutral condition, in contrast to children with ADHD-only. In the face of reward, the performance improvement in the ADHD+ODD group was disproportionally larger than that of controls. Taken together the findings suggest that, in terms of neurocognitive functioning, comorbid ADHD+ODD is a substantial different entity than ADHD-only.     

ChoiceKey: A real-time speech recognition program for psychology experiments with a small response set

Psychological experiments often collect choice responses using buttonpresses. However, spoken responses are useful in many cases—for example, when working with special clinical populations, or when a paradigm demands vocalization, or when accurate response time measurements are desired. In these cases, spoken responses are typically collected using a voice key, which usually involves manual coding by experimenters in a tedious and error-prone manner. We describe ChoiceKey, an open-source speech recognition package for MATLAB. It can be optimized by training for small response sets and different speakers. We show ChoiceKey to be reliable with minimal training for most participants in experiments with two different responses. Problems presented by individual differences, and occasional atypical responses, are examined, and extensions to larger response sets are explored. The ChoiceKey source files and instructions may be downloaded as supplemental materials for this article from brm.psychonomic-journals.org/content/supplemental.