Preservice teachers’ knowledge of proof by mathematical induction

There is a growing effort to make proof central to all students’ mathematical experiences across all grades. Success in this goal depends highly on teachers’ knowledge of proof, but limited research has examined this knowledge. This paper contributes to this domain of research by investigating preservice elementary and secondary school mathematics teachers’ knowledge of proof by mathematical induction. This research can inform the knowledge about preservice teachers that mathematics teacher educators need in order to effectively teach proof to preservice teachers. Our analysis is based on written responses of 95 participants to specially developed tasks and on semi-structured interviews with 11 of them. The findings show that preservice teachers from both groups have difficulties that center around: (1) the essence of the base step of the induction method; (2) the meaning associated with the inductive step in proving the implication P(k) ⇒ P(k + 1) for an arbitrary k in the domain of discourse of P(n); and (3) the possibility of the truth set of a sentence in a statement proved by mathematical induction to include values outside its domain of discourse. The difficulties about the base and inductive steps are more salient among preservice elementary than secondary school teachers, but the difficulties about whether proofs by induction should be as encompassing as they could be are equally important for both groups. Implications for mathematics teacher education and future research are discussed in light of these findings.

Assessing working memory capacity in a non-native language

The present studies directly test the usefulness of two English-language working memory capacity (WMC) assessments with two samples of students whose native language was not English. Participants completed two widely used complex span tasks, Reading Span (RSpan) and Operation Span (OSpan), in English. To determine whether the well-established relationship between WMC and Raven's Advanced Progressive Matrices (RAPM) would be observed when span tasks were not given in the native language of the participant, span scores were regressed against performance on the RAPM. Results indicated that while OSpan was a reliable and valid predictor of RAPM in non-native-English speakers, RSpan administered in English was not.     

Sex differences in science learning: Closing the gap through animations

Males traditionally outperform females on measures of both visuospatial ability and science achievement. This experiment directly tests a manipulation designed to compensate for such differences through the presentation of relevant illustrations or animations to support the construction of understanding of a specific scientific phenomenon. Males and females read a scientific text about plate tectonics that contained static illustrations, animated versions of the static illustrations, or no illustrations. Participants were assessed on their visuospatial ability and also working memory capacity. Results indicated that while males outperformed females on both the visuospatial measure and overall science learning, the presence of animations effectively eliminated performance differences for this science topic. These results suggest that sex differences in learning outcomes can be overcome by supporting the visualization of scientific phenomena.     

Mathematics for teaching: A form of applied mathematics

In this article we elaborate a conceptualisation of mathematics for teaching as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics) and we examine implications of this conceptualisation for the mathematical preparation of teachers. Specifically, we focus on issues of design and implementation of a special kind of mathematics tasks whose use in mathematics teacher education can support the development of knowledge of mathematics for teaching. Also, we discuss broader implications of the article for mathematics teacher education, including implications for mathematics teacher educators' knowledge for promoting mathematics for teaching.     

Implementing an institution-wide electronic lab notebook initiative

Background:To strengthen institutional research data management practices, the Indiana University School of Medicine (IUSM) licensed an electronic lab notebook (ELN) to improve the organization, security, and shareability of information and data generated by the school''s researchers. The Ruth Lilly Medical Library led implementation on behalf of the IUSM''s Office of Research Affairs.Case Presentation:This article describes the pilot and full-scale implementation of an ELN at IUSM. The initial pilot of the ELN in late 2018 involved fifteen research labs with access expanded in 2019 to all academic medical school constituents. The Ruth Lilly Medical Library supports researchers using the electronic lab notebook by (1) delivering trainings that cover strategies for adopting an ELN and a hands-on demo of the licensed ELN, (2) providing one-on-one consults with research labs or groups as needed, and (3) developing best practice guidance and template notebooks to assist in adoption of the ELN. The library also communicates availability of the ELN to faculty, students, and staff through presentations delivered at department meetings and write-ups in the institution''s newsletter as appropriate.Conclusion:As of August 2021, there are 829 users at IUSM. Ongoing challenges include determining what support to offer beyond the existing training, sustaining adoption of the ELN within research labs, and defining “successful” adoption at the institution level. By leading the development of this service, the library is more strongly integrated and visible in the research activities of the institution, particularly as related to information and data management.     

Practicing a maximal performance task: a cooperative strategy for muscle activity

The effect of practice on predicting elbow flexion movement time was studied. Participants (N = 18) performed 400 elbow flexion trials to a target in the horizontal plane. The trials were distributed equally over four sessions. The goal was to decrease the movement time (MT) for the same degree of accuracy. The electromyographic (EMG) activity of the biceps and triceps brachii was monitored with standard Beckman Ag/AgCl surface electrodes. The EMG measures formed two variable sets within one prediction equation. One variable set was composed of the onset of muscle activity relative to the start of movement (motor time) and the duration of muscle activity. The other variable set consisted of the mean amplitude value of the entire burst and of the first 30 ms (Q30) of activity. As the maximal speed of limb movement increased, the duration of muscle activity (motor time and EMG duration) decreased, and the magnitude of muscle activity (MAV and Q30) increased. Most of the change in the duration of muscle activity occurred in Session 1, while the magnitude of muscle activity continued to increase until Session 3. Multiple regression analysis revealed a cooperative strategy between the magnitude and duration of muscle activity. Early in learning, participants adjusted the magnitude of muscle activity to increase limb movement speed. As practice continued, alterations in the duration of muscle activity became more important, while the magnitude changes were less involved. Late in learning, both dimensions of muscle activity were used to decrease MT. We suggest that the interplay between the magnitude and duration of muscle activity may be due to: (a) cognitive factors related to the division of attention in a motor skill, (b) an increase in the frequency of motor unit firing that affects both dimensions of muscle activity, or (c) some combination of (a) and (b).