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.

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).     

A technology gap interpretation of growth paths in Asia and Latin America

This paper presents a North-South technology gap model which combines the Schumpeterian approach to technical and structural change with the Keynesian perspective on effective demand and the Balance-of-Payments (BOP) constraint as drivers of growth. Three are the contributions of the paper. First, it develops a model in which the technology gap, relative productivity and relative wages co-evolve and may generate different paths of convergence or divergence between South and North depending on the parameters of the model. Second, the parameters of the model are associated with different types of policies, which allows for discussing how these policies may change the growth path. Finally, the model is used to discuss the contrasting experiences of Asia and Latin America since 1970. Convergence in Asia and divergence in Latin America have been extensively debated topics in the literature on comparative economic development, which highlights the crucial role of industrial policy. It is argued that the results of the technology gap model are consistent with the findings of this literature and helps understand the forces behind convergence and divergence.     

Incorrect order of draw could be mitigate the patient safety: a phlebotomy management case report

Procedures involving phlebotomy are critical for obtaining diagnostic blood specimens and represent a well known and recognized problem, probably among the most important issues in laboratory medicine. The aim of this report is to show spurious hyperkalemia and hypocalcemia due to inadequate phlebotomy procedure. The diagnostic blood specimens were collected from a male outpatient 45 years old, with no clinical complaints. The tubes drawing order were as follows: i) clot activator and gel separator (serum vacuum tube), ii) K₃EDTA, iii) a needleless blood gas dedicated-syringe with 80 I.U. lithium heparin, directly connected to the vacuum tube holder system. The laboratory testing results from serum vacuum tube and dedicated syringe were 4.8 and 8.5 mmol/L for potassium, 2.36 and 1.48 mmol/L for total calcium, respectively. Moreover 0.15 mmol/L of free calcium was observed in dedicated syringe. A new blood collection was performed without K₃EDTA tube. Different results were found for potassium (4.7 and 4.5 mmol/L) and total calcium (2.37 and 2.38 mmol/L) from serum vacuum tube and dedicated syringe, respectively. Also free calcium showed different concentration (1.21 mmol/L) in this new sample when compared with the first blood specimen. Based on this case we do not encourage the laboratory managers training the phlebotomists to insert the dedicated syringes in needle-holder system at the end of all vacuum tubes. To avoid double vein puncture the dedicated syringe for free calcium determination should be inserted immediately after serum tubes before EDTA vacuum tubes.     

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.     

Contamination of lithium heparin blood by K2-ethylenediaminetetraacetic acid (EDTA): an experimental evaluation

Introduction:

The contamination of serum or lithium heparin blood with ethylenediaminetetraacetic acid (EDTA) salts may affect accuracy of some critical analytes and jeopardize patient safety. The aim of this study was to evaluate the effect of lithium heparin sample contamination with different amounts of K₂EDTA.

Materials and methods:

Fifteen volunteers were enrolled among the laboratory staff. Two lithium heparin tubes and one K₂EDTA tube were collected from each subject. The lithium-heparin tubes of each subject were pooled and divided in 5 aliquots. The whole blood of K₂EDTA tube was then added in scalar amount to autologous heparinised aliquots, to obtained different degrees of K₂EDTA blood volume contamination (0%; 5%; 13%; 29%; 43%). The following clinical chemistry parameters were then measured in centrifuged aliquots: alanine aminotranspherase (ALT), bilirubin (total), calcium, chloride, creatinine, iron, lactate dehydrogenase (LD), lipase, magnesium, phosphate, potassium, sodium.

Results:

A significant variation starting from 5% K₂EDTA contamination was observed for calcium, chloride, iron, LD, magnesium (all decreased) and potassium (increased). The variation of phosphate and sodium (both increased) was significant after 13% and 29% K₂EDTA contamination, respectively. The values of ALT, bilirubin, creatinine and lipase remained unchanged up to 43% K₂EDTA contamination. When variations were compared with desirable quality specifications, the bias was significant for calcium, chloride, LD, magnesium and potassium (from 5% K₂EDTA contamination), sodium, phosphate and iron (from 29% K₂EDTA contamination).

Conclusions:

The concentration of calcium, magnesium, potassium, chloride and LD appears to be dramatically biased by even modest K₂EDTA contamination (i.e., 5%). The values of iron, phosphate, and sodium are still reliable up to 29% K₂EDTA contamination, whereas ALT, bilirubin, creatinine and lipase appear overall less vulnerable towards K₂EDTA contamination.     

Avoidance to wipe alcohol before venipuncture is not a source of spurious hemolysis

Background

It is still uncertain whether or not avoidance to let disinfectant alcohol dry at the site of venipuncture is a source of spurious hemolysis when drawing venous blood.

Methods:

In a consecutive series of 52 outpatients referred for routine laboratory testing, venous blood was drawn by direct venipuncture with (odd group) or without (pair group) wiping 70% isopropyl alcohol at the site of venipuncture. A 3.5 mL evacuated tube with clot activator and gel separator was drawn from a vein of the upper limb, serum was immediately separated with standard centrifugation and tested for potassium, lactate dehydrogenase (LD), aspartate aminotransferase (AST) and hemolysis index (HI) on Roche Cobas.

Results:

No specimen was discarded for unsatisfactory venipuncture. No differences for age and gender were observed between groups. As regards the four parameters investigated, no significant differences could be observed between patients in whom blood was drawn with or without letting the alcohol dry. It is also noteworthy that no sample in both groups exceeded the conventional sample rejection threshold of cell-free hemoglobin.

Conclusions:

The results of our prospective, randomized study attest that failure to wipe alcohol at the site of venipuncture should not be considered as a potential source of spurious hemolysis when drawing blood.     

Towards a heuristic frame for transferring e-government technology

This article addresses challenges in accomplishing technology transfer process involving the adaptation and implementation of e-government applications from a donor country to a recipient country. Here it is claimed that prior e-government research has overlooked existing technology transfer literature from the field of knowledge management. This work is aimed at addressing the underlying issues associated with the transfer of e-government technology, given different characteristics of donor and recipient organizations in terms of the socio-economic context and the dynamics of the technological infrastructure. Based on a review, interpretation, and synthesis of a broad range of both technology transfer, e-government and knowledge management literature, we extend the Information Technology Transfer Life-Cycle Model, as this well-known model was derived entirely based on empirical evidence. To this end, we propose a heuristic frame for e-government technology transfer. Finally, five propositions accrued from both the literature review and the proposed heuristic frame are set forth to be further tested, in order to better understand the process dynamics of e-government technology transfer between countries.