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.

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.     

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).     

Cultural consultation: Implications for hispanic mental health services in the United States

The need to maximize the influence of the limited number of Hispanic mental health professionals in the United States requires the development of new roles. One possible role is that of cultural consultant to non-Hispanic providers. Cultural consultation can serve to help mental health providers differentiate between cultural differences and cognitive, affective and social deficits. This article will operationalize the concept and goats of cultural consultation, issues related to non- Hispanic staff providing services to Hispanics will be outlined, and a series of recommendations will be presented to assist individuals and organizations in developing cultural consultation programs.     

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.     

Applying the technology acceptance model to a Spanish City Hall

This paper examines the relative importance and significance of the four technology enablers introduced by Davis (1989) in the technology acceptance model (TAM) (perceived ease of use, perceived usefulness, attitude towards using and behavioural intention) for use on four different levels of citizen engagement in e-government (null, publish, interact and transact). An extended technology acceptance model (TAM) is developed to test citizen engagement towards online e-government services from a sample of 307 citizens who used the benefits advisor tool within a Spanish City Hall. Although the proposed model follows TAM and explains the intention towards the actual use of e-government by postulating four direct determinants, “A, PU, PEOU and BI” have been considered as parallel processes, meaning that each can have separate influence in different levels of citizen engagement. To achieve this goal, a multinomial logistic regression is developed and tested to confirm the explanatory power of the four technology enablers on the four different levels of e-government. Our findings further suggest that in order to implement e-government, some of the enablers matter more than others to move from one level of citizen engagement to another. The main contribution of the paper is to question the use of existing models which seek to represent the relationship between technology enablers and the adoption of e-government services without considering their impacts on citizens’ engagement. The implications of the findings are discussed and useful insights are provided in relation to policy recommendations geared to create appropriate conditions to build citizens’ engagement intent of use of e-government services.     

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.