K-8 Pre-service Teachers’ Algebraic Thinking: Exploring the Habit of Mind Building Rules to Represent Functions

In this study, through the lens of the algebraic habit of mind Building Rules to Represent Functions, we examined 18 pre-service middle school teachers\u27 ability to use algebraic thinking to solve problems. The data revealed that pre-service teachers\u27 ability to use different features of the habit of mind Building Rules to Represent Functions varied across the features. Significant correlations existed between 8 pairs of the features. The ability to justify a rule was the weakest of the seven features and it was correlated with the ability to chunk information. Implications for mathematics teacher education are discussed

Exploring the Relationship between K-8 Prospective Teachers’ Algebraic Thinking Proficiency and the Questions They Pose during Diagnostic Algebraic Thinking Interviews

In this study, we explored the relationship between prospective teachers’ algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers’ algebraic thinking proficiency across 125 algebra-based tasks and we analyzed the characteristics of questions they posed during the interviews. We found that prospective teachers with lower algebraic thinking proficiency did not ask any probing questions. Instead, they either posed questions that simply accepted and affirmed student responses or posed questions that guided the students toward an answer without probing student thinking. In contrast, prospective teachers with higher algebraic thinking proficiency were able to pose probing questions to investigate student thinking or help students clarify their thinking. However, less than half of their questions were of this probing type. These results suggest that prospective teachers’ algebraic thinking proficiency is related to the types of questions they ask to explore the algebraic thinking of students. Implications for mathematics teacher education are discussed

Exploring Prospective 1-8 Teachers\u27 Number and Operation Sense in the Context of Fractions

This exploratory study examined prospective elementary teachers’ (PSTs’) number and operation sense (NOS) in the context of solving problems with fractions. Drawing on the existing literature, we identified seven skills that characterize fraction-related NOS. We analyzed 230 responses to 23 tasks completed by 10 PSTs for evidence of PSTs’ use of different fraction-related NOS skills. The analysis revealed that PSTs did not use all seven fractionrelated NOS skills to the same extent. PSTs’ responses documented their frequent reasoning about the meaning of symbols and formal mathematical language in the context of fractions. To a lesser extent, PSTs’ responses documented their reasoning about different representations of fractions and operations, about the composition of numbers, and about the effects of operations on pairs of fractions. We also examined possible relationships among the seven fraction-related NOS skills identified across the analyzed responses. The results reveal that some of the fraction-related NOS skills appear to support one another. Given that NOS skills provide a foundation for effective mental computation strategies, our study shows the need for explicit attention in teacher preparation programs to supporting PSTs in developing a strong awareness of and facility with a range of fraction-related NOS skills. Our study also raises questions about the relationship between PSTs’ conceptual understanding of fractions and their fraction-related NOS skills and provides suggestions for future research that explores further connections among the fraction-related NOS skills

Subtalar versus triple arthrodesis after intra-articular calcaneal fractures

Depending upon initial treatment, between 2 and 30% of patients with a displaced intra-articular calcaneal fracture require a secondary arthrodesis. The aim of this study was to investigate the effect of subtalar versus triple arthrodesis on functional outcome. A total of 33 patients with 37 secondary arthrodeses (17 subtalar and 20 triple) with a median follow-up of 116 months were asked to complete questionnaires regarding disease-specific functional outcome (Maryland Foot Score, MFS), quality of life (SF-36) and overall satisfaction with the treatment (Visual Analogue Scale, VAS). Patient groups were comparable considering median age at fracture, initial treatment (conservative or operative), time to arthrodesis, median follow-up, and post-arthrodesis radiographic angles. The MFS score was similar after subtalar versus triple arthrodesis (59 vs. 56 points; P = 0.79). No statistically significant difference was found for the SF-36 (84 vs. 83 points; P = 0.67) and the VAS (5 vs. 6; P = 0.21). Smoking was statistically significantly associated with a non-union (χ2 = 6.60, P = 0.017). The current study suggests that there is no significant difference in functional outcome between an in situ subtalar or triple arthrodesis as a salvage technique for symptomatic arthrosis after an intra-articular calcaneal fracture. Smoking is a risk factor for non-union

Serum magnesium, hepatocyte nuclear factor 1β genotype and post-transplant diabetes mellitus: a prospective study

BACKGROUND: Retrospective studies suggest that tacrolimus-induced hypomagnesaemia is a risk factor for post-transplant diabetes mellitus (PTDM), but prospective studies are lacking. METHODS: This was a prospective study with measurements of serum magnesium and tacrolimus at pre-specified time points in the first year after living donor kidney transplantation (KT). The role of single nucleotide polymorphisms (SNPs) in hepatocyte nuclear factor 1β (HNF1β) was also explored because HNF1β regulates insulin secretion and renal magnesium handling. Repeated measurement and regression analyses were used to analyse associations with PTDM. RESULTS: In our cohort, 29 out of 167 kidney transplant recipients developed PTDM after 1 year (17%). Higher tacrolimus concentrations were significantly associated with lower serum magnesium and increased risk of hypomagnesaemia. Patients who developed PTDM had a significantly lower serum magnesium trajectory than patients who did not develop PTDM. In multivariate analysis, lower serum magnesium, age and body mass index were independent risk factors for PTDM. In recipients, the HNF1β SNP rs752010 G > A significantly increased the risk of PTDM [odds ratio (OR) = 2.56, 95% confidence interval (CI) 1.05-6.23] but not of hypomagnesaemia. This association lost significance after correction for age and sex (OR = 2.24, 95% CI 0.90-5.57). No association between HNF1β SNPs and PTDM was found in corresponding donors. CONCLUSIONS: A lower serum magnesium in the first year after KT is an independent risk factor for PTDM. The HNF1β SNP rs752010 G > A may add to this risk through an effect on insulin secretion rather than hypomagnesaemia, but its role requires further confirmation

Pedobarographic analysis and quality of life after lisfranc fracture dislocation

Background: Few studies on tarsometatarsal fracture dislocations report on plantar pressure analysis and quality of life. The primary aim of this study was to determine the added value of plantar pressure analysis. The secondary aim was to determine quality of life and functional outcome. Materials and Methods: With a median followup of 76 months, 26 patients with an isolated Lisfranc injury participated. The Short Form 36 (SF-36) was used to determine the health related

Objectives, design and main findings until 2020 from the Rotterdam Study

The Rotterdam Study is an ongoing prospective cohort study that started in 1990 in the city of Rotterdam, The Netherlands. The study aims to unravel etiology, preclinical course, natural history and potential targets for intervention for chronic diseases in mid-life and late-life. The study focuses on cardiovascular, endocrine, hepatic, neurological, ophthalmic, psychiatric, dermatological, otolaryngological, locomotor, and respiratory diseases. As of 2008, 14,926 subjects aged 45 years or over comprise the Rotterdam Study cohort. Since 2016, the cohort is being expanded by persons aged 40 years and over. The findings of the Rotterdam Study have been presented in over 1700 research articles and reports. This article provides an update on the rationale and design of the study. It also presents a summary of the major findings from the preceding 3 years and outlines developments for the coming period

Governing methods:policy innovation labs, design and data science in the digital governance of education

Policy innovation labs are emerging knowledge actors and technical experts in the governing of education. The article offers a historical and conceptual account of the organisational form of the policy innovation lab. Policy innovation labs are characterised by specific methods and techniques of design, data science, and digitisation in public services such as education. The second half of the article details how labs promote the use of digital data analysis, evidence-based evaluation and ‘design-for-policy’ techniques as methods for the governing of education. In particular, they promote the ‘computational thinking’ associated with computer programming as a capacity required by a ‘reluctant state’ that is increasingly concerned to delegate its responsibilities to digitally enabled citizens with the ‘designerly’ capacities and technical expertise to ‘code’ solutions to public and social problems. Policy innovation labs are experimental laboratories trialling new methods within education for administering and governing the future of the state itself