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This article proposes an in-depth mathematics analysis of simple and compound interest through an exploration of the mathematical structures underlying these concepts. Financial numeracy concepts (simple and compound interest, interest rates, interest period, present and future value, etc.) have been added to the mathematics curriculum of the Canadian province of Quebec in 2016. Yet, little is known with regards to mathematics teachers' knowledge of financial concepts. We mobilized the relational paradigm framework in the context of simple and compound interest to construct an assessment instrument of teacher knowledge. Based on 36 teachers' responses to the questionnaire, we observed that the majority of teachers did not use mathematical structures in problem solving; they were not able to make sense of simple and compound interest in ways that do not involve standard formulas. Such results indicate opportunities for professional development in regard to secondary mathematics teachers' knowledge of mathematics in the context of simple and compound interest situations.

The transition from arithmetic to algebra in middle school can be critical for students having persistent difficulties in mathematics. The leading perception in our project is that holistic relational thinking is an effective problem-solving tool in both arithmetic and algebra. We worked in collaboration with two teachers of special classes to implement elements of this approach with Secondary I students. We implemented several problem-solving-related activities with students. We collected data through individual interviews with students before and after the intervention. Our data shows the positive effects of the intervention in students changing their strategies as well as overall success in solving word problems requiring relational analysis.

Abstract Background The desired (therapeutic) and undesired (side) effects of methylphenidate might have underlying correlations. The aim of this study was to explore the strength and the possible sources of these correlations. Methods One hundred and fifty-seven children with ADHD (6-12 years) were administered placebo and methylphenidate (0.5 mg/kg in a divided b.i.d. dose), each for a one-week period, in a double-blind, crossover trial. Therapeutic response was assessed using the Conners' Global Index for parents (CGI-Parents) and teachers (CGI-Teachers), while side effects were assessed using the Barkley Side Effects Rating Scale (SERS). Results The side effect profile as assessed by the SERS was similar to that of previous studies with insomnia, decreased appetite, and headaches showing significant treatment effects (p < 0.005). These "somatic/physical" side effects did not correlate with CGI-Parents or CGI-Teachers. However, the side effects of "irritability", "proneness to crying", and "anxiousness" showed significant relationships with CGI-Parents. These "mood/anxiety" side effects showed no significant correlations with the CGI-Teachers. Conclusion The greater "mood/anxiety" side effects on methylphenidate and placebo, the less the parents observe improvement of their children while treated with methylphenidate. This suggests that the correlations between "mood/anxiety" side effects and poor response to treatment may be driven by observer effects rather than biological commonalities between therapeutic and side effects of methylphenidate.

Abstract Background Attention-Deficit/Hyperactivity Disorder (ADHD) is a heterogeneous disorder from both clinical and pathogenic viewpoints. Executive function deficits are considered among the most important pathogenic pathways leading to ADHD and may index part of the heterogeneity in this disorder. Methods To investigate the relationship between the dopamine transporter gene (SLC6A3) 3'-UTR VNTR genotypes and executive function in children with ADHD, 196 children diagnosed with ADHD were sequentially recruited, genotyped, and tested using a battery of three neuropsychological tests aimed at assessing the different aspects of executive functioning. Results Taking into account a correction for multiple comparisons, the main finding of this study is a significant genotype effect on performances on the Tower of London (F = 6.902, p = 0.009) and on the Wechsler Intelligence Scale for Children, Third Edition (WISC-III) Freedom From Distractibility Index (F = 7.125, p = 0.008), as well as strong trends on Self Ordered Pointing Task error scores (F = 4,996 p = 0.026) and WISC-III Digit Span performance (F = 6.28, p = 0.023). Children with the 9/10 genotype exhibited, on average, a poorer performance on all four measures compared to children with the 10/10 genotype. No effect of genotype on Wisconsin Card Sorting Test measures of performance was detected. Conclusion Results are compatible with the view that SLC6A3 genotype may modulate components of executive function performance in children with ADHD.

The multiplicative reasoning that students should develop in elementary school is a key area of research in contemporary mathematics education. Researchers employ various views including multiplication as arithmetic operation, multiplicative structures, and multiplicative relationships. They also propose various classifications of multiplicative structures to support students' development of multiplicative reasoning and problem solving. Our work contributes to this conversation by focusing on simple multiplicative relationships. Drawing on Davydov's Theory of Developmental Instruction, we employ the relational view to analyze some multiplicative structures identified by researchers and practitioners. We propose a typology of basic multiplicative relationships as well as their specific graphical representations as a set of mental tools allowing for a holistic flexible understanding of the multiplicative situations, simple and complex, primary school students usually encounter (in grades 1-6). We suggest that the new approach may better support students' multiplicative and relational reasoning and problem solving.

Pupils' difficulties in solving word problems continue to attract attention: while researchers highlight the importance of relational reasoning and modelling, school curricula typically use short word problems to develop pupils' knowledge of arithmetic operations and calculation strategies. The Relational Paradigm attributes the leading role in mathematics learning to the development of relational thinking. Using this perspective, we implemented a new approach to teaching additive word problem-solving in primary school, encouraging relational thinking and modelling. We compared the overall results of additive word problems solved by Grade 2 elementary pupils in the experimental group (N = 216) and in the control group (N = 196). Our data show: (a) on average, the experimental group performed significantly better in problem-solving than the control group; and (b) in the control group, there was a considerable lack of success in solving problems that require relational thinking--there was no such effect in the experimental group.

Mathematical relationships are crucial elements to consider for learning mathematics. However, too often students pay more attention to the calculations to be done rather than the reasons for doing them. Relying on the relational paradigm to support elementary school students, we proposed two specially designed tasks to help students recognize and formalize the relationships in additive and multiplicative word problems. These tasks were also designed to have them learn how to represent the relationships using models and to manipulate the mathematical structure of a problem to find the required arithmetic operation. In this paper, we present the task design principles to create mathematically incoherent situation (MIS) tasks and we highlight their implementation with elementary school students. Our findings suggest that students working on MIS tasks really engage in the analysis of the mathematical relationships, which corresponds to the teacher's intentions in problem-solving activities.

In Canada, as in other Western countries, solving word problems has comprised an important part of mathematics curricula. Traditionally, arithmetic thinking has largely been privileged as the main strategy for solving word problems at the elementary level, thus postponing the introduction of algebraic thinking to the secondary school. Drawing on the work of the Russian psychologist Davydov, we suggest that algebraic ways of thinking can be fostered as early as primary grades within the context of problem solving, thus enabling understanding of relational aspects of a problem's mathematical structure. In particular, we used Elkonin and Davydov's notion of "learning activity" to design a computer-based task that helps young students (ages 7-8) to analyse word problems and eventually engage in an algebraic way of thinking. The task also involves a whole-class discussion in which students probe their understanding of the problem and model its solution in a relational way, instead of instantly locking themselves into a numerical operation. Macro- and micro-levels of analyses were conducted using, inter alia, the lens of the didactical tetrahedron, which highlights the association between design of learning tasks and students' capacity building in analysing and expressing relationships between quantities through non-numerical symbols. While further research on the relational approach is still needed, this paper demonstrates its potential to contribute to progressively shifting young children's understanding from one that relies heavily on arithmetic processes toward one that builds on algebraic thinking.

The main goal of this paper is to show how Vasily Davydov's powerful ideas about the nature of mathematical thinking and learning can transform the teaching and learning of additive word problem solving. The name Vasily Davydov is well known in the field of mathematics education in Russia. However, the transformative value of Davydov's theoretical work in this field has not yet been fully recognised by the larger international community. In this article, I use Davydov's vision of mathematics as the study of quantitative relationships--the vision underlying the relational paradigm in teaching and learning of mathematics. I use the example of one research project to demonstrate how the relational paradigm changes and reforms teaching practices. I discuss the teaching approach, developed within this paradigm, as well as the learning outcomes demonstrating the transformative power of Davydov's ideas.

According to numerous studies (Barrouillet & Camos 2002; Brousseau 1988; Chevallard 1988; Riley et al. 1984; Schubauer-Leoni & Ntamakiliro, "Revue Des Sciences de L'éducation," 20(1): 87-113, 1994; Vergnaud 1982; Xin, "The Journal of Educational Research," 100(6):347-360, 2007), a combination of many factors, including curriculum, didactic contract and task design, can potentially lead to students experiencing difficulties in developing of a full understanding of addition and subtraction and their relationship in problem solving. Few studies (Conne, Recheche En "Didactique Des Mathématiques," 5, 269-332, 1985; DeBlois, "Éducation et Francophonie," 25(1), 102-120, 1997; Giroux & Ste-Marie, "European Journal of Psychology of Education," 16(2), 141-161, 2001) describe the misinterpretations of problems as a factor related to learning difficulties. We have studied how and why elementary school students misinterpret the mathematical structure of a simple additive word problem and what kind of possible (hidden) misinterpretation may occur. We analysed possible mechanisms of misinterpretations in word problem solving, discussing various examples of correct and incorrect solutions resulting from the misinterpretation of a problem. We gave the elementary school students a word problem, which could potentially be misinterpreted, and observed their solving strategies. Our results show how the particular form of mathematical misinterpretation--structure substitution--may help students obtain a correct answer and thereby hinder the development of their mathematical reasoning. We further discuss different ways of addressing this phenomenon in teaching practice.

This essay proposes a reflection on the learning difficulties and teaching approaches associated with arithmetic word problem solving. We question the development of word problem solving skills in the early grades of elementary school. We are trying to revive the discussion because first, the knowledge in question--reversibility of arithmetic operations and flexibility of mathematical thinking--are the key elements in elementary mathematics, and second, because we hope to create a shift in the understanding of this knowledge development in students. Using the folk tale "The Three Little Pigs" as a metaphor, we analyze difficulties students experience while learning to solve word problems involving addition and subtraction. We formulate a hypothesis about cognitive duality of word problem-solving. This hypothesis explains some well-known learning difficulties and suggests teaching principles which would help to avoid developmental obstacles and pitfalls within the teaching/learning process.

Children who are unhealthy are at higher risk for school problems than students who are free from medical problems. Students with poor health have a higher probability of school failure, grade retention, and dropout. The relationship between student health and academic success is complex. Common manageable factors of student health are nutrition, maintaining healthy weight, and physical fitness. Through a comprehensive literature review the relationships among school achievement and nutrition, maintaining healthy weight, and physical fitness are examined. Furthermore, the efficacy of educational programs to improve nutrition, maintain healthy weight, and increase physical fitness is evaluated. The complexity of the relationship among variables is presented and areas for future research and practice for school psychologists are described.

Objective: In a recent study, Thapar and colleagues reported that COMT "gene variant and birth weight predict early-onset antisocial behavior in children" with attention-deficit/hyperactivity disorder. We have attempted to replicate these findings in a group of ADHD children using a similar research design. Method: Children (n = 191) between 6 and 12 years of age who were diagnosed with ADHD were included in the study. Conduct disorder was diagnosed according to DSM-IV criteria based on clinical evaluation and a structured interview (Diagnostic Interview Schedule for Children-IV). The mother's report on the child's birth weight was used in the analysis. Logistic regression analysis, with genotype and birth weight as independent variables and DSM-IV conduct disorder as the dependent variable, was conducted. Results: No significant main effects of genotype and birth weight or interaction effects on conduct disorder were observed. Conclusion: In this sample of children diagnosed with ADHD, we find no association between the COMT Val[superscript 108/158] Met gene variant, birth weight, and conduct disorder. Further investigations are required before using birth weight and COMT genotype as predictors of conduct disorder in children with attention-deficit/hyperactivity disorder, especially given the societal and legal ramifications of conduct disorder. (Contains 1 figure and 2 tables.)

Human cancers over-expressing mdm2, through a T to G variation at a single nucleotide polymorphism at position 309 (mdm2 SNP309), have functionally inactivated p53 that is not effectively degraded. They also have high expression of the alternatively spliced transcript, mdm2-C. Alternatively spliced mdm2 transcripts are expressed in many forms of human cancer and when they are exogenously expressed they transform human cells. However no study to date has detected endogenous MDM2 protein isoforms. Studies with exogenous expression of splice variants have been carried out with mdm2-A and mdm2-B, but the mdm2-C isoform has remained virtually unexplored. We addressed the cellular influence of exogenously expressed MDM2-C, and asked if endogenous MDM2-C protein was present in human cancers. To detect endogenous MDM2-C protein, we created a human MDM2-C antibody to the splice junction epitope of exons four and ten (MDM2 C410) and validated the antibody with in vitro translated full length MDM2 compared to MDM2-C. Interestingly, we discovered that MDM2-C co-migrates with MDM2-FL at approximately 98 kDa. Using the validated C410 antibody, we detected high expression of endogenous MDM2-C in human cancer cell lines and human cancer tissues. In the estrogen receptor positive (ER+) mdm2 G/G SNP309 breast cancer cell line, T47D, we observed an increase in endogenous MDM2-C protein with estrogen treatment. MDM2-C localized to the nucleus and the cytoplasm. We examined the biological activity of MDM2-C by exogenously expressing the protein and observed that MDM2-C did not efficiently target p53 for degradation or reduce p53 transcriptional activity. Exogenous expression of MDM2-C in p53-null human cancer cells increased colony formation, indicating p53-independent tumorigenic properties. Our data indicate a role for MDM2-C that does not require the inhibition of p53 for increasing cancer cell proliferation and survival.

Our group (Patschan S, Chen J, Gealekman O, Krupincza K, Wang M, Shu L, Shayman JA, Goligorsky MS; Am J Physiol Renal Physiol 294: F100-F109, 2008) previously observed an accumulation of gangliosides coincident with development of cell senescence and demonstrated lysosomal permeabilization in human umbilical vein endothelial cells exposed to glycated collagen I (GC). Therefore, we investigated whether the lysosome-dependent, caspase-independent or type 2-programmed cell death (autophagy) is involved in development of premature senescence of endothelial cells. The cleaved microtubule-associated protein 1 light-chain 3 (LC3), a marker of autophagosome formation, was overexpressed within 24 h of GC treatment; however, by 4-5 days, it was nearly undetectable. Early induction of autophagosomes was associated with their fusion with lysosomes, a phenomenon that later became subverted. Autophagic cell death can be triggered by the products of damaged plasma membrane, sphingolipids, and ceramide. We observed a clustering of membrane rafts shortly after exposure to GC; later, after 24 h, we observed an internalization, accompanied by an increased acid sphingomyelinase activity and accumulation of ceramide. Pharmacological inhibition of autophagy prevented development of premature senescence but did lead to the enhanced rate of apoptosis in human umbilical vein endothelial cells exposed to GC. Pharmacological induction of autophagy resulted in reciprocal changes. These observations appear to represent a mechanistic molecular cascade whereby advanced glycation end products like GC induce sphingomyelinase activity, accumulation of ceramide, clustering, and later internalization of lipid rafts. advanced glycation end product; lysosomes; sphingomyelinase activity; lipid rafts

Objective: There is considerable evidence that maternal stress is associated with behavioural disturbances in offspring. The objective of this study was to examine whether there is an association between the [...]