Which notion of implication is the right one? From logical considerations to a didactic perspective

Implication is at the very heart of mathematical reasoning. As many authors have shown, pupils and students experience serious difficulties in using it in a suitable manner. In this paper, we support the thesis that these difficulties are closely related with the complexity of this notion. In order to study this complexity,we refer to Tarski's semantic truth theory,which contributes to clarifying the different aspects of implication: propositional connective, logically valid conditional, generalized conditional,inference rules. We will show that for this purpose, it is necessary to extend the classical definition of implication as a relation between propositions to a relation between open sentences with at least one free variable. This permits to become aware of the fact that, in some cases, the truth-value of a given mathematical statement is not constrained by the situation, contrary to the common standpoint that, in mathematics, a statement is either true or false. In the present paper, the didactic relevance of this theoretical stance will be illustrated by an analysis of two problematic situations and the presentation of some experimental results from our research on first-year university students' understanding of implication. This revised version was published online in August 2006 with corrections to the Cover Date.     

Making the Case for Early Identification and Intervention for Young Children at Risk for Learning Disabilities

The early identification of children with learning disabilities (LD) is difficult but can be accomplished. Observation of key behaviors which are indicators of LD by preschool and kindergarten teachers can assist in this process. This early identification facilitates the use of intervention strategies to provide a positive early experience for children at risk for academic difficulties.     

Using Family Backpacks as a Tool to Involve Families in Teaching Young Children About Healthy Eating

Children’s obesity rates have increased substantially over the past several decades, due in part to unhealthy eating habits. About 75% of preschool-aged children consume fewer fruits and vegetables than recommended for health. Because children begin developing eating habits during early childhood, obesity prevention programs are increasingly targeting young children in early childhood education (ECE) settings and are involving their families in teaching about healthy eating. The purpose of this pilot study is to assess the effectiveness of a family involvement activity known as the family backpack in increasing fruit and vegetable consumption among 4- and 5-year-old children and their parents through hands-on activities that encourage them to explore and discuss fruits and vegetables at home. Forty-two families (22 experimental, 20 control) participated in the study. Families received a family backpack from their child’s ECE teacher and completed activities with their child at home during a specific week. Experimental-group backpacks contained a children’s book and three activities to encourage parent–child discussion about fruits and vegetables; control-group backpacks contained an unrelated book and activities. Children’s and parents’ fruit and vegetable consumption and frequency of serving fruits and vegetables at home were assessed using parent self-report surveys before and after completing backpack activities. Parents in the experimental group, but not the control group, reported increases in their own and their children’s fruit and vegetable consumption after completing family backpack activities. Family backpacks show promise as a tool for early childhood educators to help families reinforce and expand children’s learning and encourage healthy eating habits at home.     

Children’s Extracurricular Activities

Why do children learn in different ways: some are good students who show interest and zeal, while others are lazy and have to be taught against their will? Why do schools have over- and underachievers? Of course, there are a multitude of reasons. But almost 50 years ago it was shown using large data sets that families with high socioeconomic status are more likely to have children who are good students. Of course, there are many examples of successful students from poor families. However, they tend to be the exception to the rule. The certainty of success in school increases with rising socioeconomic status.     

Parental reactions to children's negative emotions: longitudinal relations to quality of children's social functioning

Relations between self-reported parental reactions to children's negative emotions (PNRs) and children's socially appropriate/problem behavior and negative emotionality were examined longitudinally. Evidence was consistent with the conclusion that relations between children's externalizing (but not internalizing) emotion and parental punitive reactions to children's negative emotions are bidirectional. Reports of PNRs generally were correlated with low quality of social functioning. In structural models, mother-reported problem behavior at ages 10-12 was at least marginally predicted from mother-reported problem behavior, children's regulation, and parental punitive or distress reactions. Moreover, parental distress and punitive reactions at ages 6-8 predicted reports of children's regulation at ages 8-10, and regulation predicted parental punitive reactions at ages 10-12. Father reports of problem behavior at ages 10-12 were predicted by earlier problem behavior and parental distress or punitive reactions; some of the relations between regulation and parental reactions were similar to those in the models for mother-reported problem behavior. Parental perceptions of their reactions were substantially correlated over 6 years. Some nonsupportive reactions declined in the early to mid-school years, but all increased into late childhood/early adolescence.     

Teaching Against the Grain as an Act of Love: Disrupting White Eurocentric Masculinist Frameworks Within Teacher Education

What is radical love in teaching? How can radical love incite change and transformation within teacher education? What does radical love entail to prepare critically minded teachers for urban schools? In this conceptual paper, we respond to these questions through our individual and collective experiences as social justice oriented teacher educators preparing students to teach in urban schools. We engage with our womanist ways of knowing (Walker in In search of our mothers’ gardens: womanist prose, Houghton Mifflin Harcourt, Boston, 2004) and “theory in flesh” (Moraga and Anzaldúa in This bridge called my back: writings by radical women of color, 2nd edn, Kitchen Table/Women of Color Press, New York, 1983) to collaboratively reflect and analyze our conversations, reflective journaling, meetings, and other telling moments about what it means to practice radical love in teaching. More specifically, we identify three central concepts of what love as an act of resistance or teaching against the grain entails: (1) vulnerability, (2) collective support and healing, and (3) critique. Through these concepts we offer a framework from which to practice radical love in teaching and work in solidarity with others to transform oppressive systems in urban (teacher) education.     

Interaction of LDL and platelets in ischaemic and ischaemic risk subjects

Platelets play a vital role in the progression of atherosclerosis and thrombosis, a major cause of death worldwide. Platelets are activated by many triggers like elevated LDL in blood resulting in aggregation and formation of plaque. The purpose of this study was to investigate the effect of LDL and signal transduction inhibitor on the activation of platelets in Ischaemic risk subjects. Platelets from IHD and hyperlipidemic subjects were hypersensitive to ADP, as higher levels of platelet aggregation were observed in these groups. LDL from IHD hyperlipidemic subjects was more effective in activating platelets from any other group. Ox-LDL was more effective in activating platelets than native-LDL as monitored by level of platelet aggregation induced by PAF and thrombin. Calcium channel blocker, nifedipine and verapamil inhibited platelet aggregation at micromolar level. Protein kinase inhibitor, staurosporine was effective in inhibiting ADP induced aggregation at nanomolar level.     

Clinico-Biochemical indexing of calcium urolithiasis on the basis of urinary citrate to calcium ratio and inhibition of mineralisation of urinary stone forming minerals by human urine

Urinary citric acid and calcium levels have been estimated in the urine of 20 normal healthy persons as well as 12 urinary stone patients. Inhibition efficiency of these urine samples towards the mineralisation of urinary stone forming minerals, viz., calcium phosphate, oxalate or carbonate, has been studied in an experimental model. Statistical correlation of the above data has been made by computing the coefficient of determination and unexplained variance. Clinico-biochemical indexing of calcium urolithiasis risk factor has been attempted in the light of the data.