Can teachers and mathematicians communicate productively? The case of division with remainder

Is it possible that a meeting of mathematicians and primary school teachers will be productive? This question became intriguing when one professor of mathematics initiated a professional development course for practicing primary school teachers, which he taught alongside a group of mathematics Ph.D. students. This report scrutinizes the uncommon meeting of these two communities, who have very different perspectives on mathematics and its teaching. The instructors had no experience in primary school teaching, and their professed goal was to deepen the teachers’ understanding of the mathematics they teach, while teachers were expecting the course to be pedagogically relevant for their teaching. Surprisingly, despite this mismatch in expectations, the course was considered a success by teachers and instructors alike. In our study, we analyzed a lesson on division with remainder for teachers of grades 3–6, taught by the professor. The framework used for the data analysis was mathematical discourse for teaching, a discursive adaptation of the well-known mathematical knowledge for teaching framework. Our analysis focuses on the nature of the interactions between the parties and the learning opportunities they afforded. We show how different concerns, which might have hindered communication, in fact fueled discussions, leading to understandings of the topic and its teaching that were new to all the parties involved. The findings point to a feasible model for professional development where mathematicians may contribute to the education of practicing teachers, while they are gaining new insights themselves.     

Children's Responses to Contrasting `Realistic' Mathematics Problems: Just how realistic are children ready to be?

In recent years there has been an increasing emphasis within the world of mathematics education on realistic problem solving. At the same time research has shown that children typically remain apparently unwilling or unable to introduce realistic considerations when solving supposedly realistic word problems, though research has also shown that children's behaviour in this domain does vary as a function of the nature of the item, its context and the child's social background. This paper analyses 11–12 year-old English children's responses to two realistic problems. The first is taken from English national tests; the second is a revised version of this item which has been rewritten to encourage a more realistic pattern of responses. Through a comparison of responses to the two items it is suggested that, given suitable realistic problems, many children may be more willing and able to introduce realistic responses in a testing context than earlier research might lead us to expect.This revised version was published online in September 2005 with corrections to the Cover Date.     

Foraging on the radial-arm maze: Effects of altering the reward at a target location

Thirsty rats were trained to collect small water rewards from the end of each arm of an eight-arm radial maze. During these training trials and subsequent testing trials, the subjects were allowed to choose a maximum of eight arms. “Preference” for a target maze location was studied by noting when, in the sequence of eight choices, the target was selected. During testing, when one maze location was consistently devoid of water, rats decreased their preference for this arm over trials (Experiment 1). Similarly, rats that learned a saccharin-lithium association demonstrated lower preferences for a maze location that consistently held the conditioned saccharin solution. This was true for animals that received saccharin-lithium conditioning on the maze (Experiment 3A) and for animals conditioned to saccharin in a separate context (Experiment 3B). An increase in preference for a target maze location consistently containing a sweet chocolate milk solution was observed in animals that were water- and food-deprived (Experiment 2). These studies demonstrate that animals will modify their responses toward (preferences for) maze locations that predictably contain an altered reward.     

The Maintenance of Order and Use of Space in Primary School Buildings

An empirically grounded discussion of relationships which can exist between the maintenance of order in teaching situations and the use of space in primary school buildings is offered in this paper. Attention is specifically focused on verbal directives issued by teachers to their charges about what they deem acceptable behaviour in teaching areas during lesson periods. Examples of these directives are presented in order to illustrate both how teachers may manipulate children's use of space to impose on them particular definitions of educational order and also how they may use space as a means of disciplining those who transgress against that order.     

Teacher–Child Interactions in Early Head Start Classrooms: Associations With Teacher Characteristics

ABSTRACT

Research Findings: The current study examined characteristics of 71 Early Head Start lead teachers in relation to classroom interactions with infants and toddlers. Measured teacher characteristics included education, years of experience, beliefs about child rearing, depressive symptoms, and the temperamental characteristics of positivity and frustration. Teacher–child interactions were measured using the Classroom Assessment Scoring System, Toddler Version (La Paro, Hamre, & Pianta, 2012). Results indicated that field of degree was directly associated with the majority of dimensions of teacher–child interactions. Examination of teachers’ years of experience and intrapersonal characteristics revealed a number of significant interactions, indicating that teacher experience and appropriate beliefs may serve as protective factors in the presence of psychosocial risk factors. Practice or Policy: Overall, our findings suggest that both early childhood education degrees and years of experience are directly or indirectly associated with multiple dimensions of teacher–child interactions, confirming that these patterns established for preschool teachers hold for teachers of infants and toddlers. These results also suggest that years of experience and progressive beliefs about children may be especially important for teachers who are depressed or who have low levels of positivity and high levels of frustration. Implications for future research, as well as preservice and in-service professional development, are discussed.     

Perceptions of sleep duration,patterns and emotional and behavioural difficulties: a study of Greek adolescents

The study investigated adolescent students’ perceptions of sleep duration and patterns, and the way they relate to emotional and behavioural difficulties. Five hundred and two students from public schools in Greece completed the Sleep Questionnaire and the Strengths and Difficulties Questionnaire (SDQ). It was demonstrated that consistency in sleep duration and quality in sleep patterns were associated with a reduction in adolescents’ reports of emotional and behavioural difficulties. Sleep duration was similarly distributed across gender, while sleep patterns were gender‐specific. Distinct differential effects of gender, sleep duration and patterns to adolescents’ emotional and behavioural difficulties were also found. These findings and their implications for research and practice are discussed, within the scope of the biopsychosocial framework in education.     

Predictors of Criminal Justice Undergraduates’ Intentions to Pursue Graduate Education in Criminology or Criminal Justice

This study relies on data from 388 junior and senior criminal justice majors to examine predictors of intentions to pursue graduate education in criminology, criminal justice, or a closely related field. Logistic regression results demonstrate that women, students who receive greater encouragement to attend graduate school, students with a lower aversion to reading, writing, and statistics, and students who perceive greater diversity intolerance are more likely to report graduate school intentions. Although students’ race was not found to be significant in the overall model, split-sample models revealed that the significance of predictors varied by race and ethnicity. In discussing the findings, special attention is given to the need for primarily White institutions (PWIs) to partner with historically Black college and universities (HBCUs). We conclude by calling for departments to redouble their efforts to diversify their faculty and student bodies.     

Toward a constructivist perspective: The impact of a mathematics teacher inservice program on students

A constructivist-oriented inservice program provided teachers of mathematics (K-12) with intensive two-week summer institutes and weekly classroom follow-up. Pre- and post-program data on student outcomes indicate that, along with transformations in the nature and quality of mathematics activity in the classroom, students' beliefs about learning mathematics changed and elementary students' attitudes toward mathematics improved. Although the instruction they now received focused more on conceptual understanding and less on computational skill, students' scores on standardized tests assessing routine knowledge were maintained.An earlier version of this paper appeared in R. Underhill (ed.),Proceedings of the Thirteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education 1, 43–49, Backsburg, VI.     

Educating students with FASD: linking policy,research and practice

Fetal alcohol spectrum disorder (FASD ) is a prevalent neurodevelopmental disability with significant implications for learning and behaviour. International research suggests that the prevalence of FASD in school‐aged children is 2.3–6.3%. In this paper, we address the questions: (1) what is FASD ; (2) what is the prevalence of FASD in schools; (3) what is the impact of FASD ; and (4) why develop special FASD education strategies and programmes? We summarise the 18‐year history of W innipeg S chool D ivision's development of its FASD P rogramme of services, describe the specialised FASD classrooms and then present the results from a consensus‐generating workshop comprised of 36 FASD education professionals, with over 209 years of collective FASD education programme experience, who were asked to identify and reach consensus on best strategies and lessons learned in FASD education programmes. We then suggest that effectively educating children with FASD is critical to get right if positive educational outcomes are to be realised.