Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Data modeling in elementary and middle school classes : a shared experience

This paper argues for a renewed focus on statistical reasoning in the elementary school years, with opportunities for children to engage in data modeling. Data modeling involves investigations of meaningful phenomena, deciding what is worthy of attention, and then progressing to organizing, structuring, visualizing, and representing data. Reported here are some findings from a two-part activity (Baxter Brown’s Picnic and Planning a Picnic) implemented at the end of the second year of a current three-year longitudinal study (grade levels 1-3). Planning a Picnic was also implemented in a grade 7 class to provide an opportunity for the different age groups to share their products. Addressed here are the grade 2 children’s predictions for missing data in Baxter Brown’s Picnic, the questions posed and representations created by both grade levels in Planning a Picnic, and the metarepresentational competence displayed in the grade levels’ sharing of their products for Planning a Picnic.

A Randomized Controlled Trial Evaluation of an After-School Pro-Social Behavior Program in an Area of Socioeconomic Disadvantage

A randomized controlled trial was used to evaluate the effects of a pro-social behavior after-school program called Mate-Tricks for nine and ten year old children and their parents living in an area of significant socioeconomic disadvantage. The children were randomly assigned to an intervention (n=220) or a control group (n=198). Children were compared on measures of pro-social behavior, anti-social behavior and related outcome measures. The trial found adverse effects on four outcomes among the intervention group compared to the control group: anti-social behavior increased on two different measures (d=+0.20) and (d=+0.18); child reported liberal parenting increased (d=+0.16); and child reported authoritarian parenting also increased (d=+0.20). In addition, parental participation was significantly associated with several program outcomes. It was concluded, that group based after-school behavior programs may have the potential to cause iatrogenic effects and must be designed, piloted, evaluated and implemented with a high degree of care.

Effects of a specialist-led, school physical education program on bone mass, structure and strength in primary school children: a 4-year cluster randomised controlled trial

This 4-year cluster randomised controlled trial of 365 boys and 362 girls (mean age 8.1 ± 0.3 years) from grade 2 in 29 primary schools investigated the effects of a specialist-taught physical education (PE) program on bone strength and body composition. All children received 150 min/week of common practice (CP) PE from general classroom teachers but in 13 schools 100 min/week of CP PE was replaced by specialized-led PE (SPE) by teachers who emphasized more vigorous exercise/games combined with static and dynamic postural activities involving muscle strength. Outcome measures assessed in grades 2, 4, and 6 included: total body bone mineral content (BMC), lean mass (LM) and fat mass (FM) by DXA, and radius and tibia (4% and 66% sites) bone structure, volumetric density and strength, and muscle cross-sectional area (CSA) by pQCT. After 4-years, gains in total body BMC, FM and muscle CSA were similar between the groups in both sexes, but girls in the SPE group experienced a greater gain in total body LM [mean (95%CI), 1.0kg (0.2, 1.9)]. Compared to CP, girls in the SPE group also had greater gains in cortical area (CoA) and cortical thickness (CoTh) at the mid-tibia [CoA, 5.0% (0.2, 1.9); CoTh 7.5% (2.4, 12.6)] and mid-radius [CoA, 9.3% (3.5, 15.1); CoTh 14.4% (6.1, 22.7)], while SPE boys had a 5.2% (0.4, 10.0) greater gain in mid-tibia CoTh. These benefits were due to reduced endocortical expansion. There were no significant benefits of SPE on total bone area, cortical density or bone strength at the mid-shaft sites, nor any appreciable effects at the distal skeletal sites. This study indicates that a specialist-led school-based PE program improves cortical bone structure, due to reduced endocortical expansion. This finding challenges the notion that periosteal apposition is the predominant response of bone to loading during the pre- and early-pubertal period. This article is protected by copyright. All rights reserved.

A year's supervision of elementary instruction in Caroline County, 1923-1924.

Mode of access: Internet.

Integrating Engineering Experiences within the Elementary Mathematics Curriculum

Engineering education for elementary school students is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to use the data to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results provide evidence that engineering model-eliciting activities can be successfully integrated in the elementary mathematics curriculum. These activities provide rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.

Preservice Elementary Teachers’ Beliefs toward Mathematics and Mathematics Teaching

As they began their one-year teacher education program 138 elementary school teacher candidates completed a questionnaire designed to measure their beliefs concerning the nature of mathematics, measured on a scale from absolutist to fallibilist, and their beliefs concerning effective mathematics instruction, measured on a scale from traditional to constructivist. Interviews were conducted with volunteer questionnaire participants, with selection based on the questionnaire results and using two sets of criteria. Study 1. involved 8 teacher candidates showing distinct absolutist or fallibilist views of mathematics and individual interviews explored participants' beliefs concerning the use of information and communication technology, particularly interactive whiteboards (IWB), in the teaching and learning of mathematics. Participants with absolutist beliefs about the nature of mathematics tended to focus on the IWB as a presentation tool, while those with fallibilist beliefs appreciated the use of the IWB to support student exploration. Study 2. involved 8 teacher candidates with apparently misaligning absolutist beliefs concerning the nature of mathematics and constructivist beliefs concerning teaching. Interviews exploring participants' favoured instructional approaches, particularly those involving the use of manipulatives, showed that constructivist views involved essentially surface beliefs and that in fact manipulatives would be employed to support traditional direct instruction.

Understanding Parental Influence on Educational Outcomes Among 9 Year Olds in Ireland: The Mediating Role of Resources, Attitudes and Children's Own Perspectives

The relationship between parental background and children's educational outcomes has been a dominant theme within the sociology of education. There has been an on-going debate as to the relative merits of explanations which focus on the role of socio-cultural reproduction and those which focus on rational choice. However, many empirical studies within the social stratification tradition fail to allow for children's own agency in shaping the relationship between social background and schooling outcomes. This paper draws on the first wave of a large-scale longitudinal study of over 8,000 nine-year-old children in Ireland, which combines information from parents, school principals, teachers and children themselves. Both social class and parental education are found to have significant effects on reading and mathematics test scores among nine year olds. These effects are partly mediated by home-based educational resources and activities, parents' educational expectations for their child, and parents' formal involvement in the school. More importantly, children's own engagement with, and attitudes to, school significantly influence their academic performance. The influence of children's own attitudes and actions can thus reinforce or mitigate the effect of social background factors. The analysis therefore provides a bridge between the large body of research on the intergenerational transmission of inequality and the emerging research and policy literature on children's rights.

Spiritual journeys in the classroom: elementary public school teachers' perspectives /

This thesis explored 5 public elementary school teachers ' perceptions of spirituality and its implications for classroom practice. A generic qualitative study was conducted where each teacher shared her experiences and perceptions in one audiotaped semistructured interview. Transcripts were generated and coded for themes which emerged, resulting in the findings of the study. Following this process, the participants verified the accuracy of the transcripts and findings through a member-checking system. The research found that each teacher has her own definition of spirituality. Furthermore, one's personal connection with spirituality can involve a relationship with religion, the self, a higher being, others, and nature. These spiritual relationships were nurtured through a variety of methods outlined by the teachers. This resulted in the creation of a personal spiritual profile for each teacher which contained each teacher's spiritual connections or facets and the methods used to develop these facets. The teachers identified spiritual needs in their students warranting the need for and importance of spiritual education. Given this, a number of classroom practices were identified with the intention of meeting the spiritual needs of students. Among these practices, the teacher as role model was identified as a significant practice for students' spiritual development in the classroom. The teachers further outlined a number of professional development initiatives with the intention to promote greater awareness for spiritual education and to provide resources for educators.

Two School Administrators’ Perspectives on How Intercultural Education is Promoted in Their Elementary Schools

This study examined the perspectives of 2 elementary school administrators (1 principal of a faith based school, and 1 vice-principal of a public school) towards intercultural education and how it was implemented in their schools. A generic qualitative research methodology guided this study. Face-to-face interviews that used a guide with open-ended questions were used to collect data. Participants were administrators in their respective schools, had been involved in intercultural activities at their school, and were professional acquaintances of the researcher. The interviews were digitally recorded and the interview transcripts were reviewed by participants to ensure accuracy. The administrators’ understanding of intercultural education tended to be limited to learning and celebration of various cultures. The intercultural education strategies used in the respective schools focussed on developing a knowledge base and provided limited intercultural interaction. The public school had greater resources available than the private faith-based school. However, the resources were not always used to facilitate intercultural education. Teachers and administrators were provided with very few professional development opportunities focussed on intercultural education.

Les effets d’un cercle pédagogique sur le regard professionnel et les pratiques pédagogiques des enseignants du 3e cycle du primaire en grammaire actuelle

Notre recherche doctorale vise à décrire les effets d’un cercle pédagogique sur les pratiques pédagogiques et didactiques d’enseignants du 3e cycle du primaire en grammaire actuelle. Ce projet s’inscrit dans une recherche plus large intitulée « Étude des effets, sur les pratiques pédagogiques des enseignants et la compétence à écrire des élèves, d’un dispositif de formation à la grammaire nouvelle qui intègre des exemples de pratiques sur vidéo et permet un partage d'expertise ». Elle vise à éclairer les conditions d’efficacité d’une formation continue sur différentes dimensions du développement professionnel au regard de la formation elle-même et de son effet sur le transfert des pratiques en classe. Pour y parvenir, nous avons analysé les échanges provenant des cercles pédagogiques vécus durant une année scolaire. Nous avons également analysé deux activités de grammaire, avant et après la formation en grammaire offerte sous forme de capsules. Ces observations en classe ont été captées sur vidéo, dans la classe de 18 enseignants participant à notre expérimentation. Nous avons enfin analysé les réponses des participants à un questionnaire sur leur perception à l’égard du dispositif de formation auquel ils ont participé pendant neuf mois. Nos analyses montrent qu’un dispositif de formation à la grammaire actuelle qui met au cœur de la formation l’analyse d’exemples de pratiques sur vidéo soutient le développement du regard professionnel des enseignants dans le contexte du cercle. Ceux-ci observent plus d’interactions et les interprètent mieux, de manière plus approfondie. Nos observations ont également montré que les enseignants développent majoritairement des pratiques dans leur classe, qu’ils développent de nouveaux savoirs en lien avec le cadre théorique de la nouvelle grammaire et qu’ils modifient la vision qu’ils ont de la grammaire actuelle au fil des rencontres. Cette recherche peut enrichir les connaissances scientifiques sur le développement professionnel et influencer les formateurs d’enseignants de même que les cadres des milieux scolaires pour ajuster l’offre de formation continue afin de la rendre plus efficace.

Development and reliability of a self-report questionnaire to examine children's perceptions of the physical activity environment at home and in the neighbourhood

Background: Environmental factors are increasingly being implicated as key influences on children's physical activity. Few studies have comprehensively examined children's perceptions of their environment, and there is a paucity of literature on acceptable and reliable scales for measuring these. This study aimed to develop and test the acceptability and reliability of a scale which examined a broad range of environmental perceptions among children.
Methods: Based on constructs from ecological models, a survey incorporating items on children's perceptions of the physical and social environment at home and in the neighbourhood was developed. This was administered on two occasions, nine days apart, to a sample of 39 children aged 11 years (54% boys), attending a metropolitan Australian elementary school. The acceptability of the survey was determined by the proportion of missing responses to each item. The test-retest reliability of individual items, scores and scales were determined using Kappa statistics and percent agreement for categorical variables, and intraclass correlation coefficients (ICC) for continuous variables.
Results: There were few missing responses to each question, with only 4% of all responses missing. Although some Kappa values were low, all categorical variables showed acceptable reliability when examined for percent agreement between test and retest (range 68%–100% agreement). Continuous variables all showed moderate to good ICC values (range 0.72–0.92).
Conclusion: Findings suggest this questionnaire is reliable and acceptable to children for assessing environmental perceptions relevant to physical activity among 11-year-old children.

Six year follow-up of students who participated in a school-based physical activity interventions : a longitudinal cohort study

Background
The purpose of this paper was to evaluate the long-term impact of a childhood motor skill intervention on adolescent motor skills and physical activity.

Methods
In 2006, we undertook a follow-up of motor skill proficiency (catch, kick, throw, vertical jump, side gallop) and physical activity in adolescents who had participated in a one-year primary school intervention Move It Groove It (MIGI) in 2000. Logistic regression models were analysed for each skill to determine whether the probability of children in the intervention group achieving mastery or near mastery was either maintained or had increased in subsequent years, relative to controls. In these models the main predictor variable was intervention status, with adjustment for gender, grade, and skill level in 2000. A general linear model, controlling for gender and grade, examined whether former intervention students spent more time in moderate-to-vigorous physical activity at follow-up than control students.

Results
Half (52%, n = 481) of the 928 MIGI participants were located in 28 schools, with 276 (57%) assessed. 52% were female, 58% in Grade 10, 40% in Grade 11 and 54% were former intervention students. At follow-up, intervention students had improved their catch ability relative to controls and were five times more likely to be able to catch: ORcatch = 5.51, CI (1.95 – 15.55), but had lost their advantage in the throw and kick: ORthrow = .43, CI (.23 – .82), ORkick = .39, CI (.20 – .78). For the other skills, intervention students appeared to maintain their advantage: ORjump = 1.14, CI (.56 – 2.34), ORgallop = 1.24, CI (.55 – 2.79). Intervention students were no more active at follow-up.

Conclusion
Six years after the 12-month MIGI intervention, whilst intervention students had increased their advantage relative to controls in one skill, and appeared to maintain their advantage in two, they lost their advantage in two skills and were no more active than controls at follow up. More longitudinal research is needed to explore whether gains in motor skill proficiency in children can be sustained and to determine the intervention characteristics that translate to subsequent physical activity.

Driving down daily step counts: the impact of being driven to school on physical activity and sedentary behavior

This study investigated whether being driven to school was associated with lower weekday and weekend step counts, less active out-of-school leisure pursuits, and more sedentary behavior. Boys aged 10–13 years (n = 384) and girls aged 9–13 years (n = 500) attending 25 Australian primary schools wore a pedometer and completed a travel diary for one week. Parents and children completed surveys capturing leisure activity, screen time, and sociodemographics. Commute distance was objectively measured. Car travel was the most frequent mode of school transportation (boys: 51%, girls: 58%). After adjustment (sociodemographics, commute distance, and school clustering) children who were driven recorded fewer weekday steps than those who walked (girls: –1,393 steps p < .001, boys: –1,569 steps, p = .009) and participated in fewer active leisure activities (girls only: p = .043). There were no differences in weekend steps or screen time. Being driven to and from school is associated with less weekday pedometer-determined physical activity in 9- to 13-year-old elementary-school children. Encouraging children, especially girls, to walk to and from school (even for part of the way for those living further distances) could protect the health and well-being of those children who are insufficiently active.