Codeship: Financing growth: Case study and Teaching note

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics

An examination of grade three mathematics textbooks for problem solving strategies

Three grade three mathematics textbooks were selected arbitrarily (every other) from a total of six currently used in the schools of Ontario. These textbooks were examined through content analysis in order to determine the extent (i. e., the frequency of occurrence) to which problem solving strategies appear in the problems and exercises of grade three mathematics textbooks, and how well they carry through the Ministry's educational goals set out in The Formative Years. Based on Polya's heuristic model, a checklist was developed by the researcher. The checklist had two main categories, textbook problems and process problems and a finer classification according to the difficulty level of a textbook problem; also six commonly used problem solving strategies for the analysis of a process problem. Topics to be analyzed were selected from the subject guideline The Formative Years, and the same topics were selected from each textbook. Frequencies of analyzed problems and exercises were compiled and tabulated textbook by textbook and topic by topic. In making comparisons, simple frequency count and percentage were used in the absence of any known criteria available for judging highor low frequency. Each textbook was coded by three coders trained to use the checklist. The results of analysis showed that while there were large numbers of exercises in each textbook, not very many were framed as problems according to Polya' s model and that process problems form a small fraction of the number of analyzed problems and exercises. There was no pattern observed as to the systematic placement of problems in the textbooks.

Etude de pratiques enseignantes et de différenciations dans les apprentissages mathématiques scolaires à l’école primaire

Dans le cadre du réseau RESEIDA (REcherches sur la Socialisation, l’Enseignement, les Inégalités et les Différenciations dans les Apprentissages, co-piloté par E. Bautier et J-Y. Rochex), je participe depuis plusieurs années à une recherche qui vise à étudier des pratiques enseignantes contextualisées et leurs effets potentiellement différenciateurs sur les apprentissages d’élèves, en croisant des points de vue issus de différentes didactiques et de la sociologie de l'éducation. Dans ce contexte, un imposant corpus de données a été recueilli dans deux classes françaises de CM2 (élèves de 10-11 ans) considérées comme hétérogènes (d'après les résultats d'évaluations nationales, les caractéristiques familiales) en 2004-2005: composé à la fois de données filmiques orientées vers les pratiques d’enseignantes et d’élèves en situation de classe, de photocopies de cahiers ou de productions d’élèves. Ma présentation se centre sur l’analyse d’une partie de ces données, concernant l’enseignement des mathématiques observé dans une des deux classes de CM2. Plus précisément, j’effectue un zoom sur deux situations observées dans cette classe: une situation de résolution de problèmes et une situation d’enseignement des pourcentages. Ces deux situations apparaissent contrastées (gestion enseignante, apprentissages mathématiques potentiels, etc.). Mais elles permettent précisément de montrer que derrière une hétérogénéité apparente de pratiques d’une enseignante, une façon commune de penser et de faire la classe de mathématiques se joue, dont on peut penser qu’elle pèse fortement sur les apprentissages potentiels en contexte scolaire

An investigation of post-primary students' images of mathematics

This research study investigates the image of mathematics held by 5th-year post-primary students in Ireland. For this study, “image of mathematics” is conceptualized as a mental representation or view of mathematics, presumably constructed as a result of past experiences, mediated through school, parents, peers or society. It is also understood to include attitudes, beliefs, emotions, self-concept and motivation in relation to mathematics. This study explores the image of mathematics held by a sample of 356 5th-year students studying ordinary level mathematics. Students were aged between 15 and 18 years. In addition, this study examines the factors influencing students‟ images of mathematics and the possible reasons for students choosing not to study higher level mathematics for the Leaving Certificate. The design for this study is chiefly explorative. A questionnaire survey was created containing both quantitative and qualitative methods to investigate the research interest. The quantitative aspect incorporated eight pre-established scales to examine students‟ attitudes, beliefs, emotions, self-concept and motivation regarding mathematics. The qualitative element explored students‟ past experiences of mathematics, their causal attributions for success or failure in mathematics and their influences in mathematics. The quantitative and qualitative data was analysed for all students and also for students grouped by gender, prior achievement, type of post-primary school attending, co-educational status of the post-primary school and the attendance of a Project Maths pilot school. Students‟ images of mathematics were seen to be strongly indicated by their attitudes (enjoyment and value), beliefs, motivation, self-concept and anxiety, with each of these elements strongly correlated with each other, particularly self-concept and anxiety. Students‟ current images of mathematics were found to be influenced by their past experiences of mathematics, by their mathematics teachers, parents and peers, and by their prior mathematical achievement. Gender differences occur for students in their images of mathematics, with males having more positive images of mathematics than females and this is most noticeable with regards to anxiety about mathematics. Mathematics anxiety was identified as a possible reason for the low number of students continuing with higher level mathematics for the Leaving Certificate. Some students also expressed low mathematical self-concept with regards to higher level mathematics specifically. Students with low prior achievement in mathematics tended to believe that mathematics requires a natural ability which they do not possess. Rote-learning was found to be common among many students in the sample. The most positive image of mathematics held by students was the “problem-solving image”, with resulting implications for the new Project Maths syllabus in post-primary education. Findings from this research study provide important insights into the image of mathematics held by the sample of Irish post-primary students and make an innovative contribution to mathematics education research. In particular, findings contribute to the current national interest in Ireland in post-primary mathematics education, highlighting issues regarding the low uptake of higher level mathematics for the Leaving Certificate and also making a preliminary comparison between students who took part in the piloting of Project Maths and students who were more recently introduced to the new syllabus. This research study also holds implications for mathematics teachers, parents and the mathematics education community in Ireland, with some suggestions made on improving students‟ images of mathematics.

Reducing high levels of communication apprehension among primary school students

This study focused on a group of primary school teachers as they implemented a variety of intervention actions within their class programs aimed towards supporting the reduction of high levels of communication apprehension (CA) among students.Six teachers and nine students, located across three primary schools, four year levels,and six classes, participated in this study. For reasons of confidentiality the schools,principals, parents, teachers, teacher assistants, and students who were involved in this study were given fictitious names. The following research question was explored in this study: What intervention actions can primary school teachers implement within their class programs that support the reduction of high CA levels among students? Throughout this study the term CA referred to "an individual's level of fear or anxiety associated with either real or anticipated (oral) communication with another person or persons" (McCroskey, 1984, p. 13). The sources of CA were explained with reference to McCroskey's state-trait continuum. The distinctions between high and appropriate levels of CA were determined conceptually and empirically. The education system within which this study was conducted promoted the philosophy of inclusion and the practices of inclusive schooling. Teachers employed in this system were encouraged to create class programs inclusive of and successful for all students. Consequently the conceptual framework within which this study was conducted was based around the notion of inclusion. Action research and case study research were the methodologies used in the study. Case studies described teachers' action research as they responded to the challenge of executing intervention actions within their class programs directed towards supporting the reduction of high CA levels among students. Consequently the teachers and not the researcher were the central characters in each of the case studies. Three principal data collection instruments were used in this study: Personal Report of Communication Fear (PRCF) scale, semistructured interviews, and dialogue journals. The PRCF scale was the screening tool used to identify a pool of students eligible for the study. Data relevant to the students involved in the study were gathered during semistructured interviews and throughout the dialogue journaling process. Dialogue journaling provided the opportunity for regular contact between teachers and the researcher, a sequence to teacher and student intervention behaviours, and a permanent record of teacher and student growth and development. The majority of teachers involved in this study endeavoured to develop class programs inclusive of all students.These teachers acknowledged the importance of modifying aspects of their class programs in response to the diverse and often multiple needs of individual students with high levels of CA. Numerous conclusions were drawn regarding practical ways that the teachers in this study supported the reduction of high CA levels among students. What this study has shown is that teachers can incorporate intervention actions within their class programs aimed towards supporting students lower their high levels of CA. Whilst no teacher developed an identical approach to intervention, similarities and differences were evident among teachers regarding their selection, interpretation, and implementation of intervention actions. Actions that teachers enacted within their class programs emerged from numerous fields of research including CA, inclusion, social skills, behaviour teaching, co-operative learning, and quality schools. Each teacher's knowledge of and familiarity with these research fields influenced their preference for and commitment to particular intervention actions. Additional factors including each teacher's paradigm of inclusion and exclusion contributed towards their choice of intervention actions. Possible implications of these conclusions were noted with reference to teachers,school administrators, support personnel, system personnel, teacher educators, parents, and researchers.