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.

The effects of teaching a mathematics problem solving strategy on the problem solving ability of grade nine students

Forty grade 9 students were selected from a small rural board in southern Ontario. The students were in two classes and were treated as two groups. The treatment group received instruction in the Logical Numerical Problem Solving Strategy every day for 37 minutes over a 6 week period. The control group received instruction in problem solving without this strategy over the same time period. Then the control group received the treat~ent and the treatment group received the instruction without the strategy. Quite a large variance was found in the problem solving ability of students in grade 9. It was also found that the growth of the problem solving ability achievement of students could be measured using growth strands based upon the results of the pilot study. The analysis of the results of the study using t-tests and a MANOVA demonstrated that the teaching of the strategy did not significaritly (at p s 0.05) increase the problem solving achievement of the students. However, there was an encouraging trend seen in the data.

The impact of integrated programming on student attitude and achievement in grade 9 academic mathematics and science

This research studioo the effect of integrated instruction in mathematics and~ science on student achievement in and attitude towards both mathematics and science. A group of grade 9 academic students received instruction in both science and mathematics in an integrated program specifically developed for the purposes of the research. This group was compared to a control group that had received science and mathematics instruction in a traditional, nonintegrated program. The findings showed that in all measures of attitude, there was no significant difference between the students who participated in the integrated science and mathematics program and those who participated in a traditional science and mathematics program. The findings also revealed that integration did improve achievement on some of the measures used. The performance on mathematics open-ended problem-solving tasks improved after participation in the integrated program, suggesting that the integrated students were better able to apply their understanding of mathematics in a real-life context. The performance on the final science exam was also improved for the integrated group. Improvement was not noted on the other measures, which included EQAO scores and laboratory practical tasks. These results raise the issue of the suitability of the instruments used to gauge both achievement and attitude. The accuracy and suitability of traditional measures of achievement are considered. It is argued that they should not necessarily be used as the measure of the value of integrated instruction in a science and mathematics classroom.

Teachers' professional learning within communities of mathematics-for-teaching practice

Ontario bansho is an emergent mathematics instructional strategy used by teachers working within communities of practice that has been deemed to have a transformational effect on teachers' professional learning of mathematics. This study sought to answer the following question: How does teachers' implementation of Ontario bansho within their communities of practice inform their professional learning process concerning mathematics-for-teaching? Two other key questions also guided the study: What processes support teachers' professional learning of content-for-teaching? What conditions support teachers' professional learning of content-for-teaching? The study followed an interpretive phenomenological approach to collect data using a purposive sampling of teachers as participants. The researcher conducted interviews and followed an interpretive approach to data analysis to investigate how teachers construct meaning and create interpretations through their social interactions. The study developed a model of professional learning made up of 3 processes, informing with resources, engaging with students, and visualizing and schematizing in which the participants engaged and 2 conditions, ownership and community that supported the 3 processes. The 3 processes occur in ways that are complex, recursive, nonpredictable, and contextual. This model provides a framework for facilitators and leaders to plan for effective, content-relevant professional learning by placing teachers, students, and their learning at the heart of professional learning.

The effect of social skills training on grade 3 students' self-esteem, moral development and perceptions of classroom environment

Two Grade 3 classes were used to study the effects of a formal social skills training program. Specifically, comparisons were made on self-esteem, classroom environment, and moral development to see whether changes occurred as a direct result of social skills training. One group participated in the social skills program, while the other group did not. It was hypothesized that formal social skills training would improve students' selfesteem, moral development, and the classroom environment. At the end of the program, however, data from class observations, teacher interviews, journal of the social skills training group teacher, and measures of self-esteem, classroom environment and moral development did not support this hypothesis. Although the social skills training group scored significantly higher in class cohesiveness, they did not show marked improvement in the other measures. In fact, in some measures (e.g., friction and competitiveness), they demonstrated greater scores at both pretest and posttests. The social skills training group was, however, able to vocalize and utilize the strategies of several skills which had been a focus of the program, suggesting that formal social skills training is a useful tool for presenting and reinforcing some specific behaviours.

The generation effect and word learning: a test of the effect of the language experience approach versus the text approach in the acquisition of new reading vocabulary

A class of twenty-two grade one children was tested to determine their reading levels using the Stanford Diagnostic Reading Achievement Test. Based on these results and teacher input the students were paired according to reading ability. The students ages ranged from six years four months to seven years four months at the commencement of the study. Eleven children were assigned to the language experience group and their partners became the text group. Each member of the language experience group generated a list of eight to be learned words. The treatment consisted of exposing the student to a given word three times per session for ten sessions, over a period of five days. The dependent variables consisted of word identification speed, word identification accuracy, and word recognition accuracy. Each member of the text group followed the same procedure using his/her partner's list of words. Upon completion of this training, the entire process was repeated with members of the text group from the first part becoming members of the language experience group and vice versa. The results suggest that generally speaking language experience words are identified faster than text words but that there is no difference in the rate at which these words are learned. Language experience words may be identified faster because the auditory-semantic information is more readily available in them than in text words. The rate of learning in both types of words, however, may be dictated by the orthography of the to be learned word.

The impact of a digital children's literature program on primary students' reading motivation

This qualitative study stemmed from a concern of the perceived decline in students' reading motivation after the early years of schooling, which has been attributed to the disconnect between the media students are accustomed to using outside the classroom and the media they predominantly use within the classroom. This research documented the effectiveness of a digital children's literature program and a postreading multimedia program on eight grade 1 students' reading motivation, word recognition, and comprehension abilities. Eight students were given ten 25-minute sessions with the software program over 15 weeks. Preprogram, interim-program, and postprogram qualitative data were collected from students, teachers, and parents through questionnaires, interviews, standardized reading assessment tools, classroom observations, field notes, and student behaviour observation checklists. Findings are summarized into 3 themes. The motivational aspects and constructivist styles of instruction in the digital reading programs may have contributed to 5 student participants' increased participation in online storybook reading at home. Qualitative data revealed that the digital children's literature program and multimedia postreading activities seemed to have a positive influence on the majority of grade 1 student participants' reading motivation, word recognition, and listening comprehension skills. These findings suggest the promise of multimedia and Internet-based reading software programs in supporting students with reading andlor behavioural difficulties. In keeping with current educational initiatives and efforts, increased use of media literacy practices in the grade 1 curriculum is suggested.

Writing and science connections : integrated instruction and assessment

Learning to write is a daunting task for many young children. The purpose of this study was to examine the impact of a combined approach to writing instruction and assessment on the writing performance of students in two grade 3 classes. Five forms and traits of writing were purposefully connected during writing lessons while exhibiting links to the four strands of the grade 3 Ontario science curriculum. Students then had opportunities to engage in the writing process and to self-assess their compositions using either student-developed (experimental group/teacher-researcher's class) or teachercreated (control group/teacher-participant's class) rubrics. Paired samples t-tests revealed that both the experimental and control groups exhibited statistically significant growth from pretest to posttest on all five integrated writing units. Independent samples t-tests showed that the experimental group outperformed the control group on the persuasive + sentence fluency and procedure + word choice writing tasks. Pearson product-moment correlation r tests revealed significant correlations between the experimental group and the teacher-researcher on the recount + ideas and report + organization tasks, while students in the control group showed significant correlations with the teacher-researcher on the narrative + voice and procedure + word choice tasks. Significant correlations between the control group and the teacher-participant were evident on the persuasive + sentence fluency and procedure + word choice tasks. Qualitative analyses revealed five themes that highlighted how students' self-assessments and reflections can be used to guide teachers in their instructional decision making. These findings suggest that educators should adopt an integrated writing program in their classrooms, while working with students to create and utilize purposeful writing assessment tools.

The impact of a training program in phonological awareness on children's early writing

This study examined the effects that a training program in phonological awareness had on the early writing skills of children in a Grade One class in the Lincoln County Separate school system. The intent of the training program was to provide consistent and systematic practice in the manipulation of the phonological structure of language. The games and activities of the training program were related to a framework of developmental phonological skills and practised in a group setting during an unstructured period of the regular classroom schedule. The training program operated three days in a six-day cycle for approximately twenty minutes a day, from November until mid-March. All children were tested at the outset and conclusion of the study to determine level of functioning in letter identification, word recognition, verbal intelligence, phonological awareness and spelling. Results of the pre-tests and post-tests were compared to determine differences between the experimental and control groups over time. In addition, a systematic analysis of the children's writing looked at the development of the spelling of regular and irregular words. The results of this study provided strong support for the hypothesis that the treatment group would progress through the stages of early writing development more quickly than children without such training. On the basis of differences between the groups over time, it was evident that training in phonological awareness had a direct positive effect on the spelling of regular words for children during the early stages of writing. The training program did not have a significant effect on the spelling of irregular words. Test results evaluating phonological awareness indicated a significant difference within each group over time but no significance between the groups during the experimental period. It would appear that the results of these tests reflect maturational changes in the child rather than causal effects of the training program. Nor did the effects of the training program transfer significantly to other aspects of language. Although some of the hypotheses considered were not supported by the study, the results do indicate that children during the early stages of writing development can benefit from a training program in phonological awareness. The theoretical direction for effective programming as a result of this study is discussed. The educational implications of training phonological awareness concurrent to beginning efforts in writing are considered.

An after-school literacy program : investigating the experiences of students with literacy difficulties, their volunteer tutors, and the tutors' transition into the teaching profession

This research responds to a pervasive call for our educational institutions to provide students with literacy skills, and teachers with the instructional supports necessary to facilitate this skill acquisition. Questions were posed to gain information concerning the efficacy ofteaching literacy strategies to students with learning difficulties, the impact of this training on their volunteer tutors, and the influence of this experience on these tutors' ensuing instructional practice as teacher candidates in a preservice education program. Study #1 compared a nontreatment group of students with literacy difficulties who participated in the program and found that program participants were superior at reading letter patterns and at comprehending the elements of story grammar. Concurrently, the second study explored the experiences of 19 volunteer tutors and uncovered that they acquired instructional skills as they established a knowledge base in teaching reading and writing, and they affirmed personal goals to become future teachers. Study #3 tracked 6 volunteer tutors into their pre-service year and identified their constructions, and beliefs about literacy instruction. These teacher candidates discussed how they had intended to teach reading and writing strategies based on their position that effective teaching ofthese skills in the primary grades is integral to academic success. The teacher candidates emphasized the need to build rapport with students, and the need to exercise flexibility in lesson plan delivery while including activities to meet emotional and developmental requirements of students. The teacher candidates entered their pre-service education with an initial cognition set based on the limited teaching context of tutoring. This foundational ii perception represented their prior knowledge of literacy instruction, a perception that appeared untenable once they were immersed in a regular instructional setting. This disparity provoked some of the teacher candidates to denounce their teacher mentors for not consistently employing literacy strategies and individualized instruction. This critical perspective could have been a demonstration of cognitive dissonance. In the end, when the teacher candidates began to look toward the future and how they would manage the demands of an inclusive classroom, they recognized the differences in the contexts. With an appreciation for the need for balance between prior and present knowledge, the teacher candidates remained committed to implementing their tutoring strategies in future teaching positions. This document highlights the need for teacher candidates with instructional experience prior to teacher education, to engage in cognitive negotiations to assimilate newly acquired pedagogies into existing pedagogies.

Introduction to engineering : a case study of an interdisciplinary course in Mathematics, Science and Technology

This thesis research was a qualitative case study of a single class of Interdisciplinary Studies: Introduction to Engineering taught in a secondary school. The study endeavoured to explore students' experiences in and perceptions of the course, and to investigate the viability of engineering as an interdisciplinary theme at the secondary school level. Data were collected in the form of student questionnaires, the researcher's observations and reflections, and artefacts representative of students' work. Data analysis was performed by coding textual data and classifying text segments into common themes. The themes that emerged from the data were aligned with facets of interdisciplinary study, including making connections, project-based learning, and student engagement and affective outcomes. The findings of the study showed that students were positive about their experiences in the course, and enjoyed its project-driven nature. Content from mathematics, physics, and technological design was easily integrated under the umbrella of engineering. Students felt that the opportunity to develop problem solving and teamwork skills were two of the most important aspects of the course and could be relevant not only for engineering, but for other disciplines or their day-to-day lives after secondary school. The study concluded that engineering education in secondary school can be a worthwhile experience for a variety of students and not just those intending postsecondary study in engineering. This has implications for the inclusion of engineering in the secondary school curriculum and can inform the practice of curriculum planners at the school, school board, and provincial levels. Suggested directions for further research include classroom-based action research in the areas of technological education, engineering education in secondary school, and interdisciplinary education.

A Study of role conflict, role ambiguity, locus of control, job satisfaction and participation in decision making among front-line vocational service workers for mentally retarded adults

This study was an investigation of individual and organizational factors, as perceived by front-line vocational service workers from Adult Rehabilitation Centres (ARC Industries) for mentally retarded adults. The specific variables which were measured included role conflict/role ambiguity (role factors), internal/external locus of control (individual differences), job satisfaction with work and supervision (job attitudes) and participation in deci~ion making (organizational factor). The exploration of these constructs was conducted by means of self-report questionnaires which were completed by sixty-nine out of a total of ninety front-line employees. The surveys were distributed in booklet form to nine distinct rehabilitation facilities from St. Catharines, West Lincoln, Greater Niagara, Port Colborne, WeIland, Fort Erie, Hamilton, Guelph and Brantford. The survey data was evaluated by the statisti.cal Package for the Social Sciences (SPSS) which used the Pearson Product Moment Correlation procedure and a compar~son of means test. A comparison of correlation coefficients test was also conducted. This statistical procedure was calculated mathematically. The results obtained from the statistical evaluation confirmed the prediction that self-reported measures of participation in decision making and satisfaction (work and supervision) would be negatively correlated with role conflict and role ambiguity. As well, the speculation that perceived satisfaction (work and supervision) would be positively correlated with participation in decision making was empirically supported. Internal and external locus of control did not contribute to a significant difference in r~sponses to role perceptions (conflict and ambiguity) , satisfaction (work and supervision) or the correlational relationship between participation in decision making and satisfaction (work and supervision). Overall, the findings from this study substantiated the importance of examining employee perceptions in the workplace and the interrelationships among individual and organizational variables. This research was considered a contribution to the general area of occupational stress and to the study of individuals in work organizations.

Creativity and the working artist/teacher : the relationships

The purpose of this qualitative study was to understand the relationships between creativity and the working artist/teacher employed by an art college. The topic emerged from my job as an instructor at The Ontario College of Art which was used as the primary data resource and provided the highest caliber of professionals to chose from. Existent data were used to facilitate the study generated by the research of Cawelti, Rappaport, and Wood (1992). The data were generated by a group of 5 faculty members from The University of Northern Iowa, recognized for their expertise in the arts (a painter, a poet, a sculptor, a novelist, and a photographer). They were asked to respond to the following statement: "In as much detail as you like, list the things that you did, thought, or felt the last time you created an artistic product. II Cawelti, Rappaport, and Wood (1992) produced three models of the creative process, each building on the previous, with the resultant third,being in my opinion, an excellent illustration (text/visual) of the creative process. Model three (Appendix D) presented a "multi-dimensional view of the creative process: time, space, observatility, and consciousnessll (p. 90). Model three utilized a visual mapping device along the bottom of the page linked to text segments above. Both the visual and the text were interrelated so that they harmonized into a comprehensive "picture." The parti'cipants of this qualitative study were asked to consider model three from their professional perspective as artist/teachers. The interpretive sciences directed the methodology. The hermeneutic circle of continuous reflection from the whole to the part and back to the whole was an important aspect of the data analyses. Four members of the Foundation Department at The Ontario College of Art were the key participants. A series of conversational interviews was the primary source of data collection, this was augmented by observation, fie,ldnotes, and follow up telephone interviews. Transcripts of interviews were returned to participants for reflection and the telephone was used to discuss any additional -points raised. Analysis consisted of coding and organizing data according to emerging themes. These themes formed the basis for the narrative stories. The text of the narrative stories were given back to each participant for further comment. Revisions were made until both the researcher and the participants felt that the stories reflected reality. The resultant whole was critiqued from the researcher's perspective. The significance of this study was discussed as it pertains to the working artist/teacher and areas in need of further study are pointed out.

Sentence combining and thinking : a study of adult ESL learners

Thesis (M.Ed.)--Brock University, 2003.

The association of faculty's teaching philosophy and teaching behaviour, and critical thinking and self- direction in learning

The intent in this study was to investigate in what ways teachers· beliefs about education and teaching are expressed in the specific teaching behaviours they employ, and whether teaching behaviours, as perceived by their students, are correlated with students· critical thinking and self-directed learning. To this end the relationships studied were: among faCUlty members· philosophy of teaching, locus of control orientation, psychological type, and observed teaching behaviour; and among students· psychological type, perceptions of teaching behaviour, self-directed learning readiness, and critical thinking. The overall purpose of the study was to investigate whether the implicit goals of higher education, critical thinking and self-direction, were actually accounted for in the university classroom. The research was set within the context of path-goal theory, adapted from the leadership literature. Within this framework, Mezirow·s work on transformative learning, including the influences of Habermas· writings, was integrated to develop a theoretical perspective upon which to base the research methodology. Both qualitative and quantitative methodologies were incorporated. Four faCUlty and a total of 142 students participated in the study. Philosophy of teaching was described through faCUlty interviews and completion of a repertory grid. Faculty completed a descriptive locus of control scale, and a psychological type test. Observations of their teaching behaviour were conducted. Students completed a Teaching Behaviour Assessment Scale, the Self-Directed Learning Readiness Scale, a psychological type test, and the Watson-Glaser Critical Thinking Appraisal. A small sample of students were interviewed. Follow-up discussions with faculty were used to validate the interview, observation, teaching behaviour, and repertory grid data. Results indicated that some discrepancies existed between faculty's espoused philosophy of teaching and their observed teaching behaviour. Instructors' teaching behaviour, however, was a function of their personal theory of practice. Relationships were found between perceived teaching behaviour and students· self-directed learning and critical thinking, but these varied across situations, as would be predicted from path-goal theory. Psychological type of students and instructor also accounted for some of the variability in the relationships studied. Student psychological type could be shown as a partial predictor of self-directed learning readiness. The results were discussed in terms of theory development and implications for further research and practice.