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.

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.

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 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.

Using Effective Teaching Strategies and Personality Type to Enhance the Mathematics Classroom: A Handbook for Intermediate Math Teachers

This project addressed the need for more insightful, current, and applicable resources for intermediate math teachers in Canadian classrooms. A need for a handbook in this division seemed warranted by a lack of government resource support. Throughout an extensive review of the literature, themes and topics for the handbook emerged. The handbook was designed to not only provide educators with examples of effective teaching strategies within the mathematics classroom but to also inform them about the ways in which their personal characteristics and personality type could affect their students and their own pedagogical practices. Three teaching professionals who had each taught in an intermediate math class within the past year evaluated the handbook. The feedback received from these educators was directly applied to the first draft of the handbook in order to make it more accessible and applicable to other math teachers. Although the handbook was written with teachers in mind, the language and format used throughout the manual also make it accessible to parents, tutors, preservice education students, and educational administrators. Essentially, any individual who is hoping to inspire and educate intermediate math students could make use of the content within the handbook.

Emptying the bell jar: an exploration of adolescent responses to a women's literature unit /

This study examines adolescent student responses to a women's literature unit taught within a grade 12 Writer's Craft course. Current research (Gilligan, 1989, Pipher, 1994 & Slack, 1999) suggests that there is a great under-representation of female authors in the high school literature curriculum. The use of women's literature may draw attention to important literary figures who are historically overlooked within the curriculum. It gives voice to a marginalized group and presents students with alternative subjects and heroes. It encourages students to develop a critical perspective and reevaluate assumptions about institutions, ideologies, language and culture. It also allows me, as a teacher, to reflect on my own teaching practices and explore alternate feminist pedagogical principles and teaching styles encouraging multiplicity of voices, deconstruction of power relations, and alternative assessment tools within the classroom. As an educator, it is important for me to teach curriculum that is relevant and meaningful to students and help them become critical, self-reflective thinkers. It is also important for me to assist students in their exploration of self and encourage them to expand their awareness of historical, social and global issues. Sylvia Plath's (1963) The belljar is used as the primary text taught within this unit. In this novel, the bell jar is a central image that signifies entrapment and isolation. "To the person in the bell jar, blank and stopped as a dead body, the world itself is the bad dream"(p.l 54). As a metaphor, the bell jar resonates with young readers in a variety of ways.

Preparing to teach : learning from an exploration of teachers' experiences of teaching in classrooms of difference

This qualitative study explores practicing teachers' experiences of teaching in classrooms of diversity, that is, classrooms where students represent a variety of differences including race, culture, ethnicity, and class. More specifically, this study investigates the types of curricular and pedagogical practices teachers employ in their classrooms. This study attempts to make a contribution to the scholarship of critical pedagogy by drawing upon the works of critical pedagogues to make sense of participants' descriptions oftheir curricular and pedagogical practices. Four participants were involved in this study. Participants were elementary teachers in classrooms of difference in Ontario who contributed the primary sources of data by engaging in 2 individual interviews. Additional sources of data included a focus group meeting that 2 ofthe participants were able to attend, school board curriculum resource documents assisting teachers in teaching critically, as well as a research journal which the researcher kept throughout the study. The scholarship of critical pedagogy (Ellsworth, 1992; Giroux, 1993; McLaren, 1989) informs the analysis of participants' descriptions of their teaching experiences. Many of the participants did not engage in a practice of critical pedagogy. This study explores some of the challenges and possibilities of using critical pedagogy to create spaces in classrooms where teachers can build connections between the curriculum mandated by the government and the multiple identities and experiences that students bring into the classroom. This study concludes with a discussion on what teachers need to know to be able to begin creating equitable and educational experiences in classrooms of difference.

Accommodating College ESL Learner Communication Needs: Perceptions, Policies, and Practices

The purpose of this qualitative inquiry was to determine how the Practical Nursing and Pharmacy Technician programs in one southern Ontario community college could more effectively accommodate ESL learners' communication needs. The literature review examined (a) linguistic issues, such as language testing and second-language learning theories, (b) organizational matters, such as ESL curriculum and teacher training, and (c) affective issues, such as motivation for second-language learning, learning styles, and the student-teacher relationship. I gathered perceptual data from the programs' administrators, faculty members, and ESL learners. Eleven participants took part in individual interviews or a focus group session. The results suggest that ESL learners need assistance with discipline-specific vocabulary and cultural nuances. College ESL learners' weak communicative competence, together with misleading acceptance standards for ESL learners and limited support available to faculty members and to students, decrease opportunities for successful completion of the programs. The results point to re-assessment of the college's admission policies and procedures, program evaluation practices that consider the needs of ESL learners, discipline-specific language support, and strategies to enhance the ESL student-teacher relationship. The study highlights theory relating to ESL learners' self-perception and engagement, as well as the importance of including the voice of college ESL learners in educational research. The results suggest that despite ESL learners' perseverance in completing their studies, power imbalances remain. The college has yet to implement organizational strategies such as discipline-specific communications and ESL courses and extended language support that could meet the communication needs of ESL learners in the two programs.

The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

Transition into the teaching profession: induction and mentoring issues surrounding secondary music teachers /

The purpose of this study was to investigate the issues surrounding the transition into the teaching profession by specifically focusing on teacher induction and mentoring issues while explicitly addressing matters of concern by secondary music teachers in a large suburban school board in southern Ontario. Participants included beginning teachers with fewer than 5 years of teaching, mid career teachers with between 6 and 15 years of instruction, and experienced teachers with more than 16 years of practice. The ' processes of mentoring and inducting new teachers within the board were examined, along with their relationships between proteges, mentors, and administrators. Further, internal and external programs specifically designed and implemented for newer music teachers were scrutinized and discussed. An analysis of key documents and literature on the subject was performed, and data were collected through 16 personal interviews. The findings suggest that although the necessity of mentoring and induction processes has begun to be recognized, there exists a fundamental relationship between mentoring and induction and the effect of the professional attachments to mentoring; the institutional and administrative supports that are enabled; and essential processes and practices between mentors and proteges. Together these three arms combine to support successfiil induction and mentoring initiatives that will help ease the transition into teaching.

The impact of scheduling on the implementation of the new Ontario curriculum: teachers' perceptions /

This qualitative study explored secondary teachers' perceptions of scheduling in relation to pedagogy, curriculum, and observation of student learning. Its objective was to determine the best way to organize the scheduling for the delivery of Ontario's new 4-year curriculum. Six participants were chosen. Two were teaching in a semestered timetable, 1 in a traditional timetable, and 3 had experience in both schedules. Participants related a pressure cooker "lived experience" with weaker students in the semester system experiencing a particularly harsh environment. The inadequate amount of time for review in content-heavy courses, gap scheduling problems, catch-up difficulties for students missing classes, and the fast pace of semestering are identified as factors negatively impacting on these students. Government testing adds to the pressure by shifting teachers' time and attention in the classroom from deeper learning to a superficial coverage of material, from curriculum as lived to curriculum as text to be covered. Scheduling choice should be available in public education to accommodate the needs of all students. Curriculum guidelines need to be revamped to reflect the content that teachers believe is necessary for a successful course delivery. Applied level courses need to be developed for students who are not academically inferior but learn differently.

Web based content and hybrid teaching: student perceptions of the effectiveness of using web based content and hyper-linked teaching units in teaching hybrid business and marketing post secondary classes /

This exploratory, descriptive action research study is based on a survey of a sample of convenience consisting of 172 college and university marketing students, and 5 professors who were experienced in teaching in an internet based environment. The students that were surveyed were studying e-commerce and international business in 3^^ and 4*'' year classes at a leading imiversity in Ontario and e-commerce in 5^ semester classes at a leading college. These classes were taught using a hybrid teaching style with the contribution of a large website that contained pertinent text and audio material. Hybrid teaching employs web based course materials (some in the form of Learning Objects) to deliver curriculimi material both during the attended lectures and also for students accessing the course web page outside of class hours. The survey was in the form on an online questionnaire. The research questions explored in this study were: 1. What factors influence the students' ability to access and learn from web based course content? 2. How likely are the students to use selected elements of internet based curriculum for learning academic content? 3. What is the preferred physical environment to facilitate learning in a hybrid environment? 4. How effective are selected teaching/learning strategies in a hybrid environment? The findings of this study suggest that students are very interested in being part of the learning process by contributing to a course web site. Specifically, students are interested in audio content being one of the formats of online course material, and have an interest in being part of the creation of small audio clips to be used in class.

A classroom-based investigation of reciprocal teaching at the grade seven level

This study assessed the effectiveness of a reciprocal teaching program as a method of teaching reading comprehension, using narrative text material in a t.ypical grade seven classroom. In order to determine the effectiveness of the reciprocal teaching program, this method was compared to two other reading instruction approaches that, unlike rcciprocal teaching, did not include social interaction components. Two intact grade scven classes, and a grade seven teacher, participated in this study. Students were appropriately assigned to three treatment groups by reading achievement level as determined from a norm-referenced test. Training proceeded for a five week intervention period during regularly scheduled English periods. Throughout the program curriculum-based tests were administered. These tests were designed to assess comprehension in two distinct ways; namely, character analysis components as they relate to narrative text, and strategy use components as they contribute to student understanding of narrative and expository text. Pre, post, and maintenance tests were administered to measure overall training effects. Moreover, during intervention, training probes were administered in the last period of each week to evaluate treatment group performance. AU curriculum-based tests were coded and comparisons of pre, post, maintenance tests and training probes were presented in graph form. Results showed that the reciprocal group achieved some improvement in reading comprehension scores in the strategy use component of the tests. No improvements were observed for the character analysis components of the curriculum-based tests and the norm-referenced tests. At pre and post intervention, interviews requiring students to respond to questions that addressed metacomprehension awareness of study strategies were administered. The intelviews were coded and comparisons were made between the two intelVicws. No significant improvements were observed regarding student awareness of ten identified study strategies . This study indicated that reciprocal teaching is a viable approach that can be utilized to help students acquire more effective comprehension strategies. However, the maximum utility of the technique when administered to a population of grade seven students performing at average to above average levels of reading achievement has yet to be determined. In order to explore this issue, the refinement of training materials and curriculum-based measurements need to be explored. As well, this study revealed that reciprocal teaching placed heavier demands on the classroom teacher when compared to other reading instruction methods. This may suggest that innovative and intensive teacher training techniques are required before it is feasible to use this method in the classroom.

Teachers' perceptions of effects of terminal examinations on teaching and learning at the secondary school level in Zimbabwe

This study was particularly aimed at the examinations and the effect they have on schooling at the secondary school level in Zimbabwe. The views and opinions of teachers on the use of terminal examinations for certification and the influence they are seen to have on teachers' approach to the curriculum were examined. The literature has shown that there is widespread criticism of the justice and effects of terminal examinations. It is argued that they lead to an over-emphasis of that which is measured, knowledge and intellectual ability, at the expense of that kind of education progress which is almost impossible to measure in an end-of-the-course assessment. Three hundred and six secondary school teachers responded to a survey which asked for teachers' perceptions of examinations and the curriculum. The findings of this study indicated that teaching is structured towards examinations. Although teachers are trying to teach and develop reasoning skills and other activities, the pressure of examinations and the importance of doing well in them force teachers to restrict themselves to examination requirements.

Understanding the portfolio in the secondary school classroom

Four secondary school teachers were involved in this case study. Individual interviews, group reflective sessions, and participant portfolios were transcribed verbatim and analyzed. The use of the portfolio in the secondary school classroom was then discussed in relation to emergent themes. These themes included teacher attitude, portfolio structure, portfolio purpose, challenges, effect, and professional development. Teachers were able to individualize the portfolio structure to meet both program and students' needs. The portfolio structure enabled both teachers and students to assume control over the learning process. The portfolio informed teachers about their teaching. This, in tum, challenged them to reflect on their teaching practices and enabled them to redesign curriculum implementation. A collaborative professional development structure fostered a learning environment that enabled teachers to experience success, despite the challenges that they inevitably encountered. These findings were related to contemporary literature. Finally, implications for theory and practice related to portfolio use in the secondary school classroom and professional development for secondary school teachers were considered.