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.

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.

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.

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.

Investigating Formative Assessment: Exploring the Impact on the Self-Efficacy and Motivation of Mathematics Students

This is a study of the implementation and impact of formative assessment strategies on the motivation and self-efficacy of secondary school mathematics students. An explanatory sequential mixed methods design was implemented where quantitative and qualitative data were collected and analyzed sequentially in 2 different phases. The first phase involved quantitative data from student questionnaires and the second phase involved qualitative data from individual student and teacher interviews. The findings of the study suggest that formative assessment is implemented in practice in diverse ways and is a process where the strategies are interconnected. Teachers experience difficulty in incorporating peer and self-assessment and perceive a need for exemplars. Key factors described as influencing implementation include teaching philosophies, interpretation of ministry documents, teachers’ experiences, leadership in administration and department, teacher collaboration, misconceptions of teachers, and student understanding of formative assessment. Findings suggest that overall, formative assessment positively impacts student motivation and self-efficacy, because feedback is provided which offers encouragement and recognition by highlighting the progress that has been made and what steps need to be taken to improve. However, students are impacted differently with some considerations including how students perceive mistakes and if they fear judgement. Additionally, the impact of formative assessment is influenced by the connection between self-efficacy and motivation, namely how well a student is doing is a source of both concepts.

The effect of calculators on the numerical problem-solving skills and attitudes of primary students towards mathematics /

The purpose of this study was to determine the effect that calculators have on the attitudes and numerical problem-solving skills of primary students. The sample used for this research was one of convenience. The sample consisted of two grade 3 classes within the York Region District School Board. The students in the experimental group used calculators for this problem-solving unit. The students in the control group completed the same numerical problem-solving unit without the use of calculators. The pretest-posttest control group design was used for this study. All students involved in this study completed a computational pretest and an attitude pretest. At the end of the study, the students completed a computational posttest. Five students from the experimental group and five students from the control group received their posttests in the form of a taped interview. At the end of the unit, all students completed the attitude scale that they had received before the numerical problem-solving unit once again. Data for qualitative analysis included anecdotal observations, journal entries, and transcribed interviews. The constant comparative method was used to analyze the qualitative data. A t test was also performed on the data to determine whether there were changes in test and attitude scores between the control and experimental group. Overall, the findings of this study support the hypothesis that calculators improve the attitudes of primary students toward mathematics. Also, there is some evidence to suggest that calculators improve the computational skills of grade 3 students.

Perceptions of some teachers about the similarities and/or differences in teaching online versus in a classroom environment /

The introduction of computer and communications technology, and particularly the internet, into education has opened up some new possibilities for teaching and learning. Courses designed and delivered in an online environment offer the possibility of highly interactive and individually focussed teaching and learning experiences. However, online courses also present new challenges for both teachers and students. A qualitative study was conducted to explore teachers' perceptions about the similarities and differences in teaching in the online and face-to-face (F2F) environments. Focus group discussions were held with 5 teachers; 2 teachers were interviewed in depth. The participants, 3 female and 2 male, were full-time teachers from a large College of Applied Arts & Technology in southern Ontario. Each of them had over 10 years of F2F teaching experience and each had been involved in the development and teaching of at least one online course. i - -; The study focussed on how teaching in the online environment compares with teaching in the F2F environment, what roles teachers and students adopt in each setting, what learning communities mean online and F2F and how they are developed, and how institutional policies, procedures, and infrastructure affect teaching and learning F2F and online. This study was emic in nature, that is the teachers' words determine the themes identified throughout the study. The factors identified as affecting teaching in an online environment included teacher issues such as course design, motivation to teach online, teaching style, role, characteristics or skills, and strategies. Student issues as perceived by the teachers included learning styles, role, and characteristics or skills. As well, technology issues such as a reliable infrastructure, clear role and responsibilities for maintaining the infrastructure, support, and multimedia capability affected teaching online. Finally, administrative policies and procedures, including teacher selection and training, registration and scheduling procedures, intellectual property and workload policies, and the development and communication of a comprehensive strategic plan were found to impact on teaching online. The teachers shared some of the benefits they perceived about teaching online as well as some of the challenges they had faced and challenges they perceived students had faced online. Overall, the teachers feh that there were more similarities than differences in teaching between the two environments, with the main differences being the change from F2F verbal interactions involving body language to online written interactions without body language cues, and the fundamental reliance on technology in the online environment. These findings support previous research in online teaching and learning, and add teachers' perspectives on the factors that stay the same and the factors that change when moving from a F2F environment to an online environment.

Teacher survival : staying alive in the job of teaching /

This study presents information gathered during personal interviews with dynamic and capable teachers in the areas of preparedness for teaching, teaching concerns, survival skills and strategies, and how these teachers support themselves and others in the teaching profession. The data are related to Purkey and Novak's work on invitational education and connections are made to Combs' perceptual orientation. Potential participants were gathered through personal recommendations from their colleagues. All teachers recommended were approached and asked for voluntary participation. Of those who agreed to participate, 6 were selected based on gender and years of experience. There was a male and female participant at each of the following career levels: early, mid, and late. The 4 major survival skills that became apparent were the ability to believe in oneself and others, to act decisively upon that belief through personal and professional goal-setting as well as accessing resources, to actively seek opportunities for interaction with other professionals, and to celebrate personal and professional successes.

Teaching Principled negotiation skills to parents and their children : the impact of parental involvement /

This study explored the impact of training parents and children concurrently in principled negotiation skills for the purpose of developing negotiation skills and problem solving abilities in children. A second experimental group was utilized to determine the viability of negotiation skills training of junior elementary students for the purpose of improving problem solving and conflict resolving abilities. The student population in each experimental group was trained using The Program for Young Negotiators (Curhan, 1996). A control group was also established using the remaining grade four and five students attending the participating school. These students did not receive training as part of this study. Student group distribution was as follows: Experimental group 1 (students with parent participant) consisted of 10 (5 grade five and 5 grade 4 students), Experimental group 2 students without parent participant) consisted of 48 (20 grade 4 and 28 grade 5 students), and the Control group 3 (55 grade 4 and 5 students). The impact of training was measured using the Five Factor Negotiation Scale developed for use with the Program for Young Negotiators (Curhan, 1996). This measure was employed as a pre- and post-test questionnaire to the total student population, (113 students) to determine levels of ability in each of the key elements of negotiation, personal initiative, collaboration, communication, conflict based perspective taking, and conflict resolution approach (Nakkula & Nikitopoulos, unpublished). This measure has a coefficient alpha of .75 which is acceptable for this type of affective instrument. As well, open ended ability questions designed to measure ability, knowledge, and behaviour as they relate to negotiation skill application were given to the total student population, (113 students). Finally, journals were maintained by the students in both experimental groups, and informal feedback discussions were held with students and parents participating in the study.The intent of using both qualitative and quantitative measures was to provide an overall perspective of student abilities as they related to principled negotiation skills. While the quantitative measures were from the student perspective, more qualitative information was sought from parents and teachers through informal interviews, discussions, and use of confidential feedback cards. For analysis purposes, the ability questions were randomly selected for Experimental group 2 and Control group 3 in an effort to balance the groups more equitably with Experimental group 1. The findings of this study indicate that students of the junior elementary school age can be taught how to perceive conflict in a more constructive way. However, they are not as likely to use their skills when the conflict is with a sibling as they are with a peer, a teacher, or a parent. While no statistically significant differences between mean scores for Experimental groups 1 and 2 exist some subtle differences are noted. Overall, increases in mean scores for grade 4 students exceeded the increases for grade 5 students within Experimental group 1 . The implication being that younger students benefit more from having a parent trained in principled negoUation skills than older students. The skill level of a parent in principled negotiation can not be underesUmated. Without a consistent and effective role model the likelihood of developing student skill level to a point of automaticity is greatly reduced. Enough so that perhaps the emphasis should be placed on training parents more so than the students.

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.

Gender bias in the Trends in Mathematics and Science Study 2003 (TIMMS) for Canadian students /

This study is a secondary data analysis of the Trends in Mathematics and Science Study 2003 (TIMSS) to determine if there is a gender bias, unbalanced number of items suited to the cognitive skill of one gender, and to compare performance by location. Results of the Grade 8, math portion of the test were examined. Items were coded as verbal, spatial, verbal /spatial or neither and as conventional or unconventional. A Kruskal- Wallis was completed for each category, comparing performance of students from Ontario, Quebec, and Singapore. A Factor Analysis was completed to determine if there were item categories with similar characteristics. Gender differences favouring males were found in the verbal conventional category for Canadian students and in the spatial conventional category for students in Quebec. The greatest differences were by location, as students in Singapore outperformed students from Canada in all areas except for the spatial unconventional category. Finally, whether an item is conventional or unconventional is more important than whether the item is verbal or spatial. Results show the importance of fair assessment for the genders in both the classroom and on standardized tests.

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.

Why I am not a teacher: a self-study examining why I made the decision to exit the teaching profession /

A good teacher was once described as being like a candle; consuming itself to light the way for others (Author unknown). But as Knox (2005) says, far too many yoimg flames flicker out before they ever get the opportvmity to bum their brightest. This self-study explores the phenomenon of teacher attrition through the stories and lived experiences of one elementary teacher. I strive throughout this self-study to delve deeper into the significance of my story and lived experiences in order to enhance our understanding of why teachers exit the profession. As a result, the guiding question throughout the study is, "Why do teachers, particularly those who have only taught for a few years, leave the classrooms they worked so hard to enter?" Through the writing of a narrative entitled Sarah 's Story, I was able to identify and give voice to a story openly sharing the feelings of despair; disappointment, frustration and disillusionment. This study has identified areas of tension that lead to dissatisfaction, discontent, and teacher disillusionment. It confronts the issues of complexity, uncertainty, and conflict that are experienced in teaching. It discusses the puzzling, powerfiil and upsetting experiences, highlighting the importance of talk between all members of the education system.