Discipline-specific writing for business students: Research, practice and pedagogy

In the past few years strong arguments have been made for locating academic writing in higher education within the students’ disciplinary contexts in the belief that a full understanding of the role and dynamic of writing can only be achieved if it is examined as a social practice in its context of production. This chapter reports on a study that examined the conceptualisations of writing for business by a group of undergraduate and postgraduate lecturers and students at the business school of a British university. Based on a critical analysis of the literature reviewed for the study, and the data collected, the chapter contributes to existing writing pedagogy with a number of research-informed transformative pedagogical applications for teaching discipline-specific writing for business. Such applications which combine context-oriented practices (e.g. raising awareness of the role of disciplinary values in shaping writing) and text-oriented activities (e.g. discipline-specific referencing) aim at influencing the pedagogic agenda for teaching writing in higher education. The chapter concludes with questions for reflection and discussion that provide an opportunity for readers to reflect upon their own teaching environment.

Curriculum and beyond: Mathematics support for first year life science students

The move into higher education is a real challenge for students from all educational backgrounds, with the adaptation to a new curriculum and style of learning and teaching posing a daunting task. A series of exercises were planned to boost the impact of the mathematics support for level four students and was focussed around a core module for all students. The intention was to develop greater confidence in tackling mathematical problems in all levels of ability and to provide more structured transition period in the first semester of level 4. Over a two-year period the teaching team for Biochemistry and Molecular Biology provided a series of structured formative tutorials and “interactive” online problems. Video solutions to all formative problems were made available, in order that students were able to engage with the problems at any time and were not disadvantaged if they could not attend. The formative problems were specifically set to dovetail into a practical report in which the mathematical skills developed were specifically assessed. Students overwhelmingly agreed that the structured formative activities had broadened their understanding of the subject and that more such activities would help. Furthermore, it is interesting to note that the package of changes undertaken resulted in a significant increase in the overall module mark over the two years of development.

Challenges in the creation and development of a mathematics MOOC

The fast development of distance learning tools such as Open Educational Resources (OER) and Massive Open Online Courses (MOOC or MOOCs) are indicators of a shift in the way in which digital teaching and learning are understood. MOOC are a new style of online classes that allow any person with web access, anywhere, usually free of charge, to participate through video lectures, computer graded tests and discussion forums. They have been capturing the attention of many higher education institutions around the world. This paper will give us an overview of the “Introduction to Differential Calculus” a MOOC Project, created by an engaged volunteer team of Mathematics lecturers from four schools of the Polytechnic Institute of Oporto (IPP). The MOOC theories and their popularity are presented and complemented by a discussion of some MOOC definitions and their inherent advantages and disadvantages. It will also explore what MOOC mean for Mathematics education. The Project development is revealed by focusing on used MOOC structure, as well as the quite a lot of types of course materials produced. It ends with a presentation of a short discussion about problems and challenges met throughout the development of the project. It is also our goal to contribute for a change in the way teaching and learning Mathematics is seen and practiced nowadays, trying to make education more accessible to as many people as possible and increase our institution (IPP) recognition.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

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.

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.

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.

Learning and healing: a wellness pedagogy for Aboriginal teacher education /

During the last 30 years Aboriginal peoples in Canada have made steady progress in reclaiming the responsibility for the education of their young people, especially in primary and secondary school. In comparison the education and or training of adult populations has not kept pace and many socioeconomic and sociocultural indicators demonstrate a ' , continued confinement of those populations to the margins of the dominant society of Canada. It is the adults, the mothers and the fathers, the grandmothers and grandfathers, the aunties and uncles that are the first teachers of the next generation and the nature of these relationships replicates the culture of unwellness in each subsequent generation through those teachers. There are few examples in the Aboriginal adult education literatures that give voice to the educational experience of the Learner. This study addresses that gap by exploring the perspectives embedded in the stories of a Circle of Learners who are, or were enrolled in the Bachelor of Education in Aboriginal Adult Education program at Brock University. That Circle of 1 participants included 9 women and 1 man, 6 of whom were from various i Anishinabek nations while 4 represented the Hotinonshd:ni nations in southern Ontario. They are an eclectic group, representing many professions, age groups, spiritual traditions, and backgrounds. This then is their story, the story of the heaming and Healing pedagogy and an expanded vision of Aboriginal education and research at Brock University.

Adolescent girls and mathematics: classroom performance, attitudes toward mathematics and perceptions of parental attitudes /

The purpose of this study was to determine the extent to which gender differences exist in student attitudes toward mathematics and in their performance in mathematics at the Grade Seven and Eight level. The study also questioned how parents influence the attitudes of this grade level of male and female students toward mathematics. Historically, the literature has demonstrated gender differences in the attitudes of students toward mathematics, and in parental support for classroom performance in mathematics. This study was an attempt to examine these differences at one senior public school in the Peel Board of Education. One hundred three Grade Seven and Eight students at a middle school in the Peel Board of Education volunteered to take part in a survey that examined their attitudes toward mathematics, their perceptions of their parents' attitudes toward mathematics and support for good performance in the mathematics classroom, parental expectations for education and future career choices. Gender differences related to performance levels in the mathematics classroom were examined using Pearson contingency analyses. Items from the survey that showed significant differences involved confidence in mathematics and confidence in writing mathematics tests, as well as a belief in the ability to work on mathematics problems. Male students in both the high and low performance groups demonstrated higher levels of confidence than the females in those groups. Female students, however, indicated interest in careers that would require training and knowledge of higher mathematics. Some of the reasons given to explain the gender differences in confidence levels included socialization pressures on females, peer acceptance, and attribution of success. Perceived parental support showed no significant differences across gender groups or performance levels. Possible explanations dealt with the family structure of the participants in the study. Studies that, in the past, have demonstrated gender differences in confidence levels were supported by this study, and discussed in detail. Studies that reported on differences in parental support for student performance, based on the gender of the parent, were not confirmed by this study, and reasons for this were also discussed. The implications for the classroom include: 1) build on the female students' strengths that will allow them to enjoy their experiences in mathematics; 2) stop using the boys as a comparison group; and 3) make students more aware of the need to continue studying mathematics to ensure a wider choice of future careers.

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.

Exploring the impact of a hands-on intervention on grade 7 girls and their feelings about self, mathematics, science, technology and related careers

Forty-five 12- and 13-year-old females attending Grade 7 in North York, Ontario were randomly selected from a group of 100 females who had volunteered to participate in a oneday hands-on workshop called It's Your Choice at Seneca College. The goals of this intervention were to broaden the career horizons of these students and to help them realize the need to continue mathematics and science through high school in order to keep occupational options unlimited. The young women were given a pre- and post-attitude survey to provide background information. In the month following participation in the workshop the students were interviewed in small groups (S students per group) to discover their perceptions of the impact of the workshop. The interviews revealed that participants felt that after the workshop their feelings of self-confidence increased, specifically with respect to working with their hands. Participants felt more aware of the usefulness and importance of the study of mathematics, science and technology, They also felt that It's Your Choice increased their interest in careers in these domains and helped them to see that these careers are viable choices for females. The interviews also revealed that many of the participants felt that in this society their roles and their choices were influenced and probably limited by the fact that they are female.

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.

The Clemente Course in the Humanities and critical pedagogy : a comparative analysis of Earl Shorris and bell hooks on poverty, racism, imperialism and patriarchy

The Clemente Course in the Humanities is an anti-poverty intervention for adults who self-identity as "poor" and humanities instructors. The course was created in 1995 by journalist Earl Shorris, who based the curriculum on a Socratic method of pedagogy and the "great books" canon of Robert Hutchins. It began as a community-based initiative in urban US settings, but since 1997 Mayan, Yup'ik and Cherokee iterations have been created, as well as on-campus bridge courses for non-traditional students to explore college-level education in Canada and the USA. The course potentially conflicts with critical pedagogy because the critical theories of Paulo Freire and contemporary cultural studies reject traditional notions of both the canon and teaching. However, a comparison between Shorris' and bell hooks' theories of oppression reveals significant similarities between his "surround of force" and her "capitalist imperialist white supremacist patriarchy," with implications for liberal studies and critical pedagogy.

The formation of conscience : pedagogy of the sacred

This qualitative study explores Thomas Green's (1999) treatise, Voices: The Educational Formation of Conscience; for the purpose of reconstruing the transformative usefulness of conscience in moral education. Conscience is "reflexive judgment about things that matter" (Green, 1999, p. 21). Paul Lehmann (1963) suggested that we must "do the conscience over or do the conscience in" (p. 327). Thomas Green "does the conscience over", arguing that a philosophy of moral education, and not a moral philosophy, provides the only framework from which governance of moral behaviour can be understood. Narratives from four one-to-one interviews and a focus group are analysed and interpreted in search of: (a) awareness and understanding of conscience, (b) voices of conscience, (c) normation, (d) reflexive emotions, and (e) the idea of the sacred. Participants in this study (ages 16-21) demonstrated an active awareness of their conscience and a willingness to engage in a reflective process of their moral behaviour. They understood their conscience to be a process of self-judgment about what is right and wrong, and that its authority comes from within themselves. Narrative accounts from childhood indicated that conscience is there "from the beginning" with evidence of selfcorrecting behaviour. A maturing conscience is accompanied by an increased cognitive capacity, more complicated life experiences, and individualization. Moral motivation was grounded in " a desire to connect with things that are most important." A model for conscience formation is proposed, which visualizes a critical path of reflexive emotions. It is argued that schools, striving to shape good citizens, can promote conscience formation through a "curriculum of moral skills"; a curriculum that embraces complexity, diversity, social criticism, and selfhood.