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Tutor's feedback - 75% This is an astute, and often sophisticated, essay which makes its arguments cogently.One of its strengths is that you are making excellent use of citation both to support your points but also to move your argument along (for example, see double ticks on pp.
There is also significant independent reading to secure an original, thoughtful approach to the question Where to buy an mathematics report plagiarism free double spaced 24 hours US Letter Size 144 pages / 39600 words.There is also significant independent reading to secure an original, thoughtful approach to the question.
Though tendentious, the topic is broached with a real flair for critical analysis (one is well aware of the limits of Hampson's defence of Conrad through the paragraph on p.Your conclusion is deft, with a very strong sense of the complexity of the issues.
There is also the possibility, of course, that Conrad might identify with Marlow while at the same time undercutting his 'racism' not by expressing alternative perceptions but by plotting (see Peter Brooks, READING FOR THE PLOT as one way into this; Toni Morrison's PLAYING IN THE DARK is another take on Achebe's position) Think about what we have covered in the section on Critical writing and ask yourself how these essays fit with this guidance. How easy is it to follow the student's .There is also the possibility, of course, that Conrad might identify with Marlow while at the same time undercutting his 'racism' not by expressing alternative perceptions but by plotting (see Peter Brooks, READING FOR THE PLOT as one way into this; Toni Morrison's PLAYING IN THE DARK is another take on Achebe's position).Second year student: international Security essay Discuss with examples how and why major international actors have been perceived as failing the victims of genocide pdf 98 KB Tutor's Feedback - 73% This is a well structured and fluently written essay with a clear argument, well done.The examples are appropriate and the evidence and quotations you have chosen highlight your argument well .The examples are appropriate and the evidence and quotations you have chosen highlight your argument well.You could do more to say specifically why Bosnia, Rwanda and Armenia are cases of genocide at the start of the essay ? perhaps compare them against the UN Convention.
You say they are all cases of genocide, but are they all exactly the same? Are there any differences between them that are of importance when considering outsiders' failure to prevent/end them? To push your argument further, think about the reasons why major international actors fail the victims of genocide: you give a few reasons, such as political and economic interests, reputation, the desire to avoid costly and indeterminate conflicts, UN bureaucratic inertia and so on.Could you systematise these at all? Are the reasons the same in each case, such that you can make a general claim, or does it vary case by case? In the bibliography, make sure you give the publisher of books.Second year student: Issues in Contemporary Anthropology essay Explore the meaning of 'radical evil' and the 'banality of evil' and how they might relate to understandings of evil using the cases of Idi Amin and Adolf Eichmann pdf 50 KB Tutor's Feedback - 75% Deals confidently with very complex issues (Arendt's 'banality of evil' vs Zizek's 'radical evil').Focuses on Leopold's work, but extends it considerably.Rather longer than expected, but a well constructed argument, and generally well written (however p.
2 'Disobeying orders was not an option for Eichmann.As a result conveying their agency the other Nazi officials do not qualify as banal' is unclear & may misrepresent Arendt's argument p.3 some confusion over Pottier's & Leopold's position.Interesting and original attempt to compare Arendt's analysis with Zizek's in relation to Amin.
The conclusion needs more explanation about what is meant by 'everyday understandings of one refers to with the word in the on a daily basis' (sic) (Shame to have such a typo in the final sentence!).Nevertheless, a very good, thoughtful and original argument.Third year student: English literature essay Laurence Sterne and the Erotic: The Depiction of Sensibility in ‘A Sentimental Journey' pdf 99 KB Tutor's Feedback - 73% Yours is a beautifully clear essay.You write very well, and your prose is delightful to read.You've also done your research and it shows.
There is a remarkable lack of vagary about society or feminism in your piece, and you've picked canny quotes from your secondary sources that elucidate and situate your arguments.You've also located some wonderfully specific quotations from your primary source to support your argument that Hardy's narrator sympathises with Tess.Some of your close readings are wonderfully astute, as when you point out that Tess implores Angel, rather than commanding him.Slightly less persuasive is your assertion that Tess is the victim of Alec's eyes; I suspect you might have found better quotations, descriptions, or incidents denouncing Alec's gaze.You are clearly very good at pursuing and proving an argument.
I encourage you to be a bit more experimental in your next essay; perhaps choose a less straightforward topic and see where it takes you.Please see penciled notes throughout on shortening sentences and watching for comma splices (please look this term up in a style manual if it is unfamiliar).Second year student: Biomedical science essay Discuss the new insights in the understanding of Haemolytic Uraemic Syndrome and its worldwide implications following the large scale outbreak of E.Coli O104:H4 diarrhea in Germany 2011 pdf 680KB BSRLM Contents University of Southampton, UK Assessment is an essential process for gathering information about students’ learning and achievement.This process should be integrated with learning and teaching to establish ways for teachers to understand their students’ learning and make informed decision about their instruction.
In this paper, our focus is on a new approach to mathematics assessment in Saudi Arabia, which has been implemented recently.The new assessment approach is essentially a criterion-referenced assessment which aims to support students’ learning rather than measuring their progress solely.It is employed more as part of the students’ learning process.We explain why the new assessment approach is introduced, what it is, and how teachers deal with it.Moreover, we also discuss the challenges and implications of implementing new assessment approaches to mathematics teachers, educators and policy makers.
Stockholm University The Programme of International Student Assessment (PISA) and Trends in International Mathematics and Science Study (TIMSS) create much international interest in those countries perceived as high achieving.One such system, rarely acknowledged, is Flanders, the Dutch-speaking region of Belgium.In this paper I present the results of focused analyses of four sequences of video-taped mathematics lessons taught to students aged 10 to 14 years.These confirmed a mathematics education tradition drawing on two well-known curricular movements.The first presents mathematics as a Bourbakian set of interconnected concepts.
The second exploits realistic problems in its presentation of mathematics.University of Oxford; *London South Bank University We focus on a ‘typical’ task in which students have to give a functional generalisation in algebraic form of a growing sequence of spatial structures.We analyse the contribution of this task to a coherent knowledge of functions.Despite a plethora of research about misconceptions and the teaching of functions, little is known about the overall growth of students’ understanding of functions throughout schooling.We aim to map the development of students’ understanding of concepts which contribute to understanding functions in two different curriculum systems: the UK and Israel.
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The research uses a survey instrument that was developed in collaboration with a group of teachers and the task for this paper is one of six that span several routes to understanding functions.Our data appears to contradict some other studies as well as to suggest conjectures about how students’ willingness to use covariational reasoning depending to some extent on task features.University of Southampton Enhancing ways of developing students’ algebraic expertise remains an important focus for research Helpful Teacher Recommendations What are US Colleges Looking nbsp.University of Southampton Enhancing ways of developing students’ algebraic expertise remains an important focus for research.
This paper reports on a design research study which involved a digital intervention for 17-18 year old students, implemented in nine schools in the Netherlands (N=324).For the intervention, algebra tasks for the conceptual and procedural components of algebraic expertise were placed in a sequence based on three design principles: (i) ‘crisis’ items that intentionally questioned the use of standard algorithms, (ii) feedback provided by the digital system, and (iii) the ‘fading’ of feedback during the sequence to increase transfer The University of Oxford is one of the leading universities in the world. A report on the recent Queer Modernism(s) Conference held in Oxford · book .
For the intervention, algebra tasks for the conceptual and procedural components of algebraic expertise were placed in a sequence based on three design principles: (i) ‘crisis’ items that intentionally questioned the use of standard algorithms, (ii) feedback provided by the digital system, and (iii) the ‘fading’ of feedback during the sequence to increase transfer.
Data collected included results from student pre- and post-tests, questionnaires, and scores and log files of their digital work The University of Oxford is one of the leading universities in the world. A report on the recent Queer Modernism(s) Conference held in Oxford · book .Data collected included results from student pre- and post-tests, questionnaires, and scores and log files of their digital work.Results from the study show that the intervention was effective in improving algebraic expertise, and that the aforementioned design principles have merit.This paper reports on the effects and illustrates the design principles through a case example.The intervention shows a significant effect in improving algebraic expertise.
It shows that well-thought-out design principles augment learning.
The paper fits in a broader discussion on how to integrate algebraic expertise and ICT use in the classroom through the use of educational design.Department of Education and Professional Studies, King’s College London This paper concerns a philosophical, but highly practical, issue arising at the interface between mathematics and education, and I claim that mathematics education offers insights where mathematical philosophy has ground to a halt.More specifically it concerns the two related but distinct concepts of how-many-ness (alias quotity) and rank order, whose separate identities are traditionally obscured by the language of ‘number’.(Sometimes they are called ‘cardinal number’ and ‘ordinal number’.More often they are wrapped up together as ‘natural number’.
) The teacher of young children has the advantage over the philosopher that she works with people before they have acquired all the prejudices of their native language, and we shall build on the analysis of counting by Gelman and Gallistel (1978), concluding that ‘natural number’ as normally conceived is something of an illusion, for only quotity has the properties expected of ‘number’, while rank order is a mere quality.St Angela’s College, Sligo; Stranmills University College, Belfast; St Angela’s College, Sligo Teacher-facilitated “math talk” in the early years significantly increases children’s growth in understanding of mathematical concepts (Klibanoff et al.Although young children may have a beginning understanding of early number concepts, they often lack the language to communicate their ideas.Teacher modelling and fostering of mathematical language throughout the day and across various subject areas, allows children to articulate their ideas and communicate their understanding.
Encouraging “math talk” in young children as they explain, question and discuss their strategies is important.The teacher plays a significant role in guiding children to make connections, to recognise how their thinking relates to key mathematical number concepts and to make further conjectures and generalisations.This paper will outline the theoretical perspectives underpinning the development of a resource of key vocabulary and teaching and learning strategies for teachers to support their planning and teaching in early number.National Curriculum Development Centre, Kyambogo, Kampala, Uganda The Ugandan secondary school mathematics curriculum was established in colonial times to serve a small, select minority of academic high-achievers, and it is delivered with a ‘dominant pattern of expository, whole-class teaching’ (Centre for Global Development through Education 2011).But following the introduction, in 1997 and 2007, of Universal Primary and Secondary Education Policies the curriculum has become increasingly irrelevant and inaccessible to the majority of learners.
How can mathematics education be reformed to make it more appropriate to the modern Ugandan context, with large, mixed-ability classes and very limited resources? In an effort to increase access and improve learners’ performance in the first four years of secondary education, the Ugandan National Curriculum Development Centre is developing a new mathematics curriculum with a range of materials that encourage alternative teaching and learning strategies using low-cost, locally-available resources.These have been trialled in urban, peri-urban and rural secondary schools, where lessons have been observed and learners’ work has been collected and analysed.The trials indicate that learners may be more willing to adopt a new approach when the tasks are novel and unfamiliar.When they are associated with established mathematical knowledge and techniques, pedagogical change may be more difficult to establish.Institute of Education, University of London I report on a small-scale study rooted in the UK context that was conducted with eight volunteers from a cohort of PGCE secondary mathematics students (participants).
The participants’ own understanding of the square root concept and use of the associated symbol were explored and the findings revealed that they may not possess adequate subject knowledge about and for teaching this concept.Access to instructional materials, mainly textbooks and discussions with other more experienced teachers were identified as the main external sources consulted by the participants in order to refresh their knowledge of the square root concept.During this study, those participants who became aware of the shortcomings of their conceptual understanding of the square root felt, at first, uncomfortable with modifying their personal knowledge and their long held beliefs about this concept.Group discussion helped most of the participants become aware of connections between their more advanced knowledge of mathematics and the square root concept.Such awareness empowered the participants to clarify this concept for themselves and critically scrutinise the (re)sources available.
A tension between employing their modified knowledge about the square root and adherence to the widely accepted view about this topic in school mathematics has also been identified.Malm University Similar to other curricula, the Swedish mathematics curriculum emphasises problem solving both as an end in itself and as a means to becoming a competent citizen.Thus, a goal for mathematics is the creation of a problem-solving citizen.In this paper, I explore how critical discourse analysis, and parts of social activity theory can be used to operationalise Bernstein’s pedagogic device in relation to the construction of the problem-solving citizen.It is proposed that critical discourse analysis can be used for a linguistic analysis of official documents, like the curriculum whilst social activity theory’s different domains, mainly public and esoteric, can be used to analyse the national tests.
These tests assess students’ problem solving both as a means and an end in two different senior secondary programmes, an academic orientated one and a vocational one.In this exploration, two examples are given to show how these methodological tools can be used.University of Nottingham, UK This study of recent school-leavers in Further Education explores students’ opinions of relevance and how these are influenced by their experiences of different mathematics curricula in school and college.These vocational students are taught mathematics as a functional ‘tool for life’ rather than a discipline of rules.Perceptions of relevance are influenced by personal goals and interests (Ernest, 2004) and may depend on whether students identify a value for the qualification, a practical usefulness or some transferable skills (Sealey and Noyes, 2010).
These can provide reasons for studying mathematics but, in this study, students who encountered mathematics as a ‘tool for life’ engaged in learning experiences that connected with their personal life experience.This changed their conceptual view of mathematics and added a different perspective to their views of relevance.The research is part of a larger study of the student experience of functional mathematics in colleges but this paper will focus on qualitative data from student focus groups and lesson observations.Transcriptions were coded and compared to identify common themes in student experiences.
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The results suggest how teaching mathematics as a ‘tool for life’ can influence perceptions of relevance and effect some positive changes in student attitudes.
Manchester Metropolitan University Since 2003, staff at Manchester Metropolitan University (MMU) have been involved in a number of projects related to Realistic Mathematics Education (RME).This originally involved trialing materials with 11-14 year olds and then, in collaboration with the Freudenthal Institute, writing materials for Foundation level GCSE Help me with an mathematics report Editing British Standard single spaced.This originally involved trialing materials with 11-14 year olds and then, in collaboration with the Freudenthal Institute, writing materials for Foundation level GCSE.
In 2012, these materials were published by Hodder Education as a series of books called Making Sense of Maths.Classroom trials of the original materials showed an increased willingness of students to discuss and engage with their mathematics, and to attempt to ‘make sense’ of what they were doing rather than simply to try to remember taught procedures.The results from the trials led, in 2009, to a further project designing materials for Higher level GCSE The teaching of mathematics at Cambridge University is considered in the There was very real pressure on editors to ensure their journals covered at least On August 18th the Council agreed that each month the College would buy mathematics and mathematics education were the journal's primary scientific focus..
The results from the trials led, in 2009, to a further project designing materials for Higher level GCSE.
The focus here is on the development of these materials, and how we have interpreted the original design principles of RME for UK schools how to order a calculus presentation Academic double spaced British.The focus here is on the development of these materials, and how we have interpreted the original design principles of RME for UK schools.In particular, we focus on the use of context, the notion of progressive formalisation and the use of models camin.ir/presentation/how-to-order-a-calculus-presentation-academic-double-spaced-british.In particular, we focus on the use of context, the notion of progressive formalisation and the use of models.We provide excerpts from the materials that exemplify these principles and discuss the issues for teachers attempting to integrate this approach into an examination driven curriculum.Liping Ding, Keith Jones*, Birgit Pepin** and Svein Arne Sikko** S r-Tr ndelag University College, Norway and Shanghai Soong Ching Ling School, China; * University of Southampton, UK; ** S r-Tr ndelag University College, Norway We report on one component of a study of school-based teacher professional development (TPD) in Shanghai, China.
Here we focus on an experienced primary teacher who is teaching the topic of angle measurement to 10 year-olds.
Using data from the teacher’s original lesson plans, her modified lesson plans, together with an expert teacher’s advice and the teacher’s reflections on her lesson design, we illustrate how the support of an expert teacher enabled the teacher to improve her instructional practice.This was by supporting her in thinking explicitly about the traditional classroom practice with which she was familiar and in building her ‘wisdom of practice’ within the context of instructional reform taking place in China.Education School, University of Southampton This report leads from findings of an earlier research project in which pre-service mathematics and science teachers identified areas where they felt they needed greater support during their training year.In September 2011 a closed group was set up on the social network site Facebook as a support mechanism for a cohort of pre-service secondary mathematics teachers.The rationale was that the Facebook group, which was established as a ‘secret staffroom’ would provide a common, yet secure area where the pre-service teachers could share ideas and resources as well as engage in discussion about their progress on the course.
Analysis of the data collected from the interactions that took place identifies the frequency and ways in which the social network site has been used during their training year and first year of teaching.These findings are contrasted with the results of a series of attitudinal questionnaires completed by the participants at various stages of these two years.The results indicate that Facebook can be used to support pre-service teachers; however there remains a challenge in using social networking to support teachers in their first year of teaching and beyond.Department of Curriculum and Teaching, Faculty of Education, University of Calabar, Calabar, CRS, Nigeria This paper focuses on the interactive development of junior secondary three (JS3) students’ knowledge and performance in Pythagoras theorem using project-based learning skills (collaboration and critical thinking).The purpose therefore, is to acquaint the students with the necessary mathematical skills that enrich their knowledge of formation and solution of Pythagorean triple triangles.
A non-equivalent pre-test post-test quasi-experimental design was used on a sample of 280 JS3 students from two private and two public schools to ascertain the knowledge level and cognitive achievement before and after exposing them to project-based learning strategy.Special lesson plans were developed and the teachers were trained on the use of this strategy.Mean scores, standard deviations and dependent t-tests were used to analyse the data.It was discovered that students’ performance was enhanced and they were able to construct and solve Pythagorean triple triangles easily and quickly.
Recommendations were made based on these findings.University of Nottingham, The Joseph Whitaker School, Rainworth, Toot Hill School, Nottingham The benefits of learning mathematics by comparing, reflecting on and discussing multiple approaches to a problem are well-known (Silver, 2005).However, teachers using non-routine problem-solving tasks designed to encourage multiple approaches face challenges: understanding how pupils make sense of the problem, especially when pupils use unique or unanticipated approaches and helping pupils make connections between disparate approaches and aligning these with lesson goals.In an attempt to address such challenges an extensive set of problem solving lessons were developed.Each lesson includes a range of sample solution-methods that expose pupils to multiple perspectives.
A detailed teacher guide supports each lesson.This paper focuses on the use of these sample solution-methods.It explores their development from initial design to final versions.We analyse the varied interpretations and use made of sample solution-methods, in both US classrooms and by two UK teachers, and reflect on how these interpretations align with the designers’ intention.Nottingham Trent University The purpose of this study was to discover the individual and distinct ways in which each student teacher understands fractions and their strategies for working with them.
A phenomenographical approach was adopted in order to provide insight into each student teacher’s subject knowledge of fractions.This study involved detailed scrutiny of six self-selected small groups, which enabled a range of rich and honestly reflective data to be collected.Groups undertook two collaborative tasks involving the sequencing of fractions by magnitude, followed by reflective interviews.Each group also undertook a diagnostic interview, considering a range of questions, which they had ordered in terms of their perceived difficulty.A constructivist perspective was adopted giving students the opportunity to reconstruct their own understanding of fractions through the explanation and discussion of their existing ideas.
A range of successful strategies was demonstrated, especially the use of mathematical anchors and the use of residual or gap thinking as a means of comparison.Improper fractions and reunitising were the main difficulties cited by many in the group.A common assumption was that there was a particular ‘correct’ method to be adopted.The study helps to identify misconceptions that can be addressed within teacher training.School of Education, University of Nottingham It is now almost 40 years since Skemp’s (1976) seminal division of understanding into ‘instrumental’ and ‘relational’ categories, yet the current political direction of mathematics education in the UK is decidedly towards the traditional teaching of ‘standard algorithms’ (DfE, 2013).
In this research paper, I draw on a lively staffroom discussion about different approaches to the teaching of quadratic equations, in which one method used was derided as ‘a trick’.From this, I discuss reasons why certain mathematical processes are often regarded as inherently and irretrievably ‘procedural’.Informed by recent theoretical interpretations of procedural and conceptual learning in mathematics, which increasingly stress their intertwining and iterative relationship (Star, 2005; Baroody, Feil and Johnson, 2007; Star, 2007; Kieran, 2013), I make a case that stigmatising particular methods and censoring their use may deny students valuable opportunities to make sense of mathematics.
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I argue instead that encouraging students to take a critical stance regarding the details and the value of the procedures that they encounter can cultivate in them a deeper awareness of mathematical connections and a more empowered sense of ownership over their mathematics.King’s College London, Durham University* In this paper we report on the intervention phase of an ESRC-funded project, Increasing Competence and Confidence in Algebra and Multiplicative Structures (ICCAMS).
The intervention was designed to enable teachers to use formative assessment in mathematics classrooms by evaluating what students already knew, then adapting their teaching to students’ learning needs Who can help me write an report mathematics A4 (British/European) Academic single spaced 5 days.The intervention was designed to enable teachers to use formative assessment in mathematics classrooms by evaluating what students already knew, then adapting their teaching to students’ learning needs.
A key feature was the use of models and representations, such as the Cartesian graph, both to help students better understand mathematical ideas and to help teachers appreciate students’ difficulties.Twenty-two teachers and their Year 8 classes from 11 schools took part in the intervention during 2010/11 16 May 2018 - review paper is to review research on teaching mathematics learning in pedagogy By admin redy_articles academic report, anatomy report, anatomy report Choice can how to purchase college humanities thesis Premium where to find custom writing assistance geology homework Premium Junior.Twenty-two teachers and their Year 8 classes from 11 schools took part in the intervention during 2010/11.Pre- and post-tests in algebra, decimals and ratio were administered to the students of these classes, and compared to a control group of students matched from the ICCAMS national longitudinal survey (using propensity score matching) 16 May 2018 - review paper is to review research on teaching mathematics learning in pedagogy By admin redy_articles academic report, anatomy report, anatomy report Choice can how to purchase college humanities thesis Premium where to find custom writing assistance geology homework Premium Junior.Pre- and post-tests in algebra, decimals and ratio were administered to the students of these classes, and compared to a control group of students matched from the ICCAMS national longitudinal survey (using propensity score matching).The students in the intervention group made greater progress than the matched control.
2University of the Witwatersrand, Johannesburg, 3University of East London, 4University of Manchester, 5Liverpool Hope University We report survey data collated from past Mathematics Enhancement Course (MEC) students.The survey is part of a larger project involving three UK institutions offering the MEC, a UK-based government initiative to address the shortage of secondary mathematics-teachers: whereby non-mathematics graduates enter the teaching profession via a subject enhancement course.We have reported qualitative aspects of this route (Adler et al.Here we discuss the survey conducted to ascertain MEC graduate’s experiences of appointment, retention and progression, and our interpretation of this as to whether the MEC with its particular focus on understanding mathematics in-depth is ‘fit for purpose’.We asked ex-MEC students from three institutions to respond to an on line survey and 118 participated.Findings include that a large majority (100/118) secured and retained teaching posts, with some progressing in their positions in schools.Our study of subject enhancement courses as an alternative route into teaching emerges at a critical juncture given the cultural and political scepticism concerning such routes and their longevity in the current UK education climate.Institute of Education, London We draw on analysis of assignments by primary teachers as part of the assessment for the Mathematics Specialist Teachers programme (MaST).
In the assignment teachers are asked to work on some mathematics themselves, write up the mathematical part of their work then write about how this experience has impacted on their practice as a primary teacher.We focus first on case studies of teachers who included algebraic work in the first part of their assignments and look at what they say about the connections between this and their practice as primary teachers.Connections are made in a range of ways, but an overall finding is that teachers tended to focus more on the process of doing mathematics and the consequences this had for their practice rather than knowing mathematics.A further theme was feelings about mathematics, entailing positive consequences for practice, even where the initial feelings included negative dimensions.Examination of assignments on other aspects of mathematics confirms the presence of these three themes.
Across all the assignments there was strong evidence that this experience of doing mathematics impacted positively on how teachers worked mathematically with their primary classes.Irem Egwu Igiri*, Anne Ndidi Meremikwu, Emmanuel E.Asim Primary Education Studies Department, Federal College of Education, Obudu, Cross River State, Nigeria*, Faculty of Education, University of Calabar, Calabar, Cross River State, Nigeria.The study was designed to investigate the influence of classroom environment variables on mathematics achievement of junior secondary schools students in Cross River State, Nigeria.
It was a survey research involving 1200 Junior Secondary 2 (JS2) students from 48 secondary schools in Cross River State.A valid and reliable achievement test and questionnaire were used for data collection, while multiple regression analysis technique was used to analyse the data.The research findings indicated that: there is a significant individual and combined prediction effect of the classroom environment variables on students’ mathematics achievement; twenty-seven (27) out of the thirty-six (36) paths in the hypothesised recursive model are significant at .Based on the findings, it was concluded that classroom environment variables significantly influence students’ mathematics achievement in secondary school.
It was recommended among others that teachers and school counsellors should educate the students on the need to establish a good relationship with teachers and themselves in the classroom in order to improve their performance.Also, classrooms should be furnished and equipped to enhance effective teaching and learning.University of Nottingham and The Trinity Catholic School, Nottingham It is well recognised that professional development research often struggles to demonstrate that changes in a teacher’s practice are as a result of a professional development initiative (e.One reason is that teachers are influenced by a ‘patchwork’ of learning opportunities and it is sometimes impossible to pick out how, and to what extent, each opportunity may have contributed to these changes.The research reported here was a joint effort between a mathematics teacher and a researcher.The paper, which draws on ‘research conversations’ between the authors, explores what counts as professional development for this teacher and describes his patchwork of professional development in terms of the processes in which he engages within his professional practice: exploring, experimenting and reflecting; mainly within the context of teaching but also more widely.We argue that critical reflection is crucially important within professional development, but so too is appropriate action to carry exploring and experimenting through to real development.Graduate School of Education, University of Exeter Research has shown that pupils and many adults have intuitions about probability that are often at odds with accepted probability theory.
Drawing on the literature on probabilistic reasoning, effective pedagogical approaches and the use of technology tools, our aim is to examine the relationship between students’ talk together, their use of TinkerPlots software and the development of their reasoning about uncertain outcomes.In this paper we report on findings from the first iteration of a design study conducted in an afterschool club for Year 7 students in Exeter.More specifically we describe the trajectory of two students making conjectures about the fairness of some games involving combined events, testing and revising their initial theories based on simulation data.Our analysis shows that these students’ use of dialogic talk in combination with the technology leads to a shift from intuitive reasoning to probabilistic reasoning.Institute of Education, London Debate about the interplay between social and individual aspects of mathematics teaching and learning remains at the cutting edge of theoretical understanding of mathematics education research.
In trying to make sense of the insights of these divergent perspectives I ask: How is it that social reality exists? What are the merits and limitations of considering the students in our classrooms as only collections of individual minds, in contrast with perspectives that posit the primacy of the social in determining the identity of mathematics learners? Can each be accorded its relative legitimacy in a rigorous and rational manner? Recent developments in analytical social theory may have the potential to address this issue productively.This paper covers the conflict between social-constructivist and socio-cultural perspectives in the literature and the critical role of inter-subjectivity in communicating mathematics through interaction.The paper concludes by drawing on Searle’s notion of collective intentionality to address the networking and complementary use of theories based in cognitive science and critical theory and the interplay of the individual and social in school mathematics.University of East Anglia, *University of Cambridge The study we report builds on previous research conducted by Nardi, Biza and colleagues, which examined mathematics teachers’ considerations of what makes a claim an acceptable mathematical argument in the secondary classroom.We identify teachers’ considerations in their written responses to tasks and then in semi-structured interviews that probe these written responses.
Here we present data from six teachers and one such task, a (GCSE-level) Algebra Task.The tasks we invite the teachers to engage with, of which the Algebra Task is one, are structured as follows: a mathematical problem that students are likely to encounter in typical secondary mathematics lessons; fictional student responses to the problem (grounded on student responses found by relevant research as typical); and, an invitation to teachers to solve the problem, consider the purposes of its use in the lesson, reflect on the student responses and describe the feedback they would provide to the students.
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So far, we have proposed a theoretical tool for analysing mathematics teachers’ warrants for the preferences they express in their written responses and the interviews.The tool is based on our adaptation of Toulmin’s model of argumentation in which we classify teachers’ warrants according to pedagogical, epistemological and institutional considerations.Trinity College Dublin Since 2010 there has been a phased introduction of a new post-primary mathematics curriculum in Ireland entitled ‘Project Maths’ Publications About Dulwich College.
Trinity College Dublin Since 2010 there has been a phased introduction of a new post-primary mathematics curriculum in Ireland entitled ‘Project Maths’.
This new curriculum places a greater emphasis on problem solving and on an investigative approach for students.This implies not only changes in the curriculum content, but also changes to teaching and learning approaches within the classroom 2 Apr 2012 - Editors: Mike Robinson, Neil Challis and Mike Thomlinson Education Academy Maths Stats and Operational Research Subject Network, and the Heads of In Chapter 5 we report on student and staff views of teaching, both in career considerations are primary in coming to university in the first place, .This implies not only changes in the curriculum content, but also changes to teaching and learning approaches within the classroom.This research aims to provide teachers with a school-based professional development structure through which they can engage with the curriculum and attempt new teaching and learning strategies.This structure involves mathematics teachers engaging in lesson study as a professional development intervention and is investigated in two schools (phase 1 and phase 2 of Project Maths).
Teachers engage in lesson study cycles repeated throughout the academic year and the research questions how effective an approach this may be in encouraging teachers to engage with and implement a new centralised mathematics curriculum .
Teachers engage in lesson study cycles repeated throughout the academic year and the research questions how effective an approach this may be in encouraging teachers to engage with and implement a new centralised mathematics curriculum.
The research also investigates how effective an approach this may be in developing teachers’ pedagogical practices.In this paper, initial findings will be discussed from teacher research meetings and interviews.University of Witwatersrand, Johannesburg; University of Witwatersrand and Kings College London Learning mathematics-for-teaching (MfT) involves revisiting school mathematics and learning new mathematics.The notion of revisiting is operationalised and exemplified within pre-service secondary mathematics teacher education, specifically a financial mathematics course.A framework for MfT was developed consisting of nine interrelated aspects of teachers’ mathematical knowledge, and provided an analytic tool for exploring opportunities to learn MfT within the course.
These opportunities are exemplified through a revisiting task where pre-service teachers (PSTs) were required to make sense of learners’ responses to a compound growth task.The learners’ responses provided a springboard for learning other aspects of MfT of compound growth such as essential features, modelling and applications, and knowledge of context.The decompressed nature of the learners’ responses opened opportunities for PSTs to reconsider their own knowledge of compound growth, of the mathematics that underpins the formula, the process to obtain the formula and thus the way in which the formula models compound growth in different contexts.Manchester Institute of Education, University of Manchester We here add to the sparse literature on the use of Lesson Study (LS) in initial teacher education (ITE), reporting how LS can mediate development of reflective practice (RP).A cohort of 50 student-teachers, all secondary mathematics postgraduates, were involved in lesson study subgroups: planning, teaching-and-observing, analysing and reflecting on observations, and re-teaching.
Each study group worked on their own LS in selected schools with teachers/school based mentors that had some previous experience of lesson study.We tutors/researchers/authors observed the planning, teaching and post-lesson analyses, and one of us interviewed selected participants.Two main findings were: (i) the significance of imagination for reflective practice, here prompted by the focus on improving and ‘re-teaching’ the lesson; and (ii) the importance of the ITE-peer group and its relations with more powerful others (mentors and tutors) to development.We conclude that LS may complement and even ‘lead’ the development of reflective practices of student teachers, providing a Zone of Professional Development.Nottingham Trent University This research explored assessment and e-assessment in undergraduate mathematics and proposed a novel, partially-automated approach, in which assessment is set via computer but completed and marked offline.
This potentially offers: reduced efficiency of marking but increased validity compared with examination, via deeper and more open-ended questions; increased reliability compared with coursework, by reduction of plagiarism through individualised questions; increased efficiency for setting questions compared with e-assessment, as there is no need to second-guess the limitations of user input and automated marking.Implementation was in a final year module intended to develop students’ graduate skills, including group work and real-world problem-solving.Individual work alongside a group project aimed to assess individual contribution to learning outcomes.The deeper, open-ended nature of the task did not suit timed examination conditions or automated marking, but the similarity of the individual and group tasks meant the risk of plagiarism was high.Evaluation took three forms: a second-marker experiment, to test reliability and assess validity; student feedback, to examine student views particularly about plagiarism and individualised assessment; and, comparison of marks, to investigate plagiarism.
This paper will discuss the development and evaluation of this assessment approach in an undergraduate mathematics context.Patrick’s College, Dublin City University The Irish Primary Mathematics Curriculum consists of five content strands, namely Number, Algebra, Data, Measure and Shape and Space (Government of Ireland, 1999).Children engage with material from all strands throughout their primary education.Thus the Irish education system fulfills the widespread recommendations in research of commencing algebra early (e.
Kaput, 2008; Carpenter and Levi, 2000; Cai and Knuth, 2011).However, national and international studies of student attainment suggest that many children in Irish schools may not be developing robust skills in algebraic reasoning (Eivers et al., 2010; OECD, 2009; Eivers and Clerkin, 2011).In my research I plan to investigate to what extent children in Irish primary schools are developing skills in algebraic reasoning.
In order to do so, an assessment instrument must be developed which will facilitate an exploration of children’s thinking as their skills develop.The clinical interview is an instrument which allows access to children’s emergent thinking (Ginsburg, 1997; Piaget, 1929) and in this paper I discuss the design of a clinical interview with specific relevance to children’s skills in algebraic reasoning.University of Leeds The shortage of secondary mathematics teachers is a concern for UK government.In order to increase the supply of teachers, the government has sponsored subject knowledge enhancement (SKE) courses for non-specialist graduates (‘SKE Policy’).Additionally, the government has offered financial incentives to attract high attaining graduates into teaching through differentiated bursaries (‘Bursary Policy’).
Existing research into the efficacy of these measures is limited but studies on two individual teaching courses suggest that student teachers who have taken SKE courses do no worse in their teaching course and that those who achieve more highly in their first degree do not achieve significantly higher outcomes in their teaching course respectively.This study corroborated results of these smaller studies through testing over 100 secondary mathematics student teachers on a sample of ‘mathematical knowledge for teaching’ (MKT) items, designed by the University of Michigan.Results suggest that whilst the SKE Policy may be a good strategy in that there was no overall significant difference in MKT scores between SKE students and mathematics graduates, the Bursary Policy may be a flawed since there is no evidence that higher degree classes lead to greater success on PGCE courses.University of Cambridge Teachers’ professional development (PD) has been described as an ‘unsolved problem’, particularly where there is an expectation to change teaching practices from teacher-centred orthodoxies to more student-centred approaches.This paper considers PD that has been designed to support the teaching of problem solving in secondary classes.
One of the main problems in PD design and research has been identified as the limitations of existing professional learning theory.To respond to this, the research reported in this paper is intended to contribute to the theorisation of PD.
University of oxford
I will present a case study of one teacher – taken from a larger multiple case study – as they take part in a programme of school-based PD.Social learning theory (SLT) is used to analyse and explain the learning processes as a result of participation in the PD programme.This reveals that SLT provides a useful theoretical approach letters and tips for writing them and hope they will be helpful. Bart was a student at [our school] for two years and I was his Mathematics teacher throughout this to get in the way of his academic work, or his duties in the boarding house. journalist, editing our junior newspaper as a younger boy and, as a Sixth Former, .
This reveals that SLT provides a useful theoretical approach.
As a result, I suggest the approach could be used more extensively in professional learning and PD, to understand, evaluate and develop programmes more effectively.University of Bedfordshire The purpose of my research is to explore first year undergraduate perceptions in learning mathematics and their identification of strategies to support them in this area.I work as a senior lecturer in mathematics education on a BA Applied Education Studies course where students consistently identify the mathematics education units as a source of anxiety Publications. Dulwich College Senior Prospectus cover. Senior School Prospectus Years 7-13 · Supplement to the Prospectus. Junior School Prospectus.I work as a senior lecturer in mathematics education on a BA Applied Education Studies course where students consistently identify the mathematics education units as a source of anxiety.Having established a potential link between mathematics anxiety in teachers and trainee teachers, and the potential that this anxiety could be passed on to children in classrooms, my aim is to identify whether there may be strategies that could support adults in learning mathematics camin.ir/thesis/how-to-get-custom-writing-services-law-ethics-thesis-premium-a4-british-european-formatting.
Having established a potential link between mathematics anxiety in teachers and trainee teachers, and the potential that this anxiety could be passed on to children in classrooms, my aim is to identify whether there may be strategies that could support adults in learning mathematics.
To explore this area, I tracked a sample of first year undergraduate students through their initial mathematics education unit, establishing their perceptions before and after the teaching of this unit.
Initial findings demonstrated that the students had negative perceptions about learning mathematics (twice as many negative as positive) and that this was reversed following the completion of the first mathematics education unit.A range of factors were identified as affecting how they felt about learning mathematics, including the role of the teacher, personal perceptions regarding learning mathematics and the role of discussion.Institute of Education, University of London There is growing consensus, amongst teachers, teacher educators and researchers, that a more engaging and relevant school mathematics curriculum is needed, with greater emphasis on problem-solving skills and the development of conceptual understanding.Too much focus on factual recall and procedural understanding has led to unacceptable levels of disengagement and disaffection amongst learners.This paper reports on initial findings from a project involving a group of teacher researchers who share a commitment to addressing the alienation of learners, raising their awareness of the nature of mathematics and the reason for learning it, developing student agency and an appreciation of how mathematics can be used to better understand the world around them.
I make use of a participatory action research methodology to explore how being part of a research group can help teachers to begin to develop their classroom practice in ways which resonate with a commitment to teaching mathematics for social justice.I identify four themes emerging from an analysis of an initial series of semi-structured empathetic interviews with the teacher researchers that provide a useful theoretical framework for the development of the project and useful insight for others wishing to carry out research in a similar field.Our Aim BSRLM is for people interested in research in mathematics education and provides a supportive environment for both new and experienced researchers to develop their ideas.Become a Member Members of BSRLM can attend and present at our termly Day Conferences.You will also receive the three annual issues of Research in Mathematics Education published for BSRLM by Taylor and Francis.
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