Mathematics Education

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The Construction of Identity in Secondary Mathematics Education

The Construction of Identity in Secondary Mathematics Education

One of the more persistent and widespread problems in mathematics education is that many students who are successful in mathematics give up the subject as soon as they are able to do so, even though they are aware of the limitations this places on future careers. Gender studies have sought to understand this phenomenon through a number of psychological viewpoints including attribution theory, locus of control and role modelling. Such studies have been useful in shifting the emphasis away from models of ability, but have not addressed the phenomenon as a social one. This paper represents an attempt to understand why some students will continue with their studies in senior mathematics, while others do not. We take the notion of “identity” as critical to our analysis. We contend that students who develop a sense of identity which resonates with the discourse of mathematics are more likely to continue with their studies than their peers who do not develop such a sense of identity. Critical to this proposal is the understanding of the processes through which students develop such a sense of who they are in relation to mathematics.
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STEM: Challenges and opportunities for mathematics education

STEM: Challenges and opportunities for mathematics education

Even back in 1962, Australia’s former Prime Minister, Sir Robert Menzies, identified “the flowering of science” as “the great distinguishing feature of this [then] century apart from wars and political confusions” (cited by Chubb, 2014). Further, the discipline of science seems to dominate many current STEM reports, as Marginson et al. (2013) indicated. Many nations also refer to the role of STEM education as one that fosters “broad-based scientific literacy” with a key objective in their school programs being “science for all” with increased efforts on lifting science education in the primary, junior, and middle secondary school curricula (Marginson et al., 2013, p. 70). Interestingly, Marginson et al. pointed out that STEM discussions rarely adopt the form of “mathematics for all” even though mathematics underpins the other disciplines (as evident in the discipline definitions cited previously). Marginson et al. thus argued that “the stage of mathematics for all should be shifted further up the educational scale” (p.70). Even the rise in engineering education, commencing in the early school years (e.g., Lachapelle & Cunningham, 2014), would appear to be oriented primarily towards the science strand at the expense of mathematics. Nevertheless, alongside the challenges facing mathematics education are opportunities for its advancement.
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Transforming Mathematics Education With Technology

Transforming Mathematics Education With Technology

Lot of work needs to be done in order to integrate technology in mathematics education. perhaps the area of greatest challenge is teacher preparation, developing sustainable professional development programmes for teachers which will not only enhance the skills of the teacher in terms of usage of various technological tools but also focus on improving their pedagogical content knowledge using technology. The goals of mathematics learning and assessment need to undergo a major paradigm shift in a technology integrated mathematics curriculum. Also technology must be cost effective and easy to deploy in order to achieve large scale integration in schools and teacher educational institutions which has a tremendous implication in terms of infrastructural requirements. A proper attitude and mindset needs to be prepared in order to reap the benefits of integration of technology . So a deal of work remains to be done , but the benefits would clearly be enormous.
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Navigating mathematics : making sense of purpose and activity in contemporary English mathematics education

Navigating mathematics : making sense of purpose and activity in contemporary English mathematics education

Researchers’ understanding of the decision to return to learning mathematics is also informed by the actions of those who do not make a successful return to learning mathematics. First, current summaries of provision (for instance NIACE 2011) are increasingly aware that the majority of adults who have poor numeracy do not return to formal mathematics education; NAO (2008) reports that only one in ten adults with numeracy “below functional level” have attended a numeracy course (p.10). Second, many who do attend a course drop out before completion. Drop out is a significant phenomenon in the adult education sector, although the complex patterns of attendance described in 3.1.1 make it a difficult one to explore. McGivney (2003) summarises the available research and institutional data and awards great significance to personal and social reasons. A continuation of this reasoning suggests that the decision to return is more likely to be taken when personal and social factors are conducive; for example since “combining domestic responsibilities with study is a common problem for women students” (p.105), some mothers might wait until their children have reached school-age before deciding to apply for entrance onto a mathematics course.
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Ethical dimensions of mathematics education

Ethical dimensions of mathematics education

The relationships between mathematics, mathematics education and issues such as social justice and equity have been addressed by the sociopolitical tradition in mathematics education. Others have introduced explicit discussion of ethics, advocating for its centrality. However, this is an area that is still under developed. There is a need for an ethics of mathematics education that can inform moment to moment choices to address a wide range of ethical situations. I argue that mathematics educators make ethical choices which are necessarily ambiguous and complex. This is illustrated with examples from practice. The concept of ethical dimension is introduced as a heuristic to consider the awareness of different forms of relationship and arenas of action. A framework is proposed and discussed of four important dimensions: the relationship with others, the societal and cultural, the ecological and the relationship with self. Attending to the different ethical dimensions supports the development of a plural relational ethics. Navigating ethical complexity requires embracing diverse and changing commitments. An ethics that takes account of these different dimensions supports an ethical praxis that is based on principles of flexibility and a dialogical relationship to the world and practice.
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Starting as a researcher in mathematics education

Starting as a researcher in mathematics education

Beginning with questions is a start. Yet how does a beginner get to articulate their questions, and how can the questions be investigated? Of course, there is a multitude of books available on research methods, both for the social sciences in general and for education researchers in particular, some of which are suitable for the beginning researcher. The aim of this paper is not to distillate these various sources of advice much beyond the merest outline; as such a distillation cannot be achieved within the space available in this paper. Rather the intention is to look at some of the reflections of experienced researchers who, in looking back at what motivated them as a researcher, offer some thoughts that might help a beginning researcher. The paper begins by first considering what research in mathematics education might be, and, indeed, what it might not be.
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The applications of augmented reality technologies in mathematics education

The applications of augmented reality technologies in mathematics education

Recent research in the area of multimedia conducted by the authors in Australia, Japan and North America has re-confirmed the importance and effectiveness of visual features in teaching and learning materials. According to the findings, the visual aspects and interaction with the multimedia systems are the most preferred features amongst the surveyed students. In all of these studies, the surveyed students have also indicated that the visual features play a very important role in understanding the concepts. Based on these findings, the authors have embarked on an investigation to determine the practical and innovative uses of the technologies associated with augmented reality. A very typical augmented reality product is Google Glass. Hence, this paper has initiated a study on the possible contributions this amazing device can make to mathematics education. It has been shown that Google Glass can assist leaners to access and share information, connect and engage in discussions with others by utilising a more human-like interface.
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Investigating Mathematics Teachers’ Awareness in the Use of Modeling in Mathematics Education

Investigating Mathematics Teachers’ Awareness in the Use of Modeling in Mathematics Education

Abstract: This study investigated the use of modeling by mathematics teachers in their teaching of mathematics. In the specific objectives, it sought the mathematics teachers’ awareness in the use of modeling in mathematics education as well as the level of utilization. The study was conducted in Kolokuma/Opokuma local government area of Bayelsa state in Nigeria. It adopted a survey research design with a population of 47 mathematics teachers in ten secondary schools. A sample of 20 out of this population was used. To arrive at this, purposive sampling technique was used. Instrument for data collection was Modeling Awareness Inventory (MAI) which was validated by experts. The instrument was trial tested using Cronbach Alpha formula and had a reliability coefficient of 0.86. Descriptive statistic was used to answer all the research questions asked. It was found among others that Majority of the mathematics teachers in Kolokuma/Opokuma local government area are not aware of modeling in mathematics education. Suggestions on how to improve their awareness were also made.
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Standards-Based Foundations for Mathematics Education: Standards, Curriculum, Instruction, and Assessment in Mathematics

Standards-Based Foundations for Mathematics Education: Standards, Curriculum, Instruction, and Assessment in Mathematics

The mathematics classes that students need in order to acquire the ambitious knowledge and skills required in today’s world are significantly differ- ent from the mathematics instruction many of us remember and the classes many of our children experience. In order to assure all students succeed as workers, democratic citizens, and life- long learners, mathematics education should teach children how to solve both routine and non-routine prob- lems. A routine problem requires a stu- dent to use at least one of the four basic arithmetic operations (or ratio) to solve a problem that is practical in nature. A non-routine problem is con- cerned with developing a student’s mathematical reasoning power and emphasizes heuristics (strategies) rather than practical applications. Different strategies are effective for solving routine as opposed to non-routine problems. Recognizing or creating strategies requires number sense—that is, “having an intuitive feel for number size and combinations, and the ability to work flexibly with numbers in problem situations in order to make sound decisions and reasonable judgments” 1 —and proficiency in computing, geometry, algebra, data analysis,
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Mathematical Modelling Approach in Mathematics Education

Mathematical Modelling Approach in Mathematics Education

school" in Sydney University, “Mathematical Modeling and Scientific Computing” lectures are given in the Mathematics Institute of Oxford University and "Mathematical Modelling in Finance" lectures are given in Manchester University. It is seen that mathematical modeling lectures are given in engineering faculties of some universities in our country (METU Food Engineering undergraduate lectures and Cumhuriyet University, Department of Mechanical Engineering doctorate lecture). However, "modeling in mathematics education" lectures should be made compulsory in primary school mathematics education departments, secondary education mathematics educations departments or even in primary education departments in education faculties of the universities [30]. Teachers and faculty members have an important place in terms of teaching modeling topic. Modeling topic has an important role in terms of raising and educating teachers. Teacher candidates in higher education should study mathematical modeling topic [12]. Thus, it can be easy for the teacher candidates, who encounter modeling approach before their service, to put this teaching approach into practice. For example, a teacher education program that aims to use teaching of mathematics by means of an approach based on a daily life problem perspective was developed in Italy [29]. A teacher education program, in which modeling approach is used, can be developed and implemented in our country too.
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RESEARCH IN MATHEMATICS EDUCATION IN MEXICO: ACHIEVEMENTS AND CHALLENGES

RESEARCH IN MATHEMATICS EDUCATION IN MEXICO: ACHIEVEMENTS AND CHALLENGES

in Mexico work at that institution; but this is not the case. Even though most universities in Mexico do not support large departments where research is mainly concerned with Mathematics Education, groups within Mathematics departments or even within Engineering, Psychology or Pedagogy departments have developed. Researchers in these groups are contributing to the development of new areas of research and are also playing a relevant role in research on specific traditional topics. Most of the research performed in the country, takes place at Mexico City institutions. One important group can be found there at the National Pedagogic University (UPN). This university is concerned with teachers’ education. It hosts both undergraduate and graduate programs in Mathematics Education and hosts several groups interested in different research areas. Other universities like UNAM, the Autonomous Technological Institute of Mexico (ITAM), the Metropolitan Autonomous University (UAM), and the Ibero-American University (UIA) have smaller research groups, but some of them are very productive. Against what could be expected, although these groups concentrate much research on Advanced Mathematics Education, they are also interested in research at other school levels and on the use of technology in the classroom.
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EQUITY ISSUES IN MATHEMATICS EDUCATION

EQUITY ISSUES IN MATHEMATICS EDUCATION

The paper discussed equity in mathematics education in relation to access by all students to opportunities to engage in rich mathematics. For any nation to develop technologically there must be massive education of the populace in mathematics irrespective of race, social status, health status, sex or any other discriminative or classification variables. The world over, development is not limited to a few individual. It is a collective responsibility. Education is regarded as an instrument for any form of development. The paper discussed Family, Gender, Social Status, Achievements, Earnings, Health status and Political participation among other factors that can affect equity issues in mathematics education. Inequity in education affects social mobility of citizenry negatively. Among the recommendation to achieve equity in mathematics education is fairness and inclusion. The educational design system, practices and how resources are allocated should ensure equity as much as possible.
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Mathematics education policy enactment in England’s Further Education Colleges

Mathematics education policy enactment in England’s Further Education Colleges

interpretations and translations taking place at multiple levels within increasingly large and complex multi-site organizations. Devolved responsibility gives managers considerable influence in policy enactment processes which can lead to within-college tensions between vocational and mathematics teachers. This paper examines two within-college policies effecting students’ mathematics learning opportunities: 1) subject choice, and 2) examination entry levels. These policies have produced inequitable opportunities for students on different vocational study programmes. Given the strategic importance of improving mathematics education, this paper explains how multiple actors and structures interact in the enactment of policy in complex FE college settings. Such understandings are needed to inform better policy design and implementation that in turn can improve mathematics education in Further Education colleges in England.
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Creative Mathematics Education

Creative Mathematics Education

In creative mathematics education the student is guided through and involved in actual construction of a mathematical space, introduction of concepts, statement, formulation and use of axioms and proofs of conclusions from them called theorems at the appropriate level. Since a mathematical space is defined solely by its axioms, two distinct mathematical systems are independent and a concept in one is not defined (ill-defined, ambiguous, nonsense) in the other. Therefore, the rules of in- ference rest solely on the axioms. In particular, formal logic is not valid for mathematical reasoning because it has nothing to do with the axioms (Escultura, 2009a). Part of the requirements for effective mathematics education is that the subjects or courses are consistent and its axioms are adequate; otherwise, research grinds to a halt and learning is limited. The same ap- plies to science.
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Reconsidering Approaches to Aboriginal Science and Mathematics Education

Reconsidering Approaches to Aboriginal Science and Mathematics Education

Educational approaches to Indigenous science and mathematics education involve an understanding of Indigenous knowledges. However, these approaches are not always viewed as successful. McMurchy-Pilkington (2008) investigates how Mäori, the Indigenous people of New Zealand, have developed the Pängarau, the first national mathematics curriculum document in the Mäori language. Ten Mäori teachers were contracted to write the document under the guidance of a Mäori project manager. This group was overseen by two advisory groups. Tribal input was invited to ensure that the mathematics vocabulary was inclusive of all tribes. However, the curriculum did not reflect Mäori knowledge and world views as the advisory groups insisted that this be a parallel document to the English-medium curriculum. Once the document had been submitted, the advisory groups sent it to the Mäori Language Commission to have it rewritten. In a report reviewing this curriculum process, recommendations included having Indigenous knowledges inform the curriculum in a more “comprehensive, inclusive, holistic, integrative curriculum framework that reflects Maori status as tangata whenua (Indigenous people of the land)” (p. 633). Although the intent of creating a Mäori mathematics curriculum seemed to offer an opportunity to integrate Indigenous knowledges and Western mathematics, the focus on the Mäori language became a token gesture of translation. In this case, creating a Mäori curriculum that conformed to the English-medium mathematics curriculum in both structure and outcomes seemed ineffective.
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Computer Based Support for Mathematics Education in Serbia

Computer Based Support for Mathematics Education in Serbia

The aim of this paper is to present public e- course and advantages of using digital tools (techniques) for visualization and interactive approach in mathematics education at undergraduate university level. This material consists e-lessons of the Differential Calculus created within software package GeoGebra and following topics are included: functions of a real variable, arrays, limit function, continuity of functions, derivatives, applications of derivatives and interrelationships between theory and its applications in sciences. Integral parts of each e- lesson are dynamic geometric constructions made by GeoGebra applets, very strong theoretical background and traditional calculus tools. The aims of created didactic e-material are to encourage students to make connections between visual and symbolic representations of the same mathematical notions and to let them explore links between parameters, graphs and their application in tasks, sciences and everyday life. Designed teaching and learning material, e-Differential Calculus, meets and fosters individual learning styles, interest and capabilities, which make it suitable and for inclusive and lifelong learning. Left to be discovered is how are the imagery, interactivity, motivational and self- regulated learning components related to student performance on academic tasks and cognitive issues.
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Mathematics education in the early years: Building bridges

Mathematics education in the early years: Building bridges

Effective Pedagogy in Pāngarau /Mathematics: best evidence synthesis iteration (BES) (Anthony & Walshaw, 2007) claims that pedagogies which acknowledge the complexity of learners and settings are grounded in a set of common underlying principles that appear to hold good across people and settings. In acknowledging that all students, irrespective of age, have the capacity to become powerful mathematics learners, mathematics education researchers argue that young children’s developing understandings are most appropriately situated within ‘social and cultural contexts that make sense to the children involved’ (Perry & Dockett, 2004, p. 103). Studies offer evidence that the most effective settings for young learners provide a balance between opportunities for children to benefit from teacher-initiated group work and freely chosen, yet potentially instructive, play activities. Research across early years settings also attributes increasing importance to the development of appropriate relationships and supportive learning communities – communities that foster productive mathematical dispositions and participation for diverse learners. In accord with the accepted need for sound specialist mathematical knowledge in the school sector (Ball et al, 2005), recent research in the preschool sector strongly endorses the importance of sound teacher knowledge.
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Artificial intelligence in computer science and mathematics education

Artificial intelligence in computer science and mathematics education

Purdue University’s Course Signals project predicts student performance using demographics, past academic history and learning effort as measured by interaction with their VLE, Blackboard. The predictive algorithm is run on demand by instruc- tors and the outcome is fed back to students as a personalised email as well as a traffic signal which gives an indication of each student’s prediction [7]. The Open University offers distance learning education and is the largest academic institution in the UK with more than 170,000 students. The OU Analyse project identifies and supports struggling students in more than 10 courses at different years of study. Lecturers may find it difficult to identify at-risk students without the feedback from face-to-face interactions that distance education has, but with predictive data at their finger tips they are able to identify, intervene, and support students and im- prove their virtual learning experience [60, 109]. Lastly, Dublin City University’s Predictive Educational Analytics (PredictED) project used student interaction with the university’s VLE, to predict likely performance of end-of-semester final grades for first year students across a range of topics. This project’s interventions yielded nearly 5% improvement in absolute exam grade and proved that weekly automated feedback and personalised feedback to vulnerable first year students has a significant positive effect on their exam performance [28].
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Integrating the History of Mathematics into Mathematics Education: A Case Study of Teaching the Quadratic Equations

Integrating the History of Mathematics into Mathematics Education: A Case Study of Teaching the Quadratic Equations

In the general education curriculum for mathematics, it is mentioned that “acquiring mathematical knowledge is only effective when evoking aesthetic feelings in students. Therefore, mathematics contributes to the development of aesthetic competence through familiarizing students with the history of mathematics, with biographies of mathematicians and through recognizing the beauty of mathematics in the natural world”. In addition to the content requirements required for knowledge, the mathematics program at each level also gives an appropriate amount of time to carry out practical activities and mathematical experiences for students such as: conducting topics, mathematical learning projects, especially projects and practical mathematical applications; organizing mathematical games, mathematical clubs, forums, seminars, and mathematical contests; publishing a newspaper (or magazine) on mathematics; visiting mathematical training and research institutions, interacting with students who are able and love mathematics. These activities along with mathematical history will equip students with basic general education, assisting students in applying their knowledge, skills and experience in a creative way. As a result, the students see the role of mathematics in practice, thereby making an important contribution to the learning of mathematical knowledge in the classrooms.
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Bloom's and SOLO taxonomy in mathematics education

Bloom's and SOLO taxonomy in mathematics education

Analiza nalog, ki preverjajo znanje učencev na izbrani taksonomski stopnji Bloomove oziroma SOLO taksonomije, je pokazala, da so učenci dosegli večji povprečni delež točk pri nalogah izb[r]

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