Mathematics Teaching and Learning

ISSN 1473 - 0111

This journal, which is published only in electronic form, aims to enhance mathematics teaching for all ages (and abilities) up to 18 years, through relevant articles, reviews and information from around the world. It is aimed at practitioners and educationalists, providing a medium for stimulating and challenging ideas, offering innovation and practice in all aspects of mathematics teaching and learning. |

Intending contributors are advised to read

2015 | |||||

July 17th | Opportunities of Learning through the History of Mathematics: the Example of National Textbooks in Cyprus and Greece [619] | This paper examines the ways the history of mathematics is integrated in the national textbooks of Cyprus and Greece. The data-driven analyses suggest that the references identified can be clustered in four categories: biographical references about mathematicians or historical references regarding the origins of a mathematical concept, references to the history of a mathematical method or formula containing a solution or proof, mathematical tasks of purely cognitive elements that require a solution, explanation or proof and tasks that encourage discussion or the production of a project that would connect the history of mathematics with life outside mathematics. | Constantinos Xenofontos & Christos E. Papadopoulos | ||

July 17th | New Curricula and Missed Opportunities: Crowded Curricula, Connections, and ‘Big Ideas’ [225] | This position paper looks at how the recent review of the Australian Curriculum for Primary Mathematics indicates that anticipated changes in the style of teaching have not transpired and goes on to suggest how the curriculum could be reorganised to effect such change. | Chris Hurst | ||

July 17th | Indicators of Student Engagement: What Teachers Notice during Introductory Algebra Lessons [476] | This article presents results from an empirical study of how student engagement is visible during introductory algebra. Previously, the notion of engagement in mathematics has been studied from students’ and researchers’ perspectives. This study is instead focused on teachers’ perspectives on student engagement. | Rimma Nyman | ||

April 16th | Validating Affordances as an Instrument for Design and a Priori Analysis of Didactical Situations in Mathematics [264] | The aim of the presented case study is to investigate how coherent analytical instruments may guide a priori and a posteriori analyses of a didactical situation, involving trigonometry in triangles and on the unit circle, for the specific purpose of illuminating how students in Swedish upper secondary school handle conceptually challenging tasks without making use of calculators. | Håkan Sollervall & Erika Stadler | ||

April 16th | The use of Mathematical Investigations in a Queensland Primary School and Implications for Professional Development [154] | With the introduction of Ways of Working in 2008, Queensland teachers received professional development on using investigations to teach mathematics. This case study explores the extent to which teachers in one Queensland Primary School use this pedagogy. | Margaret Marshman, Darren Clark and Michael Carey | ||

April 16th | Situating Student Errors: Linguistic-to-Algebra Translation Errors [531] | This study uses a model situated in both a cognitive-oriented frame and the translation process itself to analyze student activity in the linguistic-to-algebra translation process, defines error types made, and recognizes the frequencies of such. | Michael J. Bossé, Kwaku Adu-Gyamfi & Kayla Chandler | ||

April 16th | Turkish Primary School Students’ Strategies in Solving a Non-routine Mathematical Problem and Some Implications for the Curriculum Design and Implementation [414] | Patterns as a subject and the use of patterns as a non-routine problem solving strategy are emphasized in the Turkish curriculum. The primary purpose of this study was to determine how primary school students who learn mathematics in this context approached non-routine problems. The secondary purpose of this study was to discuss how effective this context could be for non-routine problem solving and to develop some perspectives for curriculum design and implementation. | Abdulkadir Erdogan | ||

April 16th | Multi-positioning Mathematics Class Size: Teachers’ Views [266] | This paper explores mathematics teachers’ perceptions about class size and the impact class size has on teaching and learning in secondary mathematics classrooms. It seeks to understand teachers’ views about optimal class sizes and their thoughts about the education variables that influence these views. | Boris Handal, Kevin Watson & Marguerite Maher | ||

January 20th | Investigating Students’ Modes of Thinking in Linear Algebra: The Case of Linear Independence [388] | This study aims to explore undergraduate students’ ways of thinking while solving problems in the abstract mode about linearly independent/dependent vectors. It also focuses on what students understood about linear independence/dependence concepts. The study was conducted with 186 mathematics teacher-candidates. The responses of these students to four problems and interview data conducted with eight students were used to identify a student’s way of thinking. | Derya Çelik | ||

January 20th | A Study of Students’ Conceptual, Procedural Knowledge, Logical Thinking and Creativity During the First Year of Tertiary Mathematics [454] | This study focuses on students in first year environmental science degree programs, where traditionally mathematical emphasis has been much less than within the strict science or math majors. The authors attempt to gain insight into why many students fail mathematical courses even when the mathematical requirements are not as demanding. | Gurudeo Anand Tularam and Kees Hulsman | ||

January 20th | Teaching Mathematical Modelling: Demonstrating Enrichment and Elaboration [155] | This paper uses a series of models to illustrate one of the fundamental processes of model building – that of enrichment and elaboration. The paper describes how a problem context is given which allows a series of models to be developed from a simple initial model using a queuing theory framework. | Jon Warwick | ||

January 20th | Prospective Elementary Teachers’ Conceptions of Unitizing with Whole Numbers and Fractions [508] | This article examines prospective elementary teachers’ conceptions of unitizing with whole numbers and fraction concepts and operations throughout a semester-long mathematics content course. The results indicate that the prospective teachers were successful with iterating units and developing composite units within both whole numbers and fractions. | Jennifer M. Tobias, George J. Roy & Farshid Safi | ||

January 20th | A Glimpse into Secondary Students’ Understanding of Functions [294] | This article examines how secondary school students think about functional relationships. More specifically, seven students’ intuitive knowledge in regards to representing two real-world situations with functions was examined. We found students do not tend to represent functional relationships with coordinate graphs even though they are able to do so, instead representing the physical characteristics of the situation | Jonathan L. Brendefur, Gwyneth Hughes & Robert Ely | ||

January 20th | What Have We Achieved in 50 years of Equity in School Mathematics? [139] | This paper explores the relationship between social backgrounds and geographical locations with mathematical achievement. Using the national testing system in Australia, correlations between the variables were explored and it was found that students from rural and low SES backgrounds are still being marginalised in school mathematics – in terms of their success. | Robyn Jorgensen & Tom Lowrie | ||

January 20th | A Study of Equity in Mathematics Education: Lessons from Japan for U.S. Teacher Preparation [164] | This study comes at an opportune moment for Japanese and U.S. educators, policymakers, and researchers given the trends of global policy and equity-based reform. Discussions of academic achievement in both societies allows us to examine mathematics education as a public good versus private commodity in order to best serve the needs of students. Research was conducted as a visiting scholar at the University of Tokyo, and supported by classroom experience in four public and private schools. | Dr Linda Furuto | ||

January 20th | STEM Education on a Worldwide Voyage: Curriculum to College, Career, and Community Readiness [123] | This article addresses issues in equitable and quality STEM education, and comes at a significant time as students, educators, and policymakers strive to meet federal and state standards such as the Mathematics Common Core State Standards (CCSS) and Next Generation Science Standards (NGSS). | Dr Linda Furuto | ||

2014 | |||||

September 25th | Teachers’ Beliefs about Mathematical Horizon Content Knowledge [311] | This article presents and discusses an example of how teachers’ discussions of mathematical knowledge for teaching (MKT) items elicited their beliefs about the knowledge needed to teach mathematics. One category of MKT is “horizon content knowledge,” and this can be described as mathematical knowledge not directly deployed in instruction — or knowledge behind as well as ahead of the pupils in an actual teaching situation. | Reidar Mosvold and Janne Fauskanger | ||

September 25th | Fostering Elementary Students’ Mathematics Disposition through Music-Mathematics Integrated Lessons [363] | This paper examines the effects of using music-themed activities in mathematics lessons on two groups of participating students’ mathematics achievement and dispositions, including beliefs about success, attitude, confidence, motivation, and usefulness, using a pre/post test method. | Song A. An, Daniel A. Tillman, Rachel Boren and Junjun Wang | ||

September 25th | Pre-service Teachers’ Linear and Quadratic Inequalities Understandings [447] | This research focused on mathematics pre-service teachers’ understandings of linear and quadratic inequalities to determine whether they possess common misconceptions and difficulties with inequalities. Results provided evidence that many pre-service teachers have misconceptions and difficulties that cause them to misunderstand inequalities. | Ali Bicer, Dr. Robert M. Capraro and Dr. Mary M. Capraro | ||

September 25th | Students’ Understanding of the Concept of Vertex of Quadratic Functions in Relation to their Personal Meaning of the Concept of Vertex [559] | This paper explores students’ personal meaning and interpretation of the vertex of a quadratic function in relation to their understanding of quadratic functions in two different representations, algebraic and word problem. Several categories emerged from students’ personal meaning of the vertex including vertex as maximum or minimum, vertex in relation to symmetry, vertex as a starting point or turning point, vertex as an intercept, vertex as an intersection, and miscellaneous. | Annie Burns Childers and Draga Vidakovic | ||

July 8th | Using Solution Strategies to Examine and Promote High-school Students’ Understanding of Exponential Functions: One Teacher’s Attempt [427] | Much research has been conducted on how elementary students develop mathematical understanding and subsequently how teachers might use this information. This article builds on this type of work by investigating how one high-school algebra teacher designs and conducts a lesson on exponential functions. Through a lesson study format she studies with her colleagues how other algebra students have mathematically modeled a bacteria growth problem with no prior formal instruction. | Jonathan Brendefur, Kim Bunning and Walter Secada | ||

July 8th | What do Error Patterns tell us about Hong Kong Chinese and Australian Students’ Understanding of Decimal Numbers? [540] | Mathematics educators have had a long standing interest in students’ understanding of decimal numbers. Most studies of students’ understanding of decimals have been conducted within Western cultural settings. The present study sought to gain insight into Chinese Hong Kong students’ and regional Australian students’ general performance on a variety of decimals tasks and to investigate students’ error patterns. | Mun Yee Lai and Sara Murray | ||

July 8th | Optical Topography of Evoked Brain Activity during Mental Tasks Involving Whole Number Operations [631] | Students start to memorize arithmetic facts from early elementary school mathematics activities. Their fluency or lack of fluency with these facts could affect their efforts as they carry out mental calculations as adults. This study investigated participants’ levels of brain activation and possible reasons for these levels as they solved arithmetic exercises mentally. | Enrique Ortiz | ||

July 8th | Relationships Between Visual Static Models and Students’ Written Solutions to Fraction Tasks [721] | The purpose of this study was to deconstruct the relationship between visual static models and students’ written solutions to fraction problems using a large sample of students’ solutions. Students’ written responses to open-ended tasks were examined to determine common solutions and errors when using visual static models. | Katie L. Anderson-Pence, Patricia S. Moyer-Packenham, Arla Westenskow, Jessica Shumway & Kerry Jordan | ||

July 8th | An Investigation into the Performance, Solution Strategies and Difficulties in Middle School Students’ Calculation of the Volume of a Rectangular Prism [462] | This qualitative study examined middle school students’ performance, solution strategies, difficulties and the underlying reasons for their difficulties in calculating the volume of a rectangular prism. The data was collected from 35 middle school students (6th, 7th and 8th grade students) enrolled in a private school in Istanbul, Turkey. | Reyhan Tekin-Sitrava & Mine Isiksal-Bostan | ||

July 8th | Mathematics Teachers Attending and Responding to Students’ Thinking: Diverse Paths across Diverse Assignments [648] | Professional development (PD) programs often evaluate their impact on teachers’ learning by assessing teachers either individually or in groups. The goal of this paper is to illustrate the variety of paths teachers might follow as a result of working in groups within online PD settings. Data are drawn from a PD program for grades 5-9 mathematics teachers. | Alfredo Bautista, Bárbara M. Brizuela, Corinne R. Glennie, & Mary C. Caddle | ||

July 8th | Addition and Subtraction Word Problems in Greek Grade A and Grade B Mathematics Textbooks: Distribution and Children’s Understanding [340] | Mathematics textbooks are a predominant resource in primary school in Greece, as well as in many other countries. The present study reports on both a content analysis of Greek mathematics textbooks with regard to the types of word problems represented in them and a quantitative analysis of children’s achievement in these problems. | Desli Despina & Loukidou Harikleia | ||

March 10th | Mathematics Teaching in Hong Kong Pre-schools: Mirroring the Chinese Cultural Aspiration towards Learning? [394] | This study investigates the scenes behind Chinese pre-school children's mathematics performance using teacher questionnaires and interviews. Results indicated that the Chinese number system appeared to afford advantages to Chinese children in learning individual mathematics concepts but this was not enough to explain why children perform well in other areas. | Sharon Sui Ngan Ng | ||

March 10th | Elementary Pre-Service Teachers’ Mathematics Anxiety and Mathematics Teaching Anxiety [256] | The present study examined the structure of elementary pre-service teachers’ mathematics anxiety and mathematics teaching anxiety by asking whether the two systems of anxiety are related. The Turkish Mathematics Anxiety Rating Scale Short Version and the Mathematics Teaching Anxiety Scale were administered to 260 elementary pre-service teachers. Results of the study revealed that overall pre-service teachers’ had a low-level of mathematics anxiety and mathematics teaching anxiety. | Guney Haciomeroglu | ||

March 10th | Engaging Prospective Teachers in Peer Assessment as both Assessors and Assessees: The Case of Geometrical Proofs [673] | The aim of this study is to examine the effects of engaging prospective mathematics teachers in peer assessment, both as assessors and assessees, on the development of their assessment skills in general and assessment of geometrical proofs in particular. The research was conducted within a Method course in which peer assessment activities were employed. | Ilana Lavy & Atara Shriki | ||

March 10th | Students’ Differentiated Translation Processes [668] | This study examined students’ processes in their generation of symbolic and graphic representations of given polynomial functions. The purpose was to investigate how students perform these translations. The result of the study suggests that students of different ability levels process translations differently and that students’ apparent difficulties with translations may be directly connected with their processes and obstacles encountered during translations. | Michael Bossé, Kwaku Adu-Gyamfi & Kayla Chandler | ||

2013 | |||||

December 10th | Child-centred Inquiry Learning: How Mathematics Understanding Emerges [364] | This paper examines how mathematical understandings might emerge through student-centred inquiry. Data is drawn from a research project, conducted in three New Zealand primary schools, on student-centred curriculum integration that situated mathematics within authentic problem-solving contexts and involved students in collaboratively constructed curriculum. | Nigel Calder & Chris Brough | ||

December 10th | Imagining Mathematics Teaching via Scripting Tasks [280] | An innovative task used in teacher education – Lesson Play – that involves presenting a lesson in the form of an interaction between a teacher and students is explored. The paper examines the motivation for the development of this task and, through specific examples, describes the iterative design process in which the task was refined and improved. The authors demonstrate how the task, initially designed considering mathematics, can be adapted and extended for different content areas. | Rina Zazkis & Nathalie Sinclair | ||

December 10th | Chinese Students’ Engagement with Mathematics Learning [807] | Over the past decade it has been frequently reported that East Asian students are outperforming their Western counterparts in international tests of mathematics at middle-school level. This paper probes classroom discourse in an attempt to shed some light on the reasons for this phenomenon. | Stephen Norton & Qinqiong Zhang | ||

December 10th | A New Approach to Multiple-Choice Question Writing: Example, Transparency, and Variation [196] | The goal of this article is to provide teachers with an alternative perspective in writing multiple-choice questions. To the techniques and advice available in the literature on the topic, three further aspects are added whose provenance is an emerging line of research – the exemplification of concepts. The objective is to expand multiple-choice questions from their present almost exclusive function of evaluation, and turn them also into a useful instrument for everyday classroom work. | Carlos Figueiredo, Luis Contreras, Lorenzo Blanco & Janeth Cardenas | ||

December 10th | What They Say, What They Do - Understanding Students' Perceptions [503] | Research has shown students can identify practices considered appropriate for achieving when learning mathematics. However, an individual’s espoused theory (what is said) does not necessarily match their theory-in-use (what is done). Further investigation into students’ beliefs and actions are required to explain the difference between what they say and what they do. This article presents the espoused theory, theory-in-use and the follow-up discussion of three underachieving students where the identified differences were explored. | Pamela Perger | ||

September 26th | Examining the Effects of Math Teachers’ Circles on Aspects of Teachers’ Mathematical Knowledge for Teaching [239] | This study examines the results of a three-site administration of the Learning Math for Teaching instrument, a multiple-choice instrument designed to measure aspects of Mathematical Knowledge for Teaching. Results indicate that Math Teachers’ Circles are impacting teachers’ performance on the Number Concept and Operation subsection, leading to implications for future research. | Diana White, Brianna Donaldson, Angie Hodge & Adam Ruff | ||

September 26th | From Sailing Ships to Subtraction Symbols: Multiple Representations to Support Abstraction [300] | This paper reflects on a case study of a Grade one teacher to illustrate how she uses multiple representations as a learning progression for the purposes of abstraction. A detailed description of one specific lesson is provided in which multiple representations are incorporated and also analyses her pedagogy with her four chosen representation forms. | Limin Jao | ||

September 26th | Building a Knowledge Base: Understanding Prospective Elementary Teachers’ Mathematical Content Knowledge [257] | This paper summarises the current peer-reviewed literature of the research into the mathematical content knowledge of pre-service elementary teachers. The need for further research in this area is identified. | Eva Thanheiser, Christine Browning, Alden J. Edson, Signe Kastberg & Jane-Jane Lo | ||

September 26th | Singapore Pre-service Secondary Mathematics Teachers’ Content Knowledge: Findings from an International Comparative Study [155] | This article explores the mathematical content knowledge of one entire cohort of pre-service teachers through analysing their performance in a Secondary Mathematics Audit that was developed for the International Comparative Studies in Mathematics Teacher Training that was initiated by the University of Plymouth. We study how their mathematical content knowledge evolved during their one-year postgraduate teacher education programme by using a pre and post-course test scheme. | Toh Tin Lam, Berinderjeet Kaur & Koay Phong Lee | ||

May 14th | A Framework for Understanding Teachers’ Promotion of Students’ Metacognition [489] | This is an ethnographic study of promotion of metacognition, focusing on the teaching practices in secondary mathematics classrooms of three teachers in the UK. Observations of their teaching and interviews regarding their teaching were conducted. The main aim was analysing and substantiating the parallels and differences among the teaching practices, providing an account of the patterns in the teachers’ promotion of metacognition and the underpinning factors. | Engin Ader | ||

May 14th | Testing Young Children’s Ideas of Mass Measurement [712] | This article reports an innovative use of photographs in a pencil-and-paper test which was developed to assess young children’s understanding of mass measurement. 295 tests were administered by 13 teachers of Years 1 and 2 children in 3 urban and rural schools with the aim of more closely connecting written assessment with classroom experiences of young children. | Jill Cheeseman & Andrea McDonough | ||

May 14th | Engaging Elementary Students with Mathematical Processes During Assessment: What Opportunities Exist in Tests Accompanying Published Curricula? [191] | This paper presents a framework used to analyze the extent to which assessments accompanying three published elementary grades 3-5 curricula in the United States provide students with opportunities to engage with key mathematical processes. The framework uses indicators for five criteria to assess the processes of reasoning, communication, connections, and representation. | Patricia D. Hunsader, Denisse R. Thompson & Barbara Zorin | ||

April 15th | The Autonomy to Choose – the Case of Ninth-grade Mathematics Students [533] | This study explores the effects of providing ninth-grade students with the chance to take part in decision making concerning the mathematics level they would be assigned to in high school. Decisions concerned their self-competence regarding their mathematical abilities, their learning goals and the class atmosphere. | Ilana Lavy & Orly Zarfin | ||

January 30th | Aspiring Mathematicians: Students’ Views Regarding What it Takes to be Successful in Mathematics [637] | This article explores junior high school students’ views regarding what it takes to be successful in mathematics. Qualitative and quantitative methods were employed to collect and analyse data, describe and interpret junior high school students (12-14 years) perceptions about what it takes to be successful in mathematics. | Ernest Ampadu | ||

January 30th | Mathematics Teacher's Role in Promoting Classroom Discourse [664] | This qualitative study illustrates how one high school mathematics teacher engaged his students in classroom discourse and promoted in them the use of appropriate mathematics language to communicate their thinking and make sense of mathematics concepts. The study also shares students’ perceptions of the teaching approach. | Patrick Wachira, Roland G. Pourdavood & Raymond Skitzki | ||

2012 | |||||

December 21st | Coming to ‘Know’ Mathematics through being Scaffolded to ‘Talk and Do’ Mathematics [169] | This paper adds to a discussion initiated by Askew (2007) about two contrasting views of scaffolding; as a ‘tool for results’ and a ‘tool-and-result’. The wider study the article is drawn from took place in four primary classrooms with Pasifika students within a low socioeconomic setting. | Roberta Hunter | ||

December 21st | The Importance of Teaching Power in Statistical Hypothesis Testing [387] | Statistical power analysis determines the ability of a study to detect a meaningful effect size, where the effect size is the difference between the hypothesized value of the population parameter under the null hypothesis and the true value when the null hypothesis turns out to be false. Although power is an important concept it is a topic not often covered in any depth in a basic statistics class and it is often ignored by practitioners. | Alan Olinsky, Phyllis Schumacher & John Quinn | ||

December 5th | Professional Development for Secondary School Mathematics Teachers: A Peer Mentoring Model [275] | This paper examines the role of Professional Development as a support mechanism for mathematics teachers in low socio-economic schools and reports on the results of implementing a peer mentoring model with teachers in schools of this type. | Barbara Kensington-Miller | ||

December 5th | What Do They Know? A Comparison of Pre-service Teachers’ and In-service Teachers’ Decimal Mathematical Content Knowledge [1258] | The main aim of this paper is to report on an investigation into primary pre-service and in-service teachers’ content knowledge of decimals. The participants were asked to complete four decimal tasks including the ordering of decimals, operating with decimals and converting a fraction to a decimal. The findings indicated a reliance on formal procedures and that incorrect responses indicated a fundamental lack of understanding of place value. | Tracey Muir & Sharyn Livy | ||

October 26th | The Use of Alternative Algorithms in Whole Number Computation [333] | This paper focuses on how pedagogical reform in Australia has resulted in a reduced emphasis on the teaching of computational algorithms and led to a diversity of alternative mechanisms to teach students whole number computations. A study is conducted into the current methods used by students in completing written computational tasks. | Stephen Norton | ||

June 22nd | Young Students’ Self-Beliefs About Using Representations in Relation to the Geometry Understanding [265] | The purpose of the present study was to investigate the role of various aspects of apprehension (perceptual, operative and discursive) in geometrical figure understanding and the respective students’ self-beliefs about using representations as a useful tool for understanding geometrical concepts and for solving geometrical tasks. | Areti Panaoura | ||

June 22nd | School Transition from Year 6 to Year 7: A Focus on Mathematics [214] | Moving from primary school (Year 6) to the next stage in schooling (Year 7 intermediate or middle school) can provide challenges for students, teachers, and parents. This paper examines the findings of a study carried out to investigate these challenges with a focus on mathematics for 65 students from six different urban primary schools in New Zealand. | Dr Brenda Bicknell & Dr Roberta Hunter | ||

June 6th | Geometric Mean - What Does it Mean? [418] | This paper discusses a number of the connections between conceptual understanding and procedural learning that can be made when geometric mean is taught in the mathematics classroom. | Robin S. Kalder | ||

May 10th | Encouraging Students to Think Strategically when Learning to Solve Linear Equations [511] | In this paper, the design of an online resource, Equations2go, for helping students learn to solve linear equations is investigated. Students learning to solve equations need to consider their overall strategy as well as the procedures for each step. Students were encouraged to develop strategies for solving equations with interactive software, Equations2go, which allowed students to decide on strategies while the computer carried out the procedures. | Daphne Robson, Walt Abell & Dr Therese Boustead | ||

April 19th | Teaching with Procedural Variation: A Chinese Way of Promoting Deep Understanding of Mathematics [319] | This paper examines the reasons that Chinese students, mainly using procedural methods including rote learning and memorisation, usually out perform Western students who are encourage in their learning to construct a conceptual understanding of the mathematics they learn. | Mun Yee Lai & Sara Murray | ||

April 19th | Teaching a New Method of Partial Fraction Decomposition to Senior Secondary Students: Results and Analysis from a Pilot Study [307] | This paper introduces a new approach to compute the partial fraction decompositions of rational functions and describe the results of its trials at three secondary schools in Hong Kong. The responses from the teachers and students concerned indicate this new approach has potential to be introduced at the senior secondary level, as an alternative to the method of undetermined coefficients described in common secondary mathematics textbooks. | Yiu-Kwong Man & Allen Leung | ||

April 12th | Using Dynamic Geometry Software GeoGebra in Developing Countries: A Case Study of Impressions of Mathematics Teachers in Nepal [204] | This article describes a professional development initiative for fifteen mathematics teachers in the use of dynamic geometry software GeoGebra. Teachers’ impressions and beliefs concerning both the training and the software were researched in the context of applicability in Nepalese schools. | Bhesh Raj Mainali & Mary Beth Key | ||

March 27th | Enhancing Interpretation of Natural Phenomena through a Mathematical Apparatus: A Proposal of an Interactive Unit in Optics [399] | The cognitive purpose of the paper is to show how to generalize the process of determining image characteristics by using a lens equation converted to an algebraic function. Its far-reaching goal is to ignite learners’ curiosity of interpreting natural phenomena through employing more extensive mathematical embodiments. | Andrzej Sokolowski | ||

March 27th | Determining the Views of Mathematics Student Teachers Related to Mathematical Modelling [243] | The purpose of this qualitative research is to examine the views of 21 secondary mathematics student teachers attending Mathematical Modelling Course regarding mathematical modelling in a state university in Turkey; reasons why they chose this course and their expectations from the course in question. | Ayse Tekin, Semiha Kula, Çaglar Naci Hidiroglu, Esra Bukova-Güzel & Isikhan Ugurel | ||

March 27th | Curriculum Opportunities for Number Sense Development:A Comparison of First-Grade Textbooks in China and the United States [365] | This study analyzed the representation of number sense and its connection to other mathematics concepts in both traditional and reformed first-grade textbooks in China and the United States, and explored the learning opportunities that the textbooks in each country provide for their children in developing number sense. | Qiang Cheng & Jian Wang | ||

February 3rd | Eighth Grade In-service Teachers’ Knowledge of Proportional Reasoning and Functions: A Secondary Data Analysis [271] | Using a large dataset from a study related to online professional development for eighth grade teachers of mathematics, the paper provides a snapshot of the current state of teachers’ knowledge related to proportional reasoning and functions. The paper also considers how teachers’ knowledge is related to student knowledge in these two areas. | Jessica Masters | ||

February 2nd | Treatment of Variables in Popular Middle-Grades Mathematics Textbooks in the USA: Trends from 1957 through 2009 [1133] | This study investigated the development of the concept of variables in middle grades mathematics textbooks during four eras of mathematics education in the United States. Findings revealed that each of the middle grades mathematics curricula examined used variables, but in varied proportions and levels of complexity. There were also some noticeable changes in the treatment of variable ideas found in the curriculum selected for the present NCTM era when compared with the treatment in the other three curricula. | James Dogbey & Gladis Kersaint | ||

January 25th | Numeracy at Home: Involving Parents in Mathematics Education [195] | Parental involvement in the form of ‘at-home’ interest and support has a major influence on pupils’ educational outcomes and attitudes. Many parents, however, feel uninformed about current educational practices and how they can be more involved with their child’s learning. This article provides some examples of mathematics education projects, initiatives and interventions as documented in the literature, as a context for discussing in detail two initiatives undertaken with the parents of two Australian schools. | Tracey Muir | ||

2011 | |||||

November 7th | An Analysis of Higher-Order Thinking on Algebra I End-of Course Tests [302] | This research provides insight into one US state’s effort to incorporate higher-order thinking on its Algebra I End-of-Course tests. To facilitate the inclusion of higher-order thinking, the state used Dimensions of Thinking and Bloom’s Taxonomy. An analysis of Algebra I test items found that the state’s initial interpretation and application of Dimensions of Thinking and Bloom’s Taxonomy was faulty and inconsistent; as a result, few Algebra I test items from 1998 and 2001 were found to assess higher-order thinking | Tony Thompson | ||

October 31st | Assessing the Learning of Proofs in High School [246] | This article reports on the findings of a study into the learning of mathematical proof in high school and the direct links to the level of algebra of the students. | Jerry Dwyer, Robert Byerly, Terra Stout & Jennifer Wilhelm | ||

October 31st | U.S. and Taiwanese Pre-service Teachers' Geometry Knowledge and Thinking [960] | This study investigated and compared the geometry knowledge and levels of pre-service elementary teachers from the United States and Taiwan. Forty pre-service teachers in Taiwan and 48 pre-service teachers in the United States at the beginning of their teacher education programs completed the Entering Geometry Test (EGT) and the van Hiele Geometry Test (VHGT) developed by Usiskin (1982). | Cheng-Yao Lin, Fenqjen Luo, Jane-Jane Lo & Der-Ching Yang | ||

October 31st | An Analysis of Middle School Mathematics Pre-service Teachers’ Development of Teaching Goals [500] | This longitudinal study analyzes middle school mathematics pre-service teachers’ development of teaching goals. The Teaching Goals Inventory (TGI) (Angelo & Cross, 1993) was administered on four occasions. The participants were part of a teacher preparation and master’s degree program. | Enrique Ortiz | ||

October 31st | Latvian Mathematics Teachers' Beliefs on Effective Teaching [357] | The article aims to present findings of a study on the profile of traditional/constructivist beliefs of mathematics teachers in Latvia connected with effective teaching. Latvian mathematics teachers’ beliefs about effective teaching tended towards constructivism, though in response to many questions traditional standpoints still remained. | Alesja Šapkova | ||

September 21st | The Effect of Alternative Solutions on Problem Solving Performance [129] | The purpose of this study was to investigate the effect of instruction in alternative solutions on Taiwanese eighth-grade students’ mathematical problem solving performance. This study was exploratory rather than experimental. Alternative-Solution Worksheet (ASW) was developed to encourage students’ engagement with alternative solutions to mathematical problems during instruction. | Shin-Yi Lee | ||

September 21st | Understanding Graphicacy: Students’ Making Sense of Graphics in Mathematics Assessment Tasks [428] | The ability to decode graphics is an increasingly important component of mathematics assessment and curricula. This study examined 50, 9 to 10-year-old students, as they solved items from six distinct graphical languages that are commonly used to convey mathematical information. | Tom Lowrie, Carmel M. Diezmann & Tracy Logan | ||

June 15th | Teaching Place Value Concepts to First Grade Romanian Students: Teacher Knowledge and its Influence on Student Learning [339] | This study examined four Romanian first grade teachers’ knowledge about place value concepts, and the relationship between this knowledge and their classroom practice. Findings reveal a direct relationship between teachers’ content and pedagogical content knowledge and their student learning of place value concepts. | Madalina Tanase | ||

June 15th | The Indefinite Accumulation of Finite Amounts: A Socratic Educative Experience [381] | This study is a semi-structured clinic interview designed to ease the mental construction of a suitable concept-image of the notion of convergence for series of positive numbers. | María Ángeles Navarro & Pedro Pérez Carreras | ||

June 15th | Translations Among Mathematical Representations: Teacher Beliefs and Practices [239] | This paper discusses teacher beliefs and instructional practices, investigates why some translations seem to be more difficult than others and provides instructional recommendations to assist students and teachers with mathematical translations. | Michael J. Bossé, Kwaku Adu-Gyamfi & Meredith Cheetham | ||

June 13th | Important Prerequisites to Educational Success in Mathematics in Lower Secondary School [366] | This study investigates to what extent arithmetic ability and self-regulated learning skills in the beginning of lower secondary school predicts measures of students’ performance in mathematics at the end of lower secondary school. Arithmetic ability and self-regulated learning skills were tested in the first two weeks in lower secondary school. Post-tests were performed the last two months in lower secondary school. | Joakim Samulesson | ||

May 24th | An Experience of Social Rising of Logical Tools in a Primary School Classroom: the Role of Language [286] | This paper explores the relationship between language and developmental processes of logical tools through the analysis at different levels of some ‘linguistic-manipulative’ activities in a primary school classroom. | Cristina Coppola, Monica Mollo & Tiziana Pacelli | ||

May 24th | Effects of Three Modes of Personalisation on Students’ Achievement in Mathematical Word Problems in Nigeria [229] | This study investigated the effects of modes of personalisation of instruction crossed with two levels each of verbal ability and cognitive style as moderator variables on the mathematical word problems achievement of 450 junior secondary Nigerian students. | A. Awofala, T. Balogun & M. Olagunju | ||

March 10th | Experiences of Student Mathematics Teachers in Computers-Based Mathematics Learning Environment [235] | In this paper, pre-service mathematics teachers were presented with examples in Use of Computers in Mathematics Education (UCME) course on how to use computer technology in mathematics education and how mathematical relationships are investigated. This paper attempts to reveal the mathematical thinking processes and experiences lived by pre-service teachers in the course of investigation and discovery processes. | Ilhan Karatas | ||

February 28th | An Analysis of how Proctoring Exams in Online Mathematics Offerings Affects Student Learning and Course Integrity [131] | This paper presents the results of a study focused on the issue of how proctored testing affects the learning outcomes and integrity in an Intermediate Algebra course setting. The study follows a model of assessment where students in one group have taken two of their five unit exams as proctored tests along with a proctored Comprehensive Final Exam, compared to a second group who take all unit tests online, but who do complete a proctored Comprehensive Final Exam. | Michael Flesch & Elliott Ostler | ||

2010 | |||||

November 19th | Assessing Understanding Through Reading and Writing in Mathematics [205] | The mathematics education community recognizes the integrality of reading and writing in learning and communicating mathematics knowledge. This paper explores the integrality of reading and writing in mathematics and outlines techniques that can be utilized in mathematics assessment to create experiences that promote reading and writing as tools for articulating mathematics understanding. | Kwaku Adu-Gyamfi, Michael J. Bossé & Johna Faulconer | ||

November 19th | Using Differentiated Instruction in Teacher Education [110] | The article discusses using differentiated instruction in mathematics education for pre-service teachers, including background information and details on a differentiated unit on fractions and integers. In addition, a study was conducted on this lesson and results are included which suggest that students who received the differentiated lesson did better than those students who received a more typical lesson. | Melanie Butler & Kelly Van Lowe | ||

November 19th | Relation Between Tenth Grade Students’ Attitude and Components of Attitude in Algebra with Algebra Achievement of Addis Ababa Secondary Schools, Ethiopia [185] | The purpose of this study was to examine the relation between the attitudes and components of attitude of the students towards algebra with their algebra achievements. The population for this study consists of all government tenth grade students and their mathematics teachers in Addis Ababa city administration. | Mulugeta Atnafu | ||

October 12th | The Number Line: An Auxiliary Means or an Obstacle? [270] | The aim of this paper is to investigate the ways in which the number line can function in solving mathematical tasks by first graders (6 year olds). The main research question was whether the number line functioned as an auxiliary means or as an obstacle for these students. | Chrysanthi Skoumpourdi | ||

October 12th | Transforming Pedagogical Practice in Mathematics: Moving from Telling to Listening [230] | This research article is part of a larger study that examines an initiative to expand teacher expertise in facilitating mathematical problem solving within the framework of developing and field-testing pedagogical resources. We focus on one year of the study and report on the complex process of professional development as teachers move from traditional pedagogies of teacher explanation of mathematical operations followed by student practice to a pedagogy of teacher and student exploration of number operations within a problem-solving environment. | Chris Suurtamm & Nancy Vézina | ||

October 12th | Teachers’ Senses of Obligation to Curricular Messages [215] | Whether they are acknowledged or not, resources such as textbooks, curriculum guides, assessments, and professional development programs present messages about what is most important for students to learn and how students can best learn this. At times teachers feel obligated to enact these messages, but at other times they feel free to ignore these messages. When do teachers feel obligated to follow messages that they interpret from resources and when do they feel that they can ignore these messages? | Christy D. Graybeal | ||

October 12th | Role of Mathematics Learning Development Centres in HEIs [223] | A lack of mathematical ability has been identified as a factor resulting in non-completion of courses in Higher Education Institutions. This study investigates how students become involved in mathematics development services/centres and how such services impact on their learning experience. Subsequently, the study presents informative findings and results from a recently conducted survey of the perceptions of Aston University students on the mathematics learning development centre. | C. Nzekwe-Excel | ||

October 12th | Investigating Quadrilaterals as an Ongoing Task [187] | This article discusses an open-ended problem involving quadrilaterals that is continually used each semester. The task has been posed to undergraduate and graduate students in methods and problem solving classes. The task involves drawing all possible four sided figures with corners at the dots. A four by four array of dots is included in the instructions and students are asked to develop a system for knowing when they have identified all the quadrilaterals. | Kerri Richardson, Catherine Stein Schwartz & Anne Reynolds | ||

October 12th | Building Mathematics Vocabulary [121] | This paper presents aspects of mathematics vocabulary and its impact on mathematical comprehension and performance based on representative vocabulary from standardized examinations. Direct and indirect instructional methods for math vocabulary are discussed. Instructional strategies for fostering vocabulary development are also provided. | Dr. Madeline Kovarik | ||

October 5th | Characterising Preservice Teachers' Mathematical Understanding of Algebraic Relationships [235] | Five elementary and special education preservice teachers were the focus of this study. Analysis showed that preservice teachers demonstrated different levels of mathematical understanding. The nature of the mathematical tasks they completed in class provided contexts for their developing understanding. | Leah A. Nillas | ||

October 5th | Algebra Students’ Ability to Recognise Multiple Representations and Achievement [256] | The purpose of this study was to examine whether there is an association between middle school students’ achievement level on standardized test, their ability to recognize structurally the same relationship presented in different modes and their ability to solve problems involving linear relationship with one unknown posed in different modalities. | Regina M. Panasuk & Matthew L. Beyranevand | ||

October 5th | Characterising the Cognitive Processes in Mathematical Investigation [105] | Many educators believe that mathematical investigation involves both problem posing and problem solving, but some teachers have taught their students to investigate during problem solving. The confusion about the relationship between investigation and problem solving may affect how teachers teach their students and how researchers conduct their research. Therefore, this article seeks to address these issues by first distinguishing between investigation as a task, a process and an activity; and then providing an alternative characterisation of the process of investigation. | Joseph B. W. Yeo & Ban Har Yeap | ||

October 5th | Superitem Test: An Alternative Assessment Tool to Assess Students’ Algebraic Solving Ability [185] | Superitem test based on the SOLO model (Structure of the Observing Learning Outcome) has become a powerful alternative assessment tool for monitoring the growth of students' cognitive ability in solving mathematics problems. This article focused on developing a superitem test to assess students' algebraic solving ability through interview method. The findings provided evidence on the significance of superitem test in assessing algebraic solving ability. | Lim Hooi Lian, Wun Thiam Yew & Noraini Idris | ||

October 5th | Mathematics Tasks as Experiential Therapy for Elementary Preservice Teachers [189] | This paper reports on the selection and choice criteria for mathematics tasks that are used in an elementary pre-service program. The tasks can be seen as experiential therapy. It can be argued that for teachers to see mathematics, and consequently mathematics teaching and learning, in new ways then they need to personally experience mathematics in new ways. The findings show that teachers’ engagement with such tasks may help them become better positioned to teach mathematics in what are referred to as “warm” ways. | Immaculate K. Namukasa & George Gadanidis | ||

October 5th | Secondary School Education in Assam (India) with Special Reference to Mathematics [228] | This paper describes the prevailing academic scenarios of a representative group of secondary schools in Assam (India) with special references to students' performance in general and mathematics performance in particular. | Professor N R Das & Karuna Baruah | ||

April 1st | Empowering Learning with Rich Mathematical Experience: Reflections on a Primary Lesson on Area and Perimeter [192] | In this paper, a Hong Kong primary school lesson on area and perimeter is analysed with a perspective to discuss the meaning for students to have rich mathematical experiences and how pre-designed pedagogical tools could enrich mathematics classroom learning environment which promote re-shaping, shaping and even creation of mathematical knowledge. | Allen Leung | ||

February 23rd | An Analysis of the Turkish New Elementary Mathematics Curriculum and Textbooks in terms of the Presentation of Geometric Concepts [224] | The purpose of this study was to examine how geometric concepts are presented in the Turkish elementary mathematics curriculum and in the textbooks in terms of sizes and orientations. For this purpose, the elementary school mathematics curriculum and two sets of textbook series were examined. | Veli Toptas | ||

2009 | |||||

October 20th | An Assessmnet of Number Sense Among Secondary School Students [239] | This paper reports selected findings from a study of Number Sense proficiency of students aged 13 to 16 years in a state in Malaysia. | Parmjit Singh | ||

October 20th | United States Middle School Students' Perspectives on Learning Statistics [99] | This paper describes an intervention at the 8th grade level where university mathematics researchers presented a series of lessons on introductory concepts in probability and statistics. Pre- and post-tests, and interviews were conducted to examine whether or not students at this grade level can understand these concepts. | Jerry Dwyer, Kim Moorhouse & Malinda J. Colwell | ||

October 20th | Mathematical Self-Efficacy of Middle School Students Solving the Rubik Cube [144] | A solution to the Rubik’s Cube was introduced to an eighth grade mathematics class. The purpose of this study was to determine if an introduction to a solution to the Rubik’s Cube could enhance students’ problem-solving abilities, increase their general interest in mathematics, and enhance students’ problem solving self-efficacy. | Jerry Dwyer, Omar Arizpe & Tara Stevens | ||

October 8th | Students’ Difficulties in Solving Non-Routine Problems [211] | The purpose of this paper is to explore difficulties faced by 56 Secondary students when solving problems. The difficulties experienced by students who were prevented from obtaining a correct solution were: (a) lack of comprehension of the problem posed, (b) lack of strategy knowledge, (c) inability to translate the problem into mathematical form, and (d) inability to use the correct mathematics. | Kai Kow Joseph Yeo | ||

October 8th | Using Concept Maps to Assess the Effect of Graphing Calculators Use on Students' Concept Images of the Derivative at a Point [116] | This study used concept maps to investigate the effect of using graphing calculators on students' understanding of the derivative at a point. The study looked for differences between the concept images that are held by students' who are using graphing calculators and the students who are not using them. | Derar Serhan | ||

January 5th | Students' Perceptions Abouth the Symbols, Letters and Signs in Algebra and How Do These Affect Their Learning of Algebra: A Case Study in a Govenrment Girls' Secondary School, Karachi [335] | This article looks at the misconceptions that arise in Algebra, particularly pertaining to the use and meaning of symbols and letters. | Mashooque Ali Samo | ||

January 5th | Preservice Teachers' Subject Matter Knowledge of Mathematics [77] | This article relates to the author's research into the subject knowledge of trainee teachers and then catagorises this knowledge as either traditional, pedagogical, or reflective. | Ramakrishnan Menon | ||

2008 | |||||

November 25th | How Does the Problem Based Learning Approach Compare to the Model-Eliciting Activity Approach in Mathematics? [127] | The purpose of this article is to discuss the similarities and differences in the two approaches referred to in the article title with an emphasis on implementation and outcomes. | Scott A. Chamberlin & Sidney M. Moon | ||

November 25th | Seeds of Professional Growth Nurture Students’ Deeper Mathematical Understanding [258] | This manuscript describes a group of middle school age students' exploration of virtual mathematics manipulatives and the authors' professional development process. In the manuscript, the authors share the experiences they had with middle school students and the process that they, as mathematics teachers, used to refine their own learning and teaching alongside the middle school students. | Ji-Eun Lee & Dyanne Tracy | ||

November 25th | The State of Balance Between Procedural Knowledge and Conceptual Understanding in Mathematics Teacher Education [140] | In this paper, we present the results of a survey-based study of the perspectives of mathematics teacher educators in the United States regarding the effects of the conceptual/procedural balance upon four concerns: the type of mathematics that should be learned in school, preservice teacher preparation, instructional conceptualization and design, and assessment. | Michael J. Bossé & Damon L. Bahr | ||

November 25th | An Exploration of the Effects of a Practicum-Based Mathematics Methods Course on the Beliefs of Elementary Preservice Teachers [297] | Effects of a practicum-based elementary mathematics methods course on the beliefs of preservice teachers regarding conceptual knowledge in school mathematics were explored using a pre-post design. The intensity of those beliefs was assessed before and after the methods course using the IMAP Web-Based Beliefs Survey, an instrument constructed by the “Integrating Mathematics and Pedagogy” (IMAP) research group at San Diego State University. | Damon L. Bahr & Eula Ewing Monroe | ||

November 25th | What is Good College Mathematics Teaching? [141] | This article attempts to answer the question “What is good college mathematics teaching?” by examining three sources of information: research, student course evaluations, and responses on the website RateMyProfessors.com. | Carmen M. Latterell | ||

July 3rd | Real-life Connections in Japan and the Netherlands: National Teaching Patterns and Cultural Beliefs [266] | The TIMSS 1999 Video Study revealed that Japan had the lowest (of the seven participating countries) amount of real-life connections in the eighth grade mathematics classrooms, whereas the Netherlands had the highest amount of connections with real life. This article examines more closely how these ideas were actually implemented by teachers in these two countries. | Reidar Mosvold | ||

May 20th | Teaching and Evaluating ‘Open-Ended’ Problems [325] | This paper focuses on an open-ended problem. The problem comprises a group of four numbers from which the students are asked to find the one that does not belong. Each of the numbers can be selected as not belonging, each one for different reasons. The problem was given to 164 fifth-grade students. The paper suggests tools for teachers to analyze and evaluate the work of their students when dealing with problems of this kind. | Rama Klavir & Sarah Hershkovitz | ||

2007 | |||||

November 28th | Learning and Instruction in Mathematics: A Study of Achievement in Saigon, Vietnam [67] | The purpose of this study was to investigate the relationship between learning and instruction in mathematics achievement of 12-year-old students in Saigon, Vietnam. The researcher examined several instructional practices and employed variance estimation procedures for complex sampling designs. | Thienhuong Hoang | ||

November 28th | Seventh Graders' Prealgebraic Problem Solving Strategies: Geometric, Arithmetic, and Algebraic Interplay [123] | The purpose of this paper is to report a study that explores the thinking strategies of Lebanese grade 7 students in solving a problem involving simple geometric objects and first-degree equations, prior to formal instruction in algebra. | Iman Osta & Sirine Labban | ||

November 28th | The NCTM Standards from an Axiological Perspective [86] | With the recognition of the significant role played by the NCTM Standards and the Principles and Standards within the history of mathematics education within the United States and internationally, it is necessary to consider the philosophical composition of this movement and address specific questions which naturally arise. Eclipsed by discussions of curricular content, philosophical concerns are often absent from contemporary discussions of mathematics education reform efforts. | Michael J. Bossé | ||

November 28th | Beautiful Mathematics and Beautiful Instruction: Aesthetics within the NCTM Standards [172] | Today, research often considers the content and pedagogy associated with the NCTM Principles and Standards for School Mathematics (NCTM, 2000). However, philosophic analysis of NCTM’s position remains only infrequently investigated. This paper investigates the Principles and Standards from an aesthetic perspective, asking the question, “What does NCTM believe to be ‘Beautiful Mathematics?’” | Michael J. Bossé | ||

November 28th | Teaching Elementary Statistics Concepts Through [244]ks Outliers | This paper demonstrates how the application of ks outliers can assist in the instruction of introductory statistical concepts to high school and undergraduate students. | Michael J. Bossé & Frederick W. Morgan | ||

September 13th | Actual Conditions of Operating Mathematics Instruction in Accordance with the Current 7th National Curriculum in Korea [137] | This study examines the actual conditions of instruction provided by Korean mathematics teachers while adjusting the curriculum with respect to the consideration given to the needs of individual students and regional specialization in their class. | Hye Jeang Hwang & Seung-Hyun Choe | ||

August 1st | Children’s Understanding of Equality and the Equal Symbol [189] | The concept of equality and the equal symbol is discussed in this paper. Based on an instrument derived from previous research results, a study of how fifth and sixth graders understand the concept of equality was conducted and a subsequent analysis was accomplished | Cumali Oksuz | ||

June 28th | What are the Reasons Behind the Success of Finland in PISA [35] | This paper looks into the background of why Finland performed so well in the PISA study. | George Malaty | ||

May 29th | Coordinating Learning Theories with Linear Algebra [47] | This paper describes the findings of a pilot project examining the study of dual courses in Linear Algebra and in Mathematical Learning Theories designed for secondary mathematics teachers. | Laurel Cooley, William O. Martin, Draga Vidakovic & Sergio Loch | ||

March 13th | Why So, Rather than How To [48] | This paper looks into the need for students to be able to show greater understanding of Mathematical concepts, something that current examination formats fail to do. | Ilan Samson | ||

2006 | |||||

December 7th | A Case Study of Adjustment: Looking at a Graduate Teaching Assistant’s Struggles [136] | This paper seeks to provide further evidence of the problems graduate students face as they are teaching. In order to accomplish this, this study presents a singular case study of the graduate teaching instructor of Mr. M culled from an on-going investigation of the struggles graduate teaching assistants face when front-line instructors. | David Meel | ||

December 7th | A Mathematical Problem-Formulating Strategy [79] | In this paper we propose a new thinking strategy directed to improve the mathematical problem–formulating process. Several specific strategies proposed by many authors are seen as techniques, related to the implementation of our strategy. The results have been applied in the Cuban mathematics teachers' training. | Miguel Cruz Ramírez | ||

November 30th | The Mistakes Made by the Students Taking a Calculus Course in Solving Inequalities [326] | This study tries to analyse the performances of students and explore the mistakes made by the students taking a Calculus course when they are finding solution sets for inequalities. To these purposes, an examination was given to science students who have taken a calculus course at a Turkish University. | Nezahat Çetin, Nevin Mahir & Mehmet Üreyen | ||

November 13th | ICMI/IASE Joint Discussion Paper [172] | This discussion paper looks into the teaching of statistics in primary and secondary schools. It forms part of a joint study by the International Commission on Mathematical Instruction and the International Association for Statistical Education entitled Statistics Education in School Mathematics: Challenges for Teaching and Teacher Education. | ICMI/IASE | ||

October 31st | It’s CAME; We saw; Did it Conquer? - A review of the Cognitive Acceleration in Mathematics Education Pilot Study in Northern Ireland [91] | This paper presents the findings of a pilot evaluation funded by the Belfast Education and Library Board of the Cognitive Acceleration in Mathematics Education Programme in a number of post-primary schools in Northern Ireland. It looks at the impact of the programme on teachers’ classroom practice and teaching methods and its use as a professional development tool. | Patricia Eaton & Irene Bell | ||

October 31st | Mathematical Self-Efficacy: A Pilot Study Exploring Differences Between Student Groups [117] | This paper describes the results of a pilot study designed to investigate differences in mathematical self-efficacy for two groups of students taking a general mathematics unit as part of their year 1 computing and IT undergraduate studies. | Jon Warwick | ||

May 23rd | Beyond the Soup Kitchen - Thoughts on revising the Mathematics "Strategies/Frameworks" for England [182] | This paper addresses matters of general significance to mathematics education but it does so in the context of recent developments in England. In particular, the reader is assumed to be loosely familiar with the Frameworks (also sometimes referred to as the Strategies) for Key Stages 1 and 2 (ages 5-11) and for Key Stage 3 (ages 11-14). | Tony Gardiner | ||

May 8th | The Effect of Graphing Calculators' Use on Students' Understanding of the Derivative at a Point [76] | This study examined the effect of the use of graphing calculators on students' understanding of the concept of the derivative at a point. It investigated whether or not the graphing calculator with its visual representation helps students construct an appropriate concept image of the derivative at a point. | Derar Serhan | ||

May 3rd | The Effect of Computers on Teaching the Limit Concept [396] | This study investigates whether computer support has a contribution to make in teaching by the limit concept. After splitting 52 students into two groups, the limit concept was instructed by using classical methods to one of the groups whereas using computer support was employed in the other group. | Taner Büyükköroglu et al | ||

March 29th | Use of Web-based Simulation to Learn Trigonometric Curves [1260] | The purpose of this study is to investigate the impact of using Trigonometric Graphs, a teacher created web-based simulation, and asynchronous online discussion on students understanding of and performance in sketching transformation of trigonometric curves. | Boon Kiat Ng & Chun Hu | ||

March 15th | Program Development Models and Reform in Turkish Primary School Mathematics Curriculum [30] | The purpose of this paper is to discuss the current reform in the Turkish Mathematics Education at the elementary level by summarizing the types of program development models and changes involved in the current reform. | Cem Babadogan & Sinan Olkun | ||

2005 | |||||

November 7th | Election Paradoxies: Social Choice [169] | In this paper, the writer looks at how the results of elections can vary greatly depending on the voting method used and how the most popular candidate is not always the one elected. A new proof of Arrow's impossibility theorem is presented as well. | Joerg Meyer | ||

October 25th | Knowledge Maps - Tools for Building Structure in Mathematics [127] | In this paper, two special graphical representations of mathematical networks, mind maps and concept maps, are presented. Both knowledge maps are means to show ideas and concepts connected with a topic, in a well-structured form. | Astrid Brinkmann | ||

October 25th | A Review of China's Elementary Mathematics Education [38] | This paper provides an introduction and analysis of the undergoing curriculum reform in China s elementary mathematics education. The curriculum reform is expected to bring a promising future to China s elementary mathematics education. | Linrong Zhang | ||

October 25th | A Framework for Designing Computer Assisted Constructivist Learning Activities [90] | A few computer based activities aiming to teach mathematical concepts and procedures such as digit value and permutational calculations were developed. In this paper, the guidelines to design such computer assisted activities will be discussed and developed computer based activities will be presented. | Erol Karakirik & Soner Durmus | ||

October 25th | On Pedagogical Knowledge in Mathematics: How Secondary School Mathematics Teachers Face the Challenge of Teaching a New Class [31] | The study investigated how six Filipino secondary school mathematics teachers prepared for the task of teaching a beginning college algebra class. Implications for teacher preparation programs and mathematics teacher educators are offered. | Catherine P. Vistro-Yu | ||

October 25th | Diversity as a Chance in Mathematics Classrooms [100] | This article wants to illustrate the idea of diversity as a chance by seven scenes of concrete classroom situations. In order to find such chances, it is important to realize that students do not only vary in their pace of work and their proficiency level but in many dimensions, e.g., their prior experiences, conceptions, motivations, and strategies. | Susanne Prediger | ||

October 25th | Open Source Software Resources for Numerical Analysis Teaching [105] | In this article we bring some remarks about use of Open Source Software in teaching of Numerical Analysis based on our experience with Matlab, Octave, and Pythonbased software systems. | Michal Kaukic | ||

October 12th | Special Characteristics of Engineer Students Knowledge of Functions [267] | This paper looks at the mathematical knowledge of engineering students from Debrecen University, Hungary, and investigates how their knowledge develops as the course progresses. | Rita Nagy-Kondor | ||

September 28th | A Comparison of Learning Preferences and Perceptions of Students for Statistics Concepts and Techniques [52] | This paper is an extension of a comparative study on learning style and method preference of students from culturally different parts of the world. The first sample (TMB) was selected from the undergraduate students in the University of Southern Queensland in the Darling Downs region of Queensland in Australia and the second sample (KTM) was selected from the same level of students in Apex College, Kathmandu, Nepal. | Mehryar Nooriafshar & Tek Narayan Maraseni | ||

September 21st | The Role of Visualization Approach on Student s Conceptual Learning [47] | The aim of this study is to investigate the role of visualization approach on students conceptual understanding. The results of this study, while there is no statistical difference between the control and experiment groups in terms of procedural learning, experimental group students were more succesful in conceptual learning statistically. | Serpil Konyalioglu, A.Cihan Konyalioglu, A.Sabri Ipek & Ahmet Isik | ||

July 5th | Study on 8th Grade Students' Thoughts about the Mathematics Course [26] | This paper investigates the thoughts of the 8th grade students in Turkey on the mathematics course and the relations between the mathematics courses and other variables such as the students' origins, gender and the mathematics scores students achieved. | Nezahat Çetin, Nevin Mahir, Mehmet Üreyen & Ayhan Hakan | ||

July 5th | Some Methods for Composing Mathematical Problems [76] | The article sustains the idea that the mathematical educations should be performed as a continuous research and discovery, not just as a simple transmission of already known ideas. An essential contribution to this activity would be the invention of new mathematical problems. | Radu Bairac | ||

June 30th | Differences Between Canadian and Lebanese Pre-service Elementary Teachers on Their Conception of How Children Learn Mathematics [42] | On a study that explores four-year elementary education students' understanding of how children learn mathematics through the use of concept maps. Thirteen Canadian and 9 students from Lebanon participated in the study. | Ramzi Nasser | ||

June 30th | On Crossover Math Teachers and Certification [35] | On presenting a case for the development of an alternate certification program for crossover teachers: mathematics teachers not specifically trained in mathematics but who teach mathematics. | Theodore Eisenberg | ||

June 30th | Infinite Series from History to Mathematics Education [128] | In this paper an example from the history of mathematics is presented and its educational utility is investigated, with reference to pupils aged 16-18 years. | Giorgio T. Bagni | ||

June 30th | Cooperative Learning, Mathematical Problem Solving, and Latinos [47] | On work with fifth grade Latino students, where professors engaged students in cooperative activities while solving mathematical problems. Their work was based upon theories of social interdependence, cognitive development, and behavioral learning. | Veronica Galvan Carlan, Renee Rubin & Bobbette M. Morgan | ||

June 30th | Toward a Right Way to Teach Linear Algebra [68] | In this article, an overview of the design and implementation of a development course project of linear algebra is presented. The method of instruction in the project is established upon a cooperative approach, exploration and discovery, and writing. | Ismail M. Idris | ||

May 4th | Teaching Statistics with an Interactive Tool [91] | On the use of Computer Algebra's interactive software in the teaching of probability and statistics to students and helping with their understanding of the underlying concepts. | G. Albano, C. D'Apice & R. Manzo | ||

May 4th | The Effect of Using the Geometer's Sketchpad on Jordanian Students' Understanding some Geometrical Concepts [43] | On investigating the effect of using the Geometer s Sketchpad (GSP) on students understanding of some of the geometrical concepts. The sample consisted of 52 students from the Model School, Yarmouk University, Jordan. | Dr. Farouq Almeqdadi | ||

May 4th | Understanding rate of Change Using Motion Detectors: One Teacher's Voice, Perspective and Growth [76] | This study discusses how learning experiences with computer-based motion detectors created through innovative professional development activities helped one teacher develop his own ideas about rate of change relative to velocity and position concepts. | J. Castro-Filho, J. Wilhelm & J. Confrey | ||

May 4th | Quality of Teaching and Learning Interaction for Mathematics Teachers: A Case Study [26] | This paper attempts to find out a correlation among known variables in relation to the development and improvement of the quality of teaching and learning interaction for mathematics teachers. | Martua Manullang | ||

May 4th | Four Women's Motivation for Obtaining Graduate Degrees in Mathematics [87] | This study examines the reasons why four women pursued master degrees in mathematics, in the hopes of shedding light on the question: Why is it that women do not pursue graduate degrees in mathematics to the same degree that men do? | Carmen M. Latterell | ||

May 4th | Roles of Semantic Structure of Arithmetic Word Problems on Pupils' Ability to Identify the Correct Operation [50] | This paper draws on findings from a study conducted in seven primary schools in Seychelles about pupils proficiency in one-step arithmetic word problems to discuss the roles of semantic structures of the problems on the pupils ability to identify the operation required to solve them. | Justin D. Valentin & Dr. Lim Chap Sam | ||

May 4th | A Recent Encounter with an O.C. [18] | This paper looks at how teachers can respond when there is an 'opening in the curriculum' (O.C.) during their lesson, in order to enhance and facilitate further the learning of their students. | Homer Austin | ||

April 13th | Language and Mathematics: A Mediational Approach to Bilingual Arabs [143] | On the outcome of an experiment that attempted to address the language barrier of preparatory year mathematics students, who are acquiring English as a new language of instruction at King Fahd University of Petroleum & Minerals, Saudi Arabia. | B. Yushau & M. A. Bokhari | ||

April 13th | Effects of Preservice Teachers' Math Literacy in a Tutorial Field Experience [58] | On preservice teachers and their preconceived ideas of their mathematical abilities and perceptions of them teaching maths to children who may have the same perceptions and fears of maths. | Dr. Mary Timothy & Dr. Arthur Quickenton | ||

April 13th | Building Mathematical Power: Why Change is So Difficult [56] | On the lessons gleaned from a year-long staff development teacher training experience with urban teachers. The paper addresses the current research on teacher development, describes the implementation of best practices, and shares the results of the year-long study. | Mary Mueller and Lourdes Z. Mitchel | ||

April 13th | Using lattice models to determine Greatest Common Factor and Least Common Multiple [730] | On an alternative representation of whole numbers, one that can be constructed as a manipulative model. The material is particularly useful in providing a visual representation of the Greatest Common Divisor and the Least Common Multiple of numbers. | Ana Dias | ||

April 13th | Windows into Classroom Practice: Using Instructional Videotapes in an Elementary Mathematics Methods Course [94] | On investigating preservice teachers' views about the value of and purposes for the use of instructional videotapes of teaching and learning situations in mathematics in an elementary mathematics methods course. | Lisa Wilson Carboni & Susan N. Friel | ||

April 13th | Geometric Explorations with Dynamic Geometry Applications based on van Hiele Levels [88] | On presenting classroom-tested geometry activities based on the van Hiele geometric thinking levels using dynamic geometry applications. | Sinan Olkun, N. Beylem Sinoplu & Deniz Deryakulu | ||

April 13th | Toward How to Add an Aesthetic Image to Mathematics Edcuation [65] | On suggesting how an aesthetic image can be added to mathematics education. Calls for reform in mathematics education are premised on shifting teacher attention from an absolutist toward a social constructivist philosophy of mathematics and mathematics education. | Paul Betts | ||

April 13th | Bridging the Theory-Practice Gap of Mathematics and Science Preservice Teachers Using Collegial, Peer and Mentor Coaching [56] | On reporting the professional skills that mentors and peers taught 115 Mathematics and Science (M&S) pre-service teachers on 12 weeks of teaching practice. | Lovemore J. Nyaumwe, David K. Mtetwa & Juet C. Brown | ||

April 13th | Assessing the Mathematical Achievement of College Freshman Using Piaget's Logical Operations [86] | On improving higher order thinking skills in Filipino students by assessing and improving the mathematical competencies of preservice teachers. | Jaime A. Leongson & Auxencia A. Limjap | ||

2004 | |||||

October 21st | The Development of Children's Understanding of the Quotient: A Teaching Experiment [40] | On the conceptual development of the Quotient in four children in the US who were studied through a series of parallel individual teaching experiments. | James Middleton and Zulbiye Toluk | ||

October 13th | On Some Visualizations at Different Levels of Mathematics Teaching [815] | On using geometrical or visual illustration of mathematical concepts to make the understanding of them clearer to the learner, as opposed to a purely abstract approach. | Matej Mencinger and Andreja Mencinger | ||

October 12th | Optimizing Computer-Based Developmental Math Learning at an Arabic Women's University [253] | On the use of computer-based learning courses to develop mathematical knowledge of university students and how effective this method of learning is. | D Havill, W B Hashim and S Alalawi | ||

October 12th | A Comparitive Analysis of Mathematics Curricula in Korea and England Focusing on the Content of the Algebra Domain [170] | On the current mathematics curricula followed in Korea and England and, focusing specifically on algebra, the comparison between how the two countries implement these curricula. | Hye Jeang Hwang | ||

October 12th | Predicting Student Success [44] | On the study investigating the legitmacy of using students' GCE Alternative Ordinary Level Mathematics results to predict their Advanced Level Mathematics results. The study was carried out in Trinidad and Tobago. | Betty McDonald | ||

October 12th | Exploring an Interdisciplinary Strategy of Teaching Fractions Through Musical Rhythm to Second Graders [246] | On the potential for using concrete examples in helping children to learn mathematics. Specifically here, the use of music and breaking up notes into smaller parts is used as an aid to help children understand abstract fractions. | Kenneth McGuire | ||

October 12th | Prospective Teachers' Abilty to Pose Word Problems [79] | On the study into assessing the difference in prospective teachers' ability to pose word problems, before and after an instruction intervention. | Nusrat Fatima Rizvi | ||

October 12th | The Statistical Evidence in Describing the Students' Beliefs About Mathematics [77] | On the study into Malaysian students' beliefs about mathematics. Factors that contribute to students' beliefs were identified and then statistically analysed to show their significance. | M Lazim, M Abu Osman and W Wan Salihin | ||

October 12th | The Cultivation of Problem-Solving and Reason in NCTM and Chinese National Standards [87] | On the comparison of the teaching of problem-solving and reason in the USA and China. It looks at how problem-solving skills are developed in children and the differences between methods in the two countries. | Xuehui Xie | ||

October 12th | Elementary School Children's Number Sense [57] | On the findings of a study into elementary school children's number skills in the USA. The 750 pupils involved were from grades 4 to 7. | Ramakrishnan Menon | ||

October 12th | Teacher Training with Cabri Geometry [111] | On the use of ICT software, in this instance a dynamic geometry package, in training future mathematics teachers to be more proficient at using ICT in their mathematics lesson where it is most appropriate. | Judit Jassó | ||

April 15th | FAIM - Formative Assessment In Mathematics [108] | On the trial use of formative assessment and support to improve learning amongst Mathematics undergraduates. | E M Glaister and P Glaister | ||

March 29th | Metacognitive Aspects of Solving Combinatorics Problems [74] | An analysis of the role of metacognition in mathematical problem-solving (on the example of combinatorics problems) and some recommendations for classroom instruction. | Polina Biryukov | ||

2003 | |||||

December 16th | Exploring preservice teachers understanding of two-digit multiplication [24] | On the lack of a fundamental understanding of multiplication algorithms amongst pre-service Mathematic teachers, and some suggestions on how this problem might be addressed. | Ramakrishnan Menon | ||

December 5th | Using DERIVE To Understand The Concept Of Definite Integral [107] | On the use of DERIVE in a calculus course and the effects of the use of this software on students' understanding of the definite integral. | Matías Camacho and Ramón Depool | ||

October 3rd | Instructional Styles in the Teaching of Mathematics Thematically [181] | On the styles of teaching used when teaching Maths in themes, and the extent to which teachers teach Maths in themes rather than in topics. | Boris Handal and Janette Bobis | ||

July 8th | Differentiating Instruction with Marbles: Is This Algebra or What? [75] | On how the use of a differentiated problem-solving lesson involving marbles with pre-service and in-service teachers encouraged the development of their own ability to deliver in a differentiated manner to students. | Mara Alagic and Sandy Emery | ||

May 14th | Factors Contributing to Making the Learning of Statistics an Enjoyable Experience [297] | On the perception of statistics by year-12 students of High Schools in and around Toowoomba in Queensland, and the factors which made these pupils' learning of statistics more enjoyable. | Mehryar Nooriafshar | ||

April 18th | The Mathematical Education of Primary Teachers in Spain [33] | On recent changes in Spain's educational system, its effect on Maths education, and some suggestions that may aid in improving the mathematics education of future primary teachers in Spain. | Lorenzo Blanco | ||

April 18th | Research Teaching: The Great Dilemma [33] | On whether there really is a dilemma between research and teaching. | José Carrillo | ||

April 17th | Making Connections: Improving Spatial Abilities with Engineering Drawing Activities [236] | On the provision of activities for improving middle grade students spatial ability using engineering drawing applications. | Sinan Olkun | ||

April 15th | Adding an Aesthetic Image to Mathematics Education [55] | On the possibility of adding an appreciation of the aesthetic nature of mathematics to mathematics education, and the suggestion that the goal of success for all in Mathematics cannot be achieved without providing opportunities for students to experience an aesthetic image of mathematics. | Paul Betts and Kathryn McNaughton | ||

April 15th | A Cross-National Investigation of Students Perceptions of Mathematics Classroom Environment and Academic Efficacy in Secondary Schools [48] | On the associations between classroom psychosocial environment in mathematics classrooms and academic efficacy. | Joan Adams, Jeffery Dorman & Janet Ferguson | ||

2002 | |||||

November 18th | Textbooks, Word Problems, and Student Success on Addition and Subtraction [162] | On the extent to which textbooks help to develop children's problem-solving skills, and how under-representation of certain types of addition and subtraction problems in text books affects students' success in these types of question. | Sinan Olkun & Zülbiye Toluk | ||

October 17th | Why we need to teach logic and how can we teach it? [44] | Logic is usually left out from education in mathematics. This fact has effects on understanding mathematics and even on learning languages, too. This article sketches the problems and a possible solution. | Mária Bakó | ||

October 17th | Grading Student Projects And Free-Response Questions Consistently, Through Scoring Guides [115] | On the use of scoring guides to achieve consistent assessments of students mathematical achievement | Della Caldwell, James Gleaton & Tuiren Bratina | ||

October 17th | The Use Of Innovative Teaching Methods For 'Maximising' The Enjoyment From Learning Mathematical Concepts [91] | On methods of bridging the gap between a basic mathematical background and the ability to learn and use more advanced techniques | Mehryar Nooriafshar | ||

March 18th | The More Effective Use of Computers in Teaching Mathematics [80] | On the need to use new technology in mathematics education and how teachers may be guided during their initial training and continuing development | Erika Gyöngyösi | ||

2001 | |||||

Sept 17th | Teaching Non-Parametric Statistics to Students with a Non-Mathematical Background [430] | The design and delivery of a multi-media system for teaching statistics to students of Management Science with a limited mathematical background. | Meyryar Nooriafshar | ||

Sept 17th | The Role of Information in the Comprehension and Solving of Statistics Problems [60] | The results of research carried out on a sample of 40 students, and their responses to changes in the wording of some problems in statistics. | Queena N. Lee Chua | ||

Sept 17th | The Role of Statistics in School Mathematics Teaching Today [70] | How to teach statistics in a meaningful way and help dispell some of the fallacies about probabilities | Peter Rasfield | ||

May 25th | The Impact of California's Back to Basics Policies [180] | The impact of Califoria's new mathematics policies on instructional matters and professional development. | Bill Jacob | ||

May 24th | Errors in Teaching/Learning the Basic Concepts of Geometry [150] | Work done with prospective primary teachers to reveal their misconceptions about geometry and how the lessons learned might be of benefit to others. | Lorenzo J Blanco | ||

May 17th | The Changing Educational Framework for the Teaching of Mathematics in China [90] | How the general educational system in China has changed, and an account of the current mathematics curriculum. | Yanming Wang | ||

April 18th | The Development, and Developing of, the Concept of a Fraction [100] | The historical development of fractions and how this could be of help in developing them in teaching. | László Filep | ||

2000 | |||||

Oct 26th | The role of Applications in Maths Teaching [180] | The role of applications in mathematics teaching and the enhancement of mathematics learning through project work. | E M Glaister& P Glaister | ||

July 1st | MEP: The First Three Years [120] | An outline of the problems and effects of implementing, in schools, the findings of a 3-year international comparative study on mathematical progress. | David Burghes | ||

June 13th | Mathematics Teaching & Learning in Vietnam [80] | An overview of the general educational system in Vietnam, with the framework for mathematics and examples of the standards expected. | Dat Do | ||

June 7th | Applicable Mathematics in Mathematical Education [50] | Empirical results of an investigation into the differences between teachers' and students' perceptions of some mathematics lessons | Hans Humenberger | ||

June 1st | Facts & Tendencies in Hungarian Maths Teaching [20] | An explanation for the past successes of mathematics teaching in Hungary, with a warning for the future. | Tibor Szalontai | ||

May 19th | Lessons Britain won't Learn [80] | How policy-makers have ignored much important evidence concerning the groundwork of good education. | David &Clare Mills | ||

May 5th | 'Research Based' Education Policy [120] | This paper looks at the (inevitable) conflicts which arise when a major educational framework is being designed. | Joan AkersBill Jacob | ||

April 13th | An Insight into Problem Solving [80] | An investigation of the self-monitoring strategies used by students while working on problems. | Peter GalbraithMerrilyn Goos & Peter Renshaw | ||

March 29th | The Language of Mathematics [20] | Are we always as clear as we think we are in our teaching of mathematics, or does our language let us down? | Frank Tapson | ||

Feb 22nd | The National Lotteries as a teaching aid. [20] | The authors contend that, moral issues aside, any Lottery can be a useful context for the teaching of some combinatorics, and has an appropriate place in the delivery of the mathematics curriculum. | David Burghes& Peter Galbraith |

The copyright in all of this material belongs to the originators who created it.

The material is made available through the CIMT for downloading and dissemination for