Search

The article focuses on developing a coherent approach to teaching the concept of functions in mathematics. It emphasizing the importance of understanding relationships, variables and representations; exploratory and technology-integrated curriculum that allows students to explore various mathematical relationships and engage in meaningful mathematical investigations and suggests moving away from a linear progression and instead promoting a diverse understanding of functions from an early stage.

The article offers information related to "Care" by Anne Watson, which appeared in the periodical "Mathematics Teaching" is presented. Topic includes on the extent and power of love of mathematics and of learners drives, familiarity with quantitative and spatial combinations and mathematically focused interactions were the key ingredients of good teaching: foundational content and developmental pedagogy.

The article analyzes issues associated with mathematics education research and professional knowledge associated with mathematics pedagogy. Topics discussed include "worked example effect" as the best known cognitive load theory (CLT) contribution to knowledge, effect of using worked examples for all mathematics and for all learners in all contexts and extended thinking to solve quadratics.

In the article, the author discusses the variation theories and dependency relations in mathematics education. Also cited are the invariable components in mathematics like the relationship of the elements, the additive and dependency relationships of the elements, and the use of inductive reasoning in mathematics education.

The article discusses the interpretation of P in the concrete, pictorial and/abstract (CPA) approach, stating that anticipation of p-prims can help with the choices of pedagogical examples.

The article presents the discussion on classrooms committed to care in and through mathematics learning and teaching. Topics include having an Aboriginal home language and cultural context doing not and knowing nothing of the heritage; and expecting children to learn by watching, exploring, and using physical resources among other children and adults modelling actions and behaviour.

In this article, the author describes why she sometimes sees mistakes as intelligent answers to mathematical questions. Topics discussed include application of generalizations, psychologist Daniel Kahneman's distinction between fast and slow thinking; and identification of how intuitive responses to tasks, based on prior experience lead to error identified by professors Shmuel Avital and Edward Barbeau.

In this article the authors examine their own mathematical thinking. Topics include one approach, which is started with marking the angles and doing this with marks rather than letters because one can give marks different weightings, and a dynamic geometry demonstration, which was set up, while giving a visualisation of its probable truth.

In this article, the author discusses her workshop on variation at the Association of Teachers of Mathematics (ATM) conference 2016 on mathematics. Topics discussed include use of variation with strong mathematical and pedagogical intentions, role of variation in helping avoid simplistic assumptions about graphs and the "Midlands Mathematics Experiment" that asked students to tabulate areas and perimeters in all cases.

The author presents her thoughts on why the use of sequences in the mathematics section of the British National Curriculum is incoherent and negatively impacts learning. She criticizes ideas and habits found in textbooks, assessment tasks, and teaching priorities prior to the establishment of the curriculum.

The article discusses the author's understanding of the word "consolidation," as applies to the teaching of mathematics and the "Cockcroft Report." Topics discussed include the relationship between consolidation and practice, the role of consolidation in problem-solving and investigative work, and the role of signs and meanings in mathematics.

The article presents the author's statements to questions related to mathematics teaching. The author discusses the proper lesson planning for mathematics teaching and cites the applicability of music to the said subject by referring the Bowland case studies. The author also expounds the right models and abstract ideas for the integration of the two subjects.

The article focuses on the importance on notation in supporting the children's understanding of mathematics in Great Britain. It explores the issues that makes notation powerful and obstructive as revealed in the discussion by the Annual Institute of Mathematics Pedagogy. The Institute suggests to use number lines that extend below zero to be able to overcome the difficulties of using notation.

The article presents a mathematical challenge that allows learners to discover surprising ideaa regarding the subject. It offers various tasks that can generate discussion on how surprise can be created, generated, nurtured and harnessed during mathematics training. They include the sandpiles task that requires learners to predict shapes, and the double-digit reduction task develop by Milan Hejny.

Provides information about the Improvement Attainment in Mathematics Project which identifies and develops ways to stimulate mathematical thinking. Aim of the project to improve attainment of underachiever students in K3 in mathematics; Collaboration between the University of Oxford and the University of University of Birmingham with the participation of teachers; Characteristics of teaching that took place in the project.

Illustrates the use of student-generated examples as an integral part of learning about concepts, particularly in mathematics. Use of student-generated problems for assessment purposes and to provide contexts for engagement with mathematics; Situations where students have been asked to create examples in ways which encourage them to search, question and transform their knowledge.

Deals with parallels between the complexities of teaching, of learning and that of supporting the development of teaching mathematics. Demonstration of how a complex story can hide more than it reveals; Complexity of questions and prompts for mathematical thinking; Suggestions for mathematics teachers to broaden the range of questions and prompts that they use in the classroom.

Discusses the factors that affect professional judgement among mathematics teachers in Great Britain. Effects of past teaching experiences in professional judgement; Stories about long multiplication and its correlation with teachers' informal judgements.

Presents author's personal reactions to the Russian schools she visited. Teachers and students of Mathematics; Attitudes and behaviors; Classroom discussions.

The article offers information on division as an arithmetical operation. The division algorithm does not yield enough clues about what it means. The author says that a new national curriculum is being designed in Great Britain but whatever it contains, division will continue to determine whether students are able to make sense of secondary mathematics.

The article focuses on the significance of learning algebra in mathematics. It tackles the various concepts of algebra in school levels and states that it comprises of several mathematical functions such as its relevance in transforming and solving equations, modelling situations and on learning about variables. It also notes that learning algebra means determining the use of mathematical notations and arithmetic operations.

Discusses a moment in a lesson when the teacher and students have used a strategy about mathematical thinking. Potential to confuse the form of a recommended strategy with its intended function in terms of learning and doing mathematics; Ability of a student to describe a general formula which applies to a particular structure; Different methods of doing a division calculation in a plenary session.

The article discusses a range of models for multiplication. Topics discussed include a device that uses the principle of variation with the juxtaposition of multiple formats; the principle of variation used in the format of a Structured Variation Grid (SVG); and a grid is called Drakensberg which provides comparison of static to provoke awareness of variation and invariance.

Analyzes a Japanese primary mathematics lesson which teaches six-year-old children that seven minus three equals four. Mathematical features of the lesson; Teaching techniques offered by the lesson.

Presents insights on papers presented in second and seventh International Congress on Mathematical Education (ICME). Changing concerns of the ICME; Teachers as researchers in action; Reason behind the gap between teachers and researchers in mathematics.

A personal narrative is presented which explores the author's experience of participating in a discussion at the 2015 Association of Teachers of Mathematics on values in mathematics classrooms.

The article reflects on cognitive load theory (CLT). Topics include The current dominance of CLT influence in policy and advice about mathematics teaching is in danger of limiting what is meant by ‘learning mathematics' to ‘what can be learnt by micro-managing classroom activity to what is shown to be effective for a limited range of mathematical knowledge and skill; and Crude applications of cognitive science reduce the scope of mathematics in schools.

In this article the author shares thoughts on cognitive load theory (CLT). Topics include discuss aspects of mathematics education and the value of inquiry approaches to teaching mathematics and approaches that claim to be informed by cognitive science; and considered the limited time for educational input on routes into teaching mean that generic teaching skills are focus for new teachers rather than pedagogic knowledge for mathematics.

In this article, the author discusses the relationships in secondary mathematics and makes the case for analytic responses from students rather than more immediate, less considered responses. The author emphasizes that a key difference about mathematics is that individual problems can be solved by using empirical approaches but they do not themselves lead to new mathematical knowledge or mathematical reasoning. The article also offers some recommendations for teaching secondary mathematics.

The article focuses on the importance of relations among quantities in Mathematics. It suggests that students need to achieve an understanding of number which comes from several threads of development which includes counting discrete objects, knowing about quantities of all kinds, and comparing quantities. It states that the principle of learning how to read, interpret, and represent a mathematical problem becomes more important as students learn harder mathematics.

The article presents information regarding the Association of Teachers of Mathematics-Southern Examining Group (ATM-SEG) 100% General Certificate of Secondary Education (GCSE) coursework syllabus. This syllabus was pioneered and piloted between 1986 and 1994 and defined coursework as the work done by students during their GCSE years. The ATM-SEG GCSE proved to be an important movement in learning, teaching and assessing mathematics for students.

Discusses key issues concerning the power of three, a task structure in teaching math that encourages learners to explore beyond obvious answers. Key features of the task structure in math education; Search for situations in which three is not a self-imposed number of possibilities, but turns out to be the mathematically constrained number of possibilities; Implications on mathematics education.

Discusses moments in mathematics when algebraic and geometric representations coincide. Instances where an algebraic proof exactly mirrors a spatial argument that can be seen; Search for more elegant proofs that unite multiple representations; Questions regarding proofs based on static diagrams.

Discusses activities in which proof was kept as a background objective for a number of mathematics lessons. Exercise involving long multiplication; Construction of a number of geometric shapes; Tessellation made with triangular holes by students who were tessellating with some dodecahedron mats.

Presents Anne Watson's opening speech at the Association of Teachers of Mathematics 1993 conference in Great Britain. People's perception of mathematics education; Offering of itemized till receipts and book of raffle tickets.

A correction to the article about surprise that was published previously is presented.

The article presents information about a student who was given certain mathematical problems related to algebra for solving. The student while experimenting and observing during solving the problem found out that part of the problem can be solved by a "digit sum" conjecture. He further found that the conjecture was only a parody and was not the correct way of solving the problem put forward to the student. The student was allowed to proceed at the wrong track for exploration and learning.