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As part of a reflective paper, fifth-grade student Jony offered the riddle that appears in the title of this article. His answer, 'a construction worker,' showed that he had made [...]

A visitor to Carol Pettigrew's grade-three class in North Vancouver, Canada, might be forgiven for skepticism when told that a mathematics class is about to start. The children, most wearing [...]

This article examines how mathematics teachers can incorporate multicultural education into studies of numerals and mathematic representation in different cultures. Topics include cross-cultural mathematics projects and teaching students about ancient number systems.

Issues concerning the teaching of iterative and recursive mathematical techniques are discussed. In particular methods for the understanding by students of recursive thinking are examined.

Issues concerning the use of mathematical notations are discussed. In particular the correct use and understanding of notation for algebraic variables by students is described.

Issues concerning the use of calculators by mathematics students are discussed. In particular the memory limitations of currently available calculators are investigated and methods for overcoming this problem are described.

Issues concerning the practical application of mathematics in every day situations are discussed. In particular a weight/height chart appearing in the media is analysed and questions and answers provided.

A pull-out calendar for September is presented with each day containing a mathematical problem. Answers with detailed solutions are provided.

Issues concerning the use of magic squares as mathematical teaching aids are discussed. In particular the first known magic square, the ancient Chinese Luoshu, is described.

This article provides mathematics teachers with techniques for creating more engaging and interesting curricula, in order to encourage students' complex problem-solving skills. The success of a video-based instruction format is detailed.

Techniques used to teach parametric equations using the drawing toy Spirograph are described and illustrated. Parametric equations should be taught to high school mathematics students because graphing calculators are now available to assist the teaching process.

Techniques used to create a vortex tessellation diagram featuring a single object shown multiple times are described. Rotational mapping and symmetry are discussed.

Fractals can be used to stimulate the mathematics pupil's learning and interest. They are unpredictable, easy to relate to and straightforward to teach. Techniques used to teach fractal geometry are described and illustrated.

Newspapers provide interesting data for students to analyse and relate to in terms of statistics. Techniques used to teach statistics using newspaper articles are discussed and described. Example data featuring race admission patterns at two universities is shown. Students should be encouraged to work together and debate statistical concepts within the classroom.

Funny stories can be used to enhance the teaching process in statistics. They make the subject interesting and encourage students to relate to statistics in terms of everyday life. Funny anecdotes, such as the examples given, are easy to remember.

Algebra should be introduced to mathematics students using fundamental techniques that have already been digested. Novice students can find symbol manipulation, traditionally used from the beginning of algebra courses, hard to relate to. Techniques used to give students a better understanding of the discipline are discussed.

Teachers of mathematics can introduce an approach that makes use of root problems for group work in geometry. The method involves tasks that are suitable for group investigation and requires students to work from various numerical examples toward making generalizations. This technique allows students to develop different strategies for solving the same problem, thus, promoting group discussion, problem solving and inquiry. It also fosters a learning environment that enhances the students' ability to communicate and reason mathematically.

National Council of Teachers of Mathematics (NCTM) Pres Gail Burrill believes that improving the state of mathematics education in the country is an enormous challenge. Nevertheless, she is optimistic that the challenge can be successfully met. She stresses the need for schools to adopt a coordinated and structured pre-K-12 curriculum focused on mathematics to raise students' achievement. She also argues in favor of a mathematics curriculum that emphasizes algebraic thinking and the way symbols work.

Rubrics are highly effective in teaching mathematics courses in high school. These sets of guidelines are ideal for evaluating and scoring student responses to one or more tasks. Rubrics are well-suited for evaluating a wide range of tasks such as portfolios, journals, open-ended tasks, free-response tasks, performance tasks and projects because these tasks involve either multiple strategies or multiple solutions for obtaining a single solution. Rubrics can also discern different achievement levels among high school mathematics students.

Teachers of mathematics play a significant role in making students learn how to solve rational equations in algebra through an interactive classroom discourse. Mathematics teachers serve as initiators, facilitators and experts while fostering a classroom environment that allows students to develop their problem solving skills. Rational equations may be introduced by posing a problem and asking the students to work in small collaborative groups to find different ways of solving the problem.

Students of mathematics fail to grasp concepts because of certain erroneous way of thinking. They tend to make conclusions by relating one concept to another and do not investigate the underlying principle and truism. They also absorb ideas simply because the concepts were presented by some authoritative figure and have very limited ways of comprehending. To address these concerns, teachers should become aware of these thought processes and address three intellectual requirements, namely need for calculation, need for formalization and need for elegance.

Mathematics portfolios help students to focus on their course work. They should comprise of at least five examples of a range of course work including homework and tests. Portfolio examples and subsequent teaching assessments are described.

Mathematics teachers must be aware of their pupils' knowledge base to maximize the benefits of teaching. Testing knowledge through assessment is a common approach in teaching. Closed questions help the teacher assess knowledge but do not provide much information about the individual's real understanding of mathematics. Techniques to assess knowledge in the context of individual understanding are given.

Reforms in mathematics education can change the traditional pedagogy which focuses on lectures to passive students. This is an imbalance, for learning is facilitated by doing, followed by reflection on the results. The traditional mode of student activity is by doing homework away from the lecture. Reform themes include intuitive approaches to give conceptual understanding to the average student, and technology use.

Balance is needed in mathematical education, so that reforms do not overthrow effective traditional teaching. Five questions can be asked about reforms, from a traditional viewpoint. These cover maintenance of standards, calculators' impact on basic skills, constructivism, homework and the necessity of group learning. A good interaction between teacher and student is necessary and important, and this must be balanced with any pedagogical changes.

One of several factors that affect students' learning of mathematics is their disposition towards mathematics. As used here, mathematical disposition means "a tendency to think and act in positive ways" […]

Teachers can use their personal interests or backgrounds to relate the teaching of mathematics to the real world. The linking of real world experiences to mathematics concepts and lessons helps students understand concepts better and appreciate their significance in the real world. A 5th grade teacher at the Edith Bown Laboratory School integrated the study of housing and house construction to math by allowing his students to embark on a house building project., A major theme in calls for reform in mathematics education is the recognition of the need to connect the study of mathematics to the rest of the world (American Association [...]

A multimodal approach provides a more effective alternative method for teaching mathematics. The use of pictorial-journal writing, in particular, can help students understand and retain mathematical concepts through the use of pictures, symbols, numbers and manipulatives. It also allows teachers to monitor their students' performance through their writings about the subject. This two-way process can improve the students' ability to define concepts and develop a systematic and logical approach to problem solving., Come every fall, teachers of mathematics are confronted with oversized classes filled with students who vary in both their learning style and their way of communicating what they have learned. [...]

Students' emotional responses to non-routine or creative problem solving may be negative due to the hard work and frustration involved. The responses are classified into global and local responses for problem solving. Teachers may obtain positive emotional student responses by detailing their own academic struggles to students, and may encourage problem solving by assessing solution procedures and actual answers of students. Group discussions may also contribute to a positive student response.

A new three-dimensional graphic technique and modelling method helps students gain a good perspective of complex, geometrical solids. Coordinate geometry and a three-dimensional distance equation generate models. A three-dimensional, four-parallel plane model is used to develop geometric solids such as prisms by converting the parallel plane figure into a three-dimensional graph and plotting various coordinate points.

The National Council of Teachers of Mathematics (NCTM) has developed a framework that will enable middle school mathematics teachers to use alternative methods of instruction with the support of school administrators and families. Mathematics-related games which include manipulatives satisfy four or more NCTM curriculum standards and train middle schoolers to enjoy math., It is evident that our society as a whole needs to take a new look at the way mathematics is taught. The National Council of Teachers of Mathematics (NCTM) has [...]

A classroom exercise concerning polyhedra shed light on the improvement of the teaching of mathematics. The encouraged three-step philosophy involved the action to realize concepts, the accuracy in resolving a problem, and the intention to perform steps and clearly explain their goals. The main proof that this technique and exercise worked was the sincere vehemence of students that certain shapes existed in an icosahedron. This case proves to students the usage and relevance of mathematical concepts such as polyhedra, and also reveals the impact of their individual levels of thought.

University, elementary and secondary school policies regarding mathematical tests must change if the teaching of mathematics is to improve. Teachers must make students view them as allies instead of manipulative foes, must halt the excessive emphasis on exams and must make the courses be perceived as vital sources of student enrichment instead of difficult requirements for graduation and employment. This philosophy seems overly idealistic given the situations of daily struggle for teachers and educational leaders, but experiments such as those given at Hunter College in NY are bright examples.

A strategy for solving math document problems is described. They involve three general steps - identification, problem formulation and computation. Identification entails knowing which numbers are essential for the problem to be solved. Problem formulation entails knowing how to state the problem in mathematical format. Once these two have been satisfactorily dealt with, computation is easy.

A college professor devised an unconventional mathematics course for liberal arts which encouraged its students to think and acquire a sense of curiosity despite a non-emphasis on specific mathematical details. Much of its foundation came from recreational texts and the philosophies of Polya, Harold R. Jacobs and Wayne Wickelgren. Thelong and difficult development of this course is thus recalled. It was able to achieve the essence of its goal in instilling a mode of reasoning, although much improvement in the interaction between teacher and student was still required.

Successfully developing a culture of mathematics within a supportive community lead to profound teacher growth and fulfillment. To empower teachers to work hard toward the goals of mathematics education, a supportive community that respects and values the teachers' contributions is needed. Teachers need to reflect on their teaching, on their students' learning and on how they learned mathematics themselves., Rachel's experience of mathematics is typical of that of many elementary school teachers. She experienced it as a collection of rules, rituals, and routines; an arbitrary, unconnected array of procedures; [...]

Teaching fractional operations to students must go beyond manipulation of symbols and memorization of processes. Students must be able to relate these concepts to everyday problems and understand the underlying meaning behind these. One suggested activity is to draw equal partitions on a rectangle and use this diagram to demonstrate the relationships between parts and a whole. These parts can also be used to represent mathematical sentences.

The learning of new mathematical concepts must be aided by concrete visual materials to facilitate better understanding. This enables students to enhance their reasoning ability and to become convinced of mathematical relations taught to them. One activity that could be useful in the teaching of exponents uses a sequence of shapes. Another makes use of diagrams to illustrate division of same-based powers.

The teaching of transformation geometry at the beginning of a high school geometry course is recommended. This subject, which is described as 'the geometric counterpart of functions,' can be integrated with traditional high school geometry to generate several advantages. This technique enables students to visualize geometry problems before they deal with them deductively. Visualization makes it easier for the students to understand abstract geometrical concepts.