Some of mathematics teaching is routine, like an exercise from a textbook for which you have received instruction and already know what to do. On other occasions, however, teaching mathematics is challenging, involving problems of teaching for which the solutions may not be readily apparent. These situations require the application of mathematical…

This article presents "The Two Children Problem," published by Martin Gardner, who wrote a famous and widely-read math puzzle column in the magazine "Scientific American," and a problem presented by puzzler Gary Foshee. This paper explains the paradox of Problems 2 and 3 and many other variations of the theme. Then the authors…

This paper reports how the context in which a mathematics item is embedded impacts on students' performance. The performance of Year 10 students on four PISA items was compared with performance on variants with more familiar contexts. Performance was not better when they solved items with more familiar contexts but there was some evidence that…

Changes to students' understanding of mathematical notation may be brought about by using technology within mathematics. Taking equality as a case study, the paper provides brief epistemological, historical, didactical, and computational reviews of its symbolic representation in pen-and-paper and technology-assisted mathematics, most especially in…

This study reports on the use of formative, diagnostic online assessments for the topic percentages. Two new item formats (drag-drop and slider) are described. About one-third of the school students (Years 7 to 9) could, using a slider, estimate "80% more than" a given length, in contrast with over two-thirds who could estimate "90%…

Discusses some of the aspects of problem solving that teachers can observe for assessment purposes in a student's practical and written work. Suggests that these observations can be incorporated into a student's assessment traditionally or using alternative assessment devices. (PK)

This paper reviews the presentation of problem solving and process aspects of mathematics in curriculum documents from Australia, UK, USA and Singapore. The place of problem solving in the documents is reviewed and contrasted, and illustrative problems from teachers' support materials are used to demonstrate how problem solving is now more often…

Suggests that problems designed for classroom use should include such factors as ways to introduce the problem, the skills to be developed, the mathematical prerequisites for the problem, key questions, extensions, and solutions. An example is provided which illustrates these and other points. (JN)

Discusses the implications of a research study of more than 2000 students aged 11 to 15 that explored why the students interpret algebra in certain ways. Recommends strategies that can help teachers deal with prior knowledge that students may bring to their study of algebra. (DDR)

Presents examples of the use of open-ended problems in Australia and discusses assessment of open-ended problem solving. (MKR)

Describes the different ways in which two pioneering Australian teachers adapted their teaching to use computer algebra systems (CAS). One teacher used CAS with the primary goal of increasing understanding but restricted student use. The other teacher adopted CAS as an extra technique for solving standard problems, emphasizing time saving routines…

This article describes the factors to which the classroom teacher needs to attend to enhance the mathematical problem-solving abilities of students. Emphasis is placed upon the means necessary to develop the attribute of being a problem solver, rather than focusing on the goal of becoming a problem solver. (JJK)