While there has been worldwide interest in Japanese Lesson Study as a model for teacher professional learning, there has been less research into authentic implementation of the problem-solving lesson structure that underpins mathematics research lessons in Japan. Findings from a Lesson Study project involving teachers from three Victorian primary…

Making decisions over multivariate time series is an important topic which has gained significant interest in the past decade. A time series is a sequence of data points which are measured and ordered over uniform time intervals. A multivariate time series is a set of multiple, related time series in a particular domain in which domain experts…

The mythology surrounding Hercules has been a part of human culture for over 2,500 years. In ancient Greek mythology, Eurystheus assigns various labors to Hercules, who has to perform them in order to cleanse his soul. This article treats one of the more famous labors, the fifth labor: The Augean Stables. The labor is provided verbatim from…

When studying correlations, how do the three bivariate correlation coefficients between three variables relate? After transforming Pearson's correlation coefficient r into a Euclidean distance, undergraduate students can tackle this problem using their secondary school knowledge of geometry (Pythagoras' theorem and similarity of triangles).…

Perhaps a business colleague threw out a challenge. The year: around 1200. The place: Pisa. The challenge: Calculate how many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on. The question and its solution found its way into the…

Research findings indicate that specific instructional strategies, such as the use of real-world examples and independent learning activities, are positively related to mathematics achievement. This study was designed to investigate relationships between classroom instructional strategies and mathematics achievement of elementary-school students…

Students' cognitive differences in problem solving have been the focus of much research. One classification of these differences is related to whether visualisation is used. Like mathematical thinking differences, multiple representation preferences are important when considering individual differences. Choosing an appropriate representation is an…

Many delegates at "conference" relish the opportunity, and the space, to "do some mathematics". Opportunity and space help to make the experience memorable, but how often is the quality of the starting point, or question acknowledged? Here is a set of starting points or problems that invite the reader to "do some mathematics". Deliberately, no…

Although students' difficulties in developing and understanding proofs in mathematics is well documented, less is known about how students' example use may support their proof practices, particularly at the middle school level. Research on example use suggests that strategic thinking with examples could play an important role in exploring…

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a…

This paper shows how to teach a mathematics for liberal arts class in an inquiry-based way using ideas from music to launch the mathematical activities. No musical knowledge is required to understand and teach the material. The main activity is analyzing the differences between two kinds of rhythmic palindromes. The content is mathematically…

This paper presents guided classroom activities that showcase two classic problems in which a finite limit exists and where there is a certain charm to engage liberal arts majors. The two scenarios build solely on students' existing knowledge of number systems and harness potential misconceptions about limits and infinity to guide their thinking.…

"Mathematics is more than skills... it is also the excitement of discovery." This is how Derek Holton, one of the contributing authors to this book, defines mathematics. His enthusiasm and energy are echoed throughout by many of the other writers. This is a book to delight mathematics teachers at all stages: experienced and inexperienced;…

Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…

This paper describes the utility of using simulated, rather than real, student solutions to problems within a peer-assessment setting and whether this approach can be used as a means of improving performance in chemical calculations. The study involved a small cohort of students, of two levels, who carried out a simulated peer-assessment as a…