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 author offers innovative approaches to 3 topics that are typically only briefly mentioned (if at all) in money and banking courses. The first topic is a Treasury bill auction experiment in which students have an opportunity to participate directly. The results from a class of 14 money and banking students are used to explain how an instructor…

This project was developed as an interdisciplinary application of the optimization of a single-variable function. It was used in a freshman-level single-variable calculus course. After the first month of the course, students had been exposed to the concepts of the derivative as a rate of change, average and instantaneous velocities, derivatives of…

This contribution reports about a seven-month long video-based study in two regular Flemish sixth-grade mathematics classrooms. The focus is on teachers' approaches towards problem solving. In our analysis we distinguished between a paradigmatic-oriented (focus on the mathematical structure) and a narrative-oriented (focus on the contextual…

The primary application of dimensional analysis (DA) is in problem solving. Typically, the problem description indicates that a physical quantity Y(the unknown) is a function f of other physical quantities A[subscript 1], ..., A[subscript n] (the data). We propose a qualitative problem-solving procedure which consists of a parallel decomposition…

Many students have some difficulty with calculations. Simple dimensional analysis provides a systematic means of checking for errors and inconsistencies and for developing both new insight and new relationships between variables. Teaching dimensional analysis at even the most basic level strengthens the insight and confidence of students, and…

The utility of an "ecologically rational" recognition-based decision rule in multichoice decision problems is analyzed, varying the type of judgment required (greater or lesser). The maximum size and range of a counterintuitive advantage associated with recognition-based judgment (the "less-is-more effect") is identified for a range of cue…

This article describes a geometrical solution to a problem that is usually solved geometrically as an example of how alternative solutions may enrich the teaching and learning of mathematics. (Contains 11 figures.)

Modelling is an important subject in the Bachelor curriculum of Applied Mathematics at Eindhoven University of Technology in the Netherlands. Students not only learn how to apply their knowledge to solve mathematical problems posed in non-mathematical language, but also they learn to look actively for, or even construct, mathematical knowledge…

The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…

This paper draws on a one year study of three secondary school classrooms to examine the nature of student-student-technology interaction when working in partnership with computer algebra systems (CAS) on mathematical modelling tasks and the classroom affordances and constraints that influence such interaction. The analysis of these data indicates…

This project is one of four that were issued to first semester sophomore undergraduates at the United States Military Academy as part of an integrated learning experience at the end of their Calculus II course work. This project was used during a short, seven lesson block of instruction that was intended to capitalize on their recent academic…

The objective of this research was to better understand the transfer of learning between different variations of pre-algebra problems. While the authors could have addressed a specific variation that might address transfer, they were interested in developing a general model of transfer, so we gathered data from multiple problem types and their…

This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…

Several decades ago, V. A. Krutetskii conducted a multiyear study to investigate the various types of thinking that academically advanced, or as he called them, gifted mathematicians used. Following an in-depth look at Krutetskii's nine ways of thinking, a model is proposed that will provide direction for teachers in selecting problems. The model…