The United States Military Academy (USMA) has a four course core mathematics curriculum that is studied by all students. The third course is MA205, Calculus II; a multivariate calculus course filled with practical applications. During a Problem Solving Lab (PSL), students participated in a hands-on exercise with multiple vector operations,…

In 1945, Bronislaw Knaster proposed a procedure to divide any number of indivisible goods between a finite number of players requiring the players to place monetary values or bids on all of the goods. Often discussed in math for liberal arts courses that concentrate on contemporary applications of mathematics for non-major students, Knaster's…

This article describes a unique supplementary program that teaches early childhood mathematics (Pre-K to Grade 2), through a series of six problem-solving adventure stories. The mathematics concepts are taught to the children through the medium of oral storytelling sagas in an integrated approach that addresses language arts as well as early…

The theoretical perspective outlined here offers an alternative to explanations of knowledge transfer that posit its source in the construction and application of abstract, context-independent knowledge structures. A case study analysis of an undergraduate student's attempt to solve a series of problems related to an elementary statistical…

The design of technology tools has the potential to dramatically influence how students interact with tools, and these interactions, in turn, may influence students' mathematical problem solving. To better understand these interactions, we analyzed eighth grade students' problem solving as they used a java applet designed to specifically accompany…

This study describes a classroom action research activity regarding a group of elementary school teacher candidates' perceptions of good mathematics problems. A questionnaire containing 20 problems was given, and the candidates were asked to rate the quality of each problem on a 5-point scale. The results revealed that the majority of the teacher…

In this paper, results of a questionnaire about continuity of functions are analysed. The tested students attend Novi Sad grammar school. The aim of this test was to check the student's theoretical and visual knowledge of continuous functions at the end of their high school education. The questions were given with and without the graphs of…

The authors discuss proportional reasoning as a challenging yet central concept for students in the middle grades that lays a foundation for mathematics studied later in high school. Four types of proportional reasoning problems are discussed: (1) Part-part-whole (comparing a subset (part) of a whole with its complement (other part) or the whole…

Recently, the author has been fortunate to be a visitor in a number of classrooms in the United States, England and Europe. On one such visit to an Elementary School in Columbia, Missouri, the teachers accepted him into their normal classrooms for their normal lessons. He moved between three classes: Grade 1, Grade 2 and Grade 4. A snapshot…

This paper explores the wide range of mathematics content and processes that arise in the secondary classroom via the use of unusual counting problems. A universal pedagogical goal of mathematics teachers is to convey a sense of unity among seemingly diverse topics within mathematics. Such a goal can be accomplished if we could conduct classroom…

The "I CAN Learn[R] Mathematics Curriculum" is designed to help ethnically diverse, inner-city students in grades 7 through 10 achieve parity in mathematics and problem-solving skills. It uses an interactive software program to teach pre-algebra and algebra. The "I CAN Learn[R] Algebra 1" course, which was used in all of the…

Students learn to use linear algebra covered in their first algebra course to design mobiles like those created by artist Alexander Calder. (Contains 17 figures and 2 tables.)

We report a dissociation between higher order mathematical ability and language in the case of a man (SO) with severe aphasia. Despite severely impaired abilities in the language domain and difficulties with processing both phonological and orthographic number words, he was able to judge the equivalence of and to transform and simplify…

In this article, we explore the game based on the following problem from the 1st Mathematical Olympiad of Central America and the Caribbean, held in Costa Rica in 1999: Player A turns on the calculator, presses a digit key and then presses the + key. A second later, player B presses a digit key in the same row or column of the last digit key…

Three phases of development of self-regulatory skill in the domain of mathematical problem solving were designed to examine students' behaviour and the effects on their problem solving ability. Forty-eight Grade 4 students (10 year olds) participated in this pilot study. The students were randomly assigned to one of three groups, each representing…