This paper explores the wide range of pure mathematics that becomes accessible through the use of problems involving powers. In particular we stress the need to balance an applied and context based pedagogical and curricular approach to mathematics with the powerful pure mathematics beneath the simplicity of easily stated and understandable…

In their sections on inverses most precalculus texts emphasize an algorithm for finding f [superscript -1] given f. However, inspection of precalculus and calculus texts shows that students will never again use the algorithm, which suggests the textbook emphasis may be misplaced. Inverses appear primarily when equations need to be solved, which…

A inquiry-based approach called the "modelling discussion" is introduced for structuring beginning modelling activity, teaching new mathematics from examining its applications in contextual situations, and as a general classroom management technique when students are engaged in mathematical modelling. An example which illustrates the style and…

In this note we consider a type of integral that is usually presented as an example in any textbook discussion of integration by parts. Invariably this integral is determined by integrating by parts twice and solving. We will present an alternate approach to this integral which makes use of the linearity of the integral, i.e., the fact that…

Critical thinking has long been a goal of social studies education, and its importance has been reiterated in documents delineating standards for the social studies. Yet, teaching critical thinking is problematic because there are competing definitions and practices and many barriers to its implementation (Wright 1995; Onosko 1989). In this…

This article relates to an empirical study based on the use of mathematical symbolism in problem solving, twenty-five pupils were interviewed individually at the end of grade one; each of them was asked to solve and symbolize 14 different problems. In their classical curriculum, these pupils have received a traditional education based on a…

The Chinese used the idea of generating equivalent expressions for solving problems where the problems from a historical Chinese text are studied to understand the ways in which the ideas can lead into algebraic calculations and help students to learn algebra. The texts unify algebraic problem solving through complex algebraic thought and afford…

The way in which two teachers, Elizabeth and Carolyn, posed problems to develop their own conceptual understanding of division of fractions in terms that would also be meaningful for their students is described. Carolyn and Elizabeth's approach is to pose several problems of various degrees of difficulty and complexity for each aspect of the…

The 10th International Conference on Educational Data Mining (EDM 2017) is held under the auspices of the International Educational Data Mining Society at the Optics Velley Kingdom Plaza Hotel, Wuhan, Hubei Province, in China. This years conference features two invited talks by: Dr. Jie Tang, Associate Professor with the Department of Computer…

In this paper we discuss a study that looks at the kinds of practices that Latino parents use to support their children's learning of mathematics. Some of our findings reveal that parents react to their children's mathematics education looking back to their own experiences as students. Thus, in some cases, they are faced with pedagogical…

The National Council of Teachers of Mathematics' (NCTM's) Process Standards support teaching that helps students develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every middle grades math teacher the opportunity to explore each standard in depth. The series offers friendly,…

In this study, we discuss the scaffolded design of ODRES (Observe, Discuss, and Reason with Evidence in Science), a computer tool that was designed to be used with elementary school children in science, and report on the effects of learning with ODRES on students' conceptual understandings about light, color, and vision. Succinctly, dyads of…

Research on help seeking with a computer coach providing on-demand help has not produced fully adequate models of the process from a cognitive perspective. The present study postulates a model of help seeking from a cognitive perspective and tests this model in a learning situation characterized as problem-based and computer-supported. The…

This monograph argues that the case method of instruction, used effectively in legal and medical education, offers unique potential for revitalizing the field of teacher education. A description of the use of the case method in two different teaching sessions demonstrates how the method can exemplify the way a teacher frames and solves a dilemma…

Problem-based learning (PBL) is a pedagogical method that challenges students to think intuitively, learn cooperatively in groups to seek solutions to real world problems. These problems are used as the building blocks to engage students' curiosity and initiate independent learning of subject matter. Authentic, alternative assessment plays a key…