The variation theory of learning emphasizes variation as a necessary condition for learners to be able to discern new aspects of an object of learning. In a substantial number of studies, the theory has been used to analyze teaching and students' learning in classrooms. In mathematics education, variation theory has also been used to explore…

International comparative studies of education have shown that the increase in mathematical attainment differs significantly among students in relation to the different school types in which their mathematical foundations were acquired. In tertiary education, the same differences are observed with respect to simple tasks that relate to the subject…

The National Mathematics Advisory Panel (NMAP, 2008) asserts that a foundational knowledge of fractions is crucial for students' success in algebra; however, empirical evidence for this claim is relatively nonexistent. In the present study, we examine the impact of middle school students' fraction and whole number magnitude knowledge on various…

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

This monograph offers an overview of the current research work carried out in Croatia and the surrounding countries, and specifically an interesting insight in teaching and learning issues in these countries. The authors discuss the need of the general population for becoming good problem-solvers in society of today, which is characterised by…

In this paper we demonstrate that "lesson study" may be adapted from its primary use as a professional development strategy for use as a research strategy, especially to identify principles of good lesson design. We report on a project undertaken in two Australian secondary schools where lesson study research was used to investigate the…

Pedagogical maps provide a graphic depiction of the way in which teachers exploit the presence of Computer Algebra Systems (CAS) in their classrooms. They can show differences, and can also show growth, as well as personal preferences and reactions to particular teaching assignments. They might also be used for teachers to reflect on their own…

Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

Explores the ramifications of two three-year-long experiences with different pedagogical approaches to beginning algebra. Focuses on differences in the nature of subject matter understandings and explores the impact on the teacher to support students' classroom exploration of mathematical ideas. (Contains 58 references.) (Author/ASK)

One of the workshops at the 10th SNM Stowarzyszenie Nauczcieli Matematyki (SNM) conference was entitled: Do we really need algebra? The workshop members were given several problems to consider. By doing these problems and reflecting on them the participants explored some important aspects of the question posed. Moreover they became aware of a…

This book is a collection of activities designed to complement an Algebra I program that features cooperative learning. The activity descriptions contain learning outcomes, the National Council of Teachers of Mathematics (NCTM) standards addressed in the activity, a suggested time frame for the activity, assessment opportunities, materials…

Methods of teaching students to solve equations and inequalities containing parameters are suggested. (DT)

This paper explores questions about linear relationships through the use of pattern. Participants in the session generated and extended patterns and used calculators to investigate the relationships. Examples from current Texas Instruments (TI) books and U.S. textbook series, plus examples from proposed TI materials are shared. These activities…

Topics covered are: a game to provide drill with linear equations; the relationship between area and perimeter in a triangle; a new form for factoring polynomials; and a technique for graphing inverse functions. (MP)

Demonstrates techniques for teaching quadratic equations. (KHR)