Recognizing and responding to students' thinking is essential in teaching mathematics, especially when students provide incorrect solutions. This study examined, through a teaching scenario task, elementary preservice teachers' interpretations of and responses to a student's work on a task involving reflective symmetry. Findings revealed that a…

This study examined the impact of teachers' characteristics and self-reported practices on students' Algebra achievement while controlling for students' characteristics. This study is based on the secondary analysis of data collected from a nationally representative sample of 9 th grade students and their mathematics teachers during…

We present an analysis and discussion of the "tanda," a multiperson pooled credit and savings scheme (a rotating credit association or RCA), as described by two informants from Mexican immigrant communities in California. In the tanda, participants contribute regularly to a common fund which is distributed to participants on a rotating…

This study determines whether web-based instruction (WBI) represents an improved method for helping preservice teachers learn procedural and conceptual knowledge of fractions.. The purpose was to compare the effectiveness of web-based instruction (WBI) with the traditional lecture in mathematics content and methods for the elementary school…

We present a general formula for a triple product involving four real numbers. As a particular case, we get the sum of a triple product of four odd integers. Some interesting results are recovered. We derive a general formula for more than four odd numbers.

This paper examines a real life question of gamble facing lottery players. Combinatorial dependence plays a central role in shaping the game probabilistic structure, but might not carry the merited weight in punters' considerations.

Let R be an associative ring which has a multiplicative identity element but need not be commutative. Let f(X) = a[subscript n]X[superscript n] + a[subscript n-1]X[superscript n-1] + ... + a[subscript 0] [is a member of] R[X] and [alpha] [is a member of] R. It is known that there exist uniquely determined q(X) = b[subscript n-1]X[superscript n-1]…

The mean value theorem for differentials is basically a consequence of the fundamental theorem of calculus for Lebesgue integration.

Since most students "hate" the concept of limit, in order to make them "happier," this article suggests a couple of naive "lim (h[right arrow]0)-is-missing" problems for them to try for fun. Indeed, differential functional equations that are related to difference quotients in calculus are studied in this paper. In particular, two interesting…

Interspersing easy problems among challenging problems has been shown to both increase students' preference for completing math worksheets and the fluency with which they complete challenging problems. Although early research examining the interspersal procedure in mathematics was conducted with college-age students, there are a growing number of…

The purpose of this note is to outline further enrichment exercises with rhotrices and thus to stimulate ideas on mathematical arrays and structures. Rhotrices provide students with examples on how to imagine new forms of arrays and their classifications as abstract structures.

Web Access Pattern (WAP), which is the sequence of accesses pursued by users frequently, is a kind of interesting and useful knowledge in practice. Sequential Pattern mining is the process of applying data mining techniques to a sequential database for the purposes of discovering the correlation relationships that exist among an ordered list of…

Teachers know that Differentiated Instruction (DI) helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategies that teachers can use across all math…

This study used concept maps to investigate the effect of using graphing calculators on students' understanding of the derivative at a point. The study looked for differences between the concept images that are held by students' who are using graphing calculators and the students who are not using them. Seventy one students enrolled in two…

In many practical situations scaling the data is necessary to solve linear programs. This note explores the relationships in translating the sensitivity analysis between the original and the scaled problems.