Mathematical Mediated Language (MML) is a teaching technique designed to enhance children's learning. Teachers who use MML engage in a dialogue with children about mathematics concepts that apply to the activity in which they are engaged. This dialogue links "conceptually related linguistic and mathematical knowledge." In other words, teachers…

The "Principles and Standards for School Mathematics" published in 2000 by the National Council of Teachers of Mathematics (NCTM) created a vision of mathematical concepts and processes to establish core educational guidelines for instruction from grades K to 12. The overall plan does emphasize higher level thinking, problem solving, and…

There is a common opinion that mathematics is difficult for persons with Down syndrome, because of a weakness in numeracy and in abstract thinking. Since 1996, some single case studies have suggested that new opportunities in mathematics are possible for these students: some of them learned algebra and also learned to use equations in…

"Mathematical habits of mind" include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work. Current recommendations emphasize the critical nature of developing these habits of mind: "Once this kind of thinking is established, students can apply it in the…

One of the earlier, more challenging concepts in linear algebra at university is that of basis. Students are often taught procedurally how to find a basis for a subspace using matrix manipulation, but may struggle with understanding the construct of basis, making further progress harder. We believe one reason for this is because students have…

Developing the connection between biology and mathematics is one of the most important ways to shift the paradigms of both established science disciplines. However, adding some mathematic content to biology or biology content to mathematics is not enough but must be accompanied by development of suitable pedagogical models. I propose a model of…

An nth-term problem involves a sequence. Students must determine which expression will allow them to calculate the nth position of the sequence. To solve such problems, students are to find "a rule that determines the number of elements in a step from the step number." These types of problems help students develop concepts of functions, variables,…

The mathematics of information processing and the Internet can be organized around four fundamental themes: (1) access (finding information easily); (2) security (keeping information confidential); (3) accuracy (ensuring accurate information); and (4) efficiency (data compression). In this article, the author discusses each theme with reference to…

In this article we examine the activities of 2 public lessons prepared and conducted by a group of elementary school teachers in China. We employ the conceptual lens of deliberate practice to understand how the public lesson activities possibly contributed to improvement of the teachers' knowledge and instructional performance. We found that…

Starting in September 1999, new students at ETS were required to own the TI-92 Plus or TI-89 symbolic calculator and since September 2002, the Voyage 200. Looking back at these ten years of working with a computer algebra system on every student's desk, one could ask whether the introduction of this hand-held technology has really forced teachers…

It is a pity that for so many people not involved in Teaching, and for a surprising number who are, mathematics in schools is "chiefly" all about the ability to know a set of facts, multiplication tables and addition bonds in particular, rather than the capacity to reason and explore patterns and relationships in Number and Shape.…

Making constructions with paper is called "origami" and is considered an art. The objective for many fans of origami is to design new figures never constructed before. From the point of view of mathematics education, origami is an interesting didactic activity. In this article, the authors propose to help High School students understand new…

Recommendations and standards from various stakeholders in the mathematical preparation of teachers, such as "The Mathematical Education of Teachers" (http://www.cbmsweb.org/MET_Document/chapter_2.htm) and "Beyond Crossroads" (http://beyondcrossroads.amatyc.org/doc/CH6.html), call for courses that emphasize connections within topics in…

The combination of "Carnegie Learning Curricula and Cognitive Tutor[R] Software" merges algebra textbooks with interactive software developed around an artificial intelligence model that identifies strengths and weaknesses in an individual student's mastery of mathematical concepts. The software customizes prompts to focus on areas in…

The representation of fractions in long-term memory (LTM) was investigated by examining the automatic processing of such numbers in a physical comparison task, and their intentional processing in a numerical comparison task. The size congruity effect (SiCE) served as a marker of automatic processing and consequently as an indicator of the access…