This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Student thinking, a learning cycle, and procedural fluency are discussed in this article, which is the second installment in the series. [For the first installment in this series see "Promoting a Conceptual Understanding…

Student ability to demonstrate mathematical creativity positively affects their mathematical learning. Further, creativity-based mathematical instruction (CBMI) may enhance divergent thinking and precipitate a highly creative mathematical learning environment. In this literature review and discussion, it is posited that CBMI has distinctively…

In this paper, we draw on the contemporary perspective of inclusive materialism offered by de Freitas and Sinclair to contribute to current discussions on the role of the body in the learning of mathematics. Using the notions of "distributed agency" and "assemblage," we illustrate the way in which three students engage with a…

Empirical arguments rely on examples without necessarily addressing all cases. Students should be skeptical of empirical evidence and should seek more secure arguments for generalizations, such as those that explain why a generalization is true for all cases. Generalizing on the basis of patterns in data is an important mathematical practice;…

Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object's geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is…

In this article, the author wishes to emphasize two fundamental points related to theory that were significantly underplayed in Simon et al.'s "A Developing Approach to Studying Students' Learning through Their Mathematical Activity" (2010). The author believes these points are central to any study of children's mathematical learning. The first…

This paper describes a program of research aimed at better understanding mathematics conceptual learning. Rather than studying the products of learning (conceptual steps), it focuses on the process (mechanism) of students' learning -- learning that occurs through their mathematical activity in the context of a sequence of mathematical tasks.…

This book provides a landscape of learning that helps teachers recognize, support, and celebrate their students' capacity to structure their worlds algebraically. It identifies the models, contexts, and landmarks that facilitate algebraic thinking in young students and provides insightful and practical methods for teachers, math supervisors, and…

Simon's (1995) development of the construct of hypothetical learning trajectory (HLT) offered a description of key aspects of planning mathematics lessons. An HLT consists of the goal for the students' learning, the mathematical tasks that will be used to promote student learning, and hypotheses about the process of the students' learning.…

The aim of this paper is to contribute to the understanding of the possible influence of the use in class of Internet resources which offer mathematical exercises for the students' activity and learning processes. I present an exploratory study grounded on a teaching design set up in two French grade six classes about proportional reasoning…

Reviews communication as a fundamental component in implementing a balanced and effective mathematics program. Presents a classroom episode in which students solve problems, use rubrics to rate the written response of a peer, and discuss solutions and decisions for rating their peers' papers. (KHR)

The Internet, an exciting and radically different medium infiltrating pop culture, business, and education, is also a powerful educational tool with teaching and learning potential for mathematics. Web-based instructional tools allow students and teachers to actively and interactively participate in the learning process (Lynch, Moyer, Frye & Suh,…

Discusses the mathematics learning related to NCTM standards that emerges as children engage in play in early childhood and kindergarten settings and offers suggestions for the effective use of play in teaching young children mathematics. Focuses on the use of blocks and manipulatives. Discusses how teachers' assumptions and mathematics knowledge…

This article discusses how children learn to understand the decimal system in very concrete ways, while having fun using beads. When counting the beads, the children learn 5,491 is not simply "five thousand four hundred and ninety-one" but actually 5 thousands, 4 hundreds, 9 tens, and 1 unit. They begin to understand that as they get 10 units,…

This article talks about the Cognitive Recess Curriculum as a cognitive approach to elementary school recess. The concept of a cognitive recess curriculum is based on three research studies conducted by the author. The largest study involved over 1,564 educators (superintendents, principals, teachers K 12). It sought to determine the subjects'…