Curriculum and cognitive level alignment among the intended, the enacted, and the assessed curricula were explored and measured. In particular, the focus of the study was on two domains: content/operations and cognitive levels/processes. Results indicated that cognitive level alignment among the intended, enacted and assessed curricula was 0.07.…

Collaborative gestures in the mathematics classroom occur when multiple learners coordinate their bodies in concert to accomplish mathematical goals. Collaborative gestures show how cognition becomes distributed across a system of dynamic agents, allowing for members of groups of students to act and gesture as one. We explore ways high school…

This case study contrasts the strategies used by two students in solving bilateral symmetry and reflection tasks, based on the differential properties they attended to. The ninth grader focussed on congruence of sides as the main property of reflection whereas the eighth grader focussed on perpendicularity and equi-distance, as is the normative…

This paper explores the algebraic expressions of deaf learners as they explore and construct sequences using the digital microworld Mathsticks. More specifically, it attempts to identify how the deaf students coordinated bodily, discursive and digital resources in order to attribute their own personal senses to the notion of variable. Examples of…

This study uses the Mathematical Tasks Framework (Stein & Smith, 1998) to assess the cognitive demand of mathematical tasks implemented in four mathematics classrooms, and to investigate the role of technology in both low- and high-level cognitive demand tasks. The metaphor of using technology as an amplifier or reorganizer (Pea, 1987) is used…

The cognitive significance of the body has become one of the major topics in current psychology. However, it is our contention that claims about the embodied nature of thinking must come to terms with the problem of the relationship between the body as a locus for the constitution of students' subjective mathematical meanings and the historical…

Research in mathematical problem solving has produced significant results in trying to understand what people do to solve problems. An important part of the solution process is the presence of both cognitive and metacognitive strategies. This paper documents the extent to which 13 ninth grade students are able to recognize the basic structure of a…

Starting from a situated cognition perspective, this paper reports on the activity of 9th grade students who are interpreting the shape of a graph arising from the motion of a bouncing ball. In an unfamiliar context, informed by previous knowledge of similar experiments, the obstacle of understanding why the graph does not start from the origin is…

The goal of this research is to compare the effectiveness of two teaching methods (inducing a cognitive conflict, or ICC, versus direct teaching, DT) for students of two academic levels (low versus high) regarding gains in the ability to use the control of variables strategy. 121 students who learned in a heterogeneous school were divided into…

Reported is another study related to the Project on an Information Memory Model. This study involved using information theory to investigate the concepts of primacy and recency as they were exhibited by ninth-grade science students while processing a biological sorting problem and an immediate, abstract recall task. Two hundred randomly selected…

This paper addresses components of a 3-year longitudinal study in which 9th and 10th grade students in Australia, Canada, and Zambia participated in data-handling programs through networked learning communities. Of interest here are the students' responses to a selection of "ends-in-view" problems, which formed the major part of the…

A case study is presented on what is learned by a very advanced Math student in a ninth grade class (fifteen years old, approximately). This case was obtained from an exploratory study carried out in a classroom of eighteen students when the employment of certain cultural artifacts was introduced to approach the theme of basic geometrical…

The paper considers a teaching experiment carried out with secondary school students (9th grade), who face modelling tasks to approach some basic concepts of algebra and early calculus. The focus is on an embodied analysis of students' cognitive processes. The analysis highlights the use of metaphors as a means of sharing knowledge. (Contains 2…

A study examined the effects of pictorial and verbal illustrations on the initial learning and long term retention of written instruction. Subjects were eighth and ninth grade students randomly assigned to one of two text conditions (literal or analogous instructions) under one of four pictorial conditions (no picture, functional drawing,…

To probe beyond declarative knowledge about real numbers in secondary school, the authors interviewed students in Grades 9, 10 and 12. The main question seems to be whether the length of a decimal expansion is "indefinite" or "infinite." It blurs the mental representation of rational numbers as well. (Contains 3 footnotes.) [For complete…