Affordances of spreadsheets in mathematical investigation: Potentialities for learning

This article, is concerned with the ways learning is shaped when mathematics problems are investigated in spreadsheet environments. It considers how the opportunities and constraints the digital media affords influenced the decisions the students made, and the direction of their enquiry pathway. How might the leraning trajectory unfold, and the learning process and mathematical understanding emerge? Will the spreadsheet, as the pedagogical medium, evoke learning in a distinctive manner? The article reports on an aspect of an ongoing study involving students as they engage mathematical investigative tasks through digital media, the spreadsheet in particular. In considers the affordances of this learning environment for primary-aged students

Toward a Semiotic Framework for Using Technology in Mathematics Education: The Case of Learning 3D Geometry

This paper proposes and examines a semiotic framework to inform the use of technology in mathematics education. Semiotics asserts that all cognition is irreducibly triadic, of the nature of a sign, fallible, and thoroughly immersed in a continuing process of interpretation (Halton, 1992). Mathematical meaning-making or meaningful knowledge construction is a continuing process of interpretation within multiple semiotic resources including typological, topological, and social-actional resources. Based on this semiotic framework, an application named VRMath has been developed to facilitate the learning of 3D geometry. VRMath utilises innovative virtual reality (VR) technology and integrates many semiotic resources to form a virtual reality learning environment (VRLE) as well as a mathematical microworld (Edwards, 1995) for learning 3D geometry. The semiotic framework and VRMath are both now being evaluated and will be re-examined continuously

K-8 Pre-service Teachers’ Algebraic Thinking: Exploring the Habit of Mind Building Rules to Represent Functions

In this study, through the lens of the algebraic habit of mind Building Rules to Represent Functions, we examined 18 pre-service middle school teachers\u27 ability to use algebraic thinking to solve problems. The data revealed that pre-service teachers\u27 ability to use different features of the habit of mind Building Rules to Represent Functions varied across the features. Significant correlations existed between 8 pairs of the features. The ability to justify a rule was the weakest of the seven features and it was correlated with the ability to chunk information. Implications for mathematics teacher education are discussed

Methodological issues in using sequential representations in the teaching of writing

This study looks at a specific application of Ainsworth’s conceptual framework for learning with multiple representations in the context of using multiple sequential graphic organizers that are student‐generated for a process‐writing task. Process writing refers to writing that consists of multiple drafts. It may be a process of re‐writing without feedback or re‐writing based on feedback where the teacher or peers will provide feedback on the original draft and then the students will revise their writing based on the feedback given. The objective was to explore how knowledge of students’ cognitive processes when using multiple organizers can inform the teaching of writing. The literature review analyzes the interaction of the design, function and task components of the framework; culminating in instructional approaches for using multiple organizers for classes with students of different writing abilities. Extended implications for designers of concept mapping tools based on these approaches are provided

Educational Research Abstracts

Editors\u27 Note: As noted in previous issues of the Journal of Mathematics and Science: Collaborative Explorations, the purpose of this Educational Research Abstract section is to present current research on issues relevant to math and science teaching at both the K-12 and college levels. Because educational research studies are published in so many different academic journals and presented as so many different professional conferences, it is a rare public school teacher or college professor who is familiar with the range of recent reposts on a particular instructional technique or curricular advancement. Indeed, the uniqueness of various pedagogical strategies has been tacitly acknowledged by the creation of individual journals and professional organizations dedicated to teaching in a specific discipline. Yet, many of the insights gained in teaching certain physics concepts, biological principles, or computer science algorithms can have generalizability and value for those teaching in other fields or with different types of students. In this review, the focus is on cutting edge research. Abstracts are presented according to a question examined at a recent national educational research conference. Hopefully, such a format will trigger your interest in how you might incorporate new educational findings in your own teaching situation. The abstracts presented here are not intended to be exhaustive, but rather a representative sampling of recent research investigations. Please feel free to suggest future teaching or learning themes to be examined. Please send your comments and ideas via e-mail to [email protected] or by regular mail to The College of William and Mary, P. O. Box 8795, Williamsburg, VA 23185-8795

The mind's eye in blindfold chess

Visual imagery plays an important role in problem solving, and research into blindfold chess has provided a wealth of empirical data on this question. We show how a recent theory of expert memory (the template theory, Gobet & Simon, 1996, 2000) accounts for most of these data. However, how the mind’s eye filters out relevant from irrelevant information is still underspecified in the theory. We describe two experiments addressing this question, in which chess games are presented visually, move by move, on a board that contains irrelevant information (static positions, semi-static positions, and positions changing every move). The results show that irrelevant information affects chess masters only when it changes during the presentation of the target game. This suggests that novelty information is used by the mind’s eye to select incoming visual information and separate “figure” and “ground.” Mechanisms already present in the template theory can be used to account for this novelty effect

Teaching Practicum in Mathematics

A teaching preparation practicum as part of the WPI Teacher Preparation Program was completed in Mathematics in the 8th grade at Lewis-Palmer Middle School, in Monument, CO. The purpose was to accumulate specific experience (in hours of observing a licensed teacher and actual classroom teaching) and ultimately to demonstrate competence in the Five Professional Standards of Massachusetts (as specified by the Massachusetts Department of Elementary and Secondary Education)

Computational and Robotic Models of Early Language Development: A Review

We review computational and robotics models of early language learning and development. We first explain why and how these models are used to understand better how children learn language. We argue that they provide concrete theories of language learning as a complex dynamic system, complementing traditional methods in psychology and linguistics. We review different modeling formalisms, grounded in techniques from machine learning and artificial intelligence such as Bayesian and neural network approaches. We then discuss their role in understanding several key mechanisms of language development: cross-situational statistical learning, embodiment, situated social interaction, intrinsically motivated learning, and cultural evolution. We conclude by discussing future challenges for research, including modeling of large-scale empirical data about language acquisition in real-world environments. Keywords: Early language learning, Computational and robotic models, machine learning, development, embodiment, social interaction, intrinsic motivation, self-organization, dynamical systems, complexity.Comment: to appear in International Handbook on Language Development, ed. J. Horst and J. von Koss Torkildsen, Routledg