Journal of Computers in Mathematics and Science Teaching

Volume 16, Number 1 1997

---

Contents

---

Research Notes: A Review of Computer-Based ModelResearch in Precollege Science Classrooms

Microcomputer Simulated Experiments inthe Teaching of Multi-Channel Laser System in an UndergraduateCourse

Diagnostic Learning Activities UsingDERIVE

Enacting a Chaos Theory Curriculum ThroughComputer Interactions

Learning Kinematics With a V-Scope: A CaseStudy

Improving the Learning Environment inFirst-Year Programming: Integrating Lectures, Tutorials, andLaboratories

Sets, Subsets, and the Empty Set: Students'Constructions and Mathematical Conventions

---

Abstracts

---

Research Notes

A Review of Computer-Based Model Research in Precollege ScienceClassrooms

Steven J. Stratford

This review covers research conducted within the past 10 years onthe topic of using computer models and simulations to aid scienceinstruction at the precollege level. The author suggests categorizingthe research into three main areas: students running preprogrammedsimulations, students creating dynamic models using modelingenvironments, and students using programming environments to createsimulations. Because this area of research is in its infancy, fewconclusions are drawn; however, numerous suggestions for avenues offuture research are provided.

Return to Contents

Lee Sing and Chia Teck Chee

In this article, the authors describe the use of microcomputersimulated experiments in teaching the multi-channel laser system inan undergraduate course. The simulation described here was carriedout by students in the context of a Year 4 undergraduate physicslaboratory course on pulse technology. The objective of the coursewas to give the students experience in computation pulsed electricalcircuits and in comparing the computation with experiments. To helpstudents understand the sequence of firing of this multi-channelsystem, we use microcomputer simulated experiments based on circuitanalysis and numerical computation with microcomputers. Firstly, thesystem of equations is kept simple at the level of Kirchhoff's rulesapplied to a time-dependent coupled circuit. Secondly, the numericalintegration uses the simplest linear approximation. The predictionfrom the computation of the "prolong sequencing" of five laserchannels has been verified experimentally. The results show that themicrocomputer simulated experiments provide a powerful tool for amore comprehensive understanding of the multi-channel laser system.

Return to Contents

---

Diagnostic Learning Activities Using DERIVE

Nurit Zehavi

This paper includes a discussion about a method of implementingthe computer algebra system Derive for diagnosis and remediation ofbasic difficulties in mathematics. Learning activities for juniorhigh school students were developed, each activity directed at adifferent area of difficulty. The basic pedagogical strategyimplemented in these activities is replicating and completingexamples. Using partly solved examples and replication of tasks onDerive enables students to predict missing elements in a problem,even if they have not mastered the relevant mathematics. In this waythey learn not just through trial and error, but by understanding howone part of an algebraic expression relates to the whole. Experimentswith students and teachers indicate that the developed activitiesprovide the teacher with a diagnostic tool for interacting with thestudent.

Return to Contents

---

Enacting a Chaos Theory Curriculum Through ComputerInteractions

This paper begins by examining human-computer interaction from twoviews of cognition, from the representationist view and theenactivist perspective. A chaos-theory context is then discussed froman enactivist stance. In this context, high school students exploreand manipulate nonlinear dynamic computer programs. These programsgenerate (a) visual representations in the form of "cobwebs" ofiterates of functions and other graphical representations and (b)numerical iterates of functions and graphs of these iterates througha spreadsheet application program. The chaos-theory curriculum isdynamically generated with students, and an example of one student'sactivities and mathematical experiences is examined offering thepotential for increased understanding of how mathematical ideasdevelop in an interactive computer environment. The chaos-theorycontext is discussed through the enactive view. Implications of theenactive stance for education and research are then articulated.

Return to Contents

---

Learning Kinematics With a V-Scope: A CaseStudy

Ricardo Trumper

The goal of this case study was to check the effect of V-Scopeactivities in the performance of 11th-grade students in analyzingkinematics graphs. The V-Scope kinematics laboratory consisted offive double lessons that challenged students to construct differentkinds of graphs using their own movements as well as the motion of adynamics cart. The students participating in this case study were alldrawn from two parallel classes of 11th graders learning physics inthe same regional school. The experimental and control samples wererandomly chosen. The difference between them was only the treatmentgiven to the experimental sample through the V-Scope activities ofthe V-Scope kinematics laboratory. All students were requested toanswer to identical pre- and posttests at the beginning and end ofthe teaching. In all the groups there is a significant improvementbetween the pre- and posttests in students' ability to use andinterpret graphs in general; but when we compare the students'performances on the posttest alone, we find a statisticallysignificant difference only between those who worked in the V-Scopekinematics laboratory and those who did not. The results of thisstudy indicate that the V-Scope kinematics laboratory activities arepedagogically promising for the learning of kinematics concepts andgraphing skills.

Return to Contents

---

Improving the Learning Environment in First-Year Programming:Integrating Lectures, Tutorials, andLaboratories

Piyush Maheeshwari

Described in this paper is the development of a model fordelivering the first course in computer programming to large anddiverse classes. A group of team teachers, tutors, and labdemonstrators implemented this model that takes advantage of theunique characteristics of lectures, tutorials, laboratories, andreadings. Teaching methods do make a significant difference inimproving the quality of learning in a given subject. We present anintegrated approach that has been used for the last several years toimprove the learning environment in large programming classes.Instead of concentrating more on the language syntactic features,this environment emphasizes program design skills and problem-solvingskills and motivates students to learn by active processes. Theintegration of different teaching components provides a bridgebetween a surface approach and a deep approach to learning.

Return to Contents

---

Sets, Subsets, and the Empty Set: Students' Constructions andMathematical Conventions

Rina Zazkis and Chris Gunn

This study investigates students' understanding of the basicconcepts of introductory set theory: set, set element, cardinality,subset, and the empty set. The data was collected from a group ofpreservice elementary school teachers by means of written assessment,clinical interviews, and students' participation in a computer-basedproject. The project included experimentation with basic set conceptsin an open computer-based environment with mathematical computerlanguage ISETL. A constructivist-oriented framework was used inanalyzing the data. The results reveal complexities in students'understanding, especially when set elements involved are setsthemselves. Special attention is given to the description ofstudents' difficulties with the concept of the empty set.

Return to Contents