An Assessment of Web-Based Homework in the Teaching of College Algebra

Mahmoud Affouf and Thomas P. Walsh

Kean University, Union, NJ 07083, USA
maffouf@kean.edu; tpwalsh@kean.edu

The purpose of this study was to demonstrate the effectiveness of web-based homework (WBH) assignments on the overall comprehension measured by the final examination in a first year college algebra course. This study included 1653 students over a three year period. Results indicate a strong correlation between achievement on the WBH assignments and achievement in the final examination. In addition, the scores of WBH assignments can be used as a good predictor of final examination scores. Our results are independent of instructors taught the course.

 

Learning Mathematics with E-exercises: A Case Study about Proportional Reasoning

Ghislaine Gueudet

CREAD and IUFM Bretagne, Site de Rennes, 153, rue Saint Malo, 35043 Rennes, Cedex, France
Ghislaine.Gueudet@bretagne.iufm.fr

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 involving an e-exercise resource. We adopted a teaching design which used free access for the student to a wide range of exercises, and many written reports associated with the work on the computer. We observe that the students’ activity during the experiment is much richer than drill. Students develop different working patterns on the computer. These patterns can be interpreted as consequences of the different roles implicitly attributed by the student to the resource within the didactical contract. We also observe the construction of new mathematical abilities. At the end of the teaching, the students were able to use several kinds of strategies to solve proportionality problems. However the didactical contract is modified by the Internet resource and generates specific difficulties, in particular insufficient written work.

 

Reflective Implementation of DERIVE in Teaching Mathematics at the University of Food Technology, Plovdiv

Eva D. Dimitrova

Department of Mathematics, University of Food Technology, Plovdiv, Bulgaria
rektor@hiffi-plovdiv.acad.bg

The Department of Mathematics at the University of Food Technology, Plovdiv, Bulgaria, has introduced the Computer Algebra System DERIVE into the Mathematics courses with a view to increasing student motivation and understanding of the material taught as well as the efficiency of the teaching process. With the aim of investigating the effect of using CAS on the teaching and learning process regular observations of the class work have been made and special evaluation forms to measure class progress were completed by the teacher after each class. This report describes the organisation of CAS-based classes as well as the reflective approach taken in designing the materials and the CAS-based classes’ structure.

Student Misconceptions Caused by Misuse of Technology

Robert Paige, Padmanabhan Seshaiyer and Magdalena Toda

Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA
r.paige@ttu.edu; padmanabhan.seshaiyer@ttu.edu; magda.toda@ttu.edu

Calculators used widely by students, teachers, scientists, engineers and many others provide an interesting case study of a compelling technology that has helped change the way many professionals work. They not only help in enhancing problem solving skills of most individuals, but also help visualise solutions to problems in a better way. Research supports the claim that calculator use improves student performance in computation, concept development, and problem-solving although a growing number of studies show that there may be a class of errors and misconceptions that are induced by calculators. We review some basic ideas of errors in numerical analysis and discuss in detail the concept of round-off error that is often noticed by both college teachers and high school and undergraduate students when working with such computing aids. We then present experimental results on the performance of a variety of computing aids for solving two problems, perform a statistical analysis of data collected from 215 students in the freshmen calculus class at Texas Tech University, and report the findings of this analysis.

Dynamical Geometry: Analysis of Mistakes in Student Constructions

Jiří Vaníček

University of South Bohemia, Pedagogical Faculty, Czech Republic
vanicek@pf.jcu.cz

In the early stages of working with dynamical geometry environments, students make many more mistakes than if they thought out and implemented the same constructions on paper. Most Czech teachers have very little experience of doing geometry using computers. A methodology which could help them to teach students to avoid mistakes dependent on the software used could be very helpful. The main goal of the research was to classify mistakes made in the construction of dynamical figures. The example used was the construction of the figure of “dancing house”, which is typical of dynamical constructions. In the paper we cite examples of every type of mistake, documented by screen dumps of the constructions made in Cabri Geometry.

 

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