Patricia Forster

Assessing technology-based approaches for teaching and learning mathematics

When technologies are used in mathematics education it is important to assess how activities will support the development of mathematical understanding and the technical expertise that students will need. The two issues are discussed in this paper. Literature is reviewed and findings from a recent study in a high-school class are reported. The students were studying descriptive statistics. The teacher introduced regression using dynamic graphs on Java applets. The approach seemed conducive to understanding. Graphics calculators, which all students owned, were used infrequently for investigating properties and were never used to introduce new constructs—one reason was that the static graphs on the calculators did not support inference of basic statistical relationships well. However, substantial time was given to developing competence with operating the calculators, which was necessary for success in public examinations. The outcomes, overall, indicated that ongoing assessment of decisions about technology-use should occur at system level as well as in the classroom.

Process and object interpretations of vector magnitude mediated by use of the graphics calculator

This paper presents an analysis of the development of one student’s understanding of vector magnitude and how her problem solving was mediated by her use of the absolute value graphics calculator function (ABS). The context is a Year 11 class studying Geometry and Trigonometry. The analysis is cast in terms of process views of vector magnitude where magnitude is treated as resulting from mathematical operations on other concepts, and object views where magnitude is treated as a mathematical entity in its own right.

Technologies for Teaching and Learning Trend in Bivariate Data.

Research on technology-use for teaching and learning statistics is sparse compared to that in algebra and calculus. This paper addresses the deficiency with regard to teaching and learning about ‘trend’ in bivariate data. Available research findings are reviewed and an empirical inquiry in a year 12 (upper secondary) class is reported. Treatment of a single dataset by the class is described. Spreadsheet, graphics calculator and projection technologies were utilized. The main conclusions are that the dataset that the teacher downloaded from the internet supported well the identification of trend and variability and testing alternative models; and the spreadsheet graphs that were projected onto the whiteboard mediated class discussion favourably.

Assessment in Calculus in the Presence of Graphics Calculators

In this paper we explore the extent and nature of students’ calculator usage as determined from examination scripts in the Western Australian Calculus Tertiary Entrance Examination. Errors made and understanding called upon are discussed for seven questions. The inquiry highlights that skills associated with graphical interpretation need to be the subject of instruction, and that an awareness of the differing cognitive demands of graphical interpretation is needed when setting assessment items.

Applying constructivist theory to practice in a technology-based learning environment

This paper describes a research study where constructivism was used as the rationale for the design, implementation and evaluation of four technology-based investigations for Year 12 Applicable Mathematics students. Analysis is given of the successes and difficulties encountered by students and teachers of four classes, including my own, in which the investigations were implemented. The results showed that, for learning activities involving school assessment, many students chose not to work collaboratively — a strategy suggested by social constructivism. The extent to which this may have been detrimental to their learning is discussed. The study illustrates how engaging in research can be a means for teachers to understand theory. In particular, the paper describes the meaning made of constructivism through this example of teaching practice and research activity.

Working with Critical Feedback to Improve Research Writing

Is it that you come to know how to write, or is it that the writer, writing and knowing emerge together? I can say that since starting on research my writing has developed in style and, as a process of inquiry (Richardson, 1998), writing helps me work out what to say. The process includes reflection and searching for language to define the situations under interrogation. So, through writing, I have come to understand my teaching and my existence in this world in new ways. However, I still do not find the act of writing easy. I rely on the advice of others to help me revise my drafts. A friend who reads my work gets so irritated by my frequent use of participles and by commas that she says I scatter like confetti. So after I complete a paper, I do an electronic search on ‘ing’ and ‘,’ to rectify the problems. Other advice I have been given is to write in the present tense for crispness and impact, and to aim for consistency in the position of references within a paragraph – so that they are all at the beginning of a sentence, such as “van Manen (1990) said ”, or all at the end. This makes for smoother reading.

Data Analysis in Physics Examination

This paper presents a critical analysis of data analysis requirements in physics tertiary entrance examinations. The setting is Western Australia. Common aspects of the questions asked over 14 years and changes in the questions since a major syllabus reform are identified. Similar changes in other jurisdictions are referenced. The data analysis questions reflect minimally the changes in emphasis in the reform syllabus. They imply science is unassailable laws and not science is inquiry.This paper presents a critical analysis of data analysis requirements in physics tertiary entrance examinations. The setting is Western Australia. Common aspects of the questions asked over 14 years and changes in the questions since a major syllabus reform are identified. Similar changes in other jurisdictions are referenced. The data analysis questions reflect minimally the changes in emphasis in the reform syllabus. They imply science is unassailable laws and not science is inquiry.