ideas about measurement in terms of point and set paradigms

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4 A. BUFFLER ET AL. An experiment is being performed in the Physics laboratory. A wooden slope is clamped near the edge of a table. A ball is released from a height h above the table as shown in the diagram. The ball leaves the slope horizontally and lands on the floor a distance d from the edge of the table. Special paper is placed on the floor on which the ball makes a small mark when it lands. The students have been asked to investigate how the distance d on the floor changes when the height h is varied. A meter stick is used to measure d and h. Figure 1. The experimental task used for the written questionnaire. decisions are difficult to explore through written probes since respondents often have difficulty in visualizing ‘thought experiments’. In order to minimize this problem, all the probes were related to the same experimental context (see figure 1). A large-scale version of the apparatus, a ramp with a horizontal edge and a ball, was also used to demonstrate the ‘experiment’ before the probes were answered. The probes were completed by 70 students in the first year of the Science Foundation Programme (SFP) at the University of Cape Town, South Africa. The students on the SFP (see Allie and Buffler 1998) may be generally characterized as having had poor science teaching at school, learn in English as a second language and come from socio-economically disadvantaged backgrounds. The instrument was administered during registration week, before the start of coursework, and then again after the students had experienced 12 weeks of a physics laboratory course. Since almost all of the SFP students had little or no first hand laboratory experience, the prime aims of the laboratory course was to allow them to engage with a variety of experimental situations using various items of apparatus and to introduce the notion of measurement. At the same time, reporting on a completed experiment formed a central part of the experience and producing reports was seen as fundamental to the laboratory course. In general, the laboratory tasks were framed in the form of authentic problems that required an experimental investigation for their resolution and had to be reported to a particular audience (Allie and Buffler 1998). Aspects of data collection and data processing were addressed by interspersing a number of formal book-type exercises. These exercises included the drawing up tables, taking several measurements of a quantity, plotting graphs, fitting a straight line, linearizing data, forming frequency tables, calculating the mean and the standard deviation from both the statistical formulae and a plotted Gaussian curve. The laboratory course consisted of a 3 hour session every week for 12 weeks.
FIRST YEAR PHYSICS STUDENTS’ IDEAS 5 The analysis of the probes included categorizing the student responses according to the answer choice (A, B or C) together with the different types of reasoning evidenced in the justification for this choice. The coding of the responses was undertaken using an alphanumeric scheme which had been developed and tested previously (Allie et al. 1998). This coding scheme enabled the identification of whether the point or set paradigm informed a student’s procedural decision in each probe. Consistencies between the paradigms used by each student across the entire set of probes were established in order to identify the level of consistency of use of the point and set paradigms in making procedural decisions, both before and after instruction. Results Data collection Three different probes were designed to investigate students’ reasons for collecting data through repeating measurements of the same quantity. The Repeating Distance (RD) probe. The students work in groups on the experiment. Their first task is to determine d when h = 400 mm. One group releases the ball down the slope at a height h = 400 mm and, using a metre stick, they measured to be 436 mm. The following discussion then takes place between the students: A: We should roll the ball a few more times from the same height and measure d each time. B: Why? We’ve got the result already. We do not need to do any more rolling. C: We must roll the ball down the slope just one more time from the same height. The Repeating Distance Again (RDA) probe. The group of students decide to release the ball again from h = 400 mm. This time they measure d = 426 mm: First release: h = 400 mm d = 436 mm Second release: h = 400 mm d = 426 mm The following discussion then takes place between the students: A: We know enough. We don’t need to repeat the measurement again. B: We need to release the ball just one more time. C: Three releases are not enough. We must release the ball several more times. The Repeating Time (RT) probe. The students are now given a stopwatch and are asked to measure the time that the ball takes from the edge of the table to hitting the ground after being released at h = 400 mm. They discuss what to do: A: We can roll the ball once from h = 400 mm and measure the time. Once is enough. B: Let’s roll the ball twice from height h = 400 mm, and measure the time for each case. C: I think we should release the ball more than twice from h = 400 mm and measure the time in each case. The RD, RDA and RT probes were included in the pre-intervention questionnaire, whereas only the RD probe was included in the post-intervention questionnaire. The point paradigm was considered to underlie statements that repeating measurements, for time or distance, would be meaningless since identical values would be obtained, as exemplified by: We don’t need to repeat, since there is no force applied to the tennis ball. The distance will be the same because the slope is the same and the initial velocity is the same. (RD response)
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