## Teaching and Leadership - Dissertations

#### Title

Secondary teachers' understanding of probability and sampling in context

2003

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Helen Doerr

#### Keywords

Probability, Sampling

#### Subject Categories

Education | Science and Mathematics Education

#### Abstract

The need for more effective teaching of probability is well established in the literature. Probability misconceptions (e.g., the equiprobable bias, the availability heuristic, the representativeness heuristic) are frequently applied inappropriately when interpreting probabilistic situations. This qualitative study, organized as two multi-tiered teaching experiments, examines secondary mathematics teachers' knowledge of probability and sampling, their classroom strategies, and their ability to support precalculus students' reasoning about probability in the context of a sampling task situated in an instructional unit on exponential functions.

The results of this study yielded two major findings. First, I have identified a new construct which I am calling the measurement heuristic. A measurement heuristic is defined in this paper as a strategy based on scientific measurement experiments in which the variation can be minimized by reducing human error or improving the measurement device. The teachers in this study consistently applied a measurement heuristic to the sampling task. These teachers believed that a single value exists and finding that value is the goal of the experiment. The existence of a single, ideal result means that deterministic techniques may be used to predict future values. However, the variation that occurs when taking a sample of a given size from a probability distribution cannot be minimized.

Second, the results indicate that these teachers' knowledge of probability is limited and that they are uncomfortable with the subject. They knew that probability was involved in collecting the data, but they did not recognize that they were sampling from a distribution and that the variation should be reflected in the equations used for predicting results outside the domain of the task. There is some evidence of the development of teacher knowledge within this study, but the need for additional training in probability and pedagogical strategies is required before these teachers can be expected to teach probability in context.

The study was designed and the results were interpreted using the models and modeling perspective as a framework, which needs further development to support probability education. More research is also required before we can develop effective programs to support teaching probability in context.

#### Access

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