Abstract
In this paper, we analyse the knowledge of sampling in 157 prospective primary school teachers in Spain. Using two different tasks, and taking into account common and horizon content knowledge (described in the model proposed by Ball et al. in J Teacher Educ 59:389–407, 2008), we assess the teachers’ understanding of the following concepts: population and sample, frequency, proportion, estimation, variability of estimates, and the effect of sample size on this variability. Our results suggest that these prospective teachers have correct intuitions when estimating the sample proportion when the population proportion is known. However, they tend to confuse samples and populations, sometimes fail to apply proportional reasoning, misinterpret unpredictability, and show the representativeness heuristic and the equiprobability bias.
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Notes
- 1.
We can compute a confidence interval for p to better reflect the sampling uncertainty . Since 250 fish is a large sample , we can use the normal approximation. For a 95% confidence, the lower and upper limits of the interval are \( \widehat{p} \mp 1.96\sqrt {\frac{{\widehat{p}\left( {1 - \widehat{p}} \right)}}{n}} \). Substituting p with its estimate and n with 250, we obtain the interval (0.0628, 0.1372) for the population proportion.
- 2.
We can also compute a 95% confidence interval for y or for f r .
- 3.
Here, we do not count the 3.2% of the participants who responded 35 (considered to be a correct response, as explained previously).
- 4.
- 5.
The number of boys and girls in the small and large hospitals were simulated using an applet from the Rossman and Chance collection (http://www.rossmanchance.com/applets/OneProp/OneProp.htm).
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Research Projects EDU2016-74848-P (AEI, FEDER), and EDU2013-41141-P (MINECO).
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Gómez-Torres, E., Díaz, C., Contreras, J.M., Ortiz, J.J. (2018). Prospective Teachers’ Probabilistic Reasoning in the Context of Sampling. In: Batanero, C., Chernoff, E. (eds) Teaching and Learning Stochastics. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-72871-1_20
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