Challenges and Opportunities in Experimentation-Based Instruction in Probability

Nilsson, Per; Eckert, Andreas; Pratt, Dave

doi:10.1007/978-3-319-72871-1_4

Cited by 6 publications

(10 citation statements)

References 32 publications

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“…Contrary to the students in Nilsson et al (2018), the students in the present study did not fall as much into contextual reasoning for predicting or explaining obtained frequencies. The random generator used in the present study was similar to the one used in Nilsson et al (2018) and the students were of the same age. How can the difference between the two studies be understood?…”

Section: Discussion and Concluding Remarkscontrasting

confidence: 99%

“…A well-known phenomenon in statistics education research is how contextual and idiosyncratic features can turn students' attention away from data-based reasoning (Makar & Rubin, 2009;Nilsson et al, 2018;Watson et al, 2007). Contrary to the students in Nilsson et al (2018), the students in the present study did not fall as much into contextual reasoning for predicting or explaining obtained frequencies. The random generator used in the present study was similar to the one used in Nilsson et al (2018) and the students were of the same age.…”

Section: Discussion and Concluding Remarkscontrasting

confidence: 80%

“…The answer is likely to be found in how the games' design differed. In Nilsson et al (2018) the students played with the same bottle in repeated games, whereas in the present study the underlying probability distribution was changed between each game and the contents of the bottles for each game were visible on the game board. This purposeful variation (Marton et al, 2004) between the games turned the students' attention to the contents of the bottles and thus supported them in privileging the underlying probability distribution in their GoGAR in order to make sense of the outcome frequencies of the color-runs.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 94%

“…A close look was taken at how the students came to use data as evidence (Makar & Rubin, 2009). On this account, the analysis was sensitive to how the students came to be responsive to contextual features in predicting or explaining random generated outcomes (Nilsson et al, 2018). The second step of the analysis was also guided by findings from research on how students distinguish signals in noisy processes (variation) (Konold & Pollatsek, 2002).…”

Section: Methods Of Analysismentioning

confidence: 99%

“…Studies also show that students can come to overemphasize contextual reasons when explaining or predicting data from an underlying probability distribution (Makar & Rubin, 2009). In Nilsson et al (2018), for instance, students turned to material and idiosyncratic explanations (Watson et al, 2007) rather than to probabilistic and data-centered reasons when asked to predict or explain the distribution of outcomes obtained from a random generator, simulated by a bottle with colored marbles 2 .…”

Section: Relevant Research On Statistics Educationmentioning

confidence: 99%

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Students’ Informal Hypothesis Testing in a Probability Context With Concrete Random Generators

NILSSON¹

2021

SERJ

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This study examines informal hypothesis testing in the context of drawing inferences of underlying probability distributions. Through a small-scale teaching experiment of three lessons, the study explores how fifth-grade students distinguish a non-uniform probability distribution from uniform probability distributions in a data-rich learning environment, and what role processes of data production play in their investigations. The study outlines aspects of students’ informal understanding of hypothesis testing. It shows how students with no formal education can follow the logic that a small difference in samples can be the effect of randomness, while a large difference implies a real difference in the underlying process. The students distinguish the mode and the size of differences in frequencies as signals in data and used these signals to give data-based reasons in processes of informal hypothesis testing. The study also highlights the role of data production and points to a need for further research on the role of data production in an informal approach to the teaching and learning of statistical inference. First published December 2020 at Statistics Education Research Journal: Archives

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Section: Discussion and Concluding Remarkscontrasting

confidence: 99%

Section: Discussion and Concluding Remarkscontrasting

confidence: 80%

Section: Discussion and Concluding Remarksmentioning

confidence: 94%

Section: Methods Of Analysismentioning

confidence: 99%

Section: Relevant Research On Statistics Educationmentioning

confidence: 99%

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Students’ Informal Hypothesis Testing in a Probability Context With Concrete Random Generators

NILSSON¹

2021

SERJ

Self Cite

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Teaching and learning of probability

Batanero

Álvarez-Arroyo

2023

ZDM Mathematics Education

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In this paper, we develop a personal synthesis of the most outstanding research on the teaching and learning of probability in the past years. We conducted a systematic search to examine publications on this topic in mathematics education, statistics education, education, and psychology journals. This exploration was complemented by additional studies published in conference proceedings or books. We classified these papers to highlight the main recent research tendencies in the field, according to the theme studied and considering the research objectives. Epistemological analyses suggest that informal inference based on simulation diminishes the topic abstraction but reduces probability to its frequentist view. Topics receiving particular attention include children’s probabilistic knowledge, the effect of visualizations on solving conditional probability problems, teachers’ education and probability modelling. In the final section, we recommend relevant points in which more investigation is needed to complete our knowledge about teaching and learning. In particular, we miss research on teachers’ mathematical knowledge of many probability concepts and on their didactic knowledge.

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Potential of Brousseau’s guessing game in teacher education: two complementary cases

Hakamata,

Fukuda,

Otani

et al. 2024

International Journal of Mathematical Education in Science and

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Challenges and Opportunities in Experimentation-Based Instruction in Probability

Cited by 6 publications

References 32 publications

Students’ Informal Hypothesis Testing in a Probability Context With Concrete Random Generators

Students’ Informal Hypothesis Testing in a Probability Context With Concrete Random Generators

Teaching and learning of probability

Potential of Brousseau’s guessing game in teacher education: two complementary cases

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