Figure 5 - uploaded by Sibel Kazak
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Nelson's branched hair-length factory. We see a male case being produced, which has just received a hair length of 1 from the upper right mixer. Females go to the lower branch and receive a hair length of 1-12 inches.  

Nelson's branched hair-length factory. We see a male case being produced, which has just received a hair length of 1 from the upper right mixer. Females go to the lower branch and receive a hair length of 1-12 inches.  

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In current curriculum materials for middle school students in the US, data and chance are considered as separate topics. They are then ideally brought together in the minds of high school or university students when they learn about statistical inference. In recent studies we have been attempting to build connections between data and chance in the...

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... few months after this first activity, we implemented a branching capability in the software that directs cases with different values on one attribute to different sampling devices (see Figure 5). To introduce the students to it, we revisited the cat factory and pointed out the problem with how the linear factory was often misassigning males and female names. ...
Context 2
... is, although students traditionally have difficulty reasoning backwards from data to valid claims about conditional probability, these middle school students seemed quite able to reason forward from conditional situations they knew well to models and resultant data that represented those relations. Figure 5 shows Nelson's model of the hair-length problem, which he described for us: ...

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... The preparation process that both students and teachers went through while learning probability and statistics was insufficient (Koparan, 2019;Rodríguez-Alveal, Díaz-Levicoy & Vásquez, 2018). Philosophical debates around the meaning of probability, certain features of probabilistic reasoning, students' misconceptions and difficulties, and the growing diversity of technological resources reveal that teachers need special preparation to teach probability Konold, et al., 2007;Rodríguez-Alveal, Díaz-Levicoy & Vásquez, 2018). While textbooks provide some examples, some texts offer a very narrow view of probability concepts or a single approach to probability. ...
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Digital technology is indispensable for doing and learning statistics. When technology is used in mathematics education, the learning of concepts and the development of techniques for using a digital tool are known to intertwine. So far, this intertwinement of techniques and conceptual understanding, known as instrumental genesis, has received little attention in research on technology-supported statistics education. This study focuses on instrumental genesis for statistical modeling, investigating students’ modeling processes in a digital environment called TinkerPlots. In particular, we analyzed how emerging techniques and conceptual understanding intertwined in the instrumentation schemes that 28 students (aged 14–15) develop. We identified six common instrumentation schemes and observed a two-directional intertwining of emerging techniques and conceptual understanding. Techniques for using TinkerPlots helped students to reveal context-independent patterns that fostered a conceptual shift from a model of to a model for . Vice versa, students’ conceptual understanding led to the exploration of more sophisticated digital techniques. We recommend researchers, educators, designers, and teachers involved in statistics education using digital technology to attentively consider this two-directional intertwined relationship.
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We examine the challenges of teaching probability through the use of modelling. We argue how an integrated modelling approach might facilitate a coordinated understanding of distribution by marrying theoretical and data-oriented perspectives and present probability as more connected to the social lives of modern-day students. Research is, however, also showing that learning modelling is non-trivial. For example, students can easily be confused between real-world data and model-generated data. Furthermore, students tend to create models that reflect the structure of the problem context rather than its mathematical structure. The argument we present is that teaching probability through an integrated modelling approach could offer important educational benefits, but this would be an immense challenge to the skills and knowledge of teachers and would demand increased levels of resources for teacher development. The implication is that research needs to identify suitable forms of teacher development and designs for tasks and curricula.