Using students' statistical thinking to inform instruction

Jones, Graham A.; Langrall, Cynthia W.; Thornton, Carol A.; Mooney, Edward S.; Wares, Arsalan; Jones, Marion; Perry, Bob; Putt, Ian; Nisbet, Steven

doi:10.1016/s0732-3123(01)00064-5

Cited by 18 publications

(17 citation statements)

References 19 publications

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“…The results displayed that the failures, which the students made in the calculations for some probability problems included in the study (especially for the eighth problem of the study), made us conclude that they had difficulties in fractions, percentage calculations and four arithmetical operations with numbers. This overlaps the results obtained in the studies made by Jones et al (1996), and Sezgin-Memnun, Altun, and Yilmaz (2010) that the students had difficulty, especially in understanding and using the concept of sample space. It is also similar to the results obtained by Tunc (2006), and Bar-On and Or-Bach (1988) where the students had insufficient knowledge and skills regarding the subject of sets.…”

Section: Discussionsupporting

confidence: 77%

A Qualitative Research on the Difficulties and Failures about Probability Concepts of High School Students

Memnun

ÖZBİLEN

Dinç

2019

JEI

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This research aimed to examine the difficulties and failures of eleventh-grade students regarding probability concepts. With this aim, ten different open-ended probability problems were asked to the 142 eleventh-grade students. Each of these problems requires using different basic probability concepts. It is qualitative research, and the data gathered in this study were analyzed using by descriptive analysis method. The findings indicated that many of these students had difficulties in solving probability problems and failed to apply different probability concepts to these problems. Notably, it was stated that many students had difficulties in finding all the probabilities without any missing in these problems. Besides, it is essential to develop reasoning skills since the students usually used trial-and-error method and prediction to solve probability problems.

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Section: Discussionsupporting

confidence: 77%

A Qualitative Research on the Difficulties and Failures about Probability Concepts of High School Students

Memnun

ÖZBİLEN

Dinç

2019

JEI

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“…The characteristics within each of the levels of development provide guidance for the design of instructional activities and the selection of instructional strategies that will capitalize on where students are in their reasoning in this sequence of development. Results of this study provide evidence that instruction can influence the learning of probability (Jones et al 1999). …”

Section: Extending To Probabilitymentioning

confidence: 64%

“…Jones et al (1997Jones et al ( , 1999 evaluated the thinking of 3rd-grade students in an educational setting to create a "Probabilistic Thinking Framework," which describes the levels of reasoning stages related to key constructs (sample space, probability of an event, probability comparisons, and conditional probability). It is interesting to note that these key constructs maintain a striking resemblance to the four cognitive demands made on children when learning probability.…”

Section: Extending To Probabilitymentioning

confidence: 99%

Intuitive Conceptions of Probability and the Development of Basic Math Skills

Brase

Martinie

Castillo-Garsow

2014

Advances in Mathematics Education

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The idea of probabilities has been described as a "Janus-faced" concept, which can be thought of either in terms of frequencies or in terms of subjective confidence. This dualism contributes to debates about the nature of human rationality, and therefore the pedagogical assumptions and goals of education. For this reason, the present chapter explores the evidence regarding how quantitative information is intuitively understood in the human mind over the course of elementary school education. Are particular interpretations of probability equally weighted or does one interpretation predominate as mathematical concepts are being acquired? We find multiple, converging lines of evidence that indicate a frequency interpretation of probabilistic information is developmentally primary and privileged. This has implications for mathematics education, even before the introduction of actual probabilities, in areas such as learning fractions and decimals. Educational practices should work to bootstrap from these privileged representations (rather than fight them) and built towards a more inclusive and comprehensive model of probability knowledge. We conclude that a fundamental issue is not just whether students think about probabilities as a frequentist or as a subjectivist, but rather how they recognize when to be one versus the other.

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“…Hypothetical learning trajectories have been described for a number of teaching experiments in diverse areas, such as linear measurement, equivalence of fractions, and statistics (cf. Gravemeijer, 2004;Jones et al, 2001;Simon & Tzur, 2004;Stephan, Bowers, Cobb, & Gravemeijer, 2003).…”

Section: Susan D Nickerson and Ian Whitacrementioning

confidence: 99%

A Local Instruction Theory for the Development of Number Sense

Nickerson

Whitacre

2010

Mathematical Thinking and Learning

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Gravemeijer's (1999Gravemeijer's ( , 2004 construct of a local instruction theory suggests a means of offering teachers a framework of reference for designing and engaging students in a set of sequenced, exemplary instructional activities that support students' mathematical development for a focused concept. In this paper we offer a local instruction theory to guide the design of a set of instructional activities in support of the development of number sense. We make explicit the goals, assumptions, underlying rationale, and related instructional activities and provide examples from a mathematics content course for preservice elementary teachers. In this way, we contribute to an elaboration of the construct of local instruction theory.Externally-developed local instruction theories are indispensable for reform mathematics education (Gravemeijer, 2004, p. 108). Gravemeijer's (1999, 2004 construct of a local instruction theory, which was developed in the context of design research, suggests a means of offering teachers a framework of reference for designing and engaging students in a set of sequenced, exemplary instructional activities that support students' mathematical development of a focused concept. Gravemeijer (2004) described a local instruction theory with regards to learning goals, instructional activities, and the role of tools and imagery in the envisioned learning route. Gravemeijer illustrated how Realistic Mathematics Education can be used to develop a local instruction theory for an instructional sequence for addition and subtraction up to 100. Like Gravemeijer, we see a local instruction theory as indispensable to the design of instruction.The paucity of examples in the literature suggested to us that the field might benefit from further illustration and elaboration of the construct of local instruction theory. In this paper, we offer a local instruction theory in support of the development of number sense. This theory evolved out of a review of the literature, together with the results of a classroom teaching experiment, and subsequent iterations of teaching the course and fleshing out our analysis. We first discuss the differences between local instruction theory and hypothetical learning trajectory (Gravemeijer, 1999(Gravemeijer, , 2004Simon, 1995); next we discuss the literature on number sense. Within the context of our design research in a class for preservice elementary teachers, we provide an example of a local instruction theory to illustrate the relationship between the local instruction theory and resulting hypothetical learning trajectories. A colleague asked us whether we see a local instruction theory as being made up of a sequence of hypothetical learning trajectories, like Correspondence should be sent to 228 NICKERSON AND WHITACRE so many bricks in a row. We do not. Rather, we see a local instruction theory (LIT) as undergirding and informing particular hypothetical learning trajectories (HLTs).A hypothetical learning trajectory consists of learning goals for students, planned inst...

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Using students' statistical thinking to inform instruction

Cited by 18 publications

References 19 publications

A Qualitative Research on the Difficulties and Failures about Probability Concepts of High School Students

A Qualitative Research on the Difficulties and Failures about Probability Concepts of High School Students

Intuitive Conceptions of Probability and the Development of Basic Math Skills

A Local Instruction Theory for the Development of Number Sense

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