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Dani Benzvi - One of the best experts on this subject based on the ideXlab platform.
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explanations and context in the emergence of students informal Inferential Reasoning
Mathematical Thinking and Learning, 2011Co-Authors: Einat Gil, Dani BenzviAbstract:Explanations are considered to be key aids to understanding the study of mathematics, science, and other complex disciplines. This paper discusses the role of students' explanations in making sense of data and learning to reason informally about statistical inference. We closely follow students' explanations in which they utilize their experiences and knowledge of the context, statistical tools, and ideas to support their emerging informal Inferential Reasoning (IIR). This case study focuses on two independent inquiry episodes of sixth-grade students (age 12) within an unstructured, inquiry-based, technology-rich learning environment that was designed to promote students' IIR. We discuss research and practical issues related to the role of explanations and context in developing students' IIR.
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children s emergent Inferential Reasoning about samples in an inquiry based environment
7th Congress of the European Society for Research in Mathematics Education, 2011Co-Authors: Dani Benzvi, Katie Makar, Arthur Bakker, Keren AridorAbstract:Research on informal statistical inference has so far attended little to sampling. This paper analyzes children‘s Reasoning about sampling when making informal statistical inferences in an inquiry-based environment. Using data from a design experiment in Israeli Grade 5 (age 11) classrooms, we focus on the emergent Reasoning of two boys working with TinkerPlots on investigations with growing sample size. They turn out to have useful ideas about whether inferences can be made from samples of different sizes. Initially, they oscillate between deterministic and relativistic conclusions, but they come to reason in more sophisticated ways with increasing awareness of what is at stake when making inferences from samples.
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the role of context in the development of students informal Inferential Reasoning
2010Co-Authors: Dani Benzvi, Einat GilAbstract:The role of context is discussed in the setting of an extended curriculum development and research project in primary school designed to develop and study students' Reasoning about statistical inference. Qualitative research methods are used to critically dissect the roles of context in the emergence of sixth grade students' informal Inferential Reasoning (IIR). Context is examined as part of a complex network of themes, such as inquiry, norms, knowledge of statistical concepts and tools, beliefs and expectations, and meaning making and explanations. The paper analyzes and discusses these themes and the role context plays in the emerging Inferential Reasoning of these students. OVERVIEW In this paper we study the role of context in learning to make Informal Statistical Inferences (ISI), which are probabilistic (non-deterministic) generalizations from data (Makar & Rubin, 2009). We briefly present a case study of a small group of sixth graders (age 12) working within an inquiry-based and technology-rich learning environment that was designed to promote students' Informal Inferential Reasoning (IIR, Ben-Zvi, Gil & Apel, 2007), the Reasoning that underlies ISI. We briefly review the literature on IIR and context in statistics education. We use qualitative analysis methods to describe the role of context in the students' emerging IIR. When we discuss the results, we suggest that the classical distinction between data and context, although useful, represents only a partial picture of the complex processes of statistical Reasoning. LITERATURE REVIEW
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emergence of Reasoning about sampling among young students in the context of informal Inferential Reasoning
2010Co-Authors: Einat Gil, Dani BenzviAbstract:This paper discusses students’ evolving statistical Reasoning about randomness and sampling in the context of inquiry-based activities designed to develop their informal Inferential Reasoning (IIR). The knowledge of sampling and randomness are key concepts to understanding statistical inference (Garfield & Ben-Zvi, 2008). In the ‘Connections’ project (Ben-Zvi, Gil & Apel, 2007), sixth grade students were engaged in an inquiry-based learning environment using TinkerPlots (Konold & Miller, 2005) that was designed to develop their IIR. In this design experiment (Brown, 1992; Collins, 1992), the students’ intuitive concepts of sampling and randomness were used to design instructional activities that nurture the emergence of ideas of random vs. biased sample and inference. This knowledge was later applied by the students to investigate authentic data and draw informal statistical inferences from a random sample to a population. THEORETICAL BACKGROUND In this paper we study the emergence of students’ Reasoning about sample and sampling in the context of inquiry-based activities designed to develop their Informal Inferential Reasoning (IIR). IIR refers to “the cognitive activities involved in informally drawing conclusions (generalizations) from data (samples) about a ‘wider universe’ (the population), while attending to the strength and limitations of the sampling and the drawn inferences” (Ben-Zvi et al., 2007), and “articulating the uncertainty embedded in an inference” (Makar & Rubin, 2009). IIR involves a consideration of multiple dimensions: properties of data aggregates, the idea of signal and noise, various forms of variability, ideas about sample size and the sampling procedure, representativeness, controlling for bias, and tendency (Rubin, Hammerman & Konold, 2006). Ideas of sampling and using samples for statistical inference are at the heart of statistical investigations (Garfield & Ben-Zvi, 2008). Two central ideas of sampling–sampling representativeness and sampling variability–are important and related foundations for understanding statistical inference. Overreliance on sampling representativeness leads students to think that a sample tells us everything about a population, while overreliance on sampling variability leads students to think that a sample tells us nothing useful about a population (Rubin, Bruce, & Tenney, 1991). According to Tversky and Kahneman (1971), people tend to rely too much on small random samples and perceive them as representative. This has been suggested to be true also for school students (Shaughnessy, Garfield & Greer, 1996). The term randomness is related in everyday use to incidental events (contrary to intentional acts), while in statistics it is related to the principle of equal probability (Batanero & Serrano, 1999). To overcome bias in sampling that might be caused by personal choice, a statistician uses random sampling. Simple Random Sample (SRS) consists of n individuals from the population chosen in such a way that every individual has an equal chance to be in the sample, and every sample in the size n has an equal chance to be selected (Eisenbach, 2005). A larger sample is more likely to predict the desired parameter and thus to produce a smaller sampling variability (Moore & McCabe, 2006). Difficulties in understanding and using the concept of sample, random sample and sampling biases are described in the literature. For example, Metz (1999) found that many elementary school students thought that they cannot draw inferences from a sample to a population due to the need to ask everyone in the population. Watson (2004) classified children’s Reasoning about samples to six hierarchical categories of understanding that takes into account reference to sampling method (random/biased), sample size and other sample/sampling characteristics. Her findings showed that elementary school students improved their understanding of a random sample and sampling bias during the four years between one interview to another. Jacobs (1999) investigated students’ Reasoning about sampling before they learned the subject formally, and found that about a third of the students (grades 4 -5) estimated correctly the quality of the survey distinguishing between a sample taken randomly that results in a non-biased
Einat Gil - One of the best experts on this subject based on the ideXlab platform.
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explanations and context in the emergence of students informal Inferential Reasoning
Mathematical Thinking and Learning, 2011Co-Authors: Einat Gil, Dani BenzviAbstract:Explanations are considered to be key aids to understanding the study of mathematics, science, and other complex disciplines. This paper discusses the role of students' explanations in making sense of data and learning to reason informally about statistical inference. We closely follow students' explanations in which they utilize their experiences and knowledge of the context, statistical tools, and ideas to support their emerging informal Inferential Reasoning (IIR). This case study focuses on two independent inquiry episodes of sixth-grade students (age 12) within an unstructured, inquiry-based, technology-rich learning environment that was designed to promote students' IIR. We discuss research and practical issues related to the role of explanations and context in developing students' IIR.
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the role of context in the development of students informal Inferential Reasoning
2010Co-Authors: Dani Benzvi, Einat GilAbstract:The role of context is discussed in the setting of an extended curriculum development and research project in primary school designed to develop and study students' Reasoning about statistical inference. Qualitative research methods are used to critically dissect the roles of context in the emergence of sixth grade students' informal Inferential Reasoning (IIR). Context is examined as part of a complex network of themes, such as inquiry, norms, knowledge of statistical concepts and tools, beliefs and expectations, and meaning making and explanations. The paper analyzes and discusses these themes and the role context plays in the emerging Inferential Reasoning of these students. OVERVIEW In this paper we study the role of context in learning to make Informal Statistical Inferences (ISI), which are probabilistic (non-deterministic) generalizations from data (Makar & Rubin, 2009). We briefly present a case study of a small group of sixth graders (age 12) working within an inquiry-based and technology-rich learning environment that was designed to promote students' Informal Inferential Reasoning (IIR, Ben-Zvi, Gil & Apel, 2007), the Reasoning that underlies ISI. We briefly review the literature on IIR and context in statistics education. We use qualitative analysis methods to describe the role of context in the students' emerging IIR. When we discuss the results, we suggest that the classical distinction between data and context, although useful, represents only a partial picture of the complex processes of statistical Reasoning. LITERATURE REVIEW
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emergence of Reasoning about sampling among young students in the context of informal Inferential Reasoning
2010Co-Authors: Einat Gil, Dani BenzviAbstract:This paper discusses students’ evolving statistical Reasoning about randomness and sampling in the context of inquiry-based activities designed to develop their informal Inferential Reasoning (IIR). The knowledge of sampling and randomness are key concepts to understanding statistical inference (Garfield & Ben-Zvi, 2008). In the ‘Connections’ project (Ben-Zvi, Gil & Apel, 2007), sixth grade students were engaged in an inquiry-based learning environment using TinkerPlots (Konold & Miller, 2005) that was designed to develop their IIR. In this design experiment (Brown, 1992; Collins, 1992), the students’ intuitive concepts of sampling and randomness were used to design instructional activities that nurture the emergence of ideas of random vs. biased sample and inference. This knowledge was later applied by the students to investigate authentic data and draw informal statistical inferences from a random sample to a population. THEORETICAL BACKGROUND In this paper we study the emergence of students’ Reasoning about sample and sampling in the context of inquiry-based activities designed to develop their Informal Inferential Reasoning (IIR). IIR refers to “the cognitive activities involved in informally drawing conclusions (generalizations) from data (samples) about a ‘wider universe’ (the population), while attending to the strength and limitations of the sampling and the drawn inferences” (Ben-Zvi et al., 2007), and “articulating the uncertainty embedded in an inference” (Makar & Rubin, 2009). IIR involves a consideration of multiple dimensions: properties of data aggregates, the idea of signal and noise, various forms of variability, ideas about sample size and the sampling procedure, representativeness, controlling for bias, and tendency (Rubin, Hammerman & Konold, 2006). Ideas of sampling and using samples for statistical inference are at the heart of statistical investigations (Garfield & Ben-Zvi, 2008). Two central ideas of sampling–sampling representativeness and sampling variability–are important and related foundations for understanding statistical inference. Overreliance on sampling representativeness leads students to think that a sample tells us everything about a population, while overreliance on sampling variability leads students to think that a sample tells us nothing useful about a population (Rubin, Bruce, & Tenney, 1991). According to Tversky and Kahneman (1971), people tend to rely too much on small random samples and perceive them as representative. This has been suggested to be true also for school students (Shaughnessy, Garfield & Greer, 1996). The term randomness is related in everyday use to incidental events (contrary to intentional acts), while in statistics it is related to the principle of equal probability (Batanero & Serrano, 1999). To overcome bias in sampling that might be caused by personal choice, a statistician uses random sampling. Simple Random Sample (SRS) consists of n individuals from the population chosen in such a way that every individual has an equal chance to be in the sample, and every sample in the size n has an equal chance to be selected (Eisenbach, 2005). A larger sample is more likely to predict the desired parameter and thus to produce a smaller sampling variability (Moore & McCabe, 2006). Difficulties in understanding and using the concept of sample, random sample and sampling biases are described in the literature. For example, Metz (1999) found that many elementary school students thought that they cannot draw inferences from a sample to a population due to the need to ask everyone in the population. Watson (2004) classified children’s Reasoning about samples to six hierarchical categories of understanding that takes into account reference to sampling method (random/biased), sample size and other sample/sampling characteristics. Her findings showed that elementary school students improved their understanding of a random sample and sampling bias during the four years between one interview to another. Jacobs (1999) investigated students’ Reasoning about sampling before they learned the subject formally, and found that about a third of the students (grades 4 -5) estimated correctly the quality of the survey distinguishing between a sample taken randomly that results in a non-biased
Maxine Pfannkuch - One of the best experts on this subject based on the ideXlab platform.
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dynamic visualizations and the randomization test
Technology Innovations in Statistics Education, 2013Co-Authors: Stephanie Budgett, Maxine Pfannkuch, Matt Regan, C J WildAbstract:Hypothesis testing Reasoning is recognized as a difficult area for students. Changing to a new paradigm for learning inference through computer intensive methods rather than mathematical methods is a pathway that may be more successful. To explore ways to improve students’ Inferential Reasoning at the Year 13 (last year of school) and introductory university levels, our research group developed new learning trajectories and dynamic visualizations for the randomization method. In this paper we report on the findings from a pilot study including student learning outcomes and on the modifications we intend to make before the main study. We discuss how the randomization method using dynamic visualizations clarifies concepts underpinning Inferential Reasoning and why the nature of the argument still remains a challenge.
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enhancing students Inferential Reasoning from hands on to movies
Journal of Statistics Education, 2011Co-Authors: Pip Arnold, Maxine Pfannkuch, C J Wild, Matthew Regan, Stephanie BudgettAbstract:Computer simulations and animations for developing statistical concepts are often not understood by beginners. Hands-on physical simulations that morph into computer simulations are teaching approaches that can build students’ concepts. In this paper we review the literature on visual and verbal cognitive processing and on the efficacy of animations in promoting learning. We describe an instructional sequence, from hands-on to animations, developed for 14 year-old students. The instruction focused on developing students’ understanding of sampling variability and using samples to make inferences about populations. The learning trajectory from hands-on to animations is analyzed from the perspective of multimedia learning theories while the learning outcomes of about 100 students are explored, including images and Reasoning processes used when comparing two box plots. The findings suggest that carefully designed learning trajectories can stimulate students to gain access to Inferential concepts and Reasoning processes. The role of verbal, visual, and sensory cues in developing students' Reasoning is discussed and important questions for further research on these elements are identified.
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the role of context in developing informal statistical Inferential Reasoning a classroom study
Mathematical Thinking and Learning, 2011Co-Authors: Maxine PfannkuchAbstract:Context is identified as an important factor when considering the learning of informal statistical Inferential Reasoning, but research in this area is very limited. This small exploratory study in one grade 10 (14 year olds) classroom seeks to learn more about the role context plays in learners' Inferential Reasoning, where both teacher and students are positioned as learners. Two frameworks for context are used to analyze the classroom dialogue: The data-context used in statistical enquiry and in the formation of statistical concepts and the learning-experience-contexts such as prior statistical knowledge, which can affect the learning process. The analysis tracks the learning of informal Inferential Reasoning before, during, and after the introduction of sampling variability concepts. Data-context was found to assist learners in finding meaning from observed patterns, but could divert their attention during the construction of concepts and when attempting to apply newly-learned theory. Learning-experien...
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enhancing students Inferential Reasoning from hands on to movie snapshots
2010Co-Authors: Pip Arnold, Maxine PfannkuchAbstract:Computer simulations and animations for developing statistical conceptions are often not understood by beginners. Hands-on physical simulations that morph into computer simulation images are teaching approaches that can build students’ concepts. In this paper we describe an instructional sequence, from hands on to “movie snapshots”, which was trialed in a Grade 9 class. The instruction focused on developing students’ sampling variability concepts and on making inferences about populations from samples. Responses from three students’ interviews and two assessment items are explored, including the images they worked with when they reasoned and made a call from box plots. The findings suggest that students can use sampling variability ideas to support their Inferential Reasoning.
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year 11 students informal Inferential Reasoning a case study about the interpretation of box plots
Journal on Mathematics Education, 2007Co-Authors: Maxine PfannkuchAbstract:Year 11 (15-year-old) students are not exposed to formal statistical Inferential methods. When drawing conclusions from data, their Reasoning must be based mainly on looking at graph representations. Therefore, a challenge for research is to understand the nature and type of informal Inferential Reasoning used by students. In this paper two studies are reported. The first study reports on the development of a model for a teacher’s Reasoning when drawing informal inferences from the comparison of box plots. Using this model, the second study investigates the type of Reasoning her students displayed in response to an assessment task. The resultant analysis produced a conjectured hierarchical model for students’ Reasoning. The implications of the findings for instruction are discussed.
Tom Beckers - One of the best experts on this subject based on the ideXlab platform.
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the Inferential Reasoning theory of causal learning toward a multi process propositional account
Oxford library of psychology, 2017Co-Authors: Yannick Boddez, J De Houwer, Tom BeckersAbstract:Chapter 4 describes the Inferential Reasoning theory of causal learning and discusses how thinking about this theory has evolved in at least two important ways. First, the authors argue that it is useful to decouple the debate about different possible types of mental representations involved in causal learning (e.g., propositional or associative) from the debate about processes involved therein (e.g., Inferential Reasoning or attention). Second, at the process level Inferential Reasoning is embedded within a broad array of mental processes that are all required to provide a full mechanistic account of causal learning. Based on those insights, the authors evaluate five arguments that are often raised against Inferential Reasoning theory. They conclude that causal learning is best understood as involving the formation and retrieval of propositional representations, both of which depend on multiple cognitive processes (i.e., the multi-process propositional account).
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Reasoning rats forward blocking in pavlovian animal conditioning is sensitive to constraints of causal inference
Journal of Experimental Psychology: General, 2006Co-Authors: Tom Beckers, Jan De Houwer, Ralph R Miller, Kouji UrushiharaAbstract:Forward blocking is one of the best-documented phenomena in Pavlovian animal conditioning. According to contemporary associative learning theories, forward blocking arises directly from the hardwired basic learning rules that govern the acquisition or expression of associations. Contrary to this view, here the authors demonstrate that blocking in rats is flexible and sensitive to constraints of causal inference, such as violation of additivity and ceiling considerations. This suggests that complex cognitive processes akin to causal Inferential Reasoning are involved in a well-established Pavlovian animal conditioning phenomenon commonly attributed to the operation of basic associative processes.
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further evidence for the role of Inferential Reasoning in forward blocking
Memory & Cognition, 2005Co-Authors: Stefaan Vandorpe, Jan De Houwer, Tom BeckersAbstract:Previous studies on human causal learning (De Houwer & Beckers, 2003; De Houwer, Beckers, & Glautier, 2002) showed that secondary task difficulty (performing an easy vs. a difficult secondary task during the main causal learning task) and ceiling information (outcome occurs with a maximal vs. submaximal intensity) had an influence on forward blocking (i.e., lower causal ratings for cue T when AT+ trials are preceded by A+ trials than when no A+ trials are presented). We extended these studies by also examining self-reports of participants about the reasons behind their causal ratings. Blocking was found only for participants who reported an appropriate blocking inference. Furthermore, secondary task difficulty and ceiling information influenced the number of participants who reported an appropriate blocking inference. These findings point to a major impact of Inferential Reasoning in human causal learning.
Anna Cantagallo - One of the best experts on this subject based on the ideXlab platform.
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Inferential Reasoning comparison of patients with schizophrenia and patients with traumatic brain injury
Psychiatry Research-neuroimaging, 2011Co-Authors: Alessandra Geraci, Anna CantagalloAbstract:We investigated the cognitive processes underlying Inferential Reasoning, comparing performance of patients suffering from schizophrenia with that of patients with brain injury in an attempt to understand the nature of the social impairments in schizophrenia. Inferential Reasoning on mental and physical states and second-order false belief attribution were assessed in healthy controls, in patients with schizophrenia and in brain trauma patients with predominantly ventromedial prefrontal cortex or dosolateral prefrontal cortex lesions. Our finding that ventromedial prefrontal areas are involved in general Inferential Reasoning casts further light on the neural structures implicated in socio-cognitive impairments in schizophrenia.