What is Hidden Beyond the Data? Young Students Reason and Argue about Some Wider Universe 2
by Dani Ben-Zvi
A SRTL-5 paper, Warwick, UK, 2007
Download (.pdf) Integrating physical activity data technologies into elementary classrooms
by Victor Lee
Available online first, Educational Technology Research & Development. Likely press date, beginning of 2012.
This paper describes an iteration of a design-based research project that involved integrating commercial physical... more This paper describes an iteration of a design-based research project that involved integrating commercial physical activity data (PAD) sensors, such as heart rate monitors and pedometers, as technologies that could be used in two fifth-grade classrooms. Design-based research involves the development, implementation and study of new learning interventions in real-world contexts with the goal of elaborating principles or guidelines relevant to the design of new technologies and learning experiences. The current project involved the implementation of PAD technology-supported learning activities in two fifth-grade classrooms where students pursued investigations related to the distances that they walk, the relationship between heights and footsteps taken, and variations in heart rates among twins and with adults. In addition to describing some of the practical lessons learned related to the use of PAD technologies with elementary school children, we describe our initial efforts to assess students’ knowledge before and after the learning intervention. Results from the written assessments indicated that the newly designed activities indeed covered the intended content related to measures of center and averages. Results from the interviews suggested that students who participated in the unit designed to incorporate PAD technologies more reliably accessed knowledge related to measures of center and averages in scenario based problems than their counterparts who followed a traditional unit.
Learning spurious correlations instead of deeper relations
by Norma Ming
Chang, N.M., Koedinger, K.R., & Lovett, M.C. (2003). Learning spurious correlations instead of deeper relations. In R. Alterman & D. Kirsh (Eds.), Proceedings of the 25th Cognitive Science Society (pp. 228-233). Boston, MA: Cognitive Science Society.
Effective instructional design requires navigating the tradeoff between providing helpful cues to the correct... more Effective instructional design requires navigating the tradeoff between providing helpful cues to the correct solutions and supplying hints that ultimately detract from what students learn. The present study manipulated the correlations between superficial features and the correct solutions in a set of training problems in the domain of exploratory data analysis and examined their effect on novices with no prior knowledge of statistics. Students who were trained on problems with these spurious correlations performed more poorly on posttest problems lacking these associations, making errors in the direction predicted by the misleading features. The theoretical and educational implications of the outcomes of this practice are discussed.
Performance vs. learning: Knowing the right answers for the right reasons
by Norma Ming
Chang, N.M., Koedinger, K.R., & Lovett, M.C. (2005). Performance vs. learning: Knowing the right answers for the right reasons. In K. Forbus, D. Gentner, & T. Regier (Eds.), Proceedings of the 26th Cognitive Science Society (p. 1537). Mahwah NJ: Lawrence Erlbaum Associates.
An important dilemma to resolve in instruction is distinguishing between short-term performance and long-term learning... more An important dilemma to resolve in instruction is distinguishing between short-term performance and long-term learning in assessing students’ progress. Conditions that appear favorable in acquisition are not always as effective at promoting subsequent retention and transfer, due to differences in the processing activities involved in training and at test; in some cases, poor performance in training produced better performance at test (Schmidt & Bjork, 1992). Since global measures of accuracy and speed are insufficient predictors of the effectiveness of training, we have used a modeling approach to draw inferences about the knowledge structures students use to solve problems both at test and in training. We will present the results from one study demonstrating the usefulness of such qualitative measures in predicting learning outcomes from training.
The impact of spurious correlations on students' problem-solving
by Norma Ming
Chang, N.M., Koedinger, K.R., & Lovett, M.C. (2004). The impact of spurious correlations on students' problem-solving. In Y.B. Kafai, N. Enyedy, & W. Sandoval (Eds.), Proceedings of the 6th International Conference of the Learning Sciences. Mahwah NJ: Lawrence Erlbaum Associates.
Students are often susceptible to surface features when learning to solve problems in a new domain. Providing example... more Students are often susceptible to surface features when learning to solve problems in a new domain. Providing example problems where salient surface features are spuriously correlated with the same problem type may encourage their use (Ben-Zeev & Star, 2001), whereas increasing the variability among superficial features during training may yield more robust knowledge (Schmidt & Bjork, 1992). To better understand the causes and consequences of this phenomenon, we compared the impact of two instructional regimens embodying these extremes and articulated detailed models of students’ surface and deep knowledge resulting from each training procedure, enabling us to distinguish between weak correct knowledge and strong incorrect knowledge.
Data analysis skills: What and how are students learning?
by Norma Ming
Lovett, M.C., & Chang, N.M. (2007). Data analysis skills: What and how are students learning? In M. Lovett & P. Shah (Eds.), Thinking with Data: The Proceedings of the 33rd Carnegie Symposium on Cognition (pp. 293-318). Mahwah NJ: Lawrence Erlbaum Associates, Inc.
Attributing meanings to representations of data: The case of statistical process control
Hoyles, C., Bakker, A., Kent, P., & Noss, R. (2007). Attributing meanings to representations of data: The case of statistical process control. Mathematical Thinking and Learning, 9, 331-360. DOI: 10.1080/10986060701533326
This article is concerned with the meanings that employees in industry attribute to representations of data and the... more This article is concerned with the meanings that employees in industry attribute to representations of data and the contingencies of these meanings in context. Our primary concern is to more precisely characterize how the context of the industrial process is constitutive of the meaning of graphs of data derived from this process. We draw on data from a variety of sources, including ethnographic studies of workplaces and reflections on the design of prototype learning activities, supplemented by insights obtained from trying out these activities with a range of employees. The core of this article addresses how different groups of employees react to graphs used as part of statistical process control, focusing on the meanings they ascribe to mean, variation, target, specification, trend, and scale as depicted in the graphs. Using the notion of boundary crossing, we try to characterize a method that helps employees to communicate about graphs and come to data-informed decisions.
Statistical inference at work: The case of statistical process control
Bakker, A., Kent, P., Derry, J., Noss, R., & Hoyles, C. (2008). Statistical inference at work: The case of... more
Bakker, A., Kent, P., Derry, J., Noss, R., & Hoyles, C. (2008). Statistical inference at work: The case of statistical process control. Statistics Education Research Journal, 7(2), 130-145
To characterise statistical inference in the workplace this paper compares a prototypical type of statistical inference at work, statistical process control (SPC), with a type of statistical inference that is better known in educational settings, hypothesis testing. Although there are some similarities between the reasoning structure involved in hypothesis testing and SPC that point to key characteristics of statistical inference in general, there are also crucial differences. These come to the fore when we characterise statistical inference within what we call a “space of reasons” – a conglomerate of reasons and implications, evidence and conclusions, causes and effects.
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Alternative representations of statistical measures in computer tools to promote communication between employees in automotive manufacturing
Bakker, A, Kent, P, Noss, R., & Hoyles, C. (2009). Alternative representations of statistical measures in computer tools to promote communication between employees in automotive manufacturing. Technology Innovations in Statistics Education, 3(2).
In manufacturing industry, many employees need to interpret and communicate statistical information to monitor and... more In manufacturing industry, many employees need to interpret and communicate statistical information to monitor and improve production processes. Often the information is reduced to the form of numerical measures, on the logic that numbers are a convenient and understandable type of information to pass among the diverse groups of employees that make up a manufacturing operation. We investigated by means of interviews and observation how several numerical measures, ‘process capability indices’, were used in an automotive factory and how employees were trained to use them. We found that the typical introduction to the measures deployed statistical and algebraic symbolism as well as laborious manual calculations that did not appear to support employees’ understanding of the underlying mathematical relationships. These measures therefore failed to be ‘boundary objects’ – artifacts that inhabit different social worlds and satisfy the informational requirements of each. The goal of our subsequent design-based research was to design a representation of the process capability indices that would be easier to engage with than the existing formal symbolism used in shop floor calculations and in training. We did this by re-presenting relevant mathematical relationships in computer tools – technology-enhanced boundary objects (TEBOs) – developed in collaboration with company trainers. To evaluate our interaction with three trainers and 37 trainees in three courses in two factories, and the impact of the computer tools on practice, we followed the computer tools’ trajectory from the stage of co-design with the original car factory through to the stage at which the computer tools were used by factories beyond this research project. The evaluation points to the importance of aligning statistical and workplace norms and meanings, and gives illustrations of how the tools facilitated communication between employees.
Authentic practices as contexts for learning to draw inferences beyond correlated data
Dierdorp, A., Bakker, A., Eijkelhof, H. M. C., & van Maanen, J. A. (2011). Authentic practices as contexts for learning to draw inferences beyond correlated data. Mathematical Thinking and Learning, 13, 132-151.
To support 11th-grade students' informal inferential reasoning, a teaching and learning strategy was designed based on... more To support 11th-grade students' informal inferential reasoning, a teaching and learning strategy was designed based on authentic practices in which professionals use correlation or linear regression. These practices included identifying suitable physical training programmes, dyke monitoring, and the calibration of measurement instruments. The question addressed in this study is: How does a teaching and learning strategy based on authentic practices support students in making statistical inferences about authentic problems with the help of correlation and linear regression? To respond to this question we used video-recordings of lessons, audio-taped interviews, classroom field notes, and student work from a teaching experiment with 12 Dutch students (aged 16-17 years). The analysis provided insights into how the teaching and learning strategies based on authentic practices supported them to draw inferences about authentic problems using correlated data. The evidence illustrates how an understanding of the authentic problem being solved, collecting their own data to become acquainted with the situation, and learning to coordinate individual and aggregate views on data sets seemed to support these students in learning to draw inferences that make sense in the context.
The reasoning behind informal statistical inference
Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13, 152-173.
Informal statistical inference (ISI) has been a frequent focus of recent research in statistics education. Considering... more Informal statistical inference (ISI) has been a frequent focus of recent research in statistics education. Considering the role that context plays in developing ISI calls into question the need to be more explicit about the reasoning that underpins ISI. This paper uses educational literature on informal statistical inference and philosophical literature on inference to argue that in order for students to generate informal statistical inferences, there are a number of interrelated key elements that are needed to support their informal inferential reasoning. In particular, we claim that ISI is nurtured by statistical knowledge, knowledge about the problem context, and useful norms and habits developed over time, and is supported by an inquiry-based environment (tasks, tools, scaffolds). We adopt Peirce's and Dewey's view that inquiry is a sense-making process driven by doubt and belief, leading to inferences and explanations. To illustrate the roles that these elements play in supporting students to generate informal statistical inferences, we provide an analysis of three sixth-graders' (aged 12) informal inferential reasoning—the reasoning processes leading to their informal statistical inferences
Diagrammatisch redeneren als basis voor begripsontwikkeling in het statistiekonderwijs
Bakker, A. (2007). Diagrammatisch redeneren als basis voor begripsontwikkeling in het statistiekonderwijs.... more Bakker, A. (2007). Diagrammatisch redeneren als basis voor begripsontwikkeling in het statistiekonderwijs. Pedagogische Studiën, 84, 340-357.
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An Exploration into How Physical Activity Data-Recording Devices Could be Used in Computer-Supported Data Investigations
by Victor Lee
published in International Journal of Computers for Mathematical Learning. Available through the publisher only for the first year after publication. Contact me by email if you want more information.
There is a great potential opportunity to use portable physical activity monitoring devices as data collection tools... more There is a great potential opportunity to use portable physical activity monitoring devices as data collection tools for educational purposes. Using one such device, we designed and implemented a weeklong workshop with high school students to test the utility of such technology. During that intervention, students performed data investigations of physical activity that culminated in the design and implementation of their own studies. In this paper, we explore some of the mathematical thinking that took place through a series of vignettes of a pair of students engaged in analyzing some of their own activity data. A personal connection to the data appeared to aid these students in recognizing their own errors, and ultimately helped them move from a point-based analytical approach for making sense of the data to an aggregate one. From our observations of this designed learning experience, we conclude that physical activity data recording devices can afford students the opportunity to reason with personally relevant data in meaningful ways.
“VARIATION-TALK”: ARTICULATING MEANING IN STATISTICS
by Katie Makar
Little is known about the way that teachers articulate notions of variation in their own words. The study reported... more Little is known about the way that teachers articulate notions of variation in their own words. The study reported here was conducted with 17 prospective secondary math and science teachers enrolled in a preservice teacher education course which engaged them in statistical inquiry of testing data. This qualitative study examines how these preservice teachers articulated notions of variation as they compared two distributions. Although the teachers made use of standard statistical language, they also expressed rich views of variation through nonstandard terminology. This paper details the statistical language used by the prospective teachers, categorizing both standard and nonstandard expressions. Their nonstandard language revealed strong relationships between expressions of variation and expressions of distribution. Implications and the benefits of nonstandard language in statistics are outlined
Business Statistics Collaboration: A Partnership Between Business and Mathematics Departments
Two faculty members at Wilmington College (one in business and one in mathematics) experimented with a... more Two faculty members at Wilmington College (one in business and one in mathematics) experimented with a cross-departmental statistics partnership. Both teach a statistics course in different departments and decided to have the students from the classes work together on shared statistics projects that culminated in both papers and presentations. This abstract will discuss the method used, both the positive outcomes and the challenges faced, and most importantly, ways in which the project will be changed in the future.
Berdayes, Vicente (2008). "Official Statistics as Curriculum: Biopolitics and the United States Census in Schools Program". Review of Education, Pedagogy, and Cultural Studies. 30 (2): 85-114.
The United States Census Bureau’s Census in Schools targets students with the goal of increasing participation in the... more
The United States Census Bureau’s Census in Schools targets students with the goal of increasing participation in the decennial census. The program familiarizes children in grades K-12 with census practices and the political and social uses of census data. Though it ostensibly aims to demystify the practice of census-taking, an analysis of Census in Schools documents shows the program to be an expression of the bio-political desire to manage populations and direct their productive energies. In addition to diffusing the characteristic experience of space and time required by modern forms of social planning, Census in Schools cultivates an acceptance of and proficiency with social-scientific practices that allow populations to contribute to their own surveillance and rationalized administration. In spite of the instrumental purpose, there are ways in which educators can nevertheless appropriate such materials for critical and emancipatory ends.
Boredom-proneness, loneliness, social engagement and depression and their association with cognitive function in older people: a population study
by Ronan Conroy
In this study, we use data from a population survey of persons aged 65 and over living in the Irish Republic to... more
In this study, we use data from a population survey of persons aged 65 and over living in the Irish Republic to examine the relationship of cognitive impairment, assessed using the Abbreviated Mental Test, with loneliness, boredom-proneness, social relations, and depression. Participants were randomly selected community-dwelling Irish people aged 65+ years. An Abbreviated Mental Test score of 8 or 9 out of 10 was classified as 'low normal', and a score of less than 8 as 'possible cognitive impairment'. We used clustering around latent variables analysis (CLV) to identify families of variables associated with reduced cognitive function. The overall prevalence of possible cognitive impairment was 14.7% (95% CI 12.4-17.3%). Low normal scores had a prevalence of 30.5% (95% CI 27.2-33.7%). CLV analysis identified three groups of predictors: 'Low social support' (widowed, living alone, low social support), 'personal cognitive reserve' (low social activity, no leisure exercise, never having married, loneliness and boredom-proneness), and 'sociodemographic cognitive reserve' (primary education, rural domicile). In multivariate analysis, both cognitive reserve clusters, but not social support, were independently associated with cognitive function. Loneliness and boredom-proneness are associated with reduced cognitive function in older age, and cluster with other factors associated with cognitive reserve. Both may have a common underlying mechanism in the failure to select and maintain attention on particular features of the social environment (loneliness) or the non-social environment (boredom-proneness).