Readings

Frameworks, Journal Articles & Research Studies
GAISE REPORT: Franklin, C., Kader, G., Mewborn, D. S., Moreno, J., Peck, R., Perry, M. & Scheaffer, R. (2007). //Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre--K-12 Curriculum Framework//. Alexandria, VA: American Statistical Association. Retrieved from []
 * Frameworks and Guidelines **

SET: Statistical Education of Teachers [] Groth, R. E. & Bargagliotti A. E. (2012). Gaise-ing into the common core of statistics. //Mathematics Teaching in the Middle School, 18//(1) 38-45.


 * Activity Based Articles**

Cross Francis, D. I., Hudson, R. A., Lee, M. Y., Rapacki, L., & Vesperman, C. M. (2014). Motivating Play Using Statistical Reasoning. //Teaching Children Mathematics, 21//(4), 228-237. Statistical literacy is essential in everyone's personal lives as consumers, citizens, and professionals. To make informed life and professional decisions, students are required to read, understand, and interpret vast amounts of information, much of which is quantitative. To develop statistical literacy so students are able to make sense of data and interpret results meaningfully, the National Council of Teachers of Mathematics suggests in "Principles and Standards for School Mathematics" (NCTM 2000) that students should work directly with data and engage in all aspects of statistical inquiry. In this article, the authors describe a project-based statistics unit--SIMPA (Students' Ideas about Motivating Play Activities)--that they designed to support twenty sixth-grade students in authentic statistical inquiry. To maximize student learning outcomes, the unit was designed to build students' statistical reasoning through solving a problem they faced in their school environment. Students worked on the unit for approximately four hours per day for one week. They focused on determining the kinds of changes they could make, to the current playground or otherwise, that would maximize play during recess. The sections presented describe the instructional unit and how the authors engaged students in statistical inquiry with the goal of providing a unit that teachers can use with their students as well as a model for teachers to design their own units to support the development of statistical literacy.

Cross, D. I., Hudson, R. A., Lee, M. Y., & Rapacki, L. (2012). Learning to tinker. //Teaching Children Mathematics, 18//(8), 508-513. Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K-grade 6 classrooms. Technological tools such as TinkerPlots support elementary school students in constructing statistical meaning and making data-based decisions.

Fitzallen, N. (2007). Evaluating Data Analysis Software: The Case of TinkerPlots. //Australian Primary Mathematics, Classroom, 12//(1), 23-28. The ever increasing availability of mathematics education software and internet-based multimedia learning activities presents teachers with the difficult task of deciding which programs are best suited for their students' learning needs. The challenge is for teachers to select pedagogical products that not only promote significant mathematical learning but also offer user-friendly functions, and are useful in the classroom. With the aim of assisting teachers in the selection process, this article reports on a framework that may be useful for evaluating software and multimedia products. As an example, an evaluation of data-analysis software, "TinkerPlots Dynamic Data Exploration" is presented. http://tinkerplots-math.wikispaces.com/Readings

Lee, M. Y. (2014). iSTEM: Tinkering with Buoyancy. //Teaching Children Mathematics, 20//(9), 574-578. I n the technology-rich twenty-first century, students are required to actively construct their knowledge and collaboratively engage in problem solving by using such skills as adaptability, communication, self-management, and systematic thinking. In accordance with this necessity, science, technology, engineering, and mathematics (STEM) ehttp://tinkerplots-math.wikispaces.com/Readingsducation has recently been in the spotlight. The project-based unit described in this article supports STEM education for students in upper elementary or middle school. The major elements of the unit include the driving questions for the beginning of the project, specific pedagogies during the project, and guidelines for the final product. The goal of the project this month is for students to design and build a tinfoil boat that is capable of carrying the maximum weight with the least expense, learning the scientific concept of buoyancy; incorporating the technological tool of TinkerPlots; applying engineering principles to designing and building a boat; and using mathematical knowledge of area, graphs, and data analysis. Integrating Science Technology Engineering in Mathematics (iSTEM) is the venue for ideas and activities that stimulate student interest in these integrated fields in K-grade 6 classrooms.//

Watson, J.M. (2013). Resampling with TinkerPlots. //Teaching Statistics, 35//(1), 32-36 The constructivist data handling software TinkerPlots is used to carry out resampling in a manner that illustrates the stages of the process without the need for programming skills.

//Watson, JM and Beswick, K and Brown, NR and Callingham, RA and Muir, T and Wright, SE, Digging into Australian Data with Tinkerplots, Objective Learning Materials, Sandown Village, pp. 372. ISBN 978-0-9580025-2-3 (2011)//

//Watson, J. M., Fitzallen, N. E., Wilson, K. G., & Creed, J. F. (2008, August). The representational value of hats.// Mathematics Teaching in the Middle School, 14//(1), 4-10.// // The literature that is available on the topic of representations in mathematics is vast. One commonly discussed item is graphical representations. From the history of mathematics to modern uses of technology, a variety of graphical forms are available for middle school students to use to represent mathematical ideas. The ideas range from algebraic relationships to summaries of data sets. Traditionally, textbooks delineate the rules to be followed in creating conventional graphical forms, and software offers alternatives for attractive presentations. This article presents a new data representation tool called the hat plot, which is a featured tool of the data analysis software TinkerPlots Dynamic Data Exploration (Konold and Miller 2005). TinkerPlots software gives students considerable freedom to create graphs to tell the stories of their data sets. Here, the authors demonstrate the value of the hat plot in representing and interpreting data sets. //

//Watson, J., & Wright, S. (2008). Building informal inference with TinkerPlots in a measurement context.// Australian Mathematics Teacher, 64//(4), 31-40.// // This article explores the issues associated with developing ideas of informal inference and introduces the software package, TinkerPlots, as a tool to facilitate this development. The activities suggested in this article are intended for use with middle and secondary students (grades 6 to 10). The data and suggestions presented have arisen mainly from workshops with inservice middle school teachers and preservice primary teachers, and hence may provide models for similar sessions, as well as for activities in the classroom. //

//**Activity for Teachers**// //MacKinnon, D., Lynch-Davis, K., & Driskell, S. (2009). Constructing and exploring Pascal’s triangle in TinkerPlots.// Mathematics Teacher, 102//(8), 628-632.//

//**Research Articles**//

//**2015-16**// // Kazak, S., Wegerif, R., & Fujita, T. (2015). The Importance of Dialogic Processes to Conceptual Development in Mathematics. // Educational Studies In Mathematics //, // 90 // (2), 105-120. // // We argue that dialogic theory, inspired by the Russian scholar Mikhail Bakhtin, has a distinct contribution to the analysis of the genesis of understanding in the mathematics classroom. We begin by contrasting dialogic theory to other leading theoretical approaches to understanding conceptual development in mathematics influenced by Jean Piaget and Lev Vygotsky. We argue that both Piagetian and Vygotskian traditions in mathematics education overlook important dialogic causal processes enabling or hindering switches in perspective between voices in relationship. To illustrate this argument, we use Piagetian-, Vygotskian- and Bakhtinian-inspired approaches to analyse a short extract of classroom data in which two 12-year-old boys using TinkerPlots software change their understanding of a probability problem. While all three analyses have something useful to offer, our dialogic analysis reveals aspects of the episode, in particular the significance of the emotional engagement and the laughter of the students, which are occluded by the other two approaches. //

//Kazak, S., Wegerif, R., & Fujita, T. (2015). Combining Scaffolding for Content and Scaffolding for Dialogue to Support Conceptual Breakthroughs in Understanding Probability.// ZDM: The International Journal on Mathematics Education, 47//(7), 1269-1283.// // In this paper, we explore the relationship between scaffolding, dialogue, and conceptual breakthroughs, using data from a design-based research study that focuses on the development of understanding of probability in 10-12 year old students. The aim of the study is to gain insight into how the combination of scaffolding for content using technology and scaffolding for dialogue can facilitate conceptual breakthroughs. We analyse video-recordings and transcripts of pairs and triads of students solving problems using the "TinkerPlots" software with teacher interventions, focusing on moments of conceptual breakthrough. Data show that dialogue scaffolding promotes both dialogue moves specific to the context of probability and dialogue in itself. This paper focuses on episodes of learning that occur within dialogues framed and supported by dialogue scaffolding. We present this as support for our claim that combining scaffolding for content and scaffolding for dialogue can be effective in students' conceptual development. This finding contributes to our understanding of both scaffolding and dialogic teaching in mathematics education by suggesting that scaffolding can be used effectively to prepare for conceptual development through dialogue. //

//**2013-14**// Allmond, Sue and Makar, Katie (2014). From hat plots to box plots in TinkerPlots: supporting students to write conclusions which account for variability in data. In: Katie Makar, Bruno de Sousa and Robert Gould, ICOTS-9 Conference Proceedings: Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics. //ICOTS9: 9th International Conference on Teaching Statistics 2014 //, Flagstaff, AZ, USA, (1 -6 ). 13-18 July, 2014. // A statistical question acknowledges that there is variability in data that needs to be accounted for in the conclusion. Accounting for variability is problematic if students do not have an understanding that a distribution shows patterns and can be described by the centre, spread and overall shape. TinkerPlots provides opportunities to build understandings of spread and measures of centre as students work with distributions, adding and manipulating dividers and hat plots. In this exploratory study, students in a middle school inquiry classroom used hat plots to compare distributions and write justified conclusions. Results suggest that the necessity to account for variability in data within their conclusions presented students with a purpose to transition from hat plots to box plots to provide evidence to answer the question. //

Frischemeier, D., & Biehler, R. (2013). Design and exploratory evaluation of a learning trajectory leading to do randomization tests facilitated by TinkerPlots. In //Proceedings of the Eight Congress of European Research in Mathematics Education// (pp. 798-808). [|http://cerme8.metu.edu.tr/wgpapers/WG5/WG5_Frischemeier_Biehler.pdf]

//Lee, H. S. et al. (2014). Teacher's use of transnumeration in solving statistical tasks with dynamic statistical software.// Statistics Education Research Journal, 13//(1), 25-52.// // This study examined a random stratified sample (n = 62) of teachers' work across eight institutions on three tasks that utilized dynamic statistical software. We considered how teachers may utilize and develop their statistical knowledge and technological statistical knowledge when investigating a statistical task. We examined how teachers engaged in transnumerative activities with the aid of technology through representing data, using dynamic linking capabilities, and creating statistical measures and augmentations to graphs. Results indicate that while dynamic linking was not always evident in their work, many teachers took advantage of software tools to create enhanced representations through many transnumerative actions. The creation and use of such enhanced representations of data have implications for teacher education, software design, and focus for future studies. //

Podworny, S., & Biehler, R. (2014, July). A LEARNING TRAJECTORY ON HYPOTHESIS TESTING WITH TINKERPLOTS–DESIGN AND EXPLORATORY EVALUATION. In //Sustanability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9//. []

Yilmaz, Z. (2013). Usage of Tinker Plots to address and remediate 6th grade students’ misconceptions about mean and median. //Anthropologist//, //16//(1-2), 21-29. http://www.krepublishers.com/02-Journals/T-Anth/Anth-16-0-000-13-Web/Anth-16-1-2-000-2013-Abst-PDF/T-ANTH-SV-10-021-13-03/T-ANTH-SV-10-021-13-03-Tx[3].pmd.pdf

//**2010-12**// //Prodromou, T. (2011). Students’ emerging inferential reasoning about samples and sampling. Mathematics: traditions and [new] practices, 640-648. Retrieved from @http://www.merga.net.au/documents/RP_PRODROMOU_MERGA34-AAMT.pdf// // This paper investigates students’ emerging inferential reasoning about samples and sampling through observation of 13- to 14-year-olds, challenged to infer aspects of an unknown population in an inquiry–based environment. This paper reports on how students working with TinkerPlots focus on changing aspects of the samples as the sample size grew larger. Students made connections to key statistical concepts during the process of growing samples and quantified the level of confidence about their informal statistical inferences. They generally recognized the relationship between the sample size and the confidence interval for a given confidence level. //

//**<2010**// Bakker, A. (2002, July). Route-type and landscape-type software for learning statistical data analysis. In //Proceedings of the Sixth International Conference on Teaching Statistics//. @https://www.stat.auckland.ac.nz/~iase/publications/1/7f1_bakk.pdf

//Beth Chance, Dani Ben-Zvi, Joan Garfield, and Elsa Medina (2007) “The Role of Technology in Improving Student Learning of Statistics”, Technology Innovations in Statistics Education: Vol. 1: No. 1, Article 2. http://repositories.cdlib.org/uclastat/cts/tise/vol1/iss1/art2//

Ben-Moshe, O. S. (2007). //Developing fourth-grade students' statistical reasoning about distribution with TinkerPlots software// (Doctoral dissertation, University of Haifa).

//Ben-Zvi, D. (2006). Scaffolding students’ informal inference and argumentation.// ICOTS 7//(1-6). doi: 10.1.1.150.617//

// - I am not sure of the date of this article//

Hall, J. (2008). Using Census at School and TinkerPlots™ to support Ontario elementary teachers’ statistics teaching and learning. //C. Batanero, G. Burrill, C. Reading, & A. Rossman//.

Khairiree, K., & Kurusatian, P. (2009). Enhancing students’ understanding statistics with Tinker Plots: Problem-based learning approach. //Retrieved March//, //13//, 2010 by Google Scholar http://atcm.mathandtech.org/EP2009/papers_full/2812009_17324.pdf

//Lehrer, R., Kim, M., & Schauble, L. (2007). Supporting the Development of Conceptions of Statistics by Engaging Students in Measuring and Modeling Variability.// International Journal Of Computers For Mathematical Learning, 12//(3), 195-216.//

//Paparistodemou, E., & Meletiou-Mavrotheris, M. (2008). Developing Young Students' Informal Inference Skills in Data Analysis. Statistics Education Research Journal, 7(2), 83-106.//

Reddy, S., Gal, Y. A., & Shieber, S. M. (2009). Recognition of users’ activities using constraint satisfaction. In //User Modeling, Adaptation, and Personalization// (pp. 415-421). Springer Berlin Heidelberg.

Rubin, A. (2002, July). Interactive visualizations of statistical relationships: What do we gain. In //Proceedings of the Sixth International Conference on Teaching Statistics//. @http://icots6.haifa.ac.il/PAPERS/7F6_RUBI.PDF

//Watson, J. M. (2008, November). Exploring beginning inference with novice grade 7 students.// Statistics Education Research Journal, 7//(2), 59-82.//

//Watson, J., & Donne, J. (2009). TinkerPlots as a Research Tool to Explore Student Understanding.// Technology Innovations in Statistics Education, 3//(1).//

//**TinkerPlots & Fathom Background**// //Konold, C., Harradine, A., & Kazak, S., (2007). Understanding Distributions by Modeling Them.// International Journal Of Computers For Mathematical Learning, 12//(3), 217-230.//

//Finzer, W., Erickson, T., Swenson, K., & Litwin, M. (2007). On Getting More and Better Data Into the Classroom. TISE, Technology Innovations in Statistics Education, 1(1).//

//Cliff Konold (2002) ICOTS6// //@http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.590.6035&rep=rep1&type=pdf// //@http://iase-web.org/documents/papers/icots6/7f5_kono.pdf//

//Podworny, S., & Biehler, R. (2014, July). A LEARNING TRAJECTORY ON HYPOTHESIS TESTING WITH TINKERPLOTS–DESIGN AND EXPLORATORY EVALUATION. In// Sustanability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9//. []

@http://www.tinkerplots.com/research-literature

Updated - Spring 2016