ESTEEM: Enhancing Statistics Teacher Education through E-Modules

Supplementary Materials for AMTE Standards

The Enhancing Statistics Teacher Education through E-Modules [ESTEEM] project, funded by the National Science Foundation (DUE 1625713), began in 2016 to develop teacher education curriculum materials designed to support secondary (grades 6-12) mathematics teachers to learn to teach statistics. The project’s focus on the statistical education of teachers was due to increased expectations for students to learn statistics at the secondary level (e.g., CCSS-M, National Governors Association Center for Best Practice & Council of Chief State School Officers, 2010;) that needed to be matched by enhancement and prioritization of statistics teacher education (Franklin et al., 2015). Lovett and Lee (2017) found that secondary preservice mathematics teachers were leaving teacher preparation programs feeling least prepared to teach statistics out of all content strands they may be responsible for teaching. Hence, creation of high quality, modern statistics teacher education curriculum materials was identified as important for the field of mathematics teacher education.

The project also reflects the demands of today’s data-driven society and the exponential growth in the storage of and reliance on data that has created the need for a data savvy citizenry, fluent in working with data using technology (Boaler & Levitt, 2019; Finzer, 2013). The learning of modern, data-intensive statistics depends heavily on the use of technology. Hence, the ESTEEM project prepares mathematics teachers to teach statistics with the technology tool Common Online Data Analysis Platform (CODAP) (https://codap.concord.org/). CODAP is a free, web-based, educational software designed to help students learn how to analyze data. One of its designers, Bill Finzer, is a member of the ESTEEM leadership team which designed and implemented significant enhancements to CODAP to ensure its applicability and suitability for teaching secondary statistics. We use CODAP throughout ESTEEM materials, both in CODAP-based data activities and through videos of students’ use of CODAP in secondary classrooms.

Mathematics teacher preparation programs vary widely, and statistical content and pedagogy may be introduced in different courses including a general mathematics methods course, a course on teaching and learning statistics, a statistics content course, or courses focused on technology for teaching mathematics. Course modalities also vary greatly across programs, and there is an increased need for resources that support online learning. Therefore, we decided to package the materials into e-modules. Their modular format makes their use more flexible for mathematics teacher educators (MTEs), allowing them to choose the modules that work best in their teacher preparation program. The modules are easily imported into Learning Management Systems [LMSs] for adaptation and integration with other course materials. MTEs can access the entire set of ESTEEM-developed modules at the ESTEEM portal, available through free registration. At the ESTEEM portal, MTEs can view all the materials as they would appear in a Learning Management System. They can also download a version of the complete set of materials in an easy-to-use format that can be imported into CANVAS, Moodle, or Blackboard. We also offer a Common Cartridge format that can be imported into other LMSs. All materials are distributed using the Creative Commons Attribution Noncommercial Share-Alike 4.0 license. More information about the history of the ESTEEM project and its design principles can be found in Hudson et al. (2018) and Lee et al. (in press).

  1. Description of ESTEEM Materials

The ESTEEM materials include 3 modules specifically developed for online secondary mathematics education courses, with each module containing 12-16 hrs of instructional material. Although the ESTEEM materials were originally designed for undergraduate teacher preparation courses, they can, and have been, used with practicing teachers. Thus, we refer to this audience collectively as “teacher learners.”  Module 1 (Foundations in Statistics Teaching) should always be used first (parts 1.1 and 1.2).  After Module 1, MTEs can implement the Teaching Inferential Reasoning (parts A.1 and A.2) and/or the Teaching Statistical Association (parts B.1 and B.2) Modules in any order.

The modules incorporate a variety of activity types, including watching videos (e.g., interviews with teachers, classrooms with students and teachers engaged in statistics, animated videos based on research regarding how students reason about statistical concepts, how-to videos for using CODAP), reading short articles on topics like differences between mathematics and statistics or the statistical investigation cycle, investigating data in CODAP, discussing topics using online discussion boards, and taking quizzes. The Screencast and Task Design Assignments provide opportunities for teachers to demonstrate their new understandings about doing and teaching statistics. 

A complete description of all components of the ESTEEM materials, including the Screencast and Task Design assignments, is available in this annotated table of contents.

Documents for Mathematics Teacher Educators

Roller Coaster Investigation in a Statistics Classroom: Six Sample Activities from the ESTEEM Materials

The following sample activities represent critical learning experiences in the Foundations in Statistics Teaching module. Although we hope you will be interested in using many more of the ESTEEM materials, these selected activities illustrate key ideas and experiences in our materials that set the stage for teacher learners to begin their journey in developing strong statistics pedagogy. Our materials are multimedia in nature and utilize common approaches and frameworks used in mathematics teacher education (e.g., professional noticing (Jacobs et al., 2010), Five Practices model for productive classroom discussions (Smith & Stein, 2011) to support integration with other materials in teacher preparation courses.

Materials for Teacher Learners

Brief description: A 1.5 page reading highlights the key features that differentiate mathematical and statistical reasoning, including context, measurement, and anticipating variability and uncertainty. 

Brief description: A short video and reading introduce teachers to the statistical investigation cycle which involves posing a statistical question, collecting data, analyzing data, and interpreting results. A second reading and diagram describe statistical habits of mind that students should develop when they engage with statistics. 

Brief description: A seven-minute video features a teacher launching a statistical task during a classroom lesson with middle-school students.  During the launch, the teacher shares a video of a roller coaster ride to help students have a virtual experience of what such a ride may look and feel like and discuss attributes of different roller coasters.  Teacher learners are asked to attend to how the teacher makes purposeful attempts to ensure students have a strong foundation about the context of roller coasters that can help spark curiosity about variability among coasters.  

Brief description: In this CODAP-based data investigation, teacher learners investigate characteristics of roller coasters with a data set of 157 coasters with multiple attributes. Teacher learners explore features of CODAP, such as using a map and displaying data in a hierarchy. They also make comparisons using different types of bivariate data (qualitative/quantitative, quantitative/quantitative, and qualitative/qualitative). 

Brief description: A nine-minute video illustrates students in 6th grade, 7th grade, and high school AP Statistics as they investigate roller coasters with data in  CODAP. After watching the video, teacher learners may compare and contrast how the different groups of students utilized statistical habits of mind, including the role that context played in their discussion; the ways they engaged in posing questions of interest; the ways CODAP supported or hindered the students’ work; and the opportunities for each student to express their understandings. 

Brief description: An eleven-minute video shows a teacher implementing the Five Practices during a 7th grade statistics lesson, including introducing a task based on anticipating their responses, monitoring and supporting students as they work on the task, selecting and sequencing students’ work to share, and facilitating discourse by connecting and building on students’ thinking. After watching the video, teacher learners may reflect on how the teachers’ interactions with pairs of students moved their reasoning forward, why the teacher chose the sequence of students’ sharing their work, and how she used students’ ideas to build connections between the student thinking shared.

Standards and Indicators these Materials Target

The ESTEEM materials are most closely aligned with the SPTM Indicators noted below.

C.1.2 Demonstrate Mathematical (Statistical) Practices and Processes: The ESTEEM curriculum materials develop teacher learners’ skills in statistical practices and habits of mind as well as their ability to engage in the statistical investigation process. The materials introduce teacher learners to statistical practices (e.g., asking statistical questions, describing variation) and they have opportunities to demonstrate their understandings and abilities to engage in these practices as well as to design teaching materials for students to engage in such practices. For example, in the Screencast Assignment teacher learners record actions on their computer screen and talk aloud as they complete a new data investigation in CODAP. These screencasts reveal how teacher learners use CODAP to engage in statistical practices and enact statistical habits of mind. 

C.1.6 Use Mathematical (Statistical) Tools and Technology: Teacher learners using the ESTEEM materials have extensive opportunities to use the statistical technology tool CODAP. Every module includes at least two activities centered on investigating a real-world phenomenon using a large data set and advanced analysis tools in CODAP.

C.1.5. Analyze Mathematical (Statistical) Thinking: The materials illustrate various ways that students, using different levels of sophistication, reason about statistical concepts. The materials include classroom videos showing students working on statistical tasks, often using technology, along with other artifacts of students' work. These are embedded in activities that call for teacher learners to analyze the students’ thinking and craft appropriate instructional responses. These activities also support the SPTM standard C.3: Students as Learners of Mathematics by helping teacher learners learn to attend to students’ thinking about statistical content and their engagement in statistical practices.

C.2.2 Plan for Effective Instruction: The ESTEEM materials teach teacher learners to design effective statistical learning opportunities for students, with emphasis of how to launch statistical tasks, how to select and/or write high quality statistical tasks, and how to lead a productive class discussion. As a culminating activity, teacher learners have the opportunity to design their own tasks for teaching specific statistics concepts that utilize the strategies learned throughout the modules in the Task Design Assignment.

References

Boaler, J., & Levitt, S. (2019, October 23). Modern high school math should be about data science – not Algebra 2. Los Angeles Times. https://www.latimes.com/opinion/story/2019-10-23/math-high-school-algebr....

Finzer, W. (2013). The data science education dilemma. Technology Innovations in Statistics Education. http://escholarship.org/uc/item/7gv0q9dc

Franklin, C., Bargagliotti, A. E., Case, C. A., Kader, G. D., Schaeffer, R. L., & Spangler, D. A. (2015). The statistical education of teachers. American Statistical Association.

Hudson, R. A., Lee, H., Casey, S., Finzer, W., Mojica, G., Azmy, C., & Eide, A. (2018). Developing e-modules to support preservice mathematics teachers’ statistical thinking. In M.A. Sorto, A. White, & L. Guyot (Eds.), Looking back, looking forward. Proceedings of the Tenth International Conference on Teaching Statistics (ICOTS10). International Statistical Institute. http://iase-web.org/icots/10/proceedings/pdfs/ICOTS10_9A2.pdf?1531364299

Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202

Lee, H. S., Hudson, R., Casey, S., Mojica G., Harrison, T. R. (in press). Online curriculum modules for preparing teachers to teach statistics: Design, implementation, and results. In K. Hollebrands, R. Anderson, K. Oliver (Eds). Online Mathematics Teacher Education, Springer.

Lovett, J. N., & Lee, H. S. (2017). New standards require teaching more statistics: Are preservice secondary mathematics teachers ready? Journal of Teacher Education, 68(3), 299-311.

McBrien, J. L., Jones, P., & Cheng, R. (2009). Virtual spaces: Employing a synchronous online classroom to facilitate student engagement in online learning. International Review of Research in Open and Distance Learning, 10(3), 1-17. https://doi.org/10.19173/irrodl.v10i3.605

National Governors Association Center for Best Practice & Council of Chief State School Officers. (2010). Common core state standards for mathematics (CCSS-M). Washington DC: Author.

Starling, T., & Lee, H. S. (2015). Synchronous online discourse in a technology methods course for middle and secondary prospective mathematics teachers. Contemporary Issues in Technology and Teacher Education, 15(2), 106-125.

Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. National Council of Teachers of Mathematics. 

About the Authors

Hollylynne Lee, NC State University, hstohl@ncsu.edu 

Stephanie Casey, Eastern Michigan University, scasey1@emich.edu 

Rick Hudson, University of Southern Indiana, rhudson@usi.edu 

William Finzer, The Concord Consortium, wfinzer@concord.org 

Gemma Mojica, NC State University, gmmojica@ncsu.edu