# ThEMaT III

Thought Experiments in Mathematics Teaching III“Developing Rich Media-based Materials for Practice-based Teacher Education” (also known as ThEMaT III) was funded by NSF in 2013 and closed in 2020 (NSF Grant DRL–1316241). The project explored how web-based resources and tools, such as those provided by the LessonSketch platform, could support the work of teacher educators designing materials for practice based teacher education. The research focused on understanding how online, rich-media resources can instrument the work of teacher educators and their students, as well as evaluating how LessonSketch functionalities respond to the needs of teacher educators and their students. A main thrust of the project was related to materials development: a group of LessonSketch Research and Development Fellows were recruited to create and disseminate materials through a network of inquiry groups. The project was also concerned with examining how the technological mediation affects the work of teacher educators and their inquiry groups planning and enacting teacher education lessons that use the materials developed.

### Project Fellows

Wendy Rose Aaron · Emina Alibegovic · Joel Amidon · Kristen Bieda · Orly Buchbinder · Lawrence Clark · Sandra Crespo · Karl W. Kosko · Woong Lim · Janet Walkoe · Rob Wieman · Bill Zahner

The project was premised on the notion that recent technological developments have made it feasible to represent classroom work in new ways. In addition to watching recorded videos of classroom interactions or reading written cases, teacher educators and teachers can now watch animations and image sequences, realized with cartoon characters, and made to depict activities that have or could have happened in a mathematics classroom. Furthermore, teacher educators and teachers can react to such animations or image sequences by making their own depictions of alternative moves by students or teachers in classroom interaction. And all of that can take place in an online, cloud-based environment that also supports discussion fora and the kinds of capabilities associated with learning management systems. Such technologies offer important affordances to teacher educators seeking to provide candidates with course-based experiences that emphasize the development of practice-based skills.

This joint project of the University of Maryland Center for Mathematics Education and the University of Michigan gathered 12 mathematics educators, called LessonSketch Research and Development Fellows, across various teacher preparation institutions in the U.S. Fellows included Wendy Aaron (Oregon State University), Emina Alibegovic (then at the University of Utah), Joel Amidon (University of Mississippi), Kristen Bieda (Michigan State University), Orly Buchbinder (University of New Hampshire), Lawrence Clark (University of Maryland), Sandra Crespo (Michigan State University), Karl Kosko (Kent State University), Woong Lim (University of New Mexico), Janet Walkoe (University of Maryland), Rob Wieman (Rowan University), and Bill Zahner (San Diego State University). These Fellows were charged with the development of online practice-based modules for use in different courses within mathematics teacher preparation programs. Once initial drafts of materials were developed, the Fellows each gathered inquiry groups, typically composed of 3 – 4 other mathematics educators serving at distinct institutions, to help support the further development and field testing of modules. The project team engaged with the Inquiry Groups in three distinct ways. First, the team provided inquiry groups with support, both conceptual and technical, for the design of their materials. Second, using the framework of instrumental genesis, the project team documented the ways that the Fellows and their Inquiry Groups used the LessonSketch tools in conjunction with other tools. This documentation included observing the ways in which various groups used the tools, how those uses changed overtime, and challenges they faced when engaged in their work. It also included administering surveys and conducting interviews and focus groups with both Fellows and their inquiry group members. Finally, based on what had been learned from these experiences of providing support and documenting the work of the groups, the project team engaged in rounds of design-based research—making incremental changes to the LessonSketch platform and releasing those updates for piloting by various inquiry groups that had need for such updates.

As part of our own contribution to the use of rich media in teacher development, we conceived of the Story*Circles* process of teacher collaboration, which we have continued to develop in the context of other funded projects. The investigation of how teacher educators used the Lesson*Sketch* tools led to a reconceptualization and revision of two of the original Lesson*Sketch* tools: * Depict *(an online storyboarding tool for representing classroom scenarios) and

*(an online tool for annotating rich-media, such as video). Moving away from the Flash framework, two new standalone tools were coded in javascript to support similar work but with enhanced features:*

**Annotate****and**

*Lesson Depict***(ah-noh-ta-mos). An important enhancement in these tools is that they are collaborative: Users may work synchronously on the same file. Through LTI integration they are also integrated with the Canvas framework where we have begun to rebuild the capabilities of Lesson**

*Anotemos**Sketch*but relying on tools supported by a wide array of developers. While the integrated Lesson

*Sketch*platform will be decommissioned at the end of 2020, we are reconceptualizing Lesson

*Sketch*to be not a piece of software but rather a way of working. Lesson

*Sketch*, as a way of working, is anchored in Canvas and provides access to media, resources, and tools to support teacher development that uses representations of practice and research that uses scenario-based assessments.

In addition to the instrumentation work, the project produced 15 new Lesson*Sketch* modules, field-tested with ~3000 preservice teacher candidates across 42 institutions. Many of the fellows are especially interested in having an impact on how prospective teachers are prepared to teach the full range of students in the United States. Examples of some of the relevant foci of the work of the fellows include:

- Teachers’ awareness of students’ mathematical dispositions including students’ perceptions of: their mathematical ability, the importance of mathematics, and the nature of the mathematical task at hand,
- Teachers’ awareness of students’ attributions of success and failure in mathematical contexts,
- Teachers’ sensitivity to issues of equity & diversity and their impact in the mathematics classroom.

To access the materials developed by the Lesson*Sketch* Research and Development Fellows, please consult the links below

- Discourse and Teacher Feedback
- Geometry for Teachers
- Noticing of Teaching Elementary School Mathematics
- Noticing Students’ Mathematical Strengths
- Azul’s Room: A Virtual Field Placement for Learning to Teach Math
- Student Thinking Interviews to Support Classroom Practice
- Supporting Students’ Development of Productive Perceptions of their Mathematical Ability
- Understanding and Envisioning Standard for Mathematical Practice 3
- Launching rich tasks: A Lesson
*Sketch*module for teachers and teacher educators - Defining Exponents
- Argumentation

Title | Author(s) | Citation | Date |
---|---|---|---|

Data do not drive themselves | Wieman R | Wieman, R. (2018). Data do not drive themselves. Mathematics Teacher 111, no. 9 (May 2018.) | 2018 |

Learning from Mistakes: Not Just for Students. Teachers College Record | Wieman R, Hiebert J | Wieman, R. and Hiebert, J. (2018). Learning from Mistakes: Not Just for Students. Teachers College Record | 2018 |

Working collectively to design online teacher education curriculum: How do teacher educators manage to do it? | Milewski A, Gürsel U, Herbst P | Milewski, A., Gürsel, U., & Herbst, P. (2017, October). Working collectively to design online teacher education curriculum: How do teacher educators manage to do it? In Galindo, E., & Newton, J., (Eds.). Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. (pp. 112-119). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators. | 2017 |

Preservice teachers’ learning paths of classroom discourse through scripting | Lim W, Roberts-Harris D, Kim H | Lim, W., Roberts-Harris, D., & Kim, H. (2018). Preservice teachers’ learning paths of classroom discourse through scripting. In R. Zazkis and P. Herbst (Eds.), Scripting approaches in mathematics education: Mathematical dialogues in research and practice (pp. 293-319). Cham, Switzerland: Springer. | 2018 |

Investigating Patterns of Pre-service Teachers’ Written Feedback on Procedure-based Mathematics Assessment Items | Lee M Y, Lim W | Lee, M.Y. and Lim, W. (2020). Investigating Patterns of Pre-service Teachers’ Written Feedback on Procedure-based Mathematics Assessment Items. International Electronic Journal of Mathematics education. 15(1), 5946. e-ISSN: 1306-3030. Em0561 | 2020 |

“It was smart when:” Supporting prospective teachers’ noticing of students’ mathematical strengths | Kalinec‑Craig C, Bannister N, Bowen D, Jacques L, Crespo S | Kalinec-Craig, C.A., Bannister, N., Bowen, D. et al (2020). “It was smart when:” Supporting prospective teachers’ noticing of students’ mathematical strengths. Journal of Mathematics Teacher Education . | 2020 |

Directing focus and enabling inquiry with representations of practice: Written cases, storyboards, and teacher education | Herbst P, Boileau N, Clark L, Milewski A, Chieu V M, Gürsel U, Chazan D | Herbst, P., Boileau, N., Clark, L., Milewski, A., Chieu, V. M., Gürsel, U., & Chazan, D. (2017, October). Directing focus and enabling inquiry with representations of practice: Written cases, storyboards, and teacher education. In Galindo, E., & Newton, J., (Eds.). Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. (pp. 789-796). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators. | 2017 |

On dialogue and stories as representations of practice: Introduction to the book | Herbst P | Herbst, P. (2018). On dialogue and stories as representations of practice: Introduction to the book. In R. Zazkis and P. Herbst (Eds.), Scripting approaches in mathematics education: Mathematical dialogues in research and practice (pp. 1-19). Cham, Switzerland: Springer. | 2018 |

Generating, appraising, and revising representations of mathematics teaching with prospective teachers | Crespo S | Crespo, S. (2018). Generating, appraising, and revising representations of mathematics teaching with prospective teachers. In R. Zazkis and P. Herbst (Eds.), Scripting approaches in mathematics education: Mathematical dialogues in research and practice (pp. 249-264). Cham, Switzerland: Springer. | 2018 |

What can you infer from this example? Applications of online, rich-media tasks for enhancing pre-service teachers’ knowledge of the roles of examples in proving | Buchbinder O, Zodik I, Ron G, Cook A | Buchbinder, O., Zodik, I., Ron, G., & Cook, A. (2017). What can you infer from this example? Applications of online, rich-media tasks for enhancing pre-service teachers’ knowledge of the roles of examples in proving. In A. Leung, & A. Baccaglini-Frank (Eds.), Digital technologies in designing mathematics education tasks: Potential and pitfalls (215-235). Switzerland: Springer. | 2017 |

Examining the mathematical knowledge for teaching of proving in scenarios written by pre-service teachers | Buchbinder O, Cook A | Buchbinder, O., & Cook, A. (2018). Examining the mathematical knowledge for teaching of proving in scenarios written by pre-service teachers. In O. Buchbinder and S. Kuntze (Eds.), Mathematics Teachers Engaging with Representations of Practice (pp. 131-154). Springer, Cham. | 2018 |

“Who is right?” What students’ and prospective teachers’ responses to scripted dialog reveal about their conceptions of proof | Buchbinder O | Buchbinder, O. (2018). “Who is right?” What students’ and prospective teachers’ responses to scripted dialog reveal about their conceptions of proof. In R. Zazkis & P. Herbst (Eds.), Scripting approaches in mathematics education: Mathematical dialogues in research and practice (pp. 89- 113), New York, NY: Springer. | 2018 |

What can designed reference points in an animated classroom story contribute to support teachers’ study of practice? | Chieu VM, Aaron W, Herbst P | Chieu, V.M., Aaron, W., & Herbst, P. (2018). What can designed reference points in an animated classroom story contribute to support teachers’ study of practice? In R. Zazkis and P. Herbst (Eds.), Scripting approaches in mathematics education: Mathematical dialogues in research and practice (pp. 147-162). Cham, Switzerland: Springer. | 2018 |

Technology-Mediated Mathematics Teacher Development: Research on Digital Pedagogies of Practice | Herbst P, Chazan D, Chieu V M, Milewski A, Kosko K, Aaron W, | Herbst, P., Chazan, D., Chieu, V. M., Milewski, A., Kosko, K., and Aaron, W. (2016). Technology-Mediated Mathematics Teacher Development: Research on Digital Pedagogies of Practice. In M. Niess, K. Hollebrands, & S. Driskell (Eds.), Handbook of Research on Transforming Mathematics Teacher Education in the Digital Age (pp. 78-106). Hershey, PA: IGI Global. | 2016 |

Technology tools for mathematics teacher learning: How might they support the development of capacity for specific teaching assignments? | Herbst P, Chazan D, Milewski A, | Herbst, P., Chazan, D., & Milewski, A. (2020). Technology tools for mathematics teacher learning: How might they support the development of capacity for specific teaching assignments? In O. Chapman & S. Llinares (Eds.), Handbook of research in mathematics teacher education (pp. 223-251). Dordrecht, The Netherlands: Sense. | 2020 |

Mathematical Reasoning and Proving for Prospective Secondary Teachers | Buchbinder O, McCrone S, | Buchbinder, O. & McCrone, S.. "Mathematical Reasoning and Proving for Prospective Secondary Teachers," Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education, 2018, p. 115. | 2018 |

Learning to Notice and Name Students’ Mathematical Strengths: A Digital Experience | Bannister N, Kalinec-Craig C, Bowen D, Crespo S, | Bannister, N., Kalinec-Craig, C., Bowen, D., & Crespo, S.. "Learning to notice and name students? mathematical strengths: A digital experience," Journal for Technology and Teacher Education, v.26, 2018, p. 13. | 2018 |

On-Ramps to Professional Practice: Selecting and Implementing Digital Technologies for Virtual Field Experiences | Sweeney J, Milewski A, Amidon J, | Sweeney, J., Milewski, A., & Amidon, J.. "On-ramps to professional practice: Selecting and implementing digital technologies for virtual field experiences," Contemporary Issues in Technology and Teacher Education, v.18, 2018. | 2018 |

Patterns Linking Interpreting and Deciding How to Respond during the Launch of a Lesson: Noticing from an Integrated Perspective | Wieman R, Webel C, | Wieman, R. and Webel, C.. "Patterns Linking Interpreting and Deciding How to Respond During the Launch of a Lesson: Noticing from an Integrated Perspective," Mathematics Teacher Education and Development, v.20, 2019. | 2019 |

The role of simulations for supporting professional growth: Teachers’ engagement in virtual professional experimentation | Milewski A, Herbst P, Bardelli E, Hetrick C, | Milewski, A., Herbst, P., Bardelli, E.,* and Hetrick, C.*. "The role of simulations for supporting professional growth: Teachers? engagement in virtual professional experimentation," Journal of Technology and Teacher Education, v.26, 2018, p. 103. | 2018 |

Using Simulated Teaching Experiences to Perturb Preservice Teachers’ Mathematics Questioning Practices | Webel C, Conner K, | Webel, C., & Conner, K.. "Using simulated teaching experiences to perturb preservice teachers? mathematics questioning practices," Mathematics Teacher Educator, v.6, 2017, p. 9. | 2017 |

How to envision equitable mathematics instruction: Views of U.S. and Korean preservice teachers | Lee J, Kim J, Kim S, Lim W, | Lee, J., Kim, J-H., Kim, S-M., & Lim, W.. "How to envision equitable mathematics instruction: Views of U.S. and Korean preservice teachers," Teaching and Teacher Education, v.69, 2018, p. 275. | 2018 |

Meet Me in Azul’s Room: Designing a Virtual Field Placement for Learning to Teach Mathematics | Amidon J, Chazan D, Grosser-Clarkson D, Fleming E, | Amidon, J., Chazan, D., Grosser-Clarkson, D., & Fleming, E.. "Meet me in Azul?s room: Designing a virtual field placement for learning to teach mathematics," Mathematics Teacher Educator, v.6, 2017, p. 52. | 2017 |

Preservice Teachers’ Questioning: Comparing Platforms for Practice-Based Teacher Education | Weston T, Kosko K, Amador J, Estapa A, | Weston, T., Kosko, K., Amador, J. & Estapa, A.. "Preservice Teachers? Questioning: Comparing Platforms for Practice-Based Teacher Education," Journal of Technology and Teacher Education, v.26, 2018, p. 149. | 2018 |

Using Technology in Representing Practice to Support Preservice Teachers’ Quality Questioning: The Roles of Noticing in Improving Practice | Walkoe J, Levin DM, | Walkoe, J. & Levin, D.M.. "Using Technology in Representing Practice to Support Preservice Teachers? Quality Questioning: The Roles of Noticing in Improving Practice," Journal of Technology and Teacher Education, v.26, 2018, p. 127. | 2018 |

Technological supports for practice-based teacher education | Chazan D, Herbst P, Fleming E, Grosser-Clarkson D, | Chazan, D., Herbst, P., Fleming, E. & Grosser-Clarkson, D.. "Technological supports for practice-based teacher education," Journal of Technology and Teacher Education, v.26, 2018, p. 5. | 2018 |

Supporting prospective secondary mathematics teachers in creating instructional explanations through video based experience | Buchbinder O | Buchbinder, O.. "Supporting prospective secondary mathematics teachers in creating instructional explanations through video based experience," Journal of Technology and Teacher Education, v.26, 2018, p. 33. | 2018 |

A study of the quality of interaction among participants in online animation-based conversations about mathematics teaching | Chieu VM, Herbst P, | Chieu, V. M., & Herbst, P.. "A study of the quality of interaction among participants in online animation-based conversations about mathematics teaching.," Teaching and Teacher Education, v.57, 2016, p. 139-149. | 2016 |

A Cross-National Study on Pre-service Teachers’ Conceptions of Equitable Mathematics Teaching | Lee J, Kim J, Lim W, Kim S | Lee, J., Kim, J., Lim, W., & Kim, S.. "A cross-national study on pre-service teachers? conceptions of equitable mathematics teaching.," Education of Primary School Mathematics,, v.19, 2016, p. 349-360. | 2016 |

Celebrating Diversity by Sharing Multiple Solution Methods | Lim W, Kim H, Stallings L, Son J, | Lim, W., Kim, H., Stallings, L., & Son, J.. "Celebrating diversity by sharing multiple solution methods," The Mathematics Teacher, v.109, 2015, p. 209. | 2015 |

Pedagogies of practice and opportunities to learn about classroom mathematics discussions | Ghousseini H, Herbst P, | Ghousseini, H., & Herbst, P.. "Pedagogies of practice and opportunities to learn about classroom mathematics discussions.," Journal of Mathematics Teacher Education, v.19, 2016, p. 79. | 2016 |

Approximating the Practice of Mathematics Teaching: What Learning Can Web-based, Multimedia Storyboarding Software Enable? | Herbst P, Chieu VM, Rougee A, | Herbst, P., Chieu, V.M., and Rougee, A.. "Approximating the Practice of Mathematics Teaching: What Learning Can Web-based, Multimedia Storyboarding Software Enable?," Contemporary Issues in Technology and Teacher Education, CITE journal, v.14, 2014. | 2014 |

What actions do teachers envision when asked to facilitate mathematical argumentation in the classroom? | Kosko K, Rougee A, Herbst P, | Kosko, K., Rougee, A., and Herbst, P.. "What actions do teachers envision when asked to facilitate mathematical argumentation in the classroom?," Mathematics Education Research Journal, v.26, 2014, p. 459. | 2014 |

Describing Curricular Materials for Mathematics Teacher Education in an Online, Rich Media Platform | Chazan D, Herbst P, Grosser-Clarkson D, Fleming E, Walkoe J, Alibegovic E, | Chazan D., Herbst P., Grosser-Clarkson D., Fleming E., Walkoe J., Alibegović E. (2018) Describing Curricular Materials for Mathematics Teacher Education in an Online, Rich Media Platform. In: Silverman J., Hoyos V. (eds) Distance Learning, E-Learning and Blended Learning in Mathematics Education. ICME-13 Monographs. Springer, Cham | 2018 |

What StoryCircles Can Do for Mathematics Teaching and Teacher Education | Herbst P, Milewski A, | Herbst P., Milewski A. (2018) What StoryCircles Can Do for Mathematics Teaching and Teacher Education. In: Zazkis R., Herbst P. (eds) Scripting Approaches in Mathematics Education. Advances in Mathematics Education. Springer, Cham | 2018 |