Technological Innovations for Mathematics Teacher Preparation (2018 PI Meeting Reflection)

Vecihi Serbay Zambak, Marquette University

In the topical session I attended on Thursday morning, the presenters (Dr. Herbst, Dr. Grosser-Clarkson, Dr. Zahner, and Dr. Goffney) described the LessonSketch platform, providing cases and studies demonstrating the potential of LessonSketch for prospective teachers’ professional preparation.

LessonSketch is a multi-media platform for future and practicing teachers, enabling them to attend to and interpret the details of mathematical instruction presented within the “approximated” authenticity of a real classroom setting. The availability of video clips and animations in this platform allows teachers to concentrate on some previously identified mathematical content and practices and their possible representations in the classroom.

You can find further information about LessonSketch, the community, collection and tools here: https://www.lessonsketch.org/

To broaden participation and disseminate findings, the presenters also mentioned a special issue published at the beginning of this year by the Journal of Technology and Teacher Education. You may also find information about these special-issue articles in the following link: https://www.learntechlib.org/primary/j/JTATE/v/26/n/1/

The project additionally has a four-part webinar for AMTE members on materials for practice-based teacher education:

  1. https://amte.net/form/2017/08/webinar-social-contexts
  2. https://amte.net/form/2017/10/materials-practice-based-teacher-education-part-2
  3. https://amte.net/form/2018/01/materials-practice-based-teacher-education-part-3
  4. https://amte.net/content/materials-practice-based-teacher-education-4-part-series-session-4-addressing-opportunities

The topical session focused on the ways that technological innovations created and supported broader participation of students in STEM fields. While the presenters discussed effective preparation of mathematics teachers with a focus on the Pedagogies of Practice (i.e., representation, decomposition, and approximation of teaching practice, Grossman et al., 2009), I will discuss the benefits of the technological innovations on supporting teachers’ Professional Noticing abilities (Jacobs, Lamb, & Philipp, 2010). Theoretically speaking, it is hard to define either of these two constructs without touching on the other. Some researchers also approach these two constructs in an integrated way in their studies (Schack et al., 2013; McDuffie et al., 2014). For example, Schack et al. (2013) views technological innovations (e.g., video clips) as a way to represent teaching practices to prospective mathematics teachers. According to the authors, teachers’ ability to attend to and interpret students’ mathematical thinking emerges as the decomposition of teaching practice represented with technology. Finally, teachers’ ability to decide how to respond appears while they approximate the teaching practice.

I believe that technological innovations, such as video clips or animations in the LessonSketch platform, help novice teachers develop their professional noticing abilities through the approximations of teaching practices during their teacher education. The complexities of the teaching profession make it hard for novice teachers to pay attention or decide how to respond to various mathematical content, teaching practices, and students’ understanding or misunderstanding. That is why presenting teaching practices in small portions (e.g., in short video clips or animations) and in isolation from its real, but cognitively loaded, context to prospective teachers makes a functional teacher education method in order to help them efficiently develop sensitivities in interpreting students’ mathematical thinking.

Within a video clip, it is more difficult to channel prospective teachers’ attention only on mathematical content due to the existence of other pedagogical acts (e.g., teachers’ classroom management strategies) or contextual factors (e.g., students’ cultural background) implicitly represented. On the other hand, an animation in the LessonSketch platform allows prospective teachers to focus on and interpret students’ specific reasoning or misconceptions in mathematical content. For example, one of the animations presented by Dr. Zahner was developed to help prospective mathematics teachers make sense of students’ correct and incorrect reasoning about exponential rules. In his example, a student claims that the zero-power of a number is zero. According to this student’s (mis)understanding, power means how many times a number is multiplied by itself, and in this case the number is multiplied zero times. The student concludes that there is no number to multiply; therefore the result is zero []. Such conversation allows prospective teachers to be aware of students’ confusions. In this case, the student is confused about the identity properties of different operations: s/he reasons with the identity property of addition (i.e., zero) while the problem deals with multiplication. Based on the dialogue presented with the animation scripts on LessonSketch, prospective mathematics teachers could notice the importance of middle-grades students’ understanding of the concept of nothing-is-there, and how they could mistakenly reason with this concept.

The topical session also raised some key questions: what are the advantages of technological innovations that cannot be achieved or handled by other outdated media or tools? Nowadays, it seems like there is a hierarchy in technological innovations where online, computerized, and multimedia-enhanced platforms rank higher in the hierarchy compared to the written and paper-based ones (Koehler & Mishra, 2009). The latter is not even considered a type of technology, but rather as outdated media or tools. The hierarchy still requires us to question what makes the former superior to the latter for mathematics teacher preparation. Let’s revisit the student’s misconception about the zero-power of a number. The dialogue between the students could also be represented as written scripts on paper. In this case, what are the advantages (or drawbacks) of the use of written scripts on paper for prospective mathematics teachers in interpreting the student’s misconception? Either way, mathematics teachers and teacher educators face these questions and shape their instructions based on their views and experiences with technological innovations in general.

Overall, computerized platforms allow us to view mathematical content in a dynamic fashion. This cannot be achieved with written scripts on paper. Design features of computerized platforms also make the process of conjecturing and proving more efficient by reducing cognitive load for users. Finally, such platforms provide approximated opportunities for prospective teachers to gain awareness about students having diverse backgrounds. Such background details are hard to capture in a written script. While video clips are alternative means to increase prospective teachers’ awareness about students having diverse backgrounds, it is usually hard to find video clips where prospective teachers will not digress their attention to insignificant classroom details. The animation scripts in the LessonSketch platform seem to eliminate these distractions by providing unique ways for prospective teachers to professionally notice significant features of equitable teaching practices in mathematics classrooms. For example, voice integration features can emulate a mathematics classroom having a substantial proportion of English language learners. Another example was given by the presenters during the session (i.e., the case of Maya), where reassignment of a student from a lower-track to higher-track mathematics classroom was depicted in the context of a highly-segregated middle school.

The portrayal of context in the LessonSketch platform provides new opportunities for prospective teachers to increase their attention to specific conditions integrated with specific mathematical content. I believe this is the uniqueness of the LessonSketch platform compared to written scripts and video clips. Features to integrate voice and animate students and teachers within this platform allow mathematics teacher educators to create approximated mathematics instructions enhanced with various classroom contexts for future teachers to attend to, interpret and know how to respond to students’ mathematical thinking as well as to socio-mathematical norms. To that end, having such perspective for mathematics teacher education will clearly provide an exemplar for the theme of this year’s PI meeting and the intersection of three emerging forces: 1) STEM (with a bold M and T for the content of Mathematics and Technology regarding the session), 2) Broadening Participation (with a focus on preparing teachers for equitable teaching practices), and 3) Technological Innovations (with the integration of various multi-media representations in the LessonSketch platform for better teacher education opportunities).

References:

Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055-2100.

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

Koehler, M. J., & Mishra, P. (2009). What is technological pedagogical content knowledge? Contemporary Issues in Technology and Teacher Education, 9(1), 60-70.

McDuffie, A. R., Foote, M. Q., Bolson, C., Turner, E. E., Aguirre, J. M., Bartell, T. G., ... & Land, T. (2014). Using video analysis to support prospective K-8 teachers’ noticing of students’ multiple mathematical knowledge bases. Journal of Mathematics Teacher Education17(3), 245-270.

Schack, E. O., Fisher, M. H., Thomas, J. N., Eisenhardt, S., Tassell, J., & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education16(5), 379-397.


About the Author:

Dr. Vecihi Serbay Zambak is currently a postdoctoral researcher in the Department of Mathematics, Statistics and Computer Science at Marquette University.