#
The Teacher Responding Tool: Scaffolding the teacher practice of responding to student ideas in mathematics classrooms
ARTICLE

## James P. Bywater, Jennifer L. Chiu, James Hong, Vidhya Sankaranarayanan

Computers & Education Volume 139, Number 1, ISSN 0360-1315 Publisher: Elsevier Ltd

## Abstract

Research in teacher education highlights the importance of responding to student ideas. However, effectively noticing, interpreting, and then responding to students' mathematical ideas can be quite challenging for teachers as they try to balance multiple, competing goals in an authentic classroom setting. This study introduces the Teacher Responding Tool (TRT), and examines its role in scaffolding four high school teachers' responding practice. The TRT leverages natural language processing technology to provide teachers with automated, student-specific recommendations for how to respond to their student's ideas. By comparing teacher responding with and without the TRT recommendations, their interactions with the tool, their think-aloud data, and their post-project interviews, results demonstrate that the TRT recommendations helped teachers notice and respond to nuances in the mathematical ideas of their students. Implications for teaching and learning, responding tool development, and teacher professional development are discussed.

## Citation

Bywater, J.P., Chiu, J.L., Hong, J. & Sankaranarayanan, V. (2019). The Teacher Responding Tool: Scaffolding the teacher practice of responding to student ideas in mathematics classrooms. Computers & Education, 139(1), 16-30. Elsevier Ltd. Retrieved March 28, 2020 from https://www.learntechlib.org/p/209941/.

This record was imported from Computers & Education on June 3, 2019. Computers & Education is a publication of Elsevier.

Full text is availabe on Science Direct: http://dx.doi.org/10.1016/j.compedu.2019.05.004### Keywords

## References

View References & Citations Map- Aleven, V.A., & Koedinger, K.R. (2002). An effective metacognitive strategy: Learning by doing and explaining with a computer-based Cognitive Tutor. Cognitive Science, 26, pp. 147-179.
- Ball, D.L. (1993). With an eye on the mathematical horizon: Dilemmas of school mathematics. The Elementary School Journal, 93(4), pp. 373-397.
- Ball, D.L., & Forzani, F.M. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 60(5), pp. 497-511.
- Ball, D.L., Hill, H.C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide?. American Educator, 29(3), pp. 14-17.
- Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: Principles, Policy & Practice, 5(1), pp. 7-74.
- Borra, S., & Di Ciaccio, A. (2010). Measuring the prediction error. A comparison of crossvalidation, bootstrap and covariance penalty methods. Computational Statistics & Data Analysis, 54, pp. 2976-2989.
- Bransford, J.D., Brown, A.L., & Cocking, R.R. (2000). How people learn: Brain, mind, experience, and school. Washington, DC: National Academies Press.
- Brown, I.A., Davis, T.J., & Kulm, G. (2011). Pre-service teachers' knowledge for teach- ing algebra for equity in the middle grades: A preliminary report. The Journal of Negro Education, 80(3), pp. 266-283.
- Burns, M. (1995). Writing in math class: A resource for grades 2-8. Math Solutions.
- Carpenter, T.P., Fennema, E., Franke, M.L., Levi, L., & Empson, S.B. (1999). Children's mathematics: Cognitively guided instruction. Portsmouth, NH: Heinemann.
- Carpenter, T.P., Franke, M.L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
- Chapin, S.H., O'Connor, C., & Anderson, N.C. (2009). Classroom discussions: Using math talk to help students learn. Sausalito, CA: Math Solutions.
- Chi, M.T., Bassok, M., Lewis, M.W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. Cognitive science, 13(2), pp. 145-182.
- Chi, M.T., & Wylie, R. (2014). The ICAP framework: Linking cognitive engagement to active learning outcomes. Educational psychologist, 49(4), pp. 219-243.
- Coffey, J.E., Hammer, D., Levin, D.M., & Grant, T. (2011). The missing disciplinary substance of formative assessment. Journal of Research in Science Teaching, 48(10), pp. 1109-1136.
- Cohen, J. (1968). Weighted kappa: Nominal scale agreement provision for scaled disagreement or partial credit. Psychological Bulletin, 70(4), p. 213.
- Collins, A., Brown, J.S., & Holum, A. (1991). Cognitive apprenticeship: Making thinking visible. American Educator, 15(3), pp. 6-11.
- Countryman, J. (1992). Writing to learn mathematics: Strategies that work. Portsmouth, NH: Heinemann.
- Dieker, L.A., Hughes, C.E., Hynes, M.C., & Straub, C. (2017). Using simulated virtual environments to improve teacher performance. Using simulated virtual environments to improve teacher performance, Vol. 10, pp. 62-81.
- Franke, M.L., Webb, N.M., Chan, A.G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students' mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), pp. 380-392.
- Gerard, L.F., & Linn, M.C. (2016). Using automated scores of student essays to support teacher guidance in classroom inquiry. Journal of Science Teacher Education, 27(1), pp. 111-129.
- Gerard, L., Matuk, C., McElhaney, K., & Linn, M.C. (2015). Automated, adaptive guidance for K-12 education. Educational Research and Reviews, 15, pp. 41-58.
- Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), pp. 2055-2100.
- Grossman, P., Hammerness, K., & McDonald, M. (2009). Redefining teaching, re-imagining teacher education. Teachers and Teaching: Theory Into Practice, 15(2), pp. 273-289.
- Haimovitz, K., & Dweck, C.S. (2017). The origins of children's growth and fixed mindsets: New research and a new proposal. Child Development, 88(6), pp. 1849-1859.
- Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), pp. 81-112.
- Herbel-Eisenmann, B.A., Steele, M.D., & Cirillo, M. (2013). Developing) teacher discourse moves: A framework for professional development. Mathematics Teacher Educator, 1(2), p. 181.
- Jacobs, V.R., Lamb, L.L.C., & Philipp, R.A. (2010). Professional noticing of children's mathematical thinking. Source: Journal for Research in Mathematics Education Journal for Research in Mathematics Education, 41(2), pp. 169-202.
- Kazemi, E., & Stipek, D. (2009). Promoting conceptual thinking in four upper-elementary mathematics classrooms. Journal of Education, 189(1–2), pp. 123-137.
- Kluger, A.N., & DeNisi, A. (1996). The effects of feedback interventions on performance: A historical review, a meta-analysis, and a preliminary feedback intervention theory. Psychological Bulletin, 119(2), pp. 254-284.
- Lampert, M., Franke, M., Kazemi, E., Ghousseini, H., Turrou, A., & Beasley, H. (2013). Keeping it complex: Using rehearsals to support novice teacher learning of ambitious teaching. Journal of Teacher Education, 64(3), pp. 226-243.
- Liu, O.L., Brew, C., Blackmore, J., Gerard, L., Madhok, J., & Linn, M.C. (2014). Automated scoring of constructed-response science items: Prospects and obstacles. Educational Measurement: Issues and Practice, 33(2), pp. 19-28.
- Ma, T., Brown, I.A., Kulm, G., Davis, T.J., Lewis, C.W., & Allen, G.D. (2014). Constructing and role-playing student avatars in a simulation of teaching algebra for diverse learners. Urban Education, 51(5), pp. 534-555.
- McDonald, M., Kazemi, E., & Kavanagh, S.S. (2013). Core practices and pedagogies of teacher education: A call for a common language and collective activity. Journal of Teacher Education, 64(5), pp. 378-386.
- McElhone, D. (2013). Pressing for elaboration in student talk about texts. Journal of Classroom Interaction, pp. 4-15.
- Muir, T. (2012). Virtual mathematics education: Using second life to model and reflect upon the teaching of mathematics. Mathematics education: Expanding horizons. Proceedings of the 35th annual conference of the mathematics education research group of australasia, pp. 521-528. Singapore: MERGA.
- Narciss, S., & Huth, K. (2004). How to design informative tutoring feedback for multi-media learning. Instructional design for multimedia learning, pp. 181-195. Munster, NY: Waxmann.
- National Council of Teachers of Mathematics (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.
- National Council of Teachers of Mathematics (2018). Catalyzing change in high school mathematics: Initiating critical conversations. Reston, VA: Author.
- O'Connor, M.C., & Michaels, S. (1993). Aligning academic task and participation status through revoicing: Analysis of a classroom discourse strategy. Anthropology & Education Quarterly, 24(4), pp. 318-335.
- Reiser, B.J. (2004). Scaffolding complex learning: The mechanisms of structuring and problematizing student work. Journal of the Learning Sciences, 13(3), pp. 273-304.
- Robertson, A.D., Atkins, L.J., Levin, D.M., & Richards, J. (2016). What is responsive teaching?. Responsive teaching in science and mathematics, pp. 1-34. New York: Routledge.
- Rock, M.L., Gregg, M., Thead, B.K., Acker, S.E., Gable, R.A., & Zigmond, N.P. (2009). Can you hear me now? Evaluation of an online wireless technology to provide real-time feedback to special education teachers-in-training. Teacher Education and Special Education, 32(1), pp. 64-82.
- Russo, J.E., Johnson, E.J., & Stephens, D.L. (1989). The validity of verbal protocols. Memory & Cognition, 17(6), pp. 759-769.
- Sandoval, W. (2014). Conjecture mapping: An approach to systematic educational design research. Journal of the learning sciences, 23(1), pp. 18-36.
- Selling, S.K. (2016). Making mathematical practices explicit in urban middle and high school mathematics classrooms. Journal for Research in Mathematics Education, 47(5), pp. 505-551.
- Sherin, M.G. (2002). A balancing act: Developing a discourse community in a mathematics classroom. Journal of Mathematics Teacher Education, 5(3), pp. 205-233.
- Shute, V.J. (2008). Focus on formative feedback. Review of educational research, 78(1), pp. 153-189.
- Slotta, J.D., & Linn, M.C. (2009). WISE science: Web-based inquiry in the classroom. New York, NY: Teachers College Press.
- Smith, M.S., Steele, M.D., & Raith, M.L. (2017). Taking action: Implementing effective mathematics teaching practices.
- Stoyle, K.L., & Morris, B.J. (2017). Blogging mathematics: Using technology to support mathematical explanations for learning fractions. Computers in Education, 111, pp. 114-127.
- Teuscher, D., Kulinna, P.H., & Crooker, C. (2016). Writing to learn mathematics: An update. The Mathematics Educator, 24(2).
- Van Es, E.A., & Sherin, M.G. (2002). Learning to notice: Scaffolding new teachers' interpretations of classroom interactions. Jl. of Technology and Teacher Education, 10(4), pp. 571-596.
- Van Es, E.A., & Sherin, M.G. (2010). The influence of video clubs on teachers' thinking and practice. Journal of Mathematics Teacher Education, 13(2), pp. 155-176.
- Van Lehn, K. (2011). The relative effectiveness of human tutoring, intelligent tutoring systems, and other tutoring systems. Educational Psychologist, 46(4), pp. 197-221.
- Wake, D., Dailey, D., Cotabish, A., & Benson, T. (2017). The effects of virtual coaching on teacher candidates' perceptions and concerns regarding on-demand corrective feedback. Journal of Technology and Teacher Education, 25(3), pp. 327-357.
- Walker, E., Rummel, N., & Koedinger, K.R. (2011). Using automated dialog analysis to assess peer tutoring and trigger effective support. International conference on artificial intelligence in education, pp. 385-393. Berlin, Heidelberg: Springer.
- Walkoe, J. (2015). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18, pp. 523-550.
- Walkoe, J., & Levin, D.M. (2018). Using technology in representing practice to support preservice teachers' quality questioning: The roles of noticing in improving practice. Journal of Technology and Teacher Education, 26(1), pp. 127-147.
- Weston, T.L., Kosko, K.W., Amador, J.M., & Estapa, A.T. (2018). Preservice teachers' questioning: Comparing platforms for practice-based teacher education. Journal of Technology and Teacher Education, 26(1), pp. 149-172.
- Wiliam, D. (2007). Keeping learning on track: Classroom assessment and the regulation of learning. Second handbook of mathematics teaching and learning, pp. 1053-1098. Greenwich, CT: Information Age Publishing.
- Wood, T. (1998). Alternative patterns of communication in mathematics classes: Funneling or focusing?. Language and communication in the mathematics classroom, pp. 167-178. Reston, Va: NCTM.
- Xhakaj, F., Aleven, V., & McLaren, B.M. (2017). Effects of a teacher dashboard for an intelligent tutoring system on teacher knowledge, lesson planning, lessons and student learning. European conference on technology enhanced learning, pp. 315-329. Cham: Springer.
- Zehner, F., Sälzer, C., & Goldhammer, F. (2016). Automatic coding of short text responses via clustering in educational assessment. Educational and psychological measurement, 76(2), pp. 280-303.

These references have been extracted automatically and may have some errors. Signed in users can suggest corrections to these mistakes.

Suggest Corrections to References