Abstract
Despite the prevalence of undergraduate drop-in mathematics tutoring, little is known about the behaviors of this specific group of tutors. This study serves as a starting place for identifying their behaviors by addressing the research question: what observable behaviors do undergraduate drop-in mathematics tutors exhibit as they interact with students? We analyzed 31 transcripts of tutoring sessions using inductive coding, finding 83 observable behaviors. We discovered that tutors used behaviors aimed at engaging students, while primarily retaining control of the decision making and problem-solving process. Although tutors asked students to contribute to the mathematics, they often asked a less demanding question before the student had a chance to respond to the initial question. Our findings reveal the existence of opportunities for student learning in tutoring sessions as well as potential areas of growth for tutors. We present questions for future research that arose from analysis of the data and discuss how our results may be used in tutor training.
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References
Ader, S., & Carlson, M. (2021). Decentering framework: A characterization of graduate student instructors’ actions to understand and act on student thinking. Mathematical Thinking and Learning 24(2), 9-122. DOI:10.1080/10986065.2020.1844608
Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruishank, K. A., Mayer, R. E., Pintrich, P. R., & Wittrock, M. C. (2001). Taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. New York: Longman
Bentz, J. L., & Fuchs, L. S. (1996). Improving peers’ helping behavior to students with learning disabilities during mathematics peer tutoring. Learning Disability Quarterly, 19(4), 202–215
Bloom, B. S., Englehart, M. D., Furst, W. J., Hill, W. H., & Krathwohl, D. R. (1956). The taxonomy of educational objectives, the classification of educational goals, handbook I: Cognitive domain. New York: David McKay Company, Inc
Bressoud, D., Mesa, V., & Rasmussen, C. (2015). Insights and Recommendations from the MAA National Study of College Calculus. MAA Press
Byerley, C., Campbell, T., & Rickard, B. (2018). Evaluation of impact of Calculus Center on student achievement. In Weinburg, Rasmussen, Rabin, Wawro, & Brown, Eds. Proceedings of the Twenty-First Annual Conference on Research in Undergraduate Mathematics Education. San Diego, CA
Byerley, C., Moore-Russo, D., James, C., Johns, C., Rickard, B., & Mills, M. (2019). Defining the varied structures of tutoring centers: Laying a foundation for future research. Proceedings of the Twenty-second Annual Conference on Research in Undergraduate Mathematics Education, Oklahoma City, OK
Byerley, C., James, C., Moore-Russo, D., Rickard, B., Mills, M., Heasom, W., & Moritz, D. (2020). Characteristics and evaluation of ten tutoring centers. Proceedings of the Twenty-third Annual Conference on Research in Undergraduate Mathematics Education. Boston, MA
Cade, W. L., Copeland, J. L., Person, N. K., & D’Mello, S. K. (2008). Dialogue modes in expert tutoring. In International conference on intelligent tutoring systems (pp. 470–479). Springer, Berlin, Heidelberg
Carino, P. (2003). Power and authority in peer tutoring. In M. Pemberton, & J. Kinkead (Eds.), The Center Will Hold: Critical Perspectives on Writing Center Scholarship (pp. 96–113). Utah State University Press
Chi, M. T., Siler, S. A., Jeong, H., Yamauchi, T., & Hausmann, R. G. (2001). Learning from human tutoring. Cognitive Science, 25, 471–533
Fox, B. A. (1991). Cognitive and interactional aspects of correction in tutoring. In P. Goodyear (Ed.), Teaching knowledge and intelligent tutoring (pp. 149–172). Norwood, NJ: Ablex
Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111(23), 8410–8415
Fuchs, L. S., Fuchs, D., Hamlett, C. L., Phillips, N. B., Karns, K., & Dutka, S. (1997). Enhancing students’ helping behavior during peer-mediated instruction with conceptual mathematical explanations. The Elementary School Journal, 97(3), 223–249
Glaser, A. L., & Strauss, B. G. (1967). The discovery of grounded theory: Strategies for qualitative research. Chicago: Aldine Publications
Graesser, A. C., & Person, N. K. (1994). Question asking during tutoring. American Educational Research Journal, 31(1), 104–137
Graesser, A. C., Person, N. K., & Magliano, J. P. (1995). Collaborative dialogue patterns in naturalistic one-on-one tutoring. Applied Cognitive Psychology, 9, 495–522
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and Procedural Knowledge: The Case of Mathematics (pp. 1–28). Routledge
Hume, G., Michael, J., Rovick, A., & Evens, M. (1996). Hinting as a tactic in one-on-one tutoring. The Journal of Learning Sciences, 5(1), 23–47
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
Johns, C. (2019). Tutor behaviors in undergraduate mathematics drop-in tutoring. [Doctoral dissertation, The Ohio State University]. ProQuest Dissertations Publishing
Johnson, E., & Hansen, K. (2015). Academic and social supports. In D. Bressoud, V. Mesa, & C. Rasumussen (Eds.), Insights and Recommendations from the MAA National Study of College Calculus (pp. 69–82). MAA Press
Lepper, M. R., Drake, M. F., & O’Donnell-Johnson, T. (1997). Scaffolding techniques of expert human tutors. In K. Hogan, & G. M. Pressley (Eds.), Scaffolding student learning: Instructional approaches and issues (pp. 108–144). Brookline Books
Lepper, M. R., & Woolverton, M. (2002). The wisdom of practice: Lessons learned from the study of highly effective tutors. In J. Aronson (Ed.), Improving academic achievement: Impact of psychological factors on education (pp. 135–158). San Diego, CA: Academic Press
McArthur, D., Stasz, C., & Zmuidzinas, M. (1990). Tutoring techniques in algebra. Cognition and Instruction, 7(3), 197–244
Merrill, D. C., Reiser, B. J., Ranney, M., & Trafton, J. G. (1992). Effective tutoring techniques: A comparison of human tutors and intelligent tutoring systems. The Journal of Learning Sciences, 2(3), 277–305
Mills, M., Johns, C., & Ryals, M. (2019). Peer tutors attending to student mathematical thinking. Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education, (pp. 250–257). Oklahoma City, OK
Mills, M., Rickard, B., & Guest, B. (2020). Survey of mathematics tutoring centers in the USA.International Journal of Mathematical Science and Technology,1–21
National Council of Teachers of Mathematics (NCTM). (2014). Principles to Action. Reston, VA: NCTM
Pintrich, P. R. (2000). The role of goal orientation in self-regulated learning. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation (pp. 451–502). Academic Press
Putnam, R. T. (1987). Structuring and adjusting content for students: A study of live and simulated tutoring of addition. American Educational Research Journal, 24(1), 13–48
Rickard, B., & Mills, M. (2018). The effect of attending tutoring on course grades in Calculus I. International Journal of Mathematical Education in Science and Technology, 49(3), 341–354
Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91(1), 175–189
Schoenfeld, A. H. (1979). Explicit heuristic training as a variable in problem-solving performance. Journal for Research in Mathematics Education, 10(3), 173
Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press, INC
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334–370). New York, NY: Macmillan
Schoenfeld, A. H., Gamoran, M., Kessel, C., & Leonard, M. (1992). Towards a comprehensive model of human tutoring in a complex subject matter domains. The Journal of Mathematical Behavior, 11(4), 293–319
Strauss, A., & Corbin, J. (1990). Basics of qualitative research. Sage publications
Tallman, M., & Carlson, M. (2016). A characterization of calculus I final exams in U.S. colleges and universities. International Journal of Research in Undergraduate Mathematics Education, 2, 105–133
Teuscher, D., Moore, K. C., & Carlson, M. P. (2016). Decentering: A construct to analyze and explain teacher actions as they relate to student thinking. Journal of Mathematics Teacher Education, 19, 433–456
Theobald, E. J., Hill, M. J., Tran, E., Agrawal, S., Arroyo, E. N., Behling, S., & Freeman, S. (2020). Active learning narrows achievement gaps for underrepresented students in undergraduate science, technology, engineering, and math. Proceedings of the National Academy of Sciences, 117(12), 6476–6483
Topping, K., Campbell, J., Douglas, W., & Smith, A. (2003). Cross-age peer tutoring in mathematics with seven-and 11-year-olds: influence on mathematical vocabulary, strategic dialogue and self-concept. Educational Research, 45(3), 287–308
Van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education, 24, 244–276
Van Es, E., & Sherin, M. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Information Technology, 10(4), 571–596
VanLehn, K., Siler, S., Murray, C., Yamauchi, T., & Baggett, W. S. (2003). Why do only some events cause learning during human tutoring? Cognition and Instruction, 21(3), 209–249
White & Mesa, White, N., & Mesa, V. (2014). (2014). Describing cognitive orientation of Calculus I tasks across different types of coursework. ZDM., 46(4). 675–690
Zimmerman, B. J. (1998). Developing self-fulfilling cycles of academic regulation: An analysis of exemplary instructional models. In D. H. Schunk, & B. J. Zimmerman (Eds.), Self-regulated learning: From teaching to self-reflective practice (pp. 1–19). New York: NY: The Guilford Press
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Johns, C., Mills, M. & Ryals, M. An Analysis of the Observable Behaviors of Undergraduate drop-in Mathematics Tutors. Int. J. Res. Undergrad. Math. Ed. 9, 350–374 (2023). https://doi.org/10.1007/s40753-022-00197-6
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DOI: https://doi.org/10.1007/s40753-022-00197-6