Students’ REASONING WITH GRAPHS is more important than their ACCURACY IN SKETCHING GRAPHS.
What do you think of the Facilitation Guide? We want to hear from you.
Gardner, A., Smith, A, & Johnson, H. L. (in press) Humanizing the coding of college algebra students’ attitudes towards math. To appear in the Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education, Oklahoma City, OK: RUME.
Through their coding of survey responses, researchers can create spaces to humanize students’ attitudes toward math. To account for complexity in students’ attitudes beyond positive or negative, we developed three additional codes: mixed, ambiguous, and detached. In our coding methods, we account for a diversity, rather than a binary, of student attitudes.
Keywords: Attitude toward mathematics, College algebra, Humanizing, Research methods
Even before Calculus, College Algebra is a gatekeeping mathematics course, and students’ attitudes toward math can impact their persistence in such courses (Bressoud, Carlson, Mesa, & Rasumussen, 2013; Ellis, Fosdick, & Rasmussen, 2016). College Algebra students can express complex attitudes toward math, and we posit that researchers’ coding methods should begin to open space to acknowledge the complexities of students’ attitudes. Drawing on survey responses as sources of data, researchers have coded students’ attitudes toward math as positive, negative, and other/indifferent (Ding, Pepin, & Jones, 2015; Pepin, 2011). In our coding methods, we account for a wider range of students’ attitudes, to give more voice to attitudes outside the positive/negative binary. For example, students can express a mixture of positive and negative attitude, ambiguity in their attitude, or a detached attitude toward math.
We administered a fully online attitude survey to College Algebra students at the beginning and end of the Spring and Fall 2018 semesters. We used Pepin’s (2011) open-ended question stems, (e.g., “I like/dislike math because…”), because the question stems allowed students to self-narrate a range of attitudes that may not fit into binary categories. Beyond positive and negative, we included three additional codes: mixed, ambiguous, and detached. We coded mixed for a response that presented more than one attitude (e.g., positive and negative), ambiguous for responses that crossed multiple attitudes, and detached for a response that separated the person from the mathematics, treating mathematics as something “out there” or not connected to self. Table 1 shows examples of student responses we coded as mixed, ambiguous, or detached.
Table 1. Examples of responses coded as mixed, ambiguous, or detached
|Example Student Response
I love and enjoy problem solving, but I dislike having to remember a lot of rules.
I don’t care either way.
Math is the universal language.
Langer-Osuna & Nasir (2016) called for researchers to develop methods that humanize students’ experiences. Were we not to have included the additional codes, we would have coded the student responses in Table 1 as “other/indifferent,” because they are neither positive nor negative. Yet, the responses presented distinct attitudes, which we valued and wanted to name.
As researchers, our methods are never neutral. In our coding of hundreds of College Algebra students’ responses to survey questions, we worked to extend possibilities for the kinds of attitudes to which we would give voice. As a result, we created a richer landscape of possibilities, which requires more than a linear continuum to represent.
Bressoud, D. M., Carlson, M. P., Mesa, V., & Rasmussen, C. (2013). The calculus student: insights from the Mathematical Association of America national study. International Journal of Mathematical Education in Science and Technology, 44(5), 685-698.
Ding, L., Pepin, B., & Jones, K. (2015). Students’ attitudes towards mathematics across lower secondary schools in Shanghai. In B. Pepin & Roesken-Winter (Eds.), From beliefs to dynamic affect systems in mathematics education (pp. 157-178). Switzerland: Springer International Publishing.
Ellis J., Fosdick B. K., Rasmussen C. (2016) Women 1.5 times more likely to leave STEM pipeline after calculus compared to men: Lack of mathematical confidence a potential culprit. PLoS ONE 11(7): e0157447. doi:10.1371/journal. pone.0157447
Langer-Osuna, J. M., & Nasir, N. S. (2016). Rehumanizing the “Other” race, culture, and identity in education research. Review of Research in Education, 40(1), 723-743.
Pepin, B. (2011). Pupils’ attitudes towards mathematics: a comparative study of Norwegian and English secondary students. ZDM Mathematics Education, 43, 535-546.
What could a tent look like with different lengths for its height and base? In this activity, investigate and graph relationships between the height and base of a dynamic tent. Inspired by Isosceles Triangle Graphs v4 by Steve Phelps: https://www.desmos.com/calculator/yxqay82kh7
What could a kite look like with different lengths and widths? In this activity, investigate and graph relationships between the length and width of a changing kite.
Thanks to Dan Meyer and the team at Desmos for collaborating with ITSCoRe to develop these activities.
In April 2018, ITSCoRe co-PI Gary Olson presented on Desmos TECHtivities for the College Algebra Classroom at the Rocky Mountain Section Meeting of the Mathematical Association of America (MAA)
TECHtivities provide opportunities for students to use graphs to represent relationships between attributes that are capable of varying and possible to measure.
Explore the TECHtivities
Want to make a difference in students’ thinking? Integrate, don’t isolate!
Visit http://hthrlynnj.com/presentations/howgraphswork/ to access Webinar slides, video, and resources.
Keep the conversation going on Twitter with the hashtag #HowGraphsWork
Date: Friday, February 23
Time: 9:20-9:50, PST
Location: Coronado Room, Kona Kai Resort, San Diego
Heather Johnson, Evan McClintock, Jeremiah Kalir, Gary Olson, University of Colorado Denver
Since the printing of our poster, we have had a few personnel changes and additions.
Xin Wang, from RMC Research corporation, is our new Project Evaluator.
Amber Gardner and Amy Smith are the graduate research assistants serving on this project.
Download a PDF of our poster.
We have two new members of our ITSCoRe project team: Amber Gardner and Amy Smith
Amber and Amy will participate as graduate research assistants. Together, they bring over two decades of experience in K-12 education. The work of ITSCoRe will benefit from having such seasoned classroom teachers as part of our team.
Read more about Amber and Amy on our ITSCoRe team page.