Students’ REASONING WITH GRAPHS is more important than their ACCURACY IN SKETCHING GRAPHS.

## Changing Kite and Dynamic Tent Facilitation Guides

What do you think of the Facilitation Guides? We want to hear from you.

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# Author: Heather Johnson

## Changing Kite and Dynamic Tent Facilitation Guides

## Changing Kite and Dynamic Tent Facilitation Guides

## Ferris Wheel Facilitation Guide

## Ferris Wheel Facilitation Guide

## Cannon Man & Toy Car Facilitation Guides

## Humanizing the Coding of College Algebra Students’ Attitudes Toward Math

## Two New Techtivities: The Dynamic Tent and The Changing Kite

### Two new Techtivities are part of the collection:

### Tried these activities with students? Share your experiences with us.

## ITSCoRe at the Rocky Mountain MAA

## ITSCoRe Techtivities Highlighted on the Global Math Webinar

## ITSCoRe on Edutopia

## ITSCoRe at the 2018 RUME Conference [Research on Undergraduate Math Ed]

### ITSCoRe at the 2018 RUME Conference: Let’s provide opportunities for students to engage in covariational reasoning

## Networking Theories to Design Dynamic Covariation Techtivities for College Algebra Students

#### We share our work to develop opportunities for undergraduate students to engage in covariational reasoning.

#### Building from the work of mathematics education researchers (e.g., Kaput, Thompson, Moore), we developed a suite of Techtivities—free, accessible, digital media activities linking dynamic animations and graphs.

#### Using a Cannon Man Techtivity to illustrate, we provide four key design components and three theoretically based design principles underlying the Techtivities.

#### To inform design both within and across the Techtivities, we networked theories of different grain sizes: Thompson’s theory of quantitative reasoning and Marton’s variation theory.

#### Developing Techtivities for students in the gatekeeping course, College Algebra, we intend to expand students’ opportunities to employ covariational reasoning.

#### We discuss implications stemming from students’ opportunities to use free, accessible digital media activites, such as Techtivities, to promote their covariational reasoning.

## ITSCoRe at the Joint Mathematics Meetings

Implementing Techtivities to Promote Students' Covariational Reasoning in College Algebra

Students’ REASONING WITH GRAPHS is more important than their ACCURACY IN SKETCHING GRAPHS.

What do you think of the Facilitation Guides? We want to hear from you.

Students’ REASONING WITH GRAPHS is more important than their ACCURACY IN SKETCHING GRAPHS.

Ferris Wheel Distance v. Height

Ferris Wheel Distance v. Width

What do you think of the Facilitation Guide? We want to hear from you.

Students’ REASONING WITH GRAPHS is more important than their ACCURACY IN SKETCHING GRAPHS.

Promote students’ math reasoning with Desmos Cannon Man and Toy Car.

What do you think of the Facilitation Guides? 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

Code
Mixed Ambiguous 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.

References

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!

Heather Johnson, ITSCoRe project PI, highlighted the Cannon Man Activity in her Webinar for the Global Math Department (@**GlobalMathDept**)

Visit http://hthrlynnj.com/presentations/howgraphswork/ to access Webinar slides, video, and resources.

Keep the conversation going on Twitter with the hashtag #HowGraphsWork

Thought about trying one of the ITSCoRe Techtivities?

Want to help students to move beyond what graphs look like to what graphs represent?

In a February 2018 Edutopia blog post, Heather Johnson shares how the Cannon Man Techtivity can help.

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

Gary Olson, ITSCoRe project co-PI, will be discussing the ITSCoRe project scope and goals at the Joint Mathematics Meetings this week in San Diego, CA.

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.