Supplementary Materials for AMTE Standards
SEE Math: Using Case Studies to Improve Mathematics Teacher Education Coursework and Field Experiences
For developing elementary mathematics teacher candidates’ understanding of how to design, apply, and refine problemsolving tasks that are grounded in assetoriented ways and begin with what children already know.
Project information
SEE Math: Using Case Studies to Improve Mathematics Teacher Education Coursework and Field Experiences
SEE Math (Support and Enrichment Experiences in Mathematics), is a project that engages elementary teacher candidates (TCs) in purposeful tasks with children in the local community. We the authors (three mathematics teacher educators and an academic coach) will outline why the description and associated materials with SEE Math will be a useful framework for other mathematics teacher educators (MTEs) who are interested in crafting specific tasks that TCs can use to: engage children in problemsolving skills, make connections to children’s funds of knowledge, and support them to exercise their Torres’ Rights of the Learner*.
Description of SEE Math: SEE Math is an 8week program that serves two purposes: 1) it creates scaffolded experiences for elementary TCs learning to teach mathematics with a child in the community and 2) creates support and enrichment experiences for children in the local community who might not otherwise have those opportunities from the school and/or afterschool programs. SEE Math is a fundamental fieldexperience component to the elementary mathematics methods courses where TCs learn how to design, apply, and refine problemsolving tasks that are grounded in assetoriented ways and begin with what children already know. Since fall 2017, SEE Math has served almost 600 elementary TCs and almost 575 children in the local community.
History and outline of SEE Math: The history of SEE Math begins in two separate, but intersecting timelines. First, SEE Math is an extension of the Learning Case Study modules from the TEACH Math (Teachers Empowered to Advance Change in Mathematics; National Science Foundation Award #1228034 and PI Corey Drake). In the Learning Case Study, the module outlines a series of activities that bridge the two main constructs of the TEACH Math research project: children’s funds of knowledge (Moll et al., 1992) and children’s mathematical thinking (Carpenter et al., 2015), which creates a new construct called “children’s multiple mathematical knowledge bases” (Turner et al., 2012). As such, the Learning Case Study module begins with a “Getting to Know You Interview” where a TC, who is paired up with a child, asks a series of questions about the child’s experiences, interests, and activities that they do at home in their community. Based on the interview, the TCs then utilize a series of Cognitively Guided Instruction interviews to learn how to modify tasks to make them more relevant to their case study child and to eventually learn how to elicit children’s thinking across the four operations, base ten, and fractions. SEE Math stands on the shoulders of the extensive research and frameworks of the Learning Case Study module of TEACH Math and the broader research.
The second timeline of SEE Math is based on a similar literacy program at the university in which we are based. Since 1999, Roadrunner Readers supported TCs to engage in a series of casestudy mentoring activities with a child regarding literacy and reading comprehension. Because of the integrated nature of Roadrunner Readers in the elementary education program and literacybased field experiences for more than 20 years, it served as the precedent for SEE Math in the same program for mathematicsbased field experiences.
More specifically, the TCs engaged in a series of activities as briefly described in the image below.
The need for SEE Math: A review of the elementary education program since 2013 showed that TCs at our institution needed more purposeful fieldbased experiences with children in the area of mathematics education. The MTEs could already see promising advances in TCs’ learning of literacy education and reading comprehension practices by working in Roadrunner Readers that we could imagine a similar advancement of TCs’ learning of mathematics pedagogy and content. Before SEE Math, the MTEs attempted to replicate the TEACH Math Learning Case Study module during the time when the TCs were working within a practicing teacher’s classroom for 80 hours during the semester, but this proved to be challenging given the practicing teacher’s pace and schedule of activities. Therefore, by hosting SEE Math outside of the normal activities of the school (e.g., afterschool and/or as a pull out), it served at least two purposes: the TCs would be specifically mentored by the MTE in the moment and the children could reimagine their mathematical thinking outside of the structures of a traditional classroom.
Stakeholders at university and in community for SEE Math: SEE Math is based in a large university in a city located in the southcentral area of the United States. 60% of our teacher candidates are transfer students from the local community colleges, more than 50% are first generation and/or Latinx students. Many of our TCs return to the local community to teach. We partner with the large school districts in the city that serve a majority of Latinx children, many of whom are emerging bilinguals and/or are recent immigrants to the United States. Three sections of SEE Math are based on three elementary campuses where we also teach our elementary mathematics methods course; one section is taught at the downtown campus where parents from around the downtown community are encouraged to bring their children to participate. Principals from our partner elementary schools have been supportive of SEE Math since fall 2017 and continue to help us recruit families and children to participate in the program. For parents who participate in the downtown campus section, we have some siblings who have attended SEE Math since the inception.
Evolution of SEE Math: The evolution of SEE Math is one that changes with the needs of our community and needs of our TCs. Before the pandemic and remote learning, SEE Math hosted six semesters inperson. Since March 2020, our TCs have been conducting remote, Zoombased activities with their case study child. This has served multiple goals. First, TCs are learning how to use technology (e.g., Google Slides, Jamboard, prerecorded videos, etc.) to engage in problem solving tasks with children remotely. Secondly, TCs are learning how to conduct an exploration of the child’s experiences and community by taking virtual walks through Google Maps; this may mean that we can reach children in more rural settings who might not normally participate in the program. Finally, the TCs are more prepared for the upcoming clinical teaching semester in the field, most of which will be in hybrid settings.
Databased findings and Next Steps of SEE Math: The majority of the data from SEE Math comes in the form of the Mock Parent Teacher Conference that the TCs conduct either as a pre recorded video or with their instructor, who serves the role as the child’s parent. Since 2017, the program directors of SEE Math have seen demonstrable growth in TCs’ practice to design, modify, and implement tasks that support children’s problem solving skills, connect to children’s funds of knowledge, and encourage children to exercise their Torres’ Rights as Learners. Throughout the semester, TCs practice analyzing evidence from the SEE Math activities and the child’s mathematical thinking; they use strengthbased sentence frames to communicate what children know and can do (KalinecCraig et al., 2020; Jilk, 2016). We have transcriptions and video recordings of the conferences, with permission of the TCs, as well as deidentified work from the children, with permission from their guardian. Expansions to SEE Math come in the forms of replicating this program with our middle grades TCs.
*Olga Torres envisioned the Torres’ Rights of the Learners as the right for children: to be confused, the right to claim a mistake, the right to speak, listen, and be heard, and the right to write, do and represent what makes sense to them (KalinecCraig, 2017; Torres, 2020).
References
Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2015). Children's mathematics : cognitively guided instruction (Second edition. ed.). Heinemann.
Jilk, L. M. (2016, March 2016). Supporting teacher noticing of students' mathematical strengths. Mathematics Teacher Educator, 4(2), 188199.
KalinecCraig, C. A., Bannister, N., Bowen, D., Jacques, L. A., & Crespo, S. (2020). “It was smart when:” Supporting prospective teachers’ noticing of students’ mathematical strengths. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857 020094642
KalinecCraig, C. A. (2017). The rights of the learner: A framework for promoting equity through formative assessment in mathematics education. Democracy and Education, 25(2), 5.
Moll, L. C., Amanti, C., Neff, D., & Gonzalez, N. (1992). Funds of Knowledge for teaching: Using a qualitative approach to connect homes and classrooms. Theory Into Practice, 31(2), 132141.
Torres, O. (2020). Rehumanizing Schools  Rights of the Learner, YouTube.com. https://www.youtube.com/watch?v=_UndpNUCAqw
Turner, E., Drake, C., McDuffie, A., Aguirre, J., Bartell, T., & Foote, M. (2012). Promoting equity in mathematics teacher preparation: a framework for advancing teacher learning of children’s multiple mathematics knowledge bases. Journal of Mathematics Teacher Education, 15(1), 6782. https://doi.org/10.1007/s1085701191966
Documents for Mathematics Teacher Educators

PreSession Work  Read First

Site Map  Read Second

Session 1

Session 2

Session 2: Getting to Know Students’ Math Concepts and Thinking

Resources for Problem Solving Interviews (link to content in “Resources for Problem Solving Interviews” folder)

Jacobs & Ambrose (2008). Supporting, Extending, and Clarifying Student Thinking


Session 3

Session 4

Counting Cookies Task

Growing Steps Task

Session 5

Session 6

Session 7

Session 8

Session 9

Mock ParentTeacher Conference (Course Final)

Additional Materials
 Number of the Day
Standards and Indicators these Materials Target
The SEE Math program serves as a structure to support TCs during their elementary math methods course in learning to teach mathematics through iterative opportunities across the duration of several weeks working directly with an elementary student. Thus addressing Standard P.3. Opportunities to Learn to Teach Mathematics. Additionally, the program meets indicators within Standard P.4 Opportunities to Learn in Clinical Settings. Although the SEE Math program originated as a fieldbased experience during an elementary mathematics methods course that is currently taken during TCs’ preclinical year in the preparation program, it serves as a strong foundation for clinical teaching experiences. Finally, SEE Math addresses elements of Standard P.5 Recruitment and Retention of Teacher Candidates.
Below is a description of connections to key indicators within the standards.

Indicator P.3.2. Provide Foundations of Knowledge About Students as Mathematics Learners. The program focuses on providing opportunities for TCs to develop skills in eliciting and extending children’s mathematical thinking.

Indicator P.3.4. Incorporate PracticeBased Experiences. As described previously, the program also facilitates TCs in applying mathematical pedagogical practices that are grounded in children’s funds of knowledge (Moll et al., 1992), children’s mathematical thinking (Carpenter et al., 2015), and “children’s multiple mathematical knowledge bases” (Turner et al., 2012) research.

Indicator P.4.1 Collaboratively Develop and Enact Clinical Experiences. The program is mostly embedded in and done in collaboration with local public school districts.

Indicator P.4.2. Sequence SchoolBased Experiences. As shown in the image below, the activities in SEE Math are purposefully scaffolded to provide more support for TCs as they engage in oftentimes first teaching experiences to more autonomous and responsive task design as they finish the course and prepare for their clinical teaching experience.

Indicator P.4.3 Provide Teaching Experiences with Diverse Learners. SEE Math extends fieldbased experiences for TCs to include pullout or afterschool teaching contexts across elementary grades K6 and tasks include opportunities to integrate ELAR and STEM disciplines.

Indicator P.5.2 Address Diverse Community Needs. SEE Math is an essential piece of a preparation program recruiting a majority of Latinx TCs from and for a community serving a majority Latinx population of families.
About the Authors

Crystal KalinecCraig (corresponding author)  University of Texas at San Antonio

Emily Peterek Bonner  University of Texas at San Antonio

Traci Kelley University of Texas at San Antonio

Grace Trevino University of Texas at San Antonio