Supporting Elementary Teacher Candidates’ Ability to Design and Apply Problem-Solving Tasks

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 problem-solving  tasks that are grounded in asset-oriented 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 problem-solving 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 8-week 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 field-experience component to the elementary  mathematics methods courses where TCs learn how to design, apply, and refine problem-solving  tasks that are grounded in asset-oriented 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  case-study mentoring activities with a child regarding literacy and reading comprehension.  Because of the integrated nature of Roadrunner Readers in the elementary education program and literacy-based field experiences for more than 20 years, it served as the precedent for SEE Math in the same program for mathematics-based 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 field-based 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 south-central 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 in-person. Since March 2020, our TCs have been conducting remote, Zoom-based activities with their case study child. This has served multiple goals. First, TCs are learning how  to use technology (e.g., Google Slides, Jamboard, pre-recorded 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.  

Data-based 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 strength-based sentence frames to communicate what  children know and can do (Kalinec-Craig 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 (Kalinec-Craig, 2017; Torres, 2020). 



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), 188-199. 

Kalinec-Craig, 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. 020-09464-2 

Kalinec-Craig, 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), 132-141. 

Torres, O. (2020). Rehumanizing Schools - Rights of the Learner, 

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), 67-82.

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 field-based experience during an elementary mathematics methods  course that is currently taken during TCs’ pre-clinical 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 Practice-Based 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 School-Based 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 field-based experiences for TCs to include pull-out or after-school teaching  contexts across elementary grades K-6 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 Kalinec-Craig (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