SUPPORTING SECONDARY MATHEMATICS TEACHERS IN DATA ARGUMENTATION IN THE DATA INVESTIGATIVE PROCESS
Caitlin Ireland
Travis Weiland
This material is based upon work supported by the National Science Foundation under DRK-12 Grant #2143816 and #2517085. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the view of the National Science Foundation.
We present initial findings from a design-based research study aimed at supporting secondary mathematics teachers’ development of data argumentation and incorporating it into their classroom teaching through engaging in a professional learning community (PLC).
Research Questions
Toulmin et al.’s (1984) framework for argumentation includes
This approach has been used in mathematics and statistics education but provides little detail as to the specifics of how to create a strong statistical argument which relies on epistemological evidence and norms.
Abelson (1995) provides more specific details for statistical arguments by providing a set of laws and criteria for well-principled arguments.
Communication | Argumentation |
Communication or interpretation of results has long been part of the statistical and data investigative processes (Franklin et al., 2007; Lee et al., 2022; Wild & Pfannkuch, 1999). Communication is generally viewed as a rather neutral act of disseminating objective information. | Argumentation is more specific considering an actual audience for one’s communication with the goal of persuading the audience of something. Argumentation is a key component of the data investigative process and a crucial aspect of writing the world for critical data literacies (Louie, 2022; Weiland, 2017). |
Authentic Practice
We build off Lee et al.’s (2022) data investigative process.
We chose this model over others for several reasons:
We frame the data argumentation process as wrapping around the data investigation process providing further detail and support for practitioners.
We highlight the importance in framing problems in conjunction with considering and collecting data and in communicating and proposing action.
Argumentation
Process
Methods
We take a qualitative case study approach (Stake, 2000) where the case is the PLC drawing from individual and group data points.
The PLC is part of a design research project (Cobb et al., 2003) that was in its third year at the time of data collection for this paper. Most participants had been involved in 2-3 of the years of the project.
Participants
The participants in this study are 16 secondary mathematics teachers at multiple schools in a single district in southeastern United States.
The teachers have 1-16+ years of experience teaching and varying degrees of experience in teaching statistics ranging from none to teaching AP statistics (equivalent to undergraduate introduction to statistics) for several years.
Two of the teachers were international teachers (1 Filipino, 1 Jamaican) with all others coming from the same region of the country as the district.
Intervention
Time | Morning Session | Afternoon Session |
Day 1 |
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Day 2 |
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Day 3 |
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Day 4 |
| Discuss how to create a data investigation
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Day 5 |
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Day 6 |
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We focus on our summer PLC with the aim of creating data arguments in investigations. This was the first time we presented them with the data argumentation process which we designed based on feedback from the teachers during years 1 and 2.
Our qualitative data sources consist of artifacts from sixteen teachers who self-elected to participate in our workshop over a four-year period including:
Video recordings of PLC meetings were viewed for triangulation (Lincoln & Guba, 1985).
We conducted qualitative coding. Caitlin conducted open coding of the end-of-day reflection responses. Travis ran a second round of open coding, and agreement was reached on what themes were found in the data.
Data Sources & Analysis
Research Question 1: Community Supported Learning
Many teachers commented on statistical skills which had gotten stronger through work with the community. Examples from the End-of-Day Reflections include comments on binomial distributions, probability, and interpreting correlations and coefficients of determination
Research Question 1: Community Supported Learning
Another theme that arose was group discussions/collaboration. The professional learning community allowed the teachers to have a space to connect and share ideas.
As a community, the teachers were able to gain important skills together to better their content knowledge.
Research Question 2: Usefulness for Teaching
Teachers mentioned understanding the terms conjecture and hypothesis are important to their classroom activities.
Teachers also commented on the usefulness of parts of the investigative cycle, particularly exploring data, as well as having CODAP as a tool for the classroom.
Research Question 2: Usefulness for Teaching
This theme continued, as more responses about using the argumentation emerged throughout the rest of the workshop, including emphasis on using some of the resources we created such as the argumentation organizer and rubrics.
Teacher 12: “The statistical argument organizer and the presentation [were useful for the classroom]”
Teacher 13: “Using the data investigation process would go over well with my students. My AP Stats students have to do a project at the end of the semester, so the rubrics to use were handy.”
Research Question 3: Lesson Plans
We were looking for evidence of lessons that incorporated opportunities for students to gain practice with claims, evidence, and reasoning as part of the argumentation process.
Overall, the teachers did not incorporate the data argument process into the lesson plans. Reasons for this could include:
Even though the professional learning community encouraged incorporation of the data investigation process and increased skill and competence in data argumentation, current curricula create boundaries for which teachers must navigate.
Research Question 3: Lesson Plans
Teacher 4 mentions hypotheses, indicating a component of claims, in the context of her chi square lesson plan.
“Hold up a jar/bag of M&Ms and ask students to write down which color they think is coating the most candies. Then, show the students the Bag Count Breakdown visualization and ask them if their answer has changed based on what they saw and why”
As the lesson progresses, she has them formulate formal null and alternative hypotheses.
Teachers 4 and 6 created a lesson plan for statistical questions:
“In small groups, students will need to create graphical representations of the data they decide to work on. Ask them to come up with statistical questions about the given data.”
“Students will create a presentation of their other data investigation…After students have compiled their graphical representations and found measures of center, discuss as a class what they think tells us about the question.”
This excerpt is evidence that the teachers are having the students think about claims, conjectures, and questions, as well as begin exploring and visualizing data through graphical representations.
Conclusions
Our findings present mixed success.
Implications
Questions
Resources
Thank you for your time!
REFERENCES
Abelson, R. P. (1995). Statistics as principled argument. Lawrence Erlbaum Associates, Inc.
Berland, L. K., & McNeill, K. L. (2010). A learning progression for scientific argumentation: Understanding student work and designing supportive instructional contexts. Science Education, 94(5), 765–793. https://doi.org/10.1002/sce.20402
Borko, H. (2004). Professional development and teacher learning: Mapping the terrain. Educational Researcher, 33(8), 3–15.
Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.
Coners, A., Matthies, B., Vollenberg, C., & Koch, J. (2025). Data skills for everyone! An approach to assessing the integration of data literacy and data science competencies in higher education. Journal of Statistics and Data Science Education, 33(1), 90–115. https://doi.org/10.1080/26939169.2024.2334408
Davis, P., & Hersh, R. (1981). The mathematical experience. Penguin Books.
Fielding, J. (2024). Taking an argumentation approach to statistical investigations: Developing student data-ing practices. ZDM – Mathematics Education, 57(1), 31–44. https://doi.org/10.1007/s11858-024-01639-y
Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A pre-K–12 curriculum framework. American Statistical Association.
Freire, P. (1970). Pedagogy of the oppressed. Continuum.
Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge University Press.
Lee, H., Mojica, G., Thrasher, E., & Baumgartner, P. (2022). Investigating data like a data scientist: Key practices and processes. Statistics Education Research Journal, 21(2), 3. https://doi.org/10.52041/serj.v21i2.41
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REFERENCES
Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Sage Publications.
Louie, J. (2022). Critical data literacy: Creating a more just world with data (Workshop on Foundations of Data Science for Students in Grades K-12). National Academy of Sciences Engineering, and Medicine, Board on Science Education, Committee on Science Investigations and Engineering Design for Grades 6-12. https://www.nationalacademies.org/documents/embed/link/LF2255DA3DD1C41C0A42D3BEF0989ACAECE3053A6A9B/file/D16254F310D01BBDA873920E4EFB8151F2D8334181AA?noSaveAs=1
Lovett, J. N., & Lee, H. S. (2017). New standards require teaching more statistics: Are preservice secondary mathematics teachers ready? Journal of Teacher Education, 68(3), 299–311.
McNeill, K. L., Lizotte, D. J., Krajcik, J., & Marx, R. W. (2006). Supporting students’ construction of scientific explanations by fading scaffolds in instructional materials. Journal of the Learning Sciences, 15(2), 153–191. https://doi.org/10.1207/s15327809jls1502_1
Stake, R. (2000). Case Studies. In N. K. Denzin & Y. S. Lincoln (Eds.), Handbook of qualitative research (2nd ed., pp. 455–486). Sage.
Toulmin, S., Rieke, R., & Janik, A. (1984). An introduction to reasoning (2nd ed.). Macmillan.
Weiland, T. (2017). Problematizing statistical literacy: An intersection of critical and statistical literacies. Educational Studies in Mathematics, 96(1), 33–47. https://doi.org/10.1007/s10649- 017-9764-5
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–248. https://doi.org/10.2307/1403699
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Goal: Critical Data Literacy
Generative Themes to “spark” the learning process
Learning through authentic practice in a community of practice
Cycles of reflection and action (i.e. Praxis) to become enculturated to practices
Based on a sociopolitical perspective on learning drawing heavily from Communities of Practice (Lave & Wenger, 1996) and Critical Literacy (Freire, 1970).
Theory of Change
Rationale
In an era increasingly shaped by data-driven decision-making, the ability to critically interpret, construct, and communicate data-based arguments has become essential for students and for the preparation of educators (Coners et al., 2025).
Though the element communication and proposed action is in the data investigation process, we have found in practice that how to develop a strong data-based argument is not clearly articulated in an actionable way for teachers.
We also consider how to evaluate data arguments and forms of evidence for different types of investigative questions in conjunction with the explore and visualize data and model with data components of the data investigative process.
We end with examples of reasoning for pulling together pieces of evidence to support a claim which we frame as an answer to the investigative question that you started with.
Research Question 2: Usefulness for Teaching
Teacher 4:
“Having students use evidence to support their claims, the elements of a good argument. I think a smaller, less sophisticated version of this would help the Math 2 students understand the necessity of reasoning in proofs as well as help them learn how to interpret results. This also directly applies to the standards in Math 4 (of course) and IB Math! Going through this process would help my IB students understand more of what they are expected to do with their IAs. I found that last year, several students confused the requirements of the exploration with a research paper, and were missing essential pieces such as a hypothesis/claim/question and calculations or processing of data to address the hypothesis/claim/question.”