Measuring Chemistry Students' Understandings of Multiple External Representations through Cluster Analysis

Project No.
PI Name
Stacey Lowery Bretz
Miami University
Target Discipline

Abstract 1

Measuring Chemistry Students' Understandings of Multiple External Representations through Cluster Analysis

Presentation Type
Stacey Lowery Bretz, Miami University


One element of expertise within chemistry is the ability to interpret, generate, and communicate with multiple external representations. The design of AIs (assessment items) to incorporate multiple external representations of core chemistry concepts (MERC3s, pronounced "mercies") demonstrated to generate cognitive dissonance among students provides a novel detection method for studentsメ alternative conceptions (ACs) that could be used to build learning progressions to make data-driven decisions about pedagogy and curriculum. The cumulative products of this research move beyond the grain-size of "single-course" assessments and generate an integrated collection of tools to longitudinally track changes in student thinking.


The goals of this research are to
1. characterize students' misinterpretations of MERC3s across Johnstone's particulate, symbolic, and/or macroscopic domains regarding four core chemistry concepts: electron structure/periodicity, molecular shape/polarity, bond energies/heats of reaction, and solution chemistry/precipitation reactions.
2. investigate students' ACs for these core concepts.
3. construct AIs about MERC3s grounded in these misinterpretations and ACs.
4. re-examine commonly accepted practices for establishing the reliability and validity of assessment data within the CER community.
5. use cluster analysis to identify patterns in students' reasoning about MERC3s, both within a single content topic and for patterns that transcend multiple topics


This research integrates Ausubel's Meaningful Learning Framework, Geelan's Personal Constructivism, and Johnstone's Triangle of chemistry representations across the macroscopic, particulate, and symbolic domains. This research employs a four-phase sequential, mixed-methods design: 1) Multiple MERC3s will be identified to conduct semi-structured interviews in order to a) generate cognitive dissonance both within and across Johnstone's macroscopic, particulate, and symbolic domains and b) elicit chemistry students' ACs regarding four core chemistry concepts. 2) AIs will be created, paying close attention to reliability and validity, through successive iterations grounded in studentsメ ACs as revealed through their interpretations of MERC3s. 3) Data will be collected from a national sample to measure studentsメ ACs regarding four core concepts, paying close attention to establishing the reliability and validity of the data. 4) Cluster analysis will be performed on three data sets a) these four core concepts, b) the existing data sets from the previous research that established proof-of-concept, and c) a replication study where simultaneous data is collected from one sample of students using a triad of instruments.


This research includes replication studies of earlier empirical findings and further uses cluster analysis to characterize patterns in students thinking about representations across multiple studies. The interview guides, AIs, descriptions of students' ACs regarding MERC3s, and cluster analyses will be available for adoption in both instruction and research.

Broader Impacts

Capacity building workshops for 100 grad students and postdocs focus on teaching cluster analysis, and provide professional development with peer review and faculty hiring processes. The AIs can be used both as research tools and in classrooms by chemistry faculty to improve students' learning. Methodologies will be disseminated at the TRUSE Conference for STEM Education Research and through workshops for other researchers to adapt to their own research agendas at the Biennial Conference on Chemical Education.


No publications yet from this new award. This research follows up and extends the findings of NSF #0733642. Publications include:

1. Linenberger, K.J.; Bretz, S.L. "Biochemistry Students' Ideas about how an Enzyme Interacts with a Substrate," Biochemistry and Molecular Biology Education, 2015, 43(4), 213-222
2. Bretz, S.L.; McClary, L.M. "Students' Understandings of Acid Strength: How Meaningful is Reliability when Measuring Alternative Conceptions?" Journal of Chemical Education, 2015, 92(2), 212-219.
3. Bretz, S.L. (2014). "Designing Assessment Tools to Measure Students' Conceptual Knowledge of Chemistry," Tools of Chemistry Education Research, D. Bunce and R. Cole (Eds.), ACS Symposium Series, Oxford University Press, 155-168
4. Luxford, C.J.; Bretz, S.L. "Development of the Bonding Representations Inventory to Identify Student Misconceptions about Covalent and Ionic Bonding Representations," Journal of Chemical Education, 2014, 91(3), 312-320. ACS Editorsメ Choice (1st ever article in J. Chem. Educ. to earn this distinction)
5 Linenberger, K.J.; Bretz, S.L. "Biochemistry Students' Ideas about Shape and Charge in Enzyme-Substrate Interactions," Biochemistry and Molecular Biology Education, 2014, 42(3), 203-212
6. Luxford, C.J.; Bretz, S.L. "Moving Beyond Textbook Definitions: Student-Centered Models of Covalent and Ionic Bonding," Chemistry Education Research and Practice, 2013, 14, 214-222.
7. Mayo, A.V.; Bretz, S.L.; Danielson, N.D. "Flow Injection Analysis and Liquid Chromatography for Multifunctional Chemical Analysis (MCA) Systems," Journal of Chemical Education, 2013, 90(4), 500-505.
8. McClary, L.M.; Bretz, S.L. "Development and Assessment of a Diagnostic Tool to Identify Organic Chemistry Students' Alternative Conceptions Related to Acid Strength," International Journal of Science Education, 2012, 34(15), 2317-2341.
9. Linenberger, K.J.; Bretz, S.L. "A Novel Technology to Investigate Studentsメ Understandings of Enzyme Representations," Journal of College Science Teaching, 2012, 42(1), 45-49
10. Bretz, S.L.; Linenberger, K.J. "Development of the Enzyme-Substrate Interactions Concept Inventory," Biochemistry and Molecular Biology Education, 2012, 40(4), 229-233.
11. Bretz, S.L. "Navigating the Landscape of Assessment," Journal of Chemical Education, 2012, 89(6), 689-691.
12. Linenberger, K.J.; Bretz, S.L. "Generating Cognitive Dissonance in Student Interviews through Multiple Representations," Chemistry Education Research and Practice, 2012, 13, 161-171.
13. Luxford, C.J.; Crowder, M.W.; Bretz, S.L. "A Symmetry POGIL Activity for Inorganic Chemistry," Journal of Chemical Education, 2012, 89(2), 211-214.
14. Jensen, J.D.; Grundy, S.; Bretz, S.L.; Hartley, C.S. "Synthesis and Characterization of Self-Assembled Liquid Crystals: p-Alkoxybenzoic Acids," Journal of Chemical Education, 2011, 88, 1133-1136. (Cover Feature)
15. Bindis, M.P.; Bretz, S.L.; Danielson, N.D. "Preparation and Characterization of a Monolithic Column for use in HPLC: An Undergraduate Laboratory Experiment,": Journal of Chemical Education, 2011, 88, 675-678.