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Clustering methods are often used in physics education research (PER) to identify subgroups of individuals within a population who share similar response patterns or characteristics. Among these, $k$ -means (or $k$ -modes, for categorical data) is one of the most commonly used clustering methods in PER. This algorithm, however, is distance-based rather than model-based: it relies on algorithmic partitioning and assigns each individual to one subgroup through hard assignment. Researchers must also conduct analyses to relate subgroup membership to other variables. Mixture models are a model-based alternative that offers several statistical tools for choosing the optimal number of subgroups, accounts for classification errors by assigning individuals probabilities of belonging to each subgroup rather than hard assignment, and allows researchers to directly integrate subgroup membership into a broader latent variable framework. In this paper, we outline the theoretical similarities and differences between $k$ -modes clustering and latent class analysis (one type of mixture model for categorical data). We also present parallel analyses using each method to address the same research questions in order to demonstrate these similarities and differences. We provide the data and code to replicate the worked example presented in the paper for researchers interested in using mixture models. 

We introduce latent class analysis, a mixture modeling method that can explicitly model unobserved heterogeneity in a population. We provide examples of how this method could be applied to STEM education research as a means to analyze quantitative data while pursuing research goals aligned with equity, inclusion, access, and justice agendas. 

Grouping approaches are commonly employed in chemistry education research to better understand variation. Traditionally used as a tool for data dimensionality reduction, these approaches are used as a tool to help researchers interpret complex data sets that can inform instructional strategies or target interventions. Among these techniques, cluster analysis, and in particulark-means clustering, has gained popularity for its simplicity and applicability to continuous variables. However,k-means cluster analysis is limited by its algorithmic nature, including assumptions of equal variance between clusters. Latent profile analysis, a model-based alternative within the mixture modeling framework, offers greater flexibility by allowing probabilistic group membership and the modeling of individual variances and covariances across latent profiles. This methods-focused study comparesk-means clustering and latent profile analysis using data from undergraduate organic chemistry students enrolled in courses with either traditional or specifications grading. By examining students’ affective traits, this study highlights the strengths and limitations of each grouping approach. Findings support the broader adoption of mixture modeling in chemistry education research to explore heterogeneity. 

Abstract Quantitative measures in mathematics education have informed policies and practices for over a century. Thus, it is critical that such measures in mathematics education have sufficient validity evidence to improve mathematics experiences for students. This article provides a systematic review of the validity evidence related to measures used in elementary mathematics education. The review includes measures that focus on elementary students as the unit of analyses and attends to validity as defined by current conceptions of measurement. Findings suggest that one in ten measures in mathematics education include rigorous evidence to support intended uses. Recommendations are made to support mathematics education researchers to continue to take steps to improve validity evidence in the design and use of quantitative measures. 

As science teachers, you observe excitement among your middle school students when they build things, tinker with materials, and work together. The engineering design practices included in the K–12 Framework for Science Education (NRC 2012) are an attempt to harness this excitement and enthusiasm for science and engineering. Integrating engineering design into your laboratory science teaching is an engaging way to support students in learning mathematics and science concepts (Katehi, Pearson, and Feder 2009). This article describes how the three of us (an education professor, a middle school teacher who implements engineering design activities as part of a green STEM curriculum, and an engineering professor) built on student thinking to design a weeklong unit on solar energy that supported mathematics and science learning. The lesson included students designing and redesigning a model solar car and culminated in a model-solar-car race. 

The purpose of this study is to describe how analyzing student work can be used to help undergraduates reflect on the effectiveness of their service-learning experiences. The service-learning collaboration between a university and middle school was designed to increase undergraduates’ and middle school students’ knowledge of solar energy. Three undergraduates enrolled in a service-learning course that covered basic solar energy concepts and formative assessment instructional strategies. The focal point of the course was the implementation of several activities in a middle school classroom that addressed middle school students’ misconceptions about solar energy, such as the amount of solar energy production at low temperatures or on a cloudy day. Data from this study includes student work during a small-group activity on solar cells. Findings suggest that undergraduates can analyze student work and use this information to better understand how their efforts can influence middle school student learning of solar energy. 

The purpose of this study is to describe the effects of collaboration between a university and middle school that was designed to increase middle school students’ knowledge of solar energy. Three undergraduates enrolled in a service-learning course that covered basic solar energy concepts and formative assessment instructional strategies. The focal point of the course was the implementation of several activities in a middle school classroom that addressed middle school students’ misconceptions about solar energy, such as the amount of solar energy production at low temperatures or on a cloudy day. Data from this study include student performance on a written assessment, individual interviews, and student work. Findings suggest that although middle school students who participated in the activities increased their general knowledge of solar cells, many of the students’ conceptions about how exactly solar cells work were fairly persistent. This paper provides useful information on K-12 outreach efforts that can help students acquire the dispositions and knowledge they need in order to participate in STEM fields.