By Teresa Ober, Kalina Gjicali, Eduardo Vianna, and Patricia Brooks
To be informed and responsible citizens, students should be able to make sense of data—and in this day and age, we live in a world with an abundance of it! As such, developing students’ quantitative literacy (QL) has become one of the overarching goals of undergraduate education (Sons, 1994). QL is considered “an aggregate of skills, knowledge, beliefs, dispositions, habits of mind, communication, capabilities, and problem solving skills that people need in order to engage effectively in quantitative situations arising in life and work” (as cited in Steen, 2001, p. 7). QL often involves applying mathematical thinking skills to real-world data with the purpose of drawing informed conclusions about issues of personal and/or societal concern (Elrod, 2014). Students who possess strong QL skills need not have strong computational backgrounds, but should be able to identify and interpret quantitative relations (e.g., in visual graphs), organize quantitative information (e.g., in spreadsheets) and communicate effectively about the relevance of quantitative data in everyday life (Blair & Getz, 2011). It has been argued that QL is most effectively taught when embedded across the curriculum given a critical component of its application involves identifying quantitative relations in varied real-world contexts (Hughes-Hallett, 2001). Embedding QL in college classes across disciplines helps students develop skills they will need to engage effectively in work and life beyond college. In this regard, instruction around QL that uses psychology content can support development and application of practical quantitative reasoning skills outside of the classroom. Hence, psychology departments are increasingly recognizing the need to teach QL as a core cross-curricular requirement (Lutsky, 2008). This means using data and mathematical thinking in all psychology courses, and not just in statistics and research methods courses.
In this post, we offer some perspectives on how to promote QL across the psychology curriculum. Some of the tools and ideas for integrating QL activities into psychology courses were presented during a recent GSTA-sponsored workshop held at the Graduate Center of the City University of New York on March 6, 2019. During the workshop, Kalina Gjicali, PhD candidate in Educational Psychology, presented best practices for using visual graphs to help students develop quantitative concepts and skills in interpreting data. Dr. Eduardo Vianna of LaGuardia Community College shared resources developed through the Numeracy Infusion Course for Higher Education (NICHE) / Numeracy Infusion for College Educators (NICE), a consortium of educators who share a common mission of promoting quantitative reasoning across various college-level courses. He also shared information about a new CUNY-wide project to improve college students’ QL skills and his own experiences in teaching QL in an introductory (general) psychology course. Teresa Ober, PhD candidate in Educational Psychology, described sources of secondary data and free open-source statistical programs that can be used to develop students’ data analysis skills
Engaged Pedagogy and Quantitative Literacy
Educational research suggests that QL is best taught through student-centered, progressive pedagogies that promote active and inquiry-based learning (Lowney, 2008). In particular, studies have demonstrated the following strategies to be especially effective for teaching QL (Carver et al., 2016): (a) active learning, in which students are engaged learners rather than passive recipients of information; (b) inquiry-based learning, which emphasizes conceptual thinking rather than rote skills and memorization of facts as well as the use of problems and examples that are relevant to real-life situations; and (c) the use of technology to analyze actual data in real-life situations. According to constructivist learning perspectives (Cobb, 1994; Fosnot, 1996; Keeling, 2004), students learn most effectively when they explore new concepts and ideas while working out solutions to meaningful problems and considering the implications of research findings. In other words, students should figure out for themselves how new information, concepts, and ideas relate to their existing systems of knowledge and beliefs, and have opportunities to revise and expand their views in response to new knowledge.
Strategies for Teaching Quantitative Literacy
One way to build QL skills is to focus on data and visual representations of data. Introducing effective graphic displays of data into college lectures can take the focus away from text-heavy slides that summarize information as if it were established fact (as opposed to research findings that may be in need of replication) and instead towards student-centered learning and knowledge construction. By being presented with appropriate visual representations of social science data, students can be expected to (Beaudrie et al., 2013):
Articulate their ideas
Express themselves with precision
Ground their observations in evidence
Test claims and hypotheses
Participate in civil discourse
Represent what they are ill-equipped to see
Recognize and weigh uncertainty
Construct a context to attract interest and to inform critical thinking
You can build QL with your college students with the free online feature “What’s Going On in This Graph?”created by The New York Times Learning Network in partnership with the American Statistical Association. Updated on a weekly basis, this resource features graphs of different types and within different contexts, such as varied topics from labor and automation to teen smoking habits (see figure below) that can be used to ask students the following questions:
What do you notice?
What do you wonder?
What’s going on in this graph?
What are the implications for ________ (e.g., understanding health risks of teenagers)?
All releases are archived, so instructors can use previous graphs anytime. Visit this introductory post and this article about how teachers use this powerful activity.
Analyzing Data in-Class
Hands-on opportunities to work with actual data can open many doors for students, especially for those who have had limited experiences in data analysis and have anxiety about it. The concept of using secondary data to teach students about psychological science is not a novel one (see Sobel, 1981), but has received reinvigorated interest due to the vast amount of open access data currently available. In thinking through an in-class data demo, it might be useful for instructors to consider these questions:
How is this data source meaningful to students within the course?
What tools are available to students to help them analyze the data?
What strategies/resources can be made available to students to help them interpret the data?
How can we apply the findings from the data to everyday life?
Selecting a dataset for a data demo project is a crucial first step, and will depend on course content as well as the skills and reasoning abilities that you want your students to develop. Resources abound, with data sources including Kaggle, UNData, OECD, IES, and more than several amazing OSF repositories (e.g., EAMMi2) as well as data provided by local and regional government agencies. In choosing the dataset, consider what topics might be of interest to students, what problems/questions they can use the data to address, and whether there is sufficient documentation to support student learning. For example, for a course covering language development, the CHILDES database (part of Talk Bank) is an invaluable resource. This database contains transcripts of parent-child conversations in a variety of languages, often with accompanying audio or video, and includes datasets for children growing up in multilingual environments as well as datasets with various clinical populations (e.g., developmental language disorder, autism spectrum disorder, hearing loss). This resource includes CLAN software for analyzing conversational interactions and manuals to help you get started.
Another option for integrating data collection into instruction is to ask students to complete a brief survey during class time. GoogleForms is a very convenient way to collect and present such data quickly, but other survey programs can work just as well. Asking students to complete a short-form survey may be an effective way to introduce them to a dataset by helping them become familiar with the actual scales used in the original study.
Considering which statistical software programs are available and accessible to students is critical. While many undergraduate psychology courses use proprietary programs like SPSS or STATA to teach statistics, whether students own a license or actually have access to such programs off-campus is often questionable. Thus, it might be more advantageous for students long-term to consider free and open source programs, such as JASP or R. Sometimes the more sophisticated statistical programs may not even be necessary for teaching QL. Rather, in many cases, using a spreadsheet application such as GoogleSheets or Excel might actually be sufficient for teaching basic statistics (DiMaria-Ghalili & Ostrow, 2009). Many students have access to Excel on their personal computers, but benefit from instruction on how to use it to make pivot tables or charts.
In preparing a lesson around the use of secondary data, it is important to consider students’ prior knowledge, skills, and interests to ensure that the instruction is developmentally appropriate. You might start by distinguishing research questions that relate to frequencies (How often?), associations (Are X and Y related?), or causal relationships (Does X cause Y?) as this can lead to a fruitful discussion of how to fit one’s analytic approach to the research question at hand. Students may need instruction to decide what sorts of graphs are appropriate for different types of data (e.g., line graphs, bar graphs, scatterplots). This can lead to further discussion of how to present findings in APA format, determine statistical significance, and interpret p-values. Along the way, you might consider outliers, skewed distributions, and various threats to the validity of the research, such as the representativeness of the sample. As you guide your class in interpreting research findings, allow for spontaneity by offering students opportunities to test their own hypotheses and develop ideas for future research.
The Significance, … or rather, Relevance
Finally, it might be helpful to consider what possible applications can come out of the findings presented in class. Even if the findings might seem intuitive, walking students through the process of analyzing and interpreting the findings should ultimately lead them to feel empowered in working with data. When findings are non-significant and hypotheses are not supported, students have opportunities to learn that this sort of “productive failure” is part of the research process. For this reason, using secondary data as opposed to artificially generated data can lead to a more practical learning experience, particularly when resources for conducting secondary data analysis are plentiful.
Strengthening QL has been recognized as an imperative of undergraduate education, with students best served when instructors use an “across-the-curriculum” approach to ensure they have sufficient opportunities to develop QL skills. Like any well-implemented curriculum, teaching QL necessitates planning. When datasets are analyzed or in-class demonstrations are conducted, instructors should take extra precautions to ensure that the lessons achieve their objectives. Lack of clarity during a demonstration, improper analyses, or technical problems can greatly interfere with learning opportunities when conducting in-class demonstrations. Nevertheless, we hope the resources described above may at the very least offer some initial inspiration for incorporating QL instruction into all of your courses.
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Sons L. R. (1994). Quantitative reasoning for college graduates: A complement to the standards. Mathematical Association of America. Retrieved online: https://www.maa.org/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/quantitative-literacy/quantitative-reasoning-college-graduates.
Steen, L. A. (Ed.). (2001). Mathematics and democracy: The case for quantitative literacy. Report prepared by the National Council on Education and the Disciplines. Retrieved online: https://www.maa.org/sites/default/files/pdf/QL/MathAndDemocracy.pdf
Patricia J. Brooks is Professor of Psychology at the College of Staten Island and the Graduate Center, CUNY and GSTA Faculty Advisor. Brooks was recipient of the 2016 President’s Dolphin Award for Outstanding Teaching at the College of Staten Island, CUNY. Her research interests are in two broad areas: (1) individual differences in language learning, (2) development of effective pedagogy to support diverse learners.
Kalina Gjicali is a doctoral candidate in Educational Psychology at The Graduate Center, CUNY and a Quantitative Reasoning Fellow for the University at the Quantitative Research & Consulting Center (QRCC).
Teresa Ober is a doctoral candidate in Educational Psychology at the Graduate Center, CUNY. Teresa is interested in the role of executive functions in language and literacy. Her research has focused on the development of cognition and language skills, as well as how technologies, including digital games, can be used to improve learning.Eduardo Vianna
, Professor of Psychology, has taught at LaGuardia since 2005. He has a Ph.D. in developmental psychology from the GC- CUNY after completing his medical studies in Brazil. Building on recent advances in Vygotskian theory, especially the Transformative Activist Stance approach, his works focus on research with transformative agendas. His recent recent work includes applying critical-theoretical pedagogy to build the peer activist learning community (PALC), which was featured in the New York Times. In 2010 he received the Early Career Award in Cultural-Historical Research by the American Educational Research Association and currently he is chief editor of Outlines Critical Practice Studies and Co-PI in the NSF grant "Building Capacity: A Faculty Development Program to Increase Students' Quantitative Reasoning Skills.’