I research conceptual development, learning, and problem solving and have two main lines of research: a) the development of statistical literacy and b) the effects of different types of visual representations (e.g., diagrams, graphs, and illustrations) on children’s and adults’ learning and problem solving in math and statistics.

Improving Statistical Knowledge and Skills Working with Visual Representations in Mathematics How to Get Involved!

Developing Statistical Literacy

  • How do children and adults learn and use statistical thinking skills?
    • How are these cognitive processes affected by individual differences in initial knowledge levels and attitudes?
    • What types of educational materials and settings support this learning? Why are these materials and settings effective? How do these experiences influence attitudes towards statistics?

Individuals of all ages are increasingly being asked to reason with quantitative data and reach data-driven decisions, but they often have considerable difficulties and are uncomfortable working with numbers. Thus my research on the conceptual skills involved in statistical literacy, the effects of educational interventions, and the influence of attitudes is particularly timely and crucial.

Graphical literacy is a key component of representing or interpreting quantitative data. My dissertation investigated how undergraduates interpreted and constructed graphs with two independent variables. While students improved during the semester, difficulties interpreting and describing these types of graphs persisted immediately after an introductory statistics course (Cooper & Gelman, 2012). My future research on graphical literacy will continue to address why certain data patterns are more difficult; I have pilot data suggesting that the semantic content of the variable and the direction of the effect (e.g., an increase or decrease) may affect interpretation. My long-term plans on this research include incorporating how individual differences in attitudes and motivations influence performance, which I am also attending to in my other research lines. An additional goal for my research is to reveal how general statistical literacy knowledge (e.g., knowledge about variables and experimental design) interacts with graph-specific knowledge, an area that has minimal coverage in the current literature. I believe this to be necessary for a broader and deeper understanding of the multi-faceted nature of graphical literacy and to address how individuals develop their cognitive processing and understanding of graphs.

Graphical literacy is one part of statistical thinking that is increasingly being emphasized in K – 12. When I worked with preschoolers as part of research and development on an early childhood science curriculum, it became evident that supportive contexts enabled the children to show sophisticated thinking about data and graphs. In follow-up research studies, preschoolers demonstrated conceptual and procedural understanding of basic graphs (Cooper et al., 2005, 2006). A creative task context was critical here; a developmentally appropriate purpose (a story character finding items in a scavenger hunt) was necessary to support their reasoning. This general theme about context interacting with an individual’s competence to influence performance is central to my work; it reappears in my research about how visual representations are one part of the context in mathematics story problems that can affect students’ performance and engagement. One next step is to explore why the context is so essential to young children’s reasoning with data; this would be an ideal project for undergraduates interested in working with me on developmental research.

At Wesleyan, I have contributed to the development and evaluation of an innovative project-based statistics curriculum in which students learn introductory statistics concepts along with the code to work with data and run analyses. Their learning is in the service of answering their research questions; students in AP Statistics and at various colleges are a part of this project. Based on enrollment and survey data, the course increased access to statistics and programming education for underrepresented minority students (Dierker et al., 2015; Cooper & Dierker, under review) and resulted in similar, if not more positive, relationships between student experiences and outcomes for underrepresented students (Dierker et al., 2016). I am currently comparing student experiences in this innovative curriculum to experiences in non-project-based courses and also investigating how mid-semester reports about classroom climate relate to student outcomes (content mastery, attitudes towards statistics, intended future behaviors). I plan to continue this line of work related to the scholarship of teaching and learning.

Acquaintance: What type of research do you do?
Me: Part of my research looks into how people understand and use statistics.

“Oh. I hated statistics.”
“Statistics is scary.”
“I can’t do math.”

“That sounds interesting.”
“There’s so much data to think about.”
“What are you finding out?”
A lot of people feel that way! That’s one of the reasons I’m researching this – to help researchers and educators better understand children’s and adults’ existing knowledge and how they think about statistical topics. I know not everyone will love thinking about data (I do), but fleshing out and supporting these cognitive processes can further develop the contexts in which these skills are learned and used as well as helping address some of the negative experiences people have. Statistical literacy is becoming more and more important; it comes into so many different areas of our lives and jobs. I’ve looked both at statistics education as well as individuals’ knowledge and skills. It turns out that research in a project-based class may be one way to increase students’ interest in using statistics. I’ve also considered what makes certain types of graphs more difficult and am looking at what underlying skills help people read data from graphs.

Effects of Visual Representations

In another line of work, I investigate the cognitive development of reasoning processes related to visuals (diagrams and illustrations in particular) in various types of mathematical problems. Here, building on information-processing models (e.g., Mayer; Sweller), I have also incorporated a contextualization perspective that is prominent in mathematics education, to continue to address the question of when and to what extent the visuals are helpful and/or harmful to learning and problem solving. Within this research, part of the puzzle is figuring out how individuals’ attitudes and abilities affect the influence of the visuals.

So far, this work has shown that the effect of visuals for adults depends on characteristics such as their mathematical ability and their attitude. In several studies with Candace Walkington, we have also found that the effects of different types of visuals on middle school students are influenced by their ability and attitudes. With this age group though, there are more questions than answers currently as findings across studies have been inconsistent. This is problematic given the extensive use of visuals in curriculum materials for this age group. The research was initially funded as part of the National Center for Cognition and Mathematics Instruction where our research group, along with teams at other universities, focused on producing a revision of the middle school Connected Math 2 curriculum based on instructional design principles learned from cognitive science.

Learning more about the role of individual differences is an important step in understanding the processes individuals engage in when visuals are present and how those processes change as they develop different interests, attitudes, and both domain-specific and domain-general abilities.

Recently, working with undergraduates at Wesleyan University, I combined these two lines of work to address the effect of visual types when learning from a video lesson on chi square. Click here to see a short presentation about the effect of visual type in chi square instruction at the Electronic Conference On Teaching Statistics. Three undergraduates joined in on this work at different points on the project; one presented analyses of the students’ learning, opinions, and open-ended responses at the department poster session (pdf).

As I continue my research in this area, I will consider learners’ motivations, attitudes, and metacognitive judgments when presented with varying visual representations. This will help differentiate the circumstances in which different theoretical mechanisms are primary determinants of the effects of visuals on learning and cognition and the developmental patterns underlying these cognitive processes.

As with my research on the development of statistical literacy, I also hear a range of responses when I mention my research on visual representations in mathematics education. Some of these responses include their dislike of math, but more often, I hear information about visual representations. People educated in the U.S. often immediately agree about all the pictures that they had in their math textbooks in K – 12; children currently in school can be particularly talkative on this topic. As might be expected, diagrams are generally helpful, but the effects of illustrations are much more mixed.

“I really don’t like math”
“My textbook had pictures of these two kids who were …”
“What are you finding out?”

Student Involvement

  • Please email me if you are interested in researching these topics! Engaging in research is an excellent opportunity to interact closely with faculty. Depending on your interests and ongoing work, opportunities include developing research ideas, designing materials, collecting data from research participants, analyzing data, and publishing or presenting your work.
  • I also encourage you to come talk to me about other ways that you might become involved in research as well. I have a fairly interdisciplinary background with interests in cognitive development and education more generally, and there might be other areas where our interests overlap.