IES Blog

Institute of Education Sciences

Supporting STEM Transfer Through Research at the Intersection of Cognitive Science and Education

By Erin Higgins, NCER Program Officer

Wait, have I already learned that?  Can I use what I learned in math class to help me solve this physics problem? Students struggle with these types of questions every day – unsure how to identify situations where their knowledge is transferrable. Even when they do recognize opportunities to use knowledge learned in one context in a different situation, they may not apply their knowledge appropriately. This is especially true in science, technology, engineering and math (STEM) disciplines. To improve student outcomes in STEM, we need instructional strategies and curricula that help students and teachers with this enduring challenge of transfer.

At the Association for Psychological Science’s 27th Annual Convention, I put together a symposium that highlighted emerging research that addresses this complex issue. Four researchers funded through NCER’s Cognition and Student Learning topic discussed findings from their ongoing research. Each is approaching this issue from a unique perspective regarding factors that help or hinder transfer, and each is examining this issue with different learning tasks, content areas (science, math) and age groups.

Jennifer Kaminski presented research conducted in collaboration with Vladimir Sloutsky (The Role of External Representations in Learning and Transfer of Mathematical Knowledge) that demonstrates that both undergraduate and elementary students who learned a mathematical concept in a simple symbolic format were more likely to transfer their knowledge than those who learned the concept in a more contextualized and perceptually-rich format. This finding is particularly interesting given the widely-held belief that students learn mathematics concepts better with concrete objects, and suggests that there may be many instances where teaching students in a more abstract way facilitates later transfer. This research team is continuing this line of work in their more recently funded IES grant, Facilitating Transfer of Mathematical Knowledge from Classroom to Real Life.

Charles Kalish presented research with elementary-aged students and adults showing that the structure of the math practice problems students encounter affects the memory representations built in response, which then determines whether students can successfully transfer their knowledge in mathematics (Promoting Discriminative and Generative Learning: Transfer in Arithmetic Problem Solving). For instance, in a study with elementary-aged students, 2nd graders practiced arithmetic by playing a computer-based ice cream game, where they had to make ice cream flavors for monsters by combining different types of ice cream. Students who received “grounded” practice interacted with the math practice problems in a way that highlighted the underlying quantities in the arithmetic problem while students who received “symbolic” practice were given standard arithmetic problems to solve. Students who received the grounded practice showed higher performance on a later test on arithmetic problems involving quantities not seen during practice. In light of the research presented by Kaminski in this symposium, this research demonstrates that the issue of transfer in mathematics is extremely complex, and it may be the case that there are circumstances where a more concrete, grounded approach to instruction is best and other circumstances where a symbolic, abstract approach will lead to the best transfer.

Kenneth Kurtz presented research on a technique called category construction, which is a sorting task intended to teach students the conceptual principles that underlie different examples of the same science concepts (Enhancing Learning and Transfer of Science Principles via Category Construction).  Compared to students who engaged in the more standard approach of completing worksheets about science concepts, students who engaged in category construction were better able to apply the newly learned science concepts to novel situations.

Finally, Holly Taylor presented research exploring the effects of a spatial thinking program for elementary-aged children on both spatial thinking and STEM performance (An Elementary-age Origami and Pop-up Paper Engineering Curriculum to Promote the 3-D Spatial Thinking and Reasoning Underlying STEM Education).  Based on origami and paper-engineering activities, the program trains 2D to 3D spatial transformation and diagram interpretation skills. This research is ongoing, though preliminary results suggest that students’ spatial reasoning skills are improved when they engage in this program. Future research will evaluate the extent to which this intervention improves STEM achievement.

Together, these four presenters’ lines of research demonstrate the value of applying traditional cognitive psychology and cognitive development theories to challenges in education practice in order to improve education outcomes for students. By aligning instructional approaches to the ways in which the mind works (e.g., by addressing how different memory models affect how we use information, how spatial reasoning impacts math and science problem solving, and how our perceptual system impacts how we represent information in our minds), we can begin to develop approaches that more effectively impart knowledge to students in ways that will allow for the broadest and most successful transfer.

Additional summaries of the research presented at this symposium can be found at: http://www.edweek.org/ew/articles/2015/06/03/findings-show-ways-students-can-transfer-math.html and http://blogs.edweek.org/edweek/inside-school-research/2015/06/sorting_improves_science_transfer.html

Questions? Comments? Please send us an email at IESResearch@ed.gov.

Adding Knowledge, Subtracting Student Challenges: The Math Cognition and Learning Conferences

By Rob Ochsendorf (NCSER Program Officer), Joan McLaughlin (NSCER Commissioner), and Liz Berke (NCSER Intern) 


How would you solve this problem?  7 + 25 – 23 = ___.  Skilled math students recognize key features of problems and use appropriate shortcuts when solving problems but recent research led by Dr. Katherine Robinson has shown that less than a third of 7th graders actually used shortcut strategies.  Dr. Robinson noted that, “These students show strong preferences for using well-practiced rote strategies for solving these problems rather than thinking deeply and flexibly about either the problems or how they can use their knowledge of arithmetic to facilitate problem solving.”  


During May of this year, Dr. Robinson and other researchers from across the world convened in St. Louis, Missouri to share findings in the growing area of research known as math cognition. This two-day conference entitled, “Typical and Atypical Learning of Complex Arithmetic Skills and Higher-Order Mathematics Concepts,” is part of a series of five annual conferences, Math Cognition and Learning Conferences  (MCALC), funded by a grant from the National Institute of Child Health and Human Development (NICHD) with additional support from NCSER.  

Dr.  Joan McLaughlin, NCSER Commissioner, and Dr. Rob Ochsendorf attended MCALC this year and highlighted the importance of math cognition research to support students with or at risk for disabilities in their math learning.  NCSER funds a number of projects in this area, including a National Research and Development Center focused on understanding the cognitive processes involved in the development of fraction skills in elementary school children.  NCSER has taken an interest in the MCALC mission from the beginning and continues to support graduate students’ attendance and participation each year.  

 

At the conclusion of this year’s meeting, NCSER staff talked with lead investigators Dan Berch (University of Virginia) and David Geary (University of Missouri) to discuss the MCALC meetings and activities, which have included the founding of a new international society for math cognition (Mathematical Cognition and Learning) and an edited book series, in addition to the annual meetings.  


What do you think were the key takeaways from the 2015 MCALC meeting? 

The conferences really have two important, interrelated goals.  The first is social - to help researchers, especially the younger ones, develop connections with and discuss their ideas and current research with each other and senior members of the field.  This networking is important for building collaborations and for finding links between different areas of mathematical cognition and learning. The second is to more fully understand mathematical learning and cognition. The focus at this meeting on individual differences highlighted the importance of domain-general and math-specific knowledge in fostering both procedural and conceptual aspects of mathematical development, and provided directions for intervention with struggling students. 

What are the important long term contributions of this series of meetings? 

The long-term goal of the meetings and the new society is to bring together people with a shared interest in quantitative processing and development that might otherwise not be aware of one another's work, much less discuss it one-on-one. The 5-volume series coming out of the meetings is important as well.  We hope that these will provide a critical and useful reference work that highlights cutting edge advances across the whole field, from number processing in nonhumans to educational interventions.

Are there issues that you would like the IES research community to be aware of in terms of these meetings and these developments?  

I'd like to see more IES researchers entering the field. There is a clear need to better understand and foster students' mathematical development and there is now a thriving research community and literature base that makes this an exciting and rewarding field to be a part of. 


Two more MCALC meetings will be held in 2016 and 2017.  


May, 2016 - The Role of Linguistic, Cultural, SES, and Parenting Factors in Mathematical Cognitive Development  


May, 2017 - Improving Mathematical Learning: How Neurobiological, Cognitive, and Developmental Approaches Can Inform the Design of Effective Instructional Interventions 

 

If you are interested in attending one of these upcoming meetings, please contact Dr. Dan Berch.  

Other questions? Comments? Please contact us at IESResearch@ed.gov.