Visual Feature Focus in Geometry: Instructional Support for Visual Coordination During Learning (Butcher & Aleven)

Visual Feature Focus in Geometry: Instructional Support for Visual Coordination During Learning

Kirsten Butcher & Vincent Aleven

Summary Table

Study 1

PIs	Kirsten R. Butcher & Vincent Aleven
Other Contributers	Research Programmers/Associates: Octav Popescu (Research Programmer, CMU HCII), Thomas Bolster (Research Associate, CMU HCII), Michael Nugent, Research Programmer CMU HCII)
Study Start Date	December 2007
Study End Date	February 2008
LearnLab Site	Riverview High School
LearnLab Course	Geometry
Number of Students	Approximately 60
Total Participant Hours	Approximately 240
DataShop	N/A (Study is still being run)

Study 2

PIs	Kirsten R. Butcher & Vincent Aleven
Other Contributers	Research Programmers/Associates: Octav Popescu (Research Programmer, CMU HCII), Thomas Bolster (Research Associate, CMU HCII), Michael Nugent, Research Programmer CMU HCII)
Study Start Date	January 28, 2008
Study End Date	March 2008
LearnLab Site	Central Westmoreland Career & Technology Center (CWCTC)
LearnLab Course	Geometry
Number of Students	Approximately 90
Total Participant Hours	Approximately 360
DataShop	N/A (Study has not yet begun)

Abstract

Is visual-verbal integration a major source of difficulty for students learning geometry? Further, how can coordinative learning with visual and verbal knowledge components in geometry be supported by instructional events that vary the support for and type of sense making in which learners engage during problem solving? In geometry, students may have difficulty integrating visual and verbal information sources for two reasons: first, they may lack deep understanding of geometry concepts (e.g., what is an interior angle?) that are relevant to problem-solving principles (e.g., the interior angles theorem for circles); second, students may be unable to coordinate visual problem features with verbal principles during problem solving. Our research explores the robust learning effects associated with visual-verbal training of geometry features and varied levels of instructional assistance in coordinating visual diagram features with verbal geometry principles during problem solving.

Background & Significance

Successful Learning is Supported by Coordinated Visual-Verbal Knowledge

Research with both experts and more novice learners has shown that integrated visual-verbal knowledge supports successful problem solving. In geometry, for example, experts use key diagram configurations to cue retrieval of relevant schemas, and these visual configurations help successfully model expert proof (Koedinger & Anderson, 1990). In mathematics, experts are more likely than novices to generate diagrams and to use these visual representations to guide their reasoning about problem-solving steps (Stylianou, 2002).

Even for more novice learners, learning benefits are seen when visual and verbal information is processed jointly instead of in isolation. In geometry, superficial visual similarities between geometry diagrams can decrease a novice’s likelihood of problem-solving success because novices focus on irrelevant visual similarities at the expense of conceptual problem differences (Lovett & Anderson, 1994). Even when visualizations depict helpful (rather than misleading) information for learning, verbal explanations support deeper understanding. For example, the value of graphical feedback when using a physics simulation is greatly enhanced by the presence of short, embedded verbal explanations that focus learners on key principles (Rieber, Tzeng, & Tribble, 2004). Similarly, learners suffer when verbal information is processed alone. Visual representations that are designed to be informationally-equivalent to a given piece of text or audio nevertheless support deeper understanding of the text (Ainsworth & Loizou, 2003; Butcher, 2006) or audio explanations (e.g., Moreno & Mayer, 2002). Further, students benefit from activities that coordinate both visual and verbal sources; these activities include verbal comparison of self-generated and ideal diagrams (Van Meter, 2001; Van Meter, Aleksic, Schwartz, & Garner, 2006) as well as dragging and dropping verbal information into a diagram to create an integrated representation (Bodemer, Ploetzner, Feuerlein, & Spada, 2004).

The potential importance of connecting visual and verbal information also is supported by the literature on knowledge transfer following example learning, where the use of abstract rules can combat problems associated with focus on superficial similarity. Although examples often support problem solving, students frequently are unable to successfully solve transfer problems that are not superficially very similar to the trained examples (for a review, see Reeves & Weissberg, 1994). Research in reasoning and transfer has found that student performance is better supported by examples that include instruction on abstract rules when compared to learning with examples alone or instruction alone (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991). Thus, we should expect that when students connect geometry diagrams (examples) to relevant geometry principles (abstract rules), robust learning will be supported.

Further Information

Future Plans

1. To be added