1. Vincent Aleven & Kirsten Butcher
Learning with Diagrams in Geometry: Strategic Support for Robust Learning
Vincent Aleven &
Kirsten Butcher
2/18/2019
Pittsburgh Science of Learning Center

2. Placing Study within Robust Learning Framework
Primary research cluster
Interactive communication, coordinative learning, refinement & fluency
Independent variables
IC: Reflective dialog, scripting collaboration, peer tutoring, peer observation of tutoring...
CL: self-explanation, integrate conceptual & procedural, multi-representations, multi-modal, …
R&F: Feature focusing, example comparison, cognitive mastery, optimal spacing, …
Dependent variables
Normal post-test, long term retention, transfer, future learning
2/18/2019
Pittsburgh Science of Learning Center

3. Pittsburgh Science of Learning Center
Background
Close proximity between visual and verbal information improves learning
Simultaneous (vs. successive) presentation (Mayer & Anderson, 1992; Mayer & Sims, 1994)
Close (vs. distant) presentation (Mayer, 1989; Moreno & Mayer, 1999)
Students develop deeper understanding of instructional materials when they self-explain to themselves during learning
Student-generated comments (e.g., Chi, deLeeuw, Chiu, & LaVancher, 1994)
Menu-based explanations (Aleven & Koedinger, 2002)
2/18/2019
Pittsburgh Science of Learning Center

4. Pittsburgh Science of Learning Center
Research problem
Scientific Problem
Can coordination between and integration of visual and verbal information improve robust learning?
Can this integration be supported by scaffolds during tutored practice?
Application Problem
Typical problem-solving practice results in shallow learning (see next slide), poor connections between geometry principles & diagrams
Hypothesis
Interacting and self-explaining with geometry diagrams will:
Decrease use shallow problem-solving strategies
Support integration of verbal and visual knowledge
2/18/2019
Pittsburgh Science of Learning Center

5. Educational Problem Shallow Strategy, Close = Connected
Inscribed Angle: The measure of an inscribed angle is equal to half the measure of its intercepted arc.
Shallow strategies sometimes work!
An (incorrect) nearby angle can be applied to the goal angle, leading to a shallow understanding of the geometry principle.
Students often seem to have a strategy that things nearby are related. Often this is true, but it is a shallow strategy
Here, the closest elements do not allow you to solve the angle at hand.
2/18/2019
Pittsburgh Science of Learning Center

6. Study Design TABLE DIAGRAM (Contiguous)
Site of Interaction During Problem Solving
TABLE
(Non-contiguous)
DIAGRAM (Contiguous)
GEOMETRY RULE (Verbal Explanation)
GEOMETRY RULE (Verbal Explanation)
Type of Explanation
TABLE
(Non-contiguous)
DIAGRAM (Contiguous)
Students often seem to have a strategy that things nearby are related. Often this is true, but it is a shallow strategy
Here, the closest elements do not allow you to solve the angle at hand.
GEOMETRY RULE + APPLICATION (Verbal + Visual Expl.)
GEOMETRY RULE + APPLICATION (Verbal + Visual Expl.)
*Time in tutor is controlled across conditions.
2/18/2019
Pittsburgh Science of Learning Center

7. Variable 1: Site of Interaction (Table v. Diagram)
In table condition, all answers and geometry rules are entered in a separate table.
Students often seem to have a strategy that things nearby are related. Often this is true, but it is a shallow strategy
Here, the closest elements do not allow you to solve the angle at hand.
2/18/2019
Pittsburgh Science of Learning Center

8. Variable 1: Site of Interaction (Table v. Diagram)
Students often seem to have a strategy that things nearby are related. Often this is true, but it is a shallow strategy
Here, the closest elements do not allow you to solve the angle at hand.
In diagram condition, student interacts with diagram, opening nearby work areas, with accepted answers displayed in diagram
2/18/2019
Pittsburgh Science of Learning Center

9. Variable 2: Type of Explanation (Rule vs. Rule + Application)
Geometry Rule Only – Students justify their numerical answers with a relevant geometry rule.
Students often seem to have a strategy that things nearby are related. Often this is true, but it is a shallow strategy
Here, the closest elements do not allow you to solve the angle at hand.
2/18/2019
Pittsburgh Science of Learning Center

10. Variable 2: Type of Explanation (Rule vs. Rule + Application)
Rule + Application – After justifying their numerical answer with a relevant geometry rule, students indicate what known diagram elements are referents of the rule
Students often seem to have a strategy that things nearby are related. Often this is true, but it is a shallow strategy
Here, the closest elements do not allow you to solve the angle at hand.
2/18/2019
Pittsburgh Science of Learning Center

11. Robust Learning Assessments
Immediate Posttest
Short-term Retention & Transfer
Posttest given just after instruction
Delayed Posttest
Long-Term Retention and Transfer
Given 3 weeks after instruction
Computer-based assessments using CTAT
(screen shots available)
Both tests include
Isomorphic problem solving tasks (“If angle ABC = 78°, what is the measure of angle DBF?”)
Transfer: Decision-making tasks (“Is there enough information to solve this problem?”)
Transfer: Goal-free problem solving (“Derive and explain all you can”)
2/18/2019
Pittsburgh Science of Learning Center

12. How our treatment fits Robust Learning
Direct interaction with visual representations & self-explanations that connect visual & verbal info support sense-making, improving foundational skills and leading to robust learning.
How our treatment fits
Robust Learning
Outcomes: Knowledge, reasoning & learning processes
Foundational Skills
Sense-Making
Learning Processes:
Construction, elaboration, discrimination
Refinement of Features
Co-Training
Streng-thening
Scaffolds that support visual-verbal integration work because they:
Promote richer sense-making pathways
Produce better foundational skills & explicit knowledge that can be adapted to produce better transfer
Coordinative learning processes make use of visual and verbal information to refine example-based learning
Instructional Processes: (independent variables or treatments)
Multiple inputs, representations, strategies … self-explanation connects vis/verbal representations
Tutorial dialogue, peer collaboration …
Feedback, example variability, authenticity …
Schedules, part training …

13. Which pathways probably explain the results?
Accelerated Future Learning
Robust learning measures
Normal learning
Long-term Retention
Transfer
Additional reasoning during testing
Cognitive
headroom
Self-supervised
learning
Rederiv-
ation
Adapt-
ation
KCs with valid features
Stronger KCs
Knowledge outcomes
Meta-cognitive KCs
Deep, general, flexible KCs
Broad outcome categories of learning/instructional processes during training
Sense-Making
Foundational Skill Building

14. Micro-level interpretation
Site of Interaction During Problem Solving
+ Superficial Strategies
++ Improved understanding of diagram elements & geometry rules
+++Deep connections between rules & diagrams
TABLE
DIAGRAM
GEOMETRY RULE
GEOMETRY RULE
Type of Explanation
TABLE
DIAGRAM
The manipulations essentially increase the likelihood that a student will apply a deep level explanation during learning.
Geometry rules are often very difficult to understand – often not clear how to apply the information to a diagram. Essentially, each of the manipulations increase the likelihood that students will make the correct connection between the reference in a diagram and the referring expression in a geometry rule. Interacting directly with a diagram supports this process, but in a relatively passive way. Students may be more likely to notice relationships between geometry elements and rules, but are not forced to do so. But the elaborated explanations – where students name rules and also the diagram referents of those rules – are very likely to support these connections.
GEOMETRY RULE + APPLICATION
GEOMETRY RULE + APPLICATION
2/18/2019
Pittsburgh Science of Learning Center

15. Pittsburgh Science of Learning Center
Questions?
2/18/2019
Pittsburgh Science of Learning Center