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

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

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

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

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

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

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

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

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

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

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

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 …

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

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

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