Improving Students’ Understanding Through Research

Chandralekha Singh

Department of Physics and Astronomy

University of Pittsburgh

Model of Student Learning?

Typical Classroom Today

Typical Classroom 5000 Years Ago

• Goal of instruction: Guide students from Si -> Sf

• Sf depends on Si and instructional design

Model of Learning

PfS

f

Instruction

Posttest, interviews

Si

Pi

Lea

rnin

g

Pretest, interviews

Assessment

Student's knowledge state Performance

When Physical Intuition Fails

• 20 faculty and students were posed – a non-intuitive introductory physics problem

(Singh, Am. J. Phys., 70(11), 1103-1109, 2002)

Expertise and Intuition• Non-intuitive problem has two critical variables

– How much friction

– How long to start rolling

• Faculty – Difficulty solving non-intuitive problem on-the-spot

• Often focused only on one variable

– No difficulty with Ballistic pendulum which also involves two principles

• Students– Both equally difficult

Energy & Momentum Question • Two small spheres of putty, A and B, of equal mass hang from a ceiling on

massless strings of equal length. Sphere A is raised to a height h0 as

shown below and released. It collides with sphere B (which is initially at rest); they stick and swing together to a maximum height h

f. Choose all of

the following principles that must be invoked to find height hf in terms of h

0?

(I) conservation of mechanical energy (II) conservation of linear momentum

(a) (I) only 34% (b) (II) only 23% (c) both (I) and (II) 27%(d) either (I) or (II) but not both 13% (e) none of the above 3%

(Singh & Rosengrant, Am. J. Phys., 71(6), 607-617, 2003)

Expertise and Intuition

• Perceived difficulty not only depends on inherent complexity of problem– Must assess difficulty of a problem from students’

perspective

– Experience, familiarity & intuition built• Crucial for optimal scaffolding

Another Lesson : Problem Solving Heuristics• Although professors had difficulty when forced to think

``on their feet”

– They demonstrated they know how to solve problems

– Problem solving strategies initially employed were better

• Started by visualizing & analyzing problem qualitatively

• Searched for useful conservation principles before resorting to other routes

• Examined limiting cases

• Drew analogies & mapped problem to a familiar one

• Highlights importance of teaching effective problem-solving heuristics

• Design a flexible instructional tool that

– Teaches effective problem solving heuristics

– Uses Cognitive Apprenticeship model that employs• Modeling -> instructor exemplifies & demonstrates skills

• Coaching -> provides practice and guidance

• Scaffolding -> provides feedback with gradually decreasing support to develop self-reliance

– Combines qualitative & quantitative problem solving

– Can be used by students with a wide variety of skills/ability

Interactive Video Tutorials for Enhancing Problem Solving, Reasoning, and Meta-cognitive Skills of

Introductory Physics Students (supported by NSF)

Problem Solving Heuristics1) Initial qualitative analysis

• Draw picture/diagram • Write down known quantities• Determine the goal• Predict features of solution

2) Planning (decision making)• What is/are appropriate physics principles?

3) Implementation

4) Assessment

5) Reflection• What did I learn by solving this problem?

As problems get complex, it becomes increasingly important to employ a systematic approach

Layout and Design(Journal of College Science Teaching, 2010)

• Interactive tutorial based problems contain

– Problem worksheets

– Solve problem without help on worksheet

– Video tutorial on computer

• Before entering solutions on-line, students solve research-guided sub-problems (multiple-choice)

– At each stage of problem solving

– Incorrect responses direct them to help session based on difficulty

– Correct responses give choice of advancing or accessing help

Problem WorksheetProblem StatementTwo adjacent boxes (m1=5 kg, m2=2.5 kg) are in contact on a frictionless table. You apply a constant horizontal force FH=3 N to the larger box. Find the magnitude of force, F, exerted on the larger box by the smaller box.

Qualitative Analysis•Draw a picture•Give names to all known and unknown numerical quantities•Make reasonable physical assumptions•Try to make predictions about the solution

m2= 2.5 kg

m1=5 kgFH= 3 N

Problem Worksheet (continued)Planning/Decision Making•What physics principle may be useful?•Draw any diagram that may be helpful

Assessment and Reflection•Does the solution have the right dimensions?•Does the solution agree with your qualitative assessment?•Will you be able to recognize and apply this principle in a somewhat different situation?

Implementation

Problem Worksheet (Paired Problem)Problem StatementThree adjacent boxes (m1=10 kg, m2=5 kg, m3=15 kg) are in contact on a frictionless table (box with mass m2 is in the middle). You apply a constant horizontal force FH=3 N to box with mass m1 continuously. Find the forces exerted on m1 by m2 and on m2 by m3.

m2=5 kg

FH= 3 N m1=10 kg m3=15 kg

Development and Assessment• All students solved reflection sub-problem that deals with

hand exerting a force in opposite direction

• Third pass: Retention study with students– All could solve another pair problem a week later

• Assessment using other tutorial problems is also encouraging

Summary of Video-Tutorials• Self-paced video tutorials demonstrate and

exemplify systematic approach to problem solving

– Use concrete examples

– Keep students actively involved

– Provide prompt feedback as needed

– Focus on helping students develop self-reliance

– Flexible and adaptable for a variety of students

• Further development & assessment is in progress

Critical Issues in Scaffolding & Learning• Mental Load during problem solving is subjective

– Analyze problem difficulty from students’ perspective

• New knowledge builds on prior knowledge• Piaget’s “optimal mismatch” or Vygotsky’s “zone of proximal

development”

• Students must construct their own understanding

– Give students opportunity to reconstruct, extend, and organize their knowledge

• Actively engaged

Richard Hake (Interactive engagement vs traditional methods) http://www.physics.indiana.edu/~hake/

Traditional (lecture)

Interactive (active/cooperative)

<g> = Concept Inventory Gain/Total

Collaborative Learning• Learning is embedded in social context

– Easier retrieval later• Knowledge is encoded in memory with context

– Opportunity for clarifying difficulties • Especially if there is diverse opinion

– Keeps students alert & on their toes

• Students must explain their reasoning to peers– Challenges students

– Fun to work with peers

– Encourages students to monitor their learning

– Helps all students since discussing and articulating concepts helps organize and solidify concepts

• Provides opportunity for co-construction of knowledge

Effectiveness of Group Interaction during Qualitative Problem Solving

(Singh, AJP, May 2005)

• How does group performance differ from individual performance?

• Extent of unguided co-construction

• Extent of retention

Investigation Method• In a double-class period, administered CSEM test (Maloney et.

al., AJP,2001) in pairs and individually

– Calculus-based introductory physics course

– 128 students: two equivalent samples

• individual followed by group: "IG intervention"

• group followed by individual: "GI intervention"

– 50 minutes testing period each time

– 7 minute break between individual and group testing

– Students turned in first response so could not refer to it

– Test answers never discussed with students

– Students chose their partners

• Two weeks later, students took the same test individually

• Control group: no group intervention

Results

• Similar group scores in GI and IG interventions

• Large normalized gain g=0.39 in IG interventions

Co-construction in IG Intervention• Co-construction: neither student alone chose correct response but did as group

• Possible reasons–For different individual incorrect responses:

• students must explain reasoning to peers

• unravel problems in initial logic

• complementary information can help co-construct

–For same individual incorrect responses:• peers may discuss doubts• important clues can trigger recall of relevant concepts

– can help group co-construct

• Peers can relate to each other's difficulty better

Evidence for co-construction• Table displays

–Percentage of overall cases where neither, one or both group members had correct response individually

–Impact of group work

Individual gain and retention

• Two weeks later individual testing using CSEM

• "IGI" intervention

–74%, g=0.42 (between first & second individual testing)

• Control group: no group intervention

• 58% first time

• 63.8% two weeks later: g=0.14

Benefits of Collaborative Learning

• Group interaction

–Produced high gain on individual testing

–Facilitated co-construction of knowledge

–Aided in retention of material

• Students frequently noted that

–Interpretation of problems easier with peer

–Discussion forced them to think harder

• Helped rectify their initial reasoning

• Reminded them of relevant concepts

Acknowledgements

• Funding Agencies– National Science

Foundation

– Spencer Foundation

• Graduate students– Andy Mason

– Guangtian Zhu

– Shih Yin Lin

– Jing Li

– David Rosengrant

– Yvette Beck

• Undergraduates– Joshua Bilak– Daniel Hailesellassie– Nicki Zevola– Chris Pankow– Caitlin Holmes– Kimberly Smith– Suzzane Coholic– Amanda Metzger– Justin Calugar– Nick Ferrel– Chris Nelsen– John Berry– Michael Gao