Observing the Problem Solving Strategies of Students

Marsali Wallace

Ross Galloway

Introduction

• Experimental design

• A problem solving model

• Its use by introductory students

• What this means

AIMS

• To see how and if students use the problem solving model given to them in class.

• To look at the results in terms of successful and unsuccessful student behaviour in problem solving.

“Problem solving is cognitive processing directed at achieving a goal when no

solution method is obvious to the problem solver.”

Mayer, R. E. (1992). Thinking, problem solving, cognition (2nd ed.). New York: Freeman.

Think Aloud

http://www.livescribe.com/cgi-bin/WebObjects/LDApp.woa/wa/MLSOverviewPage?sid=4dNdFjpNtrV6

The QuestionsDrawbridge QuestionA man is trying to push a large stone block across a uniform drawbridge which has a mass of m = 200kg. The mass of the large stone block and the man combined is M = 300kg. The drawbridge is of length L = 5.00m and is held up by a wire. The wire can withstand a maximum tension of 5000N. The vertical distance between the drawbridge and the point where the wire is attached to the wall is h = 4.00m. How far along from the wall can the man push the stone block before the bridge collapses? Assume g = 10 ms-2

Army Cadet Question

An Army cadet uses a rope swing to cross a river. He starts on a high platform with his centre of mass 7.16 metres from the ground and grabs onto the rope which is 6m long, to swing. He lets go when the rope is vertical and his centre of mass is 1m off the ground. He needs to travel 5m horizontally to clear the river after letting go of the rope. If he successfully clears the river what is the tension in the rope just before he releases? The cadet’s weight is 80kg.

Problem Solving Model

Focus on the problem

Describe the physics

Plan a solution

Execute the plan

Evaluate the answer

Heller and Heller (1995) The Competent Problem Solver. University of Minnesota

Results: Timeline of problem solving strategies

Minnesota Model Time (Minutes)Code   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Focus on the problem

                                                                                                                                                                                       

Describing the physics

                                                                                                                                                                                       

Planning                                                                                                                                                                                       

Execution

                                                                                                                                                                                       

Evaluation

                                                                                                                                                                                       

Silence and no writing

                                                                                                                                                                                       Student 1. Drawbridge Question. Non-Major, Female

Results: Successful Student

Student 6 FDPEE Model

Focus on problem

Describe Physics

Plan Execute Evaluate Silence and no writing

Per

cent

age

of ti

me

on E

ach

Act

ivity

Results: Unsuccessful Student

Student 4 FDPEE Model

Focus on problem

Describe Physics

Plan Execute Evaluate Silence and no writing

Per

cent

age

of ti

me

on E

ach

Act

ivity

Discussion

• No use of the problem solving model given in class

• What does this mean?

• Is the model still useful?

Discussion• Across all students (successful or not) and

both questions there was a lack of Evaluation and Planning.

• Other studies agree (Kohl and Finkelstein, 2008)

• What we expect from Experts (Schoenfeld, 1985)

• Control decisions and MetacognitionKohl, P.B. and Finkelstein, N.D. (2008) “Patterns of multiple representation use by experts and novices during physics problem solving”, Physical Review Special Topics – Physics Education Research 4(1) 010111

Schoenfeld (1985) Mathematical Problem Solving. Academic Press, Florida.

Kohl and Finkelstein, 2008

Kohl, P.B. and Finkelstein, N.D. (2008) “Patterns of multiple representation use by experts and novices during physics problem solving”, Physical Review Special Topics – Physics Education Research 4(1) 010111

Discussion• Across all students (successful or not) and

both questions there was a lack of Evaluation and Planning.

• Other studies agree (Kohl and Finkelstein, 2008)

• What we expect from Experts (Schoenfeld, 1985)

• Control decisions and MetacognitionKohl, P.B. and Finkelstein, N.D. (2008) “Patterns of multiple representation use by experts and novices during physics problem solving”, Physical Review Special Topics – Physics Education Research 4(1) 010111

Schoenfeld (1985) Mathematical Problem Solving. Academic Press, Florida.

Schoenfeld, 1985

“On the surface it (the solution attempt) appears to be clumsy and unstructured… In reality, however, there was an extraordinary degree of control at all times during this solution.”

“Plans and their implementation were continually assessed, and then acted upon in accordance with the assessments.”

Page 313. Schoenfeld (1985) Mathematical Problem Solving. Academic Press, Florida.

Discussion• Across all students (successful or not) and

both questions there was a lack of Evaluation and Planning.

• Other studies agree (Kohl and Finkelstein, 2008)

• What we expect from Experts (Schoenfeld, 1985)

• Control decisions and MetacognitionKohl, P.B. and Finkelstein, N.D. (2008) “Patterns of multiple representation use by experts and novices during physics problem solving”, Physical Review Special Topics – Physics Education Research 4(1) 010111

Schoenfeld (1985) Mathematical Problem Solving. Academic Press, Florida.

Conclusions

• Students did not use the problem solving model given to them in class whether successful or unsuccessful in solving the problem.

• There was a lack of Evaluation and Planning in all students, should we be looking for more Evaluation?