1. Students' Epistemological Beliefs vis-à-vis Problem Solving Sophistication in M&I Physics
Wendi Wampler1, Lynn Bryan2,1, & Mark Haugan1
Department of Physics1, Department of Curriculum and Instruction2
Purdue University,
West Lafayette IN
This project is funded in part by the National Science Foundation grant DUE-CCLI

2. Introduction Problem solving is critical
Learning goal
Assess student knowledge
Epistemological beliefs can impact a students learning
Conceptual understanding, organization of knowledge, study habits
Little (but growing) research on relation between Problem Solving approach and epistemological beliefs in reform based curricula

3. In the M&I context: How do students approach problem solving?
What are the personal epistemological beliefs, and how do they change over the semester?
How do epistemological beliefs relate to how they approach problem solving?

4. Context: Matter and Interactions
Purdue’s large scale implementation
Restructuring pedagogical content knowledge
few fundamental principles as opposed to unconnected, discrete equations.
M&I problem solving approach:
Choose a system/surroundings.
Make diagram.
Choose initial and final times.
Apply the fundamental principle.
Add in terms accounting for objects/interactions.
Substitute known values into fundamental principle.
Check units; reasonableness.
Qualitative analysis of scenario

5. Methodology
6 students from the M&I introductory physics course, Fall 2010
Modified CLASS survey
Participants met week 3 and week 13; level of agreement with expert and gains used to characterize student beliefs
Recitation Observation
Video recorded during weeks 4 – 13
Post Recitation Interviews
Participants reviewed recitation activity

6. First level of analysis: Rubric for problem solving
SYS
0-2
Extent to which students analyze the objects and interactions in the situation
COND
0-1
Discussed and accounted for Initial and Final conditions FP
Started problem from fundamental principle
APP
Applied fundamental principle to defined system correctly
Started from conservation laws
ACCT
Accounts for objects/interactions vs. use of random terms SM
Tries to make sense of situation
Eval
Sanity check/evaluation of solution
ANS
Correct Answer

7. Second level of analysis: problem solving sophistication
Based on categories by Walsh, Howard, and Bowe, 2007
Category
Key Characteristics
4 - Scientific Approach
(M&I)
- Qualitative analyzes the situation
- Plans and carries out solution in a systematic manner based on
that analysis
- Refers to concepts to guide the solution
- Evaluates solution
3 - Structured plug
and chug
Qualitatively analyzes the situation based on the required formulas
Plans the solution based on the variables and proceeds
systematically
- Evaluates the solution
2 - Unstructured plug
- Analyzes the situation based on the required variable
- Proceeds by choosing formulas based on the variables in a trial
and error manner
- Refers to concepts as variables
- Conducts no evaluation
1 - Memory-based
approach
- Analyzes situations based on previous examples
- Proceeds by trying to “fit” the given variables to those examples
0 - No clear
- Analyzes situation based on the given variables
- Proceeds by trying to use the variables in a random way
- Refers to variables as terms

8. Epistemological Beliefs
Espoused: Modified CLASS survey
Enacted: Coded recitations and interview; based on Hammer’s Dimensions of Epistemological Beliefs in Physics and student classifications
Code
Dimension
Value
EQN
Structure of physics knowledge +1
Coherence – Physics is a connected, coherent framework -1
Pieces – Physics is collection of discrete, unrelated facts or ideas.
CONC
Content of physics knowledge
Concepts – Physics is made up of concepts represented by symbols and formulas
Formulas – Physics consists of facts and formulas to be memorized and manipulated
AUTH
Learning physics
Independence ­– Learning is a process of applying and modifying one’s own models until it makes sense
By Authority – Learning is receiving knowledge from authority and storing what is taught PS
M&I problem solving approach
Applying Fundamental Principles – Solving problems involves applying fundamental principles to defined systems of objects and their surrounding interactions
Using equations ­– Solving problems involves using equations from the instructor or book

9. Results: Problem Solving

10. Results: Epistemological Beliefs
Student
% agree PS total
% agree PS Gen
% agree M&I
% agree PS Soph
% agree Ps Con
Quant
Gains
Qual gains
John
Pre
81.25
100 80
Post
87.5 75
6.25
-12.5 20
-25 +
Derek
56.25 50 40
68.75
12.5
37.5 25
0/+
Anthony 60
-6.25
-40
0/-
Melissa
93.75
David
Laura
43.75
62.5
18.75

11. Relationship Between EB and PS
Student
EB levels
Quant EB
Qual EB
PS Gains %
Grade
John
H>H + 40 A
Derek
ML>ML
0/+ 25 A-
Anthony
0/-
43.333 C+
Melissa A+
David
13.75
Laura
ML>MH
43.75 C
Trend 1: (David and John)
High quantitative EBs with positive qualitative gains
High level of PS sophistication at start, revert to novice through mid
EBs about PS were challenged and PS back to expert-like
Trend 2: (Melissa and Derek)
Little change in EBs and PS sophistication.
Melissa remained a high level for both, Derek a lower level for both
Trend 3: (Anthony, and Laura)
Mid EBs with positive qualitative gains
Large gains in PS sophistication
EBs about PSing were quickly aligned, but lacked content knowledge

12. (YAY!!)
“I feel like the focus of this class was giving you the basic principles, showing you how all the basic formulas were derived from the basic principles, which is then a way of thinking that you can apply in life in general.” -Laura

13. Implications
Curriculum design based on increasing both sophistication of problem solving and appropriate epistemological beliefs.
When introducing a problem solving strategy, important to address epistemological beliefs about problem solving, as well as content knowledge about problem solving approach
Within M&I, course materials should be designed with this relationship in mind
Emphasis should be consistent across course in lecture, homework, recitation, and lab

14. Questions?