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-0618504

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

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?

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

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

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

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

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

Results: Problem Solving

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 66.66667 Post 87.5 75 6.25 -12.5 20 -25 + Derek 56.25 50 40 68.75 12.5 37.5 25 0/+ Anthony 16.66667 60 33.33333 -6.25 -40 0/- Melissa 93.75 David 83.33333 -16.6667 Laura 43.75 62.5 18.75

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

(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

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

Questions?