Algebraic Modeling: Pre-Service Teachers’ Opportunities to Learn Hyunyi Jung Alexia Mintos Purdue University Purdue University Preparing to Teach Algebra This research is partially supported by the National Science Foundation grant number 11-09256.
PTA Overview & Research Questions • An NSF-funded collaborative project • Mixed methods research approach o survey & case study data • What opportunities do secondary mathematics teacher preparation programs provide to learn about o algebra, o algebra teaching, o issues in achieving equity in algebra learning o algebra, functions, and modeling standards mathematical practices described in the CCSSM? Preparing to Teach Algebra This research is partially supported by the National Science Foundation grant number 11-09256.
Research Question • What opportunities do pre-service secondary mathematics teachers have to learn about and teach contexts and modeling in algebra during their teacher education program? Preparing to Teach Algebra This research is partially supported by the National Science Foundation grant number 11-09256.
Significance • Algebra: as a foundation for higher mathematics & a gatekeeper for entrance to college course work (Kilpatrick & Izsak, 2008; Rech & Harrington, 2000) • Contexts and modeling: support better conceptual understanding when learning mathematical concepts from models and solving problems in context (Brown et al., 1989; NCTM, 2000) Preparing to Teach Algebra This research is partially supported by the National Science Foundation grant number 11-09256.
Significance • Changes in standards & teacher education: whether teacher education programs are preparing teachers to teach algebra in the current standards (CCSSM) while considering CK and PCK for future teachers (National Research Council, 2010) • Opportunity to Learn (OTL): measuring the extent to which students learn about concepts by examining academic tasks, activities, and detailed accounts of content coverage (Floden, 2002; McDonnell, 1995) Preparing to Teach Algebra This research is partially supported by the National Science Foundation grant number 11-09256.
Data Sources ( 10-12 instructor interviews and 2 student teacher focus groups at each of five universities) Example Mathematics Courses Mathematics Education Courses Common Calculus Secondary Math Methods Courses Linear Algebra Middle School Math Methods across Modern Algebra Field Experience universities Probability and Statistics Student Teaching Seminar Geometry Other Discrete Mathematics Technology in Education courses Advanced Calculus: Education and Individual Single Variable Differences Teaching in a Pluralistic Society Mathematical Models/Applications Algebra Throughout the Curriculum Senior Capstone
Framework – Level 1 Learn Learn to teach What do PSTs Modeling topics Knowledge for learn? and processes teaching modeling in algebra In what ways do Ways to learn Ways to learn to PSTs learn? modeling topics teach modeling and processes topics and processes Preparing to Teach Algebra This research is partially supported by the National Science Foundation grant number 11-09256.
Framework – Level 2 Processes of Modeling • Identifying and selecting variables • Formulating a model by creating and selecting appropriate representations • Analyzing and performing operations • Interpreting the results of the mathematics • Validating the conclusions, possibly improving the model • Reporting on the conclusions and the reasoning behind them (National Governor’s Association Center for Best Practices & Council of Chief State School Officers, 2010, p. 72). Preparing to Teach Algebra This research is partially supported by the National Science Foundation grant number 11-09256.
Coding Process 1) Four themes (e.g., What to learn, how to learn, what to teach, how to teach) 2) Algebra, Mathematics 3) Process of modeling described in CCSSM (e.g., identifying and selecting variables; formulating a model by creating and selecting appropriate representations) Preparing to Teach Algebra This research is partially supported by the National Science Foundation grant number 11-09256.
Coding Example We do, actually I was thinking about this when you asked about modeling. To develop the concept of linear regression, they do an experiment where they light candles and convert with jars. Preparing to Teach Algebra This research is partially supported by the National Science Foundation grant number 11-09256.
Coding Example That's one of the things we talk about in this class too. How is modeling different from just doing story problems. Preparing to Teach Algebra This research is partially supported by the National Science Foundation grant number 11-09256.
Coding Example We did something about population of animals where we used eigenvalues and eigenvectors to decide on the long term stabilization of the population of two, sort of predator/prey model…I did something about drawing graphs and essentially computing their numbers. Preparing to Teach Algebra This research is partially supported by the National Science Foundation grant number 11-09256.
Questions • Can this framework [level1] be used for the other big ideas? (e.g., Nature and Structure of Algebra, Functions, Contexts and Modeling, Reasoning and Proof, Connections, Tools and Technology, Equity) • What other components can be added to the framework to answer the research question? Preparing to Teach Algebra This research is partially supported by the National Science Foundation grant number 11-09256.
Questions & Comments? Hyunyi Jung Alexia Mintos Purdue University Purdue University Preparing to Teach Algebra This research is partially supported by the National Science Foundation grant number 11-09256.
Frequency of Opportunities to Learn Modeling Mentioned by Participants PSTs Math Math Ed Purposes of modeling Instructors Instructors Use mathematical modeling in real-world context 5 6 7 Use problem-solving approaches to investigate and understand 2 0 3 math Understand and describe the behavior of a system or event 0 0 1 Processes of modeling (from CCSSM) Identifying and selecting variables 0 3 4 Formulating a model by creating and selecting appropriate 2 3 5 representations Analyzing and performing operations to draw conclusions 0 2 1 Interpreting the results of the mathematics 0 1 3 Validating the conclusions, possibly improving the model 0 1 2 0 0 1 Reporting on the conclusions and the reasoning behind them
OTL Comparisons across Universities Purposes of modeling A B C 5 5 8 Use mathematical modeling in real-world context 2 2 1 Use problem-solving approaches to investigate and understand math 0 1 0 Understand and describe the behavior of a system or event Processes of modeling (from CCSSM) 1 2 4 Identifying and selecting variables 3 2 5 Formulating a model by creating and selecting appropriate representations 0 1 2 Analyzing and performing operations to draw conclusions 1 1 2 Interpreting the results of the mathematics 0 0 3 Validating the conclusions, possibly improving the model 0 0 1 Reporting on the conclusions and the reasoning behind them
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