Algebraic Modeling: Pre-Service Teachers Opportunities to Learn - - PowerPoint PPT Presentation

Algebraic Modeling: Pre-Service Teachers’ Opportunities to Learn

Preparing to Teach Algebra

This research is partially supported by the National Science Foundation grant number 11-09256.

Hyunyi Jung Purdue University Alexia Mintos 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
• survey & case study data
• What opportunities do secondary mathematics

teacher preparation programs provide to learn about

• algebra,
• algebra teaching,
• issues in achieving equity in algebra learning
• 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)

Data Sources (10-12 instructor interviews and 2 student

teacher focus groups at each of five universities) Example Mathematics Courses Mathematics Education Courses Common Courses across universities Calculus Secondary Math Methods Linear Algebra Middle School Math Methods Modern Algebra Field Experience Probability and Statistics Geometry Student Teaching Seminar Other courses Discrete Mathematics Technology in Education Advanced Calculus: Single Variable Education and Individual Differences Mathematical Models/Applications

Teaching in a Pluralistic Society

Senior Capstone

Algebra Throughout the Curriculum

Preparing to Teach Algebra

This research is partially supported by the National Science Foundation grant number 11-09256.

Framework – Level 1

Learn Learn to teach What do PSTs learn? Modeling topics and processes Knowledge for teaching modeling in algebra In what ways do PSTs learn? Ways to learn modeling topics and processes Ways to learn to teach modeling 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)

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.

Alexia Mintos Purdue University Hyunyi Jung Purdue University

Questions & Comments?

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

Purposes of modeling

PSTs Math Instructors Math Ed Instructors Use mathematical modeling in real-world context 5 6 7 Use problem-solving approaches to investigate and understand math 2 3 Understand and describe the behavior of a system or event 1

Processes of modeling (from CCSSM)

Identifying and selecting variables 3 4 Formulating a model by creating and selecting appropriate representations 2 3 5 Analyzing and performing operations to draw conclusions 2 1 Interpreting the results of the mathematics 1 3 Validating the conclusions, possibly improving the model 1 2 Reporting on the conclusions and the reasoning behind them 1

OTL Comparisons across Universities

Purposes of modeling A B C

Use mathematical modeling in real-world context

5 5 8

Use problem-solving approaches to investigate and understand math

2 2 1

Understand and describe the behavior of a system or event

1

Processes of modeling (from CCSSM)

Identifying and selecting variables

1 2 4

Formulating a model by creating and selecting appropriate representations

3 2 5

Analyzing and performing operations to draw conclusions

1 2

Interpreting the results of the mathematics

1 1 2

Validating the conclusions, possibly improving the model

3

Reporting on the conclusions and the reasoning behind them

1