Models and Modeling - Mathematics

Educator investigates the use of models and modeling as they pertain to the Common Core State Standards for Mathematics (CCSSM) and investigates resources for use in classrooms.
Made by University of Wisconsin - Milwaukee
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About this Micro-credential

Key Method

The educator studies the use of models and modeling in the classroom, engages in a detailed analysis of the standards related to such, including the analysis of classroom tasks that address the standard, and devises a set of criteria for measuring student progress on the standards in that category appropriate to their grade level.

Method Components

Components and Implementation of Models and Modeling

  • Examine your own personal model of teacher decision-making used for planning, teaching, and reflection of lessons.
  • Use the model of teacher decision-making from Clough, Berg, Olson to write a reflection of a recent lesson.
  • Discuss the distinctions between models, modeling, modeling with mathematics, and mathematical modeling in the context of the Common Core State Standards for Mathematics.
  • Identify critical features of modeling tasks in mathematics and the progressions related to modeling in high school mathematics.
  • Explore pedagogical aspects of modeling, including the reasons for teaching modeling and pedagogical practices that support successful student engagement in modeling.
  • Plan and teach a modeling-focused lesson that supports student learning opportunities related to other mathematics content standards.
  • Choose or create a measurement tool (rubric, standards-based grading criteria) that capture student performance related to the standards.
  • Analyze student performance related to the standards after students engage in the target lessons.
  • Write a reflection of the planning, implementation, and assessment of the modeling lesson.

Research & Resources

Supporting Research

Prior to the advent of recent standards documents (e.g., CCSSM) and detailed reports (e.g., GAIMME), modeling in the context of teaching mathematics has had a wide array of meanings. In particular, the constructs of modeling with mathematics and mathematical modeling have been used fairly interchangeably by some, leading to confusion among teachers about what components are necessary to meet modeling standards and how to design a modeling standard. This micro-credential is designed to untangle the modeling confusion and discuss the important components of a modeling lesson as reflected in current research and policy. You will engage in readings about mathematics and modeling using the resources noted above to deepen your knowledge of modeling, then plan, implement, and study a lesson related to that content with your students.

The ideas in this micro-credential are specifically designed for the teaching and learning of secondary mathematics. Similar distinctions exist in science; the Models and Modeling (Science) micro-credential contains those resources.

Both Math and Science – A Model for Teacher Decision-Making

  • Clough, M. P., Berg, C. A., & Olson, J. K. (2009); Promoting Effective Science Teacher Education and Science Teaching: A Framework for Teacher Decision-Making. International Journal of Science and Mathematics Education, 7(4), 821-847.

Mathematics Resources

  • Hirsch, C. R. & Roth McDuffie, A. (2016). Annual Perspectives in Mathematics Education 2016: Mathematical Modeling. Reston, VA: National Council of Teachers of Mathematics.
  • Common Core Standards Writing Team. (2013, July 4). Progressions for the Common Core State Standards in Mathematics (draft). High School, Modeling. Tucson, AZ: Institute for Mathematics and Education, University of Arizona.
    http://bit.ly/2nC4TQp
  • Society for Industrial and Applied Mathematics (SIAM). (2016). Guidelines for Assessment and Instruction in Mathematical Modeling Education. Philadelphia, PA: SIAM. Accessed on 1 March 2017 from
    http://www.siam.org/reports/gaimme.php
  • Meyer, D. (2015). Missing the Promise of Mathematical Modeling.Mathematics Teacher,108(8), 578-583.
  • Wendt, T., & Murphy, K. (2016). Integrating Modeling Steps into the High School Curriculum. Mathematics Teacher, 109(5), 374-379.
  • Anhalt, C. O., & Cortez, R. (2015). Mathematical Modeling: A Structured Process.Mathematics Teacher,108(6), 446-452.

Resources

  • Zbiek, Rose M. (2016, October.) IGNITE: Teaching for Learning Mathematical Modeling. Presentation at the NCTM Regional Conference and Exposition, Philadelphia, PA. Accessed 1 March 2017 from
    https://www.youtube.com/watch?v=gZJLZ-iEUys

Learning Opportunities

  • Session 1 (Face to Face) – Math and Science Together
    A model to guide thinking about planning for instruction, while teaching and reflecting on your teaching.
    • Your current model – a diagram that represents a model of the decisions you make as a teacher when planning for lessons, teaching lessons, and then reflecting on your success regarding the impact you have on the learner.
    • Introduce the teacher decision-making article with a focus on the diagram on page 8.
    • Models and modeling

    Modeling in the Context of Mathematics
    Considering the general concept of modeling

    • Examine the conceptual category fromCCSSM and identify what you notice about the concept of modeling and what you are wondering.

    Examples of successful modeling: The Cruise Ship Task

    • Solve and discuss the cruise ship task
    • Classify the task using the GAIMME report
    • Use the GAIMME introduction to discuss and debrief the task
    • Practitioner articles?

    Modeling in Mathematics

    • Show and discuss the Zbiek IGNITE talk.
    • Discuss the distinction between“modeling with mathematics” and “mathematical modeling.”
    • “When students are modeling they need to be making genuine choices.” Present the quote and have a discussion on what we might mean by this.
    • Explore connections between characteristics of modeling tasks, content goals, and aspects of the modeling cycle.
    • Summary discussion: What criteria do we want to prioritize as we consider tasks with respect to modeling?
  • Session 2 (Online PLC)
    • Read GAIMME Report, chapters 1 and 3.
    • Read chapters 1 and 16 of Hirsch and Roth McDuffie (2016).
    • Read practitioner articles Meyer (2015), Anhalt & Cortez (2015), and Wendt & Murphy (2016).
    • Be prepared to discuss how the readings help to clarify the nature of a good mathematical modeling task and how we might plan for lessons that use those tasks.
  • Session 3 (Face to Face)
    Debrief the readings: What did you take away from each of the three types of readings (GAIMME report, APME research-based reports, practitioner articles)? What are you still wondering about related to mathematical modeling?
    • Why use modeling? What are the affordances for student learning?
    • Unpacking the modeling cycle: discussing characteristics of modeling tasks based on GAIMME and a closer read of CCSSM, progression
    • Distinction between mathematical modeling and modeling with mathematics

    Enact a three-act task/101qs task together and discuss how it connects to the characteristics.

    Discuss mathematics teaching practices that support modeling.

    Connecting modeling across mathematics and science
    Mixed Small Groups – Math and Science

    • What are common points between modeling between math and science in terms of student learning? How does it help the learner?
    • What are similarities and differences between modeling in math and science?
    • What are the similarities and differences between our assessing strategies?
  • Session 4 (Online PLC)
    • Produce a written summary of modeling in mathematics key points from Session 3 small-group discussions.
    • Read the CCSSM Progression document in Modeling and reflect.
    • Read GAIMME Appendix B on assessment.
    • Plan and teach a lesson on modeling, including a rigorous data collection component (check in with lesson plan and data collection instrument prior to teaching).
  • Session 5 (Face to Face)
    Work session focused on data analysis from taught lesson(s)
  • Session 6 (Online PLC)
    Write up documentation of lesson and evidence; prepare for public presentation.
  • Session 7 (Face to Face) – Poster Session: Results of Teaching a Modeling Lesson
    Final Reflection and Critique
    • What type of model did you use? What modeling strategy did you use?
    • How did you integrate it into the lesson?
    • What specifically did you want students to be doing during this lesson that told you it was successful?
    • What was some feedback from students and artifacts?
    • What would you change?

Submission Requirements

Submission Guidelines & Evaluation Criteria

To earn the micro-credential, you must receive a passing evaluation for Part 1 and 3 and a “Yes” for the artifacts submitted for Part 2.

Part 1. Overview Questions

Please provide responses from the following session questions:

  • Reflections on a recent lesson using the Teacher Decision Making Framework from Session 1:
  • Produce a written summary of modeling in mathematics key points from Session 3 small-group discussions.

Part 2. Work Examples/Artifacts

To earn this micro-credential, please attach your lesson plan which includes all of the following:

  • Connections to CCSSM modeling standard and other relevant content standards
  • Connection between your task and aspects of the GAIMME framework
  • Specific plans (so that someone else could read your plan and attachments and teach the lesson)
  • How you are going to assess what students learned
  • How you are going to measure the overall effectiveness of the lesson.
  • How you assess the impact on student learning (student assessments, student artifacts)
  • Reflective narrative of efforts and results

Part 3. Educator Reflection

Reflect on the effectiveness of the lesson from your perspective as a teacher.

  • How did your lesson represent aspects of mathematical modeling?
  • What instructional practices did you use to enact the modeling task?
  • What specifically did you want students to be doing during the lesson that would be indicators of success?
  • How did the student artifacts inform your practice?
  • What was some feedback from students?
  • What would you change?

Except where otherwise noted, this work is licensed under:
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
http://creativecommons.org/licenses/by-nc-nd/4.0/

Requirements

Download to access the requirements and scoring guide for this micro-credential.
How to prepare for and earn this micro-credential - in a downloadable PDF document

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