CPED 6370 & 6367
Instructors
C. Pyke, T. Sikorski, & D. Ullman
About the Course
This course is designed to provide experiences aimed at developing a deeper understanding of what it means to “do” mathematics and science. The experiences will include an examination of historical perspectives, personal engagement in math and science tasks, and consideration of research on the teaching of “practices” as described in today’s curriculum standards (see Common Core Math Standards and Next Generation Science Standards). To better focus the course the topic of modeling has been selected. This will naturally lend itself to opportunities to compare and contrast modeling with mathematics and modeling in the sciences. The course is also enacting curricular changes supported by a National Science Foundation (NSF) project aimed at improving the disciplinary focus of STEM teacher preparation (*see more detail)
Course Goals
- Appreciate history as a source for enriching understanding of the practices of math and science.
- Develop an understanding of how practices such as modeling function in similar and different ways in mathematics and science.
- Participate in a collaborative problem solving/inquiry experience.
- Prepare and present a solution to a mathematics problem or problem set.
- Improve understanding of standards for practices (e.g., modeling) in school mathematics and science.
- Examine assessments of practices (e.g., modeling) in school mathematics and science.
- Engage in critical discussion of practices as curricular goals using knowledge of research results in the teaching and learning of mathematics and science.
Course Outline
Part I
Historical perspectives on doing math and science, problem solving and modeling.
Historical perspective on inquiry & modeling in science
Historical perspective on problem solving & modeling in mathematics
Student presentations historical perspectives on modeling in math and science
Part II
Engagement in math problem solving with modeling (learning by doing, and reflecting)
Work on Julia Roberston Math Festival “Split a Pile” problems by Joshua Zucker
Present selected results from working the problem set
Part III
Study the curricular goals for modeling in school math and science curriculum
Understand evolution of “modeling” in Math and Science Ed history (precursors, courses, texts, etc)
Understand Students’ Modeling (Research from Math and Science Ed –)
Understand Modeling Standards
Understand Assessment of Modeling
Student Learning and Designs for Modeling Instruction
Course Products
Historical paper/presentations
Identify a significant problem, model, proof, experiment, etc. in the history of mathematics or science that enables examination of the primary source (or translation). Consult with the instructor on the appropriateness of the source. Prepare a paper that (a) provides some historical context for the problem, (b) describes or summaries the work, and (c) highlight the role of modeling in the production or presentation of the work. In addition, prepare a 15 min presentation. Presentations of the main ideas should include demonstrations, activities, or brief lessons to illustrate how modeling was a part of the mathematics or science created.
Journal of Modeling with Math Experience
4 journal entries of at least a page describing your engagement in the class problem solving activity including a discussion of your ideas/what you learned.
Mathematics Problem Set and Present Findings
Prepare answers to the questions in the “Split a Pile” problem set and
Present selected findings.
Position Paper on Modeling with Math and Science (30%)
Write a brief paper that outlines your views or position on teaching modeling in schools.
Prompts
- What is math modeling, how is it different from modeling in science.
- Describe and instructional design for teaching math modeling
- Present an assessment of modeling, including a rubric and anchor papers
- When did the first modeling texts appear and who where they written for?
- What is the state/status of modeling today? Is it growing in importance? Why or why not?
Course Schedule
| Date/Session | Topic | Readings/Videos/Activities: |
| Session 1
|
Goal: Introductions & Advance Org for course – a look an practices in video
Introductions and Course Overview Discussion of Research Component With exemplar of a “Video Case” Discussion Questions (see handout) -Play Math Games and think about modeling in math. -Science video that motivates thinking about science modeling? |
Sean’s Numbers (10min)
http://deepblue.lib.umich.edu/handle/2027.42/65013 Split a Pile -Play game 1 http://juliarobinsonmathfestival.org/problems/SplitPile.pdf Light Model (5min) https://www.teachingchannel.org/videos/fifth-grade-light-lesson |
| HW | Begin Historical Problem Paper: Identify sources and consult with instructor.
Complete Reading and assignment for 1/20 |
|
| Session 2
(Dr. Sikorski Leads Class) |
Goal: Explore doing science from a historical perspective.
Making sense of doing science using a primary source document
|
Reading:
Read the Franklin Letter #2 before class (pg. 10-18), and come to class with a 3-4 sentence synopsis of the Letter and one question about its contents. |
| HW | Work on Historical Problem Paper
Complete Readings for 1/27 |
|
| Session 3
|
Goal: Explore doing math from a historical perspective.
Making sense of doing math with a primary source document. - Is there something we might call modeling being done? |
Readings:
1. Reading Networks and Spanning Trees and make note of questions about it contents with special attention to the Borukvka section. http://www.cs.nmsu.edu/historical-projects/Projects/25620140928trees.pdf 2. Browse Boruvka’s original paper for style and form. Compare to translated version in reading #1 http://dml.cz/bitstream/handle/10338.dmlcz/500114/Boruvka_01-0000-6_1.pdf |
| HW | Complete Historical Problem Paper and Prepare Presentation | |
| Date/Session | Topic | Readings/Videos/Activities: |
| Session 4
|
Goal: Explore historical perspectives on doing math and science.
Student Presentations |
|
| HW | play the split a pile games | |
| Sessions 5
|
Goal: Engage in Mathematics Problem Solving/Modeling | |
| HW | HW – Journal entry and readings or problems TBD based on class progress. | |
| Session 6
|
Goal: Engage in Mathematics Problem Solving/Modeling | |
| HW | Journal entry and readings or problems TBD based on class progress. | |
| Session 7 | Goal: Engage in Mathematics Problem Solving/Modeling | |
| HW | Journal entry and readings or problems TBD based on class progress. | |
| Session 8
|
Goal: Engage in Mathematics Problem Solving/Modeling | |
| HW | Journal entry and preparation of solutions to problem set and preparation of presentation of selected results. | |
| No Class | Spring Break | |
| Session 9
|
Goal: Students Prepare and Present solutions to problems and reflect on role of modeling.
Student presentations |
|
| Date/Session | Topic | Readings/Videos/Activities: |
| HW | Review journal entries and summarize ideas about doing math and modeling | |
| Session 10
|
Goal: Reflect on doing math experience.
Finish problem presentations if needed |
|
| HW | HW – Readings for 3/31 | |
| Session 11
|
Goal: Develop understanding of modeling standards in school science
|
Readings (page #s needed):
History of Science Ed Reading Benchmarks NRC Science Ed Standards NGSS Science Modeling in College |
| HW | Readings for 4/8 | |
| Session 12
|
Goal: Develop understanding of modeling standard in school mathematics | Readings (page #s needed)
History of Math Ed Reading (Heibert concepts and procedure - or earlier) Curric and Eval Standards Benchmarks P&S 2000 Adding it-uP Common Core Middle & HS Math Modeling in College |
| HW | HW - Complete sample items | |
| Session 13
|
Goal: Explore issues in assessing modeling in math and science
|
Common Core aligned items
NGSS aligned items |
| Session 14 | Goal: Ideas for the designing lessons and units to teach practices/modeling
Discussion about instructional design |
Video Examples |
| Submit Position Paper | ||
Reading List
Books
Adding it Up: Helping Children Learn Mathematics (2001), NRC
Read it online at - http://www.nap.edu/books/0309069955/html/index.html
Readings in the History of Mathematics Education (1970) NCTM
http://www.eric.ed.gov:80/PDFS/ED038316.pdf
DeBoer, G. (1991). A history of ideas in science education: Implications for practice. New York, NY: Teachers College Press.
Science Teaching: The Role of History and Philosophy of Science
http://books.google.com/books/about/Science_Teaching.html?id=qnwzRqh5jFMC
Selected Web Sites and Standards Documents
NGSS
http://www.nextgenscience.org/next-generation-science-standards
The Common Core Standards Initiative
http://www.corestandards.org/
Principles and Standards for School Mathematics. (2000). NCTM
Read online at - http://standards.nctm.org/document/index.htm
Benchmarks for Science Literacy. (1993). AAAS
Read it online at - http://www.project2061.org/tools/benchol/bolframe.htm
Curriculum and Evaluation Standards for School Mathematics (1989). NCTM
Read online with your membership at nctm.org
Assessment Standards for School Mathematics (1995). NCTM
Read online with your membership at nctm.org
Professional Standards for School Mathematics (1991). NCTM
Read online with your membership at nctm.org
Other related materials
http://www.ams.org/samplings/feature-column/fc-2012-09
http://dartmed.dartmouth.edu/fall00/pdf/Heart_Failure.pdf
http://plato.stanford.edu/entries/models-science/
This site is going to be helpful for math people.
http://www.cs.nmsu.edu/historical-projects/
Contrasting Problems involving modeling
http://www.mathmodels.org/problems/probview.php?probnum=20027
http://juliarobinsonmathfestival.org/problems/SplitPile.pdf
http://www.comap.com/undergraduate/contests/mcm/contests/2014/problems/ICM_2014.pdf
Franklin Reading
https://archive.org/details/experimentsobser00fran
Paper
http://www.cs.nmsu.edu/historical-projects/Papers/HPM2012-projects-workshop.pdf
Student version
http://www.cs.nmsu.edu/historical-projects/Projects/25420120346Euclid-april-2012.pdf
The link below should get us close to the original document
Networks/Trees Student version
http://www.cs.nmsu.edu/historical-projects/Projects/25620140928trees.pdf
notes to instructor
http://www.cs.nmsu.edu/historical-projects/Blog/trees.temp.pdf
Boruvka’s original paper
http://dml.cz/bitstream/handle/10338.dmlcz/500114/Boruvka_01-0000-6_1.pdf
