1 / 34

In-Service Teacher Education: US

In-Service Teacher Education: US. Deborah Hughes Hallett Department of Mathematics, University of Arizona Harvard Kennedy School. The US Context. Teachers are (too) busy keeping up with everyday requirements (often non-academic)

zion
Download Presentation

In-Service Teacher Education: US

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. In-Service Teacher Education: US Deborah Hughes Hallett Department of Mathematics, University of Arizona Harvard Kennedy School

  2. The US Context • Teachers are (too) busy keeping up with everyday requirements (often non-academic) • Curriculum is often not the teachers’ own; they often work largely from a prescribed text • During the school year, in-service sessions that are immediately useful to teachers have the most impact

  3. What Works Best? • Providing copies of materials that teachers can easily copy or adapt • Illustrating pedagogical techniques that can be used in a classroom right away (don’t need equipment, further training, etc) • Exhibiting support for policies that teachers want to persuade administrators or parents • Answers to “landscape questions”: How topics fit together, where mathematics is applied

  4. http://www.teachersasscholars.org/ Some Organizations offering In-Service http://crr.math.arizona.edu/

  5. Organizations • Organizations may be private NGOs (Teachers as Scholars) or • Paid for by school districts or grants • Based at a university (CRR and IM&E) • Offer in-service teacher education to schools that want it or pay for it; not mandated • States and school districts may also have their own teacher education staff • May offer mandatory education sessions conducted either by their own staff or by outsides

  6. Scheduling • During school year: • One or two day sessions, or • 2 hours a night once a week for several weeks • Often not paid but usually give PDPs (professional development points, ) • During summers: • One day to one month, more hours per day • Often give college credit or count toward master’s degree

  7. Types of Problems and Activities Teachers Have Found Useful, and Why First, what is the mindset of the students?

  8. Student Beliefs About Mathematics:Harvard Undergraduates (about 1990) Answer choices for each question: Disagree 1 2 3 4 5 Agree • A well-written problem makes it clear what method to use to solve it • Calculus students: 4.1, precalculus: 4.6 • If you can’t do a homework problem, you should be able to find a worked example in the text that will show you how • Calculus students: 4.1, precalculus: 4.7 • Review problems should have the section of the text they come from listed after them in parentheses • Calculus students: 4.2, precalculus: 4.8

  9. Calculus

  10. Rates and Concavity From PrecalculusbtConnally, et al, Wiley2011

  11. Calculus: Derivatives From Calculus by Hughes Hallett, Gleason, McCallum, et al, Wiley 2013.

  12. Application to Medicine: Exponential Decay & Separable DesDavid Sloane MD (Harvard Medical School)

  13. Distance-Velocity Functions: Integrals-Derivatives From TAS Seminar, Deb Hughes Hallett

  14. Scatter Plots(middle school)

  15. Famous Personalities SCATTER PLOT Estimated age Actual age

  16. Guess how old? Taylor Lautner

  17. How Old? • Miley Cyrus

  18. How old? • Barrack Obama

  19. How old? • Stefani Germanotta • a.k.a Lady Gaga

  20. Actual Ages…

  21. Graphs and Algebra(middle and high school)

  22. Basic: Functions and Graphs From Functions Modeling Change by Connally, Hughes Hallett, et al

  23. Common Core State Standards:Functions and Interpretation From Algebra by McCallum, Connally, Hughes Hallett, et al

  24. Common Core State Standards: Functions and Interpretation From Algebra by McCallum, Connally, Hughes Hallett, et al

  25. Structure from the Viewpoint of Other Disciplines: Economics and Biology

  26. Economists and Algebraic Structure: Consumer Price Index (CPI) Data is as follows:

  27. Economists’ View of the CPI Data Converting to linear form enables an answer the question: “How fast has the CPI grown over last century?”

  28. Now Equation Has Linear Form: Variables are y = ln(CPI) and x = Year

  29. Biologists’ Use of Algebraic Structure • V0 is initial velocity of chemical reaction • [S]0is initial concentration of substrate • Vmax, KMare constants Michaelis-Menten Equation How Do We Know If a Reaction Follows Michaelis-Menten?

  30. Does a Chemical Reaction Follow Michaelis-Menten? Put in linear form, with variables 1/V0 and 1/[S]0

  31. Now Equation Has Linear Form: Variables are y = 1/V0and x = 1/[S]0

  32. What Should Calculus Preparation Look Like? • Algebra: Develop insight into the structure of expressions; achieve fluency through reasoning • Functions and Graphs: Qualitative behavior, parameters, families • Modeling: Create a model; interpret results in context • Stamina and Strategy: Make repeated attempts, try multiple approaches. Choose the best tools, graphs, algebra, technology

  33. Functions and Graphs: Interpretation From Functions Modeling Change by Connally, Hughes Hallett, et al

More Related