Download - In-Service Teacher Education: US
In-Service Teacher Education: US
Deborah Hughes HallettDepartment of Mathematics, University of Arizona
Harvard Kennedy School
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
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
http://www.teachersasscholars.org/
http://crr.math.arizona.edu/
Some Organizations offering In-Service
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
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
Types of Problems and Activities Teachers Have Found Useful,
and Why
First, what is the mindset of the students?
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
Calculus
Rates and Concavity
From Precalculus bt Connally, et al, Wiley2011
Calculus: Derivatives
From Calculus by Hughes Hallett, Gleason, McCallum, et al, Wiley 2013.
Application to Medicine: Exponential Decay & Separable DesDavid Sloane MD (Harvard Medical School)
Distance-Velocity Functions: Integrals-Derivatives
From TAS Seminar, Deb Hughes Hallett
Scatter Plots(middle school)
Famous Personalities
SCATTER PLOT•Estimated age
•Actual age
Guess how old?Taylor Lautner
How Old?• Miley Cyrus
How old?• Barrack Obama
How old?• Stefani Germanotta• a.k.a Lady Gaga
Actual Ages…
Graphs and Algebra(middle and high school)
Basic: Functions and Graphs
From Functions Modeling Change by Connally, Hughes Hallett, et al
Common Core State Standards:
Functions and Interpretation
From Algebra by McCallum, Connally, Hughes Hallett, et al
Common Core State Standards:
Functions and Interpretation
From Algebra by McCallum, Connally, Hughes Hallett, et al
Structure from the Viewpoint of Other Disciplines: Economics
and Biology
Economists and Algebraic Structure:
y = 8.3132e0.0326x
R² = 0.9185
0
50
100
150
200
250
0 20 40 60 80 100
CPI
Years since 1913
CPI, with 1982-84 def ined to be 100
Consumer Price Index (CPI) Data is as follows:
y = 0.0325t + 2.1214
0123456
0 50 100
y, ln
(CPI
)
t, years since 1913
Economists’ View of the CPI DataConverting to linear form enables an answer the question:“How fast has the CPI grown over last century?”
Now Equation Has Linear Form:
Variables are y = ln(CPI) and x = Year
bmxy
CPI
1214.2Year0325.0)ln(
Biologists’ Use of Algebraic Structure
• V0 is initial velocity of chemical reaction• [S]0 is initial concentration of substrate• Vmax, KM are constants
0
0max0 ][
][SKSV
Vm
Michaelis-Menten Equation
How Do We Know If a Reaction Follows Michaelis-Menten?
Does a Chemical Reaction Follow Michaelis-Menten?
Put in linear form, with variables 1/V0 and 1/[S]0
max0max0
0max
0
0
1][
11
][][1
VSVK
V
SVSK
V
M
M
Now Equation Has Linear Form:
bmxy
VSVK
VM
max0max0
1][
11
Variables are y = 1/V0 and x = 1/[S]0
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
Functions and Graphs: Interpretation
From Functions Modeling Change by Connally, Hughes Hallett, et al