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John Losse began teaching mathematics at Government Secondary School in Katsina, Nigeria. More recently he
taught at Scottsdale Community College in Arizona. He has assisted Scottsdale-area high schools with their AP* Calculus programs
since 1991. He holds an MS in Mathematics from the University of North Carolina at Chapel Hill, and has been active in applications
of technology to mathematics teaching, including graphing calculators, the CBL, and computer algebra systems. He has served
as a reader of the AP* Calculus Exam and has conducted workshops and institutes for AP* teachers for the past 12 years.
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During our week at Stanford we will look all of the topics in the AB curriculum including
limits, continuity, derivatives, applications of the derivative, local linearity, techniques of integration, applications
of integration, The Fundamental Theorem of Calculus, natural exponentials and logarithms, differential equations and slope
fields. We will explore appropriate uses of graphing calculators and computer technology. As your institute leader, I will
share my experiences and insights as a teacher and reader of recent AP* Calculus exams. Whether you are a new or experienced
calculus teacher, you will see that Calculus makes PERFECT sense - it is just a logical extension of things you and your students
already know!
Whether you stay on campus or not, you will find many opportunities to learn and share with other calculus
teachers, both inside and outside the scheduled sessions.
What follows is a tentative daily schedule for
our institute. Experience shows that it is better to be flexible with the schedule - go off on tangents, if you like. After
all, it's calculus!
Monday
Introductions. Tell us about yourself and what
you hope to get out of this week.
The Intermediate Value Theorem
Introduction to the
derivative
Meaning of difference quotient and derivative.
Average rate of change (AROC), and instantaneous rate of change (IROC)
Importance of units of measure
The derivative at a
point. Various formulations of the derivative.
The derivative as a
function
Using technology to see the relation between f and f'
Rules
for taking the derivative. The chain rule. Using the definition directly
The second derivative and interpretations
f and f ' and f '' , especially graphically
Extrema
and the AP* policy on sign charts to justify maxima and minim
The many faces of concavity
Optimization. Global max and min on a closed interval - considering all the candidates
Local linearity. The tangent line approximation and errors
Rolle's Theorem and the Mean Value Theorem
Inverse
functions and their derivatives
Definition of the definite integral as the limit of Riemann sums
The definite integral as an accumulator. The definite integral of a rate of change is total change.
The average value of
a function
Left, right, midpoint and trapezoidal sums
and associated errors
The Fundamental Theorem(s) of Calculus
Functions defined in terms of a definite integral
Antiderivatives and their computation, including substitution of variable.
Differential Equations. Analytic solutions. Initial
conditions.
Slope Fields - What they are and what is expected
Other applications of integration and antiderivatives
Differential equations for growth, including dP/dt = kP(L-P)
Teaching resources available from the internet and elsewhere.
Distribution of resources from publishers as well as the CD with our own stuff!
Graphing Calculator: We
will be using the TI-84 for some demonstrations, and will be distributing some programs for it.
Idea and Material Sharing Encouraged: If you have handouts or
other materials you would be willing to share, please bring them (as files too, if possible). Have you found good internet
resources? Bring the url's. We will be creating a CD with these for distribution on the last day.
a
*College Board, AP, Advanced Placement Program, and the acorn logo are registered
trademarks of the College Board. Used with permission.
