AP®/Advanced and Electives
Mathematics Training
16 DECEMBER, 2015
Sebastian Andino
Product Marketing
312.515.5602
Today’s Overview
– Larson and Stewart
• What sets them apart?
• Precalculus
• Calculus
– Calculus for AP®
Larson or Stewart? Which One and Why?
The approach each author takes is distinctly different. Almost every teacher
knows these authors and their approach, so this should be the first question
addressed.
Stewart emphasizes problem solving, the elegance of calculus, and conceptual
and verbal understanding along with skills.
Larson emphasizes skill building and believes that students will learn the
elegance and problem solving process by practicing skills.
Precalculus
Precalculus is a third or fourth year math course
that combines:
•
•
•
•
Functions
Trigonometry
Analytic geometry
Introduction to Calculus via instruction on Limits (in
most books).
• Statistics and probability (added to most higher ed
books because of the direction taken by high schools)
Larson
• Designed according to how
students learn math
(examples)
• Clear, easy to follow
method throughout
• Same pedagogy as
Larson’s middle- and highschool math programs,
easing transition to
Precalculus
Stewart
• Best choice for more
aspirational classes
• Written by best-selling
university Calculus author
• Focus on conceptual
understanding and its
mathematical precision
1. Which authors approach do you prefer, Larson or Stewart?
2. Do you cover limits?
If YES
“Limits” is shorthand for a chapter devoted to
the topics of Limits and content that
introduces students to calculus.
If NO
3. Would you like your students to use graphing calculators for all their exercises?
If YES
If NO
4. How much algebra do you need to review?
A lot – the students are weak in algebra
If not important, you can sell anything else
Precalculus with Limits,
3rd edition
Precalculus with Limits: AGA 7th
edition
Moderate
Minimal
For students; concise
For students; concise
Written to design; pedagogy;
side-by-side examples
Written to design; pedagogy;
side-by-side examples
Graphing Use
Optional
Required
Problem Sets
Basic skill-building to
challenging
Basic skill-building to
challenging
Algebra Review
Writing Style
Guided
Instruction
LarsonPrecalculus.com
• Larson
• Designed according to how
students learn math
(examples)
• Clear, easy to follow
method throughout
• Same pedagogy as
Larson’s middle- and highschool math programs,
easing transition to
Precalculus then Calculus
• Stewart
• Best choice for more
aspirational classes
• Written by best-selling
university Calculus author
• Focus on conceptual
understanding and its
mathematical precision
AB or BC?
For AP Calculus, the AB course is the most popular. The BC course is primarily
for students who are on a more advanced mathematics track, such as
engineering.
Single Variable or Complete?
BC Calculus is covered in both the Larson and Stewart Single Variable versions.
Our suggestion is to sample the full, complete version for BC, but either version
should work.
AP® Calculus
Which authors approach do you prefer, Larson or Stewart?
Does your course only cover single variable calculus, or do you also teach multivariable calculus?
If SINGLE VARIABLE only
If BOTH SINGLE VARIABLE & MULTIVARIABLE
AB
BC
What Does Early Transcendental Functions
Mean?
An early transcendental functions (ETF) approach simply describes when these
functions are taught. The traditional approach is teaching them at the point in
which they are used, making it more accessible.
With an ETF approach, these functions are taught earlier, which allows more
time to review for the AP exam.
AP® Calculus
Do you prefer to teach transcendental functions late or early in your course?
If LATE
If EARLY
Calculus: Graphical, Numerical, Algebraic
Finney, Demana, Waits, Kennedy, Bressoud
Pearson
What teachers like
What that
teachers
complain
More
teachers
like about
• It is aligned directly with AP®, no
extraneous content
by design.
several One
authors,
feelsconcise
• Written to
clearitand
cobbled
together
voice AND
with an AP® expert’s guidance
• It has a more conceptual approach
imprecise
• The mathematics is precise
and clear
• It is in the ETF sequence many
teachers prefer
not do to
much
align it with
• Publisher
A programdid
designed
aligntosquarely
withredesigned
the redesigned
curriculum
the
curriculum
framework
framework
Calculus for AP®
Larson and Battaglia
Table of Contents
P: Preparation for Calculus
1: Limits and Their Properties
2: Differentiation
3: Applications of Differentiation
4: Integration
5: Differential Equations
6: Applications of Integration
7: Integration Techniques, L’Hopital’s
Rule, and Improper Integrals
8: Infinite Series
9: Parametric Equations, Polar
Coordinates, and Vectors
AP® Calculus Course Redesign – Starts 2016-17
• What AP® students should know and be able to do is more clearly defined:
• Enduring Understandings
• Learning Objectives
• Essential Knowledge
• Courses should emphasize conceptual understanding through the
Mathematical Practices for AP® Calculus (MPACs)
• A few new topics to be covered:
• L’Hospital’s Rule will be included in AP® Calculus AB
• 3 new topics to be added to BC
• Exam changes
• Multiple-choice questions have four answers, not five
• Exam question have evolved to be more conceptual and this continues
• Changes on timing of multi-choice questions
Support for the AP® Student
Chapter Openers
Support for the AP® Student
Side-by-Side Examples
Chapter 2, Differentiation
Support for the AP® Student
Insights
Chapter 2, Differentiation
Support for the AP® Student
Algebra Review
Chapter 4, Integration
Support for the AP® Student
Calculus AP® – Exam Preparation Questions
Chapter 2, Differentiation
Support for the AP® Student
Mathematical Practices for AP® Calculus (MPACs)
Support for the AP® Student
Mathematical Practices for AP® Calculus (MPACs)
Chapter 4, Integration
Support for the AP® Student
End of Section Exercises
Section 2.2 QR code
Online AP® Support
LarsonCalculusforAP.com
•
•
•
CalcView – video solutions of selected
exercises
CalcChat – worked out solutions and live
tutoring
Three-dimensional graphs, lecture videos,
example grading to free-response AP®
questions, and more!
AP® Teacher Support
Teacher’s Edition
Larson Programs – A Changing of the Guard
2014 – 2015 Sales Year
2015 – 2016 Sales Year
NEW Calculus 10/e AP® Update
Calculus for AP®, 1st edition