APAdvanced and Electives Mathematics Training 16 DECEMBER 2015

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 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, 3 rd edition Precalculus with Limits: AGA 7 th edition Moderate Minimal For students; concise Written to design; pedagogy; side-by-side examples Graphing Use Optional Required Problem Sets Basic skill-building to challenging Algebra Review Writing Style Guided Instruction

Larson. Precalculus. 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 teachers complain More teachers like about • It is aligned directly with AP®, no extraneous content by design. several One authors, feels • Written to clearitand concise 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 much tosquarely align it with • Publisher A programdid designed to align withredesigned the redesigned curriculum the curriculum 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 Larson. Calculusfor. AP. com • • • Calc. View – video solutions of selected exercises Calc. Chat – 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®, 1 st edition