Barbara Kane Patrick Gierut J. Sterling Morton East High School Cicero, IL Morton East High School...

Barbara KanePatrick Gierut

Making AP Calculus as Easy as 3,4,5

J. Sterling Morton East High SchoolCicero, IL

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as easy as 3, 4, 5

Barbara Kane

Introduce ourselves. Barbara Kane 17 years teaching, taught AB Calculus for 10 years, BC Calculus for 1 year. AP Reader for 2 years. All years at Morton East.Pat Gierut 10 years teacher, taught AB Calculus for 2 years, PreCalculus for 8 years. All years at Morton East.

Collaboration & Support

Vertical Teaming

Calculus at Morton Today

2013-2014

Everyone Takes the AP Test

2004-2005

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as easy as 3, 4, 5Ten Year Timeline

Barbara Kane

In spring 2004, the AP Calculus teacher was looking to spend more time with family and relinquished teaching Calculus. THis opened up the opportunity for teaching Calculus. I took up the opportunity. I got one section of 20 students and another teacher had one section of 15 students. I was handed a binder (bring binder) of curriculum map, textbook, and answer solutions. Over the summer, I planned out what I best thought students would need to know. I taught way too much...L'Hopital, Trig Substitution, Arc Length. Limited collaboration with the other teacher, I had about 2 weeks left to review with students. I didn't know any better and told the kids all year that they all take the AP test (wasn't a school policy, but I thought they were supposed to). 3 years later, taking the Test was mandatory for all AP classes. 2 Calc teachers, but not a collaborative team. Then, 4 years later, I was the only AP Calc teacher. Drop AP Class was ok until about 2006.After that needed parent conference, now everyone must stay.

Barbara Kane

Collaboration & SupportPat -- At this point I began teaching at ME and by chance Barb had a geo class during my prep and since I was teaching geo I would sit in on her classes every day. Not only did i learn a lot about barbs teaching style, moving from activity to activity, interacting with students, but we also would talk a lot about how to best teach the students/subject. since we had this collaborative relationship from the beginning, it was natural when i was brought on board to teach calculus.

Barbara Kane

Barbara -- In 2008, other Calc teacher retired & I was team of 1. Communicated more with PreCalc teachers about expectations for Calculus students (proper notation, explaining answers); common language & terminologyAP Vertical Team workshopAP Calculus Workshop together at Plainfield in summer 2011.MathletesCRISS strategies.Find the Truesdale video.PLTs began in 2011. More vertical team discussion btn Adv Alg & PreCalc & Calc.

Barbara Kane

Barbara -- 2012-13 school year brought Morton East 4 sections of Calculus, 82 students, and Pat on to the Calculus team. We now have a Calculus team of 2. We spent the summer of 2012 discussing the details of the lessons through 1st semester. I organized my files and lessons so that they could be understood by Pat. We planned on teaching same lesson, same day, same way, same homework.Pat --as far as time commitment, barb and i met several times in the summerin order to go over the AB curriculum. we met and still meet every morning and afternoon to go over the day's lesson the next day's lesson and any questions about HW that i may have or to try and anticipate student questions or points of difficulty (past knowledge that students will need to relearn), writing rubrics. grading and regrading for consistency. taking a lot of time to thoroughly scrutinize student work so that they seek perfectioin on the AP exam. they are learning to improve themselves not just for a class grade. Barbara -- Since 2012-13 gave good data, we kept going with same style this year. But adjusting to things like retakes and standards-based grading system. We discuss every decision that is made together. With BC, I am a team of 1 again, but BC follows ABs course expectations.

Daily Homework

AP Review Sessions

Apply skills to new

situations

Summer Work

AP Calculus…as easy as 3,4,5Expectations of Students

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as easy as 3, 4, 5

Barbara Kane

MathletesGroups -- presenting homework problems, participate actively.

Summer WorkExpectations of Students

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as easy as 3, 4, 5

Barbara Kane

Summer work is for practice of concepts that they already know( i.e. unit circle, simplify expressions, solve equations, wirte equations of lines, find limits)Ask participants to brainstsorm 3 items that they would want students to know on 1st day of Calculus

Summer WorkSummer WorkExpectations of Students

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as easy as 3, 4, 5

Summer WorkExpectations of Students

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as easy as 3, 4, 5

Apply Skills to New SituationsSkill: Chain Rule

New Situation: Apply knowledge of the chain rule using a table of values instead of functions.

x

0 1 1 5.6 8.2

1 3.75 –4.2 –7.9 –5.3

Suppose that the functions f and g and their derivatives with respect to have the following values at and . If , evaluate .

Expectations of StudentsM

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as easy as 3, 4, 5

Barbara Kane

discuss having to read the question in order to figure out what skill needed to solve the problem.

Skill: Definite Integral, Increasing/Decreasing, Average Value, Average Rate of Change

Apply Skills to New SituationsExpectations of Students

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as easy as 3, 4, 5

AB Review SessionsDATE Time Type of Test Length of Test

Thurs, March 20 3pm-5pmM/C Non-Calculator 55 min

(plus 60min discussion)Sat, March 22 8am-10am

Thurs, March 27 3pm-5pmM/C Calculator 50 min

(plus 60min discussion)Sat, March 29 8am-10am

Thurs, April 10 3pm-5pmFRQ Calculator 45 min

(plus 60min discussion)Sat, April 12 8am-10am

Thurs, April 17 3pm-5pm FRQ Non-Calculator 45 min(plus 60min discussion)

Wed, April 238am-9:30am

M/C Calculator 50 min(plus 40min discussion)9:30am-11am

Sat, April 26 8am-10am FRQ Non-Calculator 45 min(plus 60min discussion)


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as easy as 3, 4, 5

Barbara Kane

viewed as students make it mandatory. We hold the expectation and then kids rise to the expectation. Add in the % of kids who came to these.

BC Review SessionsDATE Time Type of Test Length of Test

Sat, March 2210am-12pm

M/C Non-Calculator 55 min(plus 60min discussion)12pm-2pm

Sat, March 2910am-12pm

M/C Calculator 50 min(plus 60min discussion)12pm-2pm

Sat, April 1210am-12pm

FRQ Calculator 45 min(plus 60min discussion)12pm-2pm

Wed, April 238am-9:30am

M/C Calculator 50 min(plus 40min discussion)9:30am-11am

Sat, April 2610am-12pm

FRQ Non-Calculator 45 min(plus 60min discussion)12pm-2pm

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as easy as 3, 4, 5Expectations of Students

Daily Homework(Notation, Notation, Notation)


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as easy as 3, 4, 5

Barbara Kane

Remind 101Break here for questions from audience

Teach Calculus & prepare for

AP Test

Unit/Year Schedules

Consistent Teaching

Teacher Availability

AP Calculus…as easy as 3,4,5M

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Expectations of Ourselves

Teacher Availability

Tutoring/Homework Help: Before & After School every day

AP Review Sessions: After School & Saturdays

Collegial Support: Before & After School, Lunch/Prep Time, Weekends, Summer

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as easy as 3, 4, 5Expectations of Ourselves

Consistent Teaching: Planning

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as easy as 3, 4, 5Expectations of Ourselves

Consistent Teaching: RubricsQUESTION: Find the volume of the solid formed by revolving the region bounded by the graphs of and about the x-axis. SOLUTION:

Volume = 1.324

Score Qualifications0 No work or washer method never used or

used incorrectly1 Outer radius incorrect, limits incorrect2 Inner radius incorrect3 Error in computation. (AP-style answer)4 Error in notation.5 Proper notation used throughout problem.

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as easy as 3, 4, 5

Barbara Kane

Rubrics; getting together to grade; going over grades; looking at students anaswers to check for consistency; rubrics helped in process

Consistent Teaching: Strategies

In Calculus, everything comes in 3’s• AP-Style Answer

• Continuity • Differentiability• Derivatives• Riemann Sums• Value Theorems• Critical Points• Volume• BC Topics

Expectations of OurselvesM

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as easy as 3, 4, 5

Barbara Kane

Handout for the audience with the details of these items.

Unit/Year SchedulesExpectations of Ourselves

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as easy as 3, 4, 5

Barbara Kane

no surprises; students know expectations for the year/unit; plann ahead for students and teachers

Teach Calculus & Prepare for the AP TestExpectations of Ourselves

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as easy as 3, 4, 5

Barbara Kane

teachers need to put in time and effort to do extra review. Planning a balance btn material and test prep. Above & beyond classtime to fit in lots of review. Review taken seriously b/c of timing on their own.Break for audience questions here.

Growing the Program

AP Calculus

PreCalculus

Adv Alg

Geometry

Algebra (8th grade)

AP Calculus

PreCalculus

Summer Adv Alg

Geometry

Algebra

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as easy as 3, 4, 5

Math Course Sequences for AP Calculus

Barbara Kane

Summer AdvAlg was originally called Independent Study in Adv Alg, began in summer 2003. Enrollment by teacher recommendation only and was free for students. Following years were not free. Changed to student choice and for the past 5 years has been free from grant $. THis year $25 fee for kids.

Barbara Kane

Summer AdvAlg was 1st based on recommendations, then based on student choice. Maybe in 2007-2008 school year...so that correlates with the 2010 data

Growing the Program

School Year

# Students in Calculus

2013-14 97

2012-13 82

2011-12 64

2010-11 41

2009-10 38

2008-09 49

2007-08 40

2006-07 29

2005-06 32

2004-05 25

36 BC

61 ABAP Calculus

PreCalculus

Summer Adv Alg

Geometry

Algebra

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as easy as 3, 4, 5

Effect on the # of AP Calculus Students

AP Calculus

PreCalculus

Adv Alg

Summer Geometry

Algebra

AP Calculus

PreCalculus

Summer Adv Alg

Geometry

Algebra

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as easy as 3, 4, 5

Additional Course Sequence for Summer 2013 & 2014

Growing the Program

• Unit Circle/Trig Review

• Rational Expressions (including factoring)

• Solving/Simplifying Logs/Exp

• Solving/Simplifying Polynomials

• Calculator Usage (graphing functions, solving equations, etc)

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as easy as 3, 4, 5

ABBoot Camp

Barbara Kane

Developed b/c we wanted to best prepare students for start of Calclulus and best prepare them for understanding summer work. Help kids to become more vested into the summer work & course.

• Limits & Continuity

• Parametric Functions

• Vectors

• Polar Functions

• Partial Fractions

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as easy as 3, 4, 5

BC

Boot Camp

Barbara Kane

to free up more time in school year for BC topics and make their skills on these topics stronger.

AP Calculus

PreCalculus

Math 2/3

Summer Math 2

Math 1

AP Calculus

PreCalculus

Math 2/3

Math 1/2

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as easy as 3, 4, 5

CCSS Integrated Math Course Sequencesfor AP Calculus

The Future

Barbara Kane

new structure may/may not effect #s for Calculus as well as content for Calculus.Break for audience questions

2005 2006 2007 2008 2009 2010 2011 2012 20130

10

20

30

40

50

60

70

80

90

Score 5Score 4Score 3Score 2Score 1

Years

# of

stu

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AP

Calc

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as easy as 3, 4, 5

AP Calculus AB Scores from 2005 to 2013

Avg Score: 3.427

Global Avg: 2.96

3 or Higher: 75.61%

Avg Score: 1.880Global Avg: 2.94

3 or Higher: 20%

Data

Particle

Motion

Area & Volume

Modelin

g Numeric

ally/A

nalytica

lly

Modelin

g w/D

iff Eq

Graphica

l Analy

sis of F

,F',FT

C01234567

2010201120122013

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as easy as 3, 4, 5

AP Instructional Planning ReportData

Barbara Kane

Review days on specific topics based on feedback from the students. Based upon data, we focused more on graphical analysis of f,f', ftc and particle motion. We will highlight more topic specific days.

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as easy as 3, 4, 5

AP Instructional Planning Report 2013Data

Lowest 4th Second 4th Third 4th Highest 4th0

5

10

15

20

25

30

35

40

45

Multiple-Choice

2010201120122013

% o

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as easy as 3, 4, 5


Lowest 4th Second 4th Third 4th Highest 4th0

5

10

15

20

25

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35

40

45

Free-Response

2010201120122013

% o

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as easy as 3, 4, 5


Barbara Kane

this data makes us happy.Questions from participants about this data?

BC Calculus

The Birth of BC

Calculus Teacher

Student Interest

PreCalc Teachers

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as easy as 3, 4, 5

Barbara Kane

Student Interest--Mathletes expressed interest in doing BC. Andrew Franco in particular. Student choice to sign up for BC or AB, 55 student chose BC, 65 students chose AB. End of year, 36 BC, 61 AB.

Barbara Kane

PreCalc Teachers -- asked & advised students on which course they were going to chose. Prepared students for the expectations of the BC course. Told students about self-teaching during the summer required to learn about limits/continuity, polar, parametric, partial fractions. They fit in some lessons at the end of the year about polar, parametric, partial fractions.

Barbara Kane

Students wanted the course, so I asked admins to run it. Encouraged admins to do so just like AB, based upon student choice, so this made 2 sections. But for both AB & BC, students must have passed PreCalculus. Students were given BC summer work -- limits & continuity, polar functions, parametric functions, partial fractions, and vectors--to self-teach.

Attended College Board AP Summer Institute with Ruth Dover (IMSA)• Arc Length, Parametrics, Vectors• L’Hôpital’s Rule, Improper Integrals• Sequences & Series• Convergence of Series• Taylor Series• Euler’s Method• Differential Equations, Logistic Graphs• Polar graphs

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as easy as 3, 4, 5

1st StepsBC Calculus

Planned out the schedule for the year

• Ends 1st week of schoolChapter 2Limits &

Continuity• Includes Vectors, Parametric

& Polar Functions• Ends early October

Chapter 3 Derivatives

• Ends early NovemberChapter 4

Applications of Derivatives

• Includes integration by parts, partial fractions

• Ends mid-December

Chapter 5 Definite Integral

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as easy as 3, 4, 5


• Includes Euler’s method & Logistic Growth

• Ends January, before Finals

Chapter 6Slope Fields

• Includes polar curves, lengths of curves, parametric curves, distance traveled in vector

• Ends mid-February

Chapter 7 Applications of

Definite Integrals

• Ends late-February

Chapter 8 L’Hôpital’s Rule &

Improper Integrals

• Ends late-MarchChapter 9 Infinite Series

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Planning Lessons

Guided Notes

Wolfram Demonstrations

Videos & Website

Resources

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Picking Up SpeedBC Calculus

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as easy as 3, 4, 5

Guided NotesPicking Up Speed

Wolfram Demonstrations

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demonstrations.wolfram.com

Picking Up Speed

http://demonstrations.wolfram.com/

Videos & Websitewww.mathkanection.com

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as easy as 3, 4, 5Picking Up Speed

http://www.mathkanection.com/

• Remind 101 www.remind101.com

• Math Is Fun www.mathsisfun.com/calculus/index.html

• AP Calculus Stillwater apcalculusstillwater.wordpress.com/ap-calculus-videos/

• Mr. White’s AP Calculus AB https://sites.google.com/a/lusherschool.org/mrwhitecalc/

• Mr. Landry’s Online Learning Math Center www.deeringmath.com/Calculus/calculusbc/

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ResourcesPicking Up Speed

http://www.remind101.com/

http://www.mathsisfun.com/calculus/index.html

http://apcalculusstillwater.wordpress.com/ap-calculus-videos/



https://sites.google.com/a/lusherschool.org/mrwhitecalc/

http://www.deeringmath.com/Calculus/calculusbc/

http://www.deeringmath.com/Calculus/calculusbc/

Collegial Support

55 students

36 students

Frozen Days

Review Days

3 preps

Videos35 students

Series

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as easy as 3, 4, 5Reflections

Barbara Kane

Highs & lows – Admin & precalc support;, only 36 students remained by October; Frozen Days;Chapter 4 needs more polar, parametric, vector application;Need to adjust for more Time for students to let Series sink in.3 preps difficulty—next year AB Gierut, BC Kane

More AB & BC

Student Buddy System

More Vertical Teaming

100% success rate

More Teachers Involved

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as easy as 3, 4, 5What Will the Next 10 Years

Look Like?

Barbara KanePatrick Gierut

Making AP Calculus as Easy as 3,4,5

J. Sterling Morton East High SchoolCicero, IL

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as easy as 3, 4, 5

Barbara Kane Patrick Gierut J. Sterling Morton East High School Cicero, IL Morton East High School...

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