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Addressing Prerequisite Skills in AP Calculus AB

Learn how to identify and address gaps in prerequisite skills in AP Calculus AB. Discover strategies for pre-assessment, embedding instruction, and providing targeted support to ensure student success.

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Addressing Prerequisite Skills in AP Calculus AB

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  1. Calculus AB APSI 2016Day 4 Professional Development Workshop Handbook Curriculum Framework Calculus AB and BC

  2. Discussion of Homework Problems Lesson 15: Addressing Prerequisite Skills Throughout the Course Break Lesson 16: Unit Development Lunch Lesson 17: Formative Assessment: Practice and Feedback Lesson 18: Curricular Requirements and Syllabus Development Lesson 19: Next Steps, Communities, and AP Resources Thursday

  3. Multiple Choice Questions on the Calculus AB Practice Exam (p. 24-29 and 37-39 in Multi-day Workshop Handbook) Questions 21-30 and 86-90 Free Response: 2017: AB5, AB6 Sample FRQ (p. 52-55-Multi-day Workshop Handbook): 5,6 Wednesday Assignment - AB

  4. Lesson 15:Addressing Prerequisite Skills Throughout the Course Key Takeaway 15 An instructional plan incorporating targeted support can help to ensure that students who enter AP Calculus with gaps in their prerequisite understandings are successful in the course.

  5. What skills, understanding, and knowledge from previous math courses will be needed to be successful in AP Calculus?

  6. Identifying Prerequisite Skills • Many students will come to your class with gaps in knowledge across the spectrum of topics—algebraic reasoning, geometric formulas, trigonometric functions, etc. • How can you help those students get up to speed? • First, rather than assuming your students will be on level for most topics, assume your students will have gaps so you can be prepared. • Pre-assess: figure out what your students understand and know before you teach it.Are your students ready for AP Calculus? (https://www.teacherspayteachers.com/Product/Are-You-Ready-for-Calculus-AP-988389 • Embed “gap” instruction directly into the lesson on the on-level topic.Discuss the big idea behind factoring as you discuss the process or finding the limit of a rational expression involving binomials and trinomials.

  7. 2005 AB FRQ 3 (Form B) Take a few minutes to solve this problem. What prerequisite understanding, knowledge, and skills are needed for that question? Where are some additional locations in the curriculum where additional instruction can be embedded in order to address potential gaps in understanding?

  8. Practice • Your group will be assigned two sample AP Calculus Questions. Each is related to: • Derivatives • Integrals • limits/continuity • area and volume • related rates • Complete the table for the question

  9. 2003 Multiple Choice # 25

  10. 2010 FRQ #4

  11. 2012 MC #2

  12. 2012 MC #9

  13. AB 2012 MC #14 If and , then the derivative of at x = 3 is A ) B) C) D) E)

  14. Reflect • How will making a plan to address gaps in prerequisite knowledge help your students be successful in AP Calculus? • Revisit your planning calendar from Day 1For which topics will you need to pre-assess and/or provide targeted instruction to address gaps? Place a star on a stick for those topics.

  15. Lesson 16:Building Units of Instruction Key Takeaway 16 Students are more likely to be successful when learning goals and instructional practices align with assessment strategies.

  16. When designing your curriculum, it is important to ensure your learning goals, instruction, and assessments are aligned. Units and lessons should be designed so they match the learning objectives and performance standards for the AP Calculus course. • What are your first steps when planning a unit? What resources would be helpful for you to have as your begin to plan your unit?

  17. go to https://advancesinap.collegeboard.org/stem/calculus#planningopen Lindsey Bibler’s Sample Syllabus. Open Unit 9. • What are the relative strengths/advantages of the unit plan?

  18. Make Notes on the following

  19. Lesson 17: Formative Assessment: Practice and Feedback Key Takeaway 17 Formative assessments and meaningful feedback enable both teachers and students to know what the students understand.

  20. p. 161 • Generate a list of the type of assessments teachers might use to gauge what their students know.

  21. Formative Assessment Strategies (p. 162) • Formative assessment is a process used to monitor student learning and provide ongoing feedback so students can improve. • The goal of formative assessment is to monitor student learning to provide ongoing feedback • help students identify their strengths and weaknesses and target areas that need work • help faculty recognize where students are struggling and address problems immediately • Formative assessments are generally low stakes, which means that they have low or no point value. • exit tickets • hand signals • journal entries • debriefing http://www.cmu.edu/teaching/assessment/basics/formative-summative.html

  22. Using feedback to target misunderstandings (p. 184) • Effective feedback is timely, targeted, and actionable. • Think-Pair-ShareWhat do these terms mean to you? Timely: Targeted: Actionable:

  23. AP Calculus Course and Exam Description FRQ 2

  24. Sample Student Response Part a Part b Yes, IVT What feedback would you give?

  25. AP Calculus Course and Exam Description FRQ #3

  26. Sample Student Response Student Response part B g is increasing on [2,4] because g is increasing What feedback would you give?

  27. AP Calculus Course and Exam Description FRQ #1

  28. Sample student response part b only What feedback would you give?

  29. 2009 FRQ #3

  30. Scoring Guideline Student Sample Response part D From part c, Profit = so P’(k) is 0 at k=400, so 16,000 dollars is the maximum profit. What feedback would you give?

  31. Reflect • What are some challenges you might encounter when using formative assessments and providing feedback? What are some ways you can address those challenges?

  32. Lesson 18: Curricular Requirements and Syllabus Development Key Takeaway 18 The curricular requirements set expectations for teachers and ensure consistency among AP Calculus courses.

  33. Audit Options

  34. Preparing for the Audit • Log on to the Audit Site • Turn to page 194 and complete the survey relating • Syllabus Self-Evaluation Checklist • The list of Curriculum/Resource Requirements • The example textbook list

  35. Curricular Requirements

  36. Curricular Requirements What are your observations about this sample?

  37. p. 197 Check out 2 of the syllabi Share what you have found Curriculum Requirements in Syllabus Development Guide.

  38. Reflect • How will you ensure your course aligns with the expectations laid out in the curricular requirements? • If you currently have an approved syllabus, compare your syllabus with the updated curricular requirements, noting areas where you may need to account for things that are missing and how you can adjust your instructions to account for those things. • If you do not have an approved syllabus, use the planning calendar you worked on earlier in the week to begin designing a syllabus for your course. You may want to check off which curricular requirements you have already met, and consider how you will address things you still need to include. Also review the Syllabus Evaluation Checklist to see what else you should include.

  39. Lesson 19 : Next Steps, Communities, and AP Resources Key Takeaway 19 Teaching the updated AP Calculus course presents opportunities for professional learning and collaborative problem solving.

  40. Write down any questions you have about teaching the new topics and skills that have been included in the Curriculum Framework. What steps can you take to begin addressing areas of the Framework that are new to the course or that are less familiar to you?

  41. AP Resources • https://apstudent.collegeboard.org/apcourse/ap-calculus-abSample activitiesCollege Career information • http://apcentral.collegeboard.com/homeonline video and documents for parents to get students excited about AP • http://www.davidson.edu/davidsonnext/coursesFree online modules targeting challenging AP Calculus course topics with videos, interactive activities, simulations, and test questions • https://www.khanacademy.org/Free online videos walking through examples of various calculus concepts.

  42. http://apcentral.collegeboard.com/apc/public/homepage/4137.htmlInformation on how to become an AP reader • https://apcommunity.collegeboard.org/web/apcalculusProvides a forum for AP calculus teachers to post discussions and share resources • http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/2178.htmlProvides information about professional development Beginning in 2016-2017, The Teaching and Assessing AP Calculus series will be available.

  43. There are many NEXT steps you can take that are concrete and actionable to help you more forward with planning your course. Discuss your NEXT steps using the table on page 213.

  44. Graphs of f, f’ and Descriptions of f and f’

  45. Reading and Using Information from a Graph of f’

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