Ib dp hl mathematics cat 1 day 1
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- The Core Syllabus Details section (pp 17-36) which outlines the required content to be covered - The Option section (pp 37-41) related to the option that will be taught - The Notation List (pp 73-75) that defines the terminology and symbols used - The Internal Assessment Criteria (pp 68-70) that describes the standards for the exploration coursework - The Assessment Outline (p 58) that overviews the assessment objectives and weightings
Ib dp hl mathematics cat 1 day 1
- 1. IB DP Higher Level Mathematics Cat. 1 Mick Purcell
- 2. Agenda 1. Understanding the Course Guide 2. Assessment 3. Syllabus Details -- Core 4. Syllabus Details -- Options 5. The Burden of Proof 6. Exploration 7. Technology 8. Writing Tests 9. Classroom Practices 10. Relationship to Other Parts of IB 11. Writing Unit Plans
- 3. Session 0: wifi OK? Everybody will need internet access to participate effectively SSID, username, and password are written on the whiteboard.
- 4. Session 1: Introductions and the Course Guide 1. Introductions and Learning Objectives, 15 - 20 minutes 2. Activity 1.1: Natural Numbers, 10 - 15 minutes 3. Activity 1.2: Communicating with each other, 10 - 15 minutes 4. Activity 1.3: Tangents, 10 - 15 minutes
- 5. About me: @mickpurcell 1. Gmail: mickpurcell@gmail.com 2. Twitter: https://twitter.com/mickpurcell 3. LinkedIn: https://www.linkedin.com/in/mickpurcell 4. Facebook: https://www.facebook.com/mick.purcell 5. Slideshare: http://www.slideshare.net/mickpurcell 6. Geogebra: https://www.geogebra.org/mickpurcell Head of Department at Mahindra UWC in India in 2000 - 2002; teaching IB Higher Level Mathematics since 2000. A Reader, School Visit Team Leader, Workshop Leader, and Consultant for the IB. Has taught Further Mathematics 3 times. Currently Head of School at Edubridge International School in Mumbai, running PYP, MYP, and DP.
- 6. Session 1: Introductions 1. Introductions a. About me b. Line up by date you taught your first math class (name, year, school, # of years) c. Learning Objectives d. Essential Agreements e. What I know about you
- 7. Mick Hashtag #IBHLMath The key learning outcomes for this 3-day workshop are At the end of this 3-day workshop, each IBHL Mathematics teacher will: ● Be better prepared to maximize learning and get the best results for your students ● Become much more familiar with: ○ the IB Higher Level Mathematics Course Guide ○ The OCC ○ IB Exam Questions ○ The Exploration IA ● Be able to implement key aspects of IB-style pedagogy, such as Approaches to Learning, Concept-based Teaching and Learning, and Differentiation ● Be confident about teaching particular aspects of the IB, such as ToK, the Extended Essay and the Exploration IA
- 8. Basic Plan Day 1: the Course Guide Day 2: the Internal Assessment Day 3: as required ● Using the Questionbank and OCC throughout -- stay focused on these 4 things: ○ the IB Higher Level Mathematics Course Guide ○ The OCC ○ IB Exam Questions ○ The Exploration IA
- 9. Essential Agreements To best achieve our learning outcomes, we agree to: ● Be comfortable, move around, use the toilet when required, etc. ● Not use our phones for personal communications during the sessions -- if an urgent matter comes up, please step outside ● Participate but don’t dominate ● Ask questions -- in a mindful and appropriate manner
- 10. Mick Code #IBHLMath Key attributes of a successful IB mathematics teacher ● Know the maths! ● Differentiate: different styles suit different students ● Find a balance: push students but not too hard: firm and friendly ● Use technology and the internet ● Write well ○ More than “sums” ○ Write mathematical papers
- 11. What I know about you Information from the survey: ● Mostly new to IB teaching (1st or 2nd year), with a few experienced ● Use TI Family of Calculators ● More interested in mathematics than general IB stuff ● A bit nervous about Internal Assessment (Day 2)
- 12. The most important learnings from this workshop: to be successful teachers of IB HL Mathematics, We must teach students ● to read and write mathematics correctly ● the thinking skills and concepts required to solve unexpected problems
- 13. This workshop includes plenty of mathematics Disclaimer: I realize that there will be members who know more mathematics than I do, are smarter than me, or can solve a sum more quickly . . . . fine -- I welcome your contributions. However, please respect my experience and successful track record.
- 14. This workshop includes plenty of mathematics When I ask you to “do mathematics”, to answer questions, please consider these points: ● Why did he select this question? ● What are the important points about this question? ● How will this make us better teachers of IB Mathematics HL?
- 15. This workshop includes plenty of mathematics Let’s get started: Is zero a natural number? Discuss in your groups for two minutes. Note: in the context of this workshop, there IS a correct answer to this question.
- 16. This workshop includes plenty of mathematics Activity: there is a hidden gem in the Course Guide. Use this hint: Is zero a natural number? Why did he ask that question? To find the hidden gem!
- 17. Is zero a natural number? ● Why did he select this question? ○ Debate, discussion, branches, Wikipedia, Notation list ● What are the important points about this question? ○ In DP HL Mathematics, the set ℕ is {0, 1, 2, 3, 4, . . . } and the set ℤ+ is {1, 2, 3, 4, . . . } ○ This is found in the Notation List -- which every teacher must know ● How will this make us better teachers of IB Mathematics HL? ○ Your students should keep the Notation List and Formula Booklet with them at all times ○ Regardless of our personal opinions about debatable questions, it is our obligation to our students to write mathematics the IB way and to help them read the exam papers
- 18. Communicating with each other a. Todaysmeet: https://todaysmeet.com/ibhlmath b. Slideshare: http://www.slideshare.net/mickpurcell c. Use the OCC: occ.ibo.org Please make sure you have access to: 1. OCC 2. Course Guide 3. Formula Booklet 4. Email 5. Geogebra 6. Any Social media you want to use 7. A Folder of Bookmarks dedicated to Mathematics Teaching
- 19. Communicating with each other a. Go to: https://todaysmeet.com/ibhlmath b. Join, and talk: just write which Option you teach or plan to teach: i. Sets, Relations, and Groups ii. Statistics and Probability iii. Calculus iv. Discrete Mathematics v. I don’t know
- 20. ∃ Exercises and Problems in mathematics Exercise: see it and think: “I know how to do that!” Problem: see it and think: “uh-oh . . . I have no idea how to do that!” Cognitively, solving exercises or problems are much different processes
- 21. This workshop includes plenty of mathematics A simple question?? 2. The point P = (0, 1) lies on two distinct lines tangent to the parabola with equation y = x2 + 2. Find the equations of both tangent lines.
- 22. A relatively simple problem
- 23. Many students will struggle with this question: 5. The point P = (0, 1) lies on two distinct lines tangent to the parabola with equation y = x2 + 2. Find the equations of both tangent lines. Command term comes at the end Find the equation of the line tangent to y = x2 + 2 when x = -1.
- 24. Session 2: Introductions and the Course Guide 1. Activity 2.1: Functions: 40 minutes 2. Activity 2.2: Purists vs. Pragmatists 10 - 15 minutes 3. Activity 2.3: Rating the Course Guide: 10 - 15 minutes 4. Activity 2.4: Reflection: what have I learned? 10 minutes New idea: divide into 3 groups: 1. “New to IB -- not taught a single lesson -- don’t know about Course Guide or occ, etc.” 2. “In 1st or 2nd year of IB teaching -- need practical tips about how to teach the students I currently have -- know a little about Course Guide or OCC 3. “Have significant experience as a teacher or with IB, have my course outline, familiar with Course outline and occ, etc.”
- 25. Mick Code #IBHLMath Activity 2.1: The Concept of Functions: Please get into your groups (by prime number?) and spend 24 minutes working out this question Answer these Questions: ● Why did he select this question? ● What are the important points about this question? ● How will this make us better teachers of IB Mathematics HL?
- 26. Mick Code #IBHLMath Activity 1: Functions Please split into your groups, by your geometrical object take 12 minutes of silence and then 12 minutes of conversation to solve this sum
- 27. 24 = 12 + 12 minutes . . . . . HAVE FUN!
- 28. WHY???? ● How are IB Questions different than other Boards? ● The importance of notation, vocabulary and CONCEPTS ● Notation and vocabulary are stepping stones to CONCEPTS ● GRAPHING is important ● Need to know: when and how to use the Calculator ● FUNCTIONS ● Getting the early parts of the questions leads to success ● Many topics in one question ● Command Terms
- 29. COMMAND TERMS
- 30. Mick Code #IBHLMath Activity 2.2: Spectrum There are two types of IB HL Math Teachers: 1: “Pragmatists” they teach kids to get 7s -- they use words like “results”, “assessments”, “exams”, “papers’, “IAs”, etc. 2. “Purists”: they teach kids to love math -- they use words like “learning”, “elegance”, “beauty”, “theorem”, “lifelong”, etc Where do you stand? Please stand up.
- 31. 20 = 10 + 10 minutes . . . . . HAVE FUN!
- 32. Quiz: 1 step, 2 steps To what extent do you agree with each statement? 1. “There’s not enough time to cover the syllabus” (left) 2. “Learning synthetic division is important, even though it’s not on the syllabus” (right) 3. “Class time should be spent on teaching efficient use of the calculator” L 4. “ToK links are important, especially axiomatic thinking and proof”R 5. “Practicing old papers must be done early and often” L 6. “Students benefit from metacognitive skills, such as learning how to learn” R 7. “My students want top universities -- the grade is what matters.” L 8. “Regardless of career, clear mathematical thinking is always beneficial.” R
- 33. Session 3: Assessing the Course Guide 1. Activity 3.1: Assessing the Course Guide 2. Activity 3.2: Rating the Course Guide: 10 - 15 minutes 3. Activity 3.2: Detailed Examination of the Course Guide 50 minutes 4. Activity 3.4: Reflection: what Have I learned? 10 minutes
- 34. Which Sections of the Guide are Critically Important? Rank them.
- 35. We agree that the Syllabus details are important, right? 6 groups will each examine one part of the syllabus and write three slides for three minutes. You might include: ● Points that you find tricky ● Points that students will find trick ● Questions for me or for the group ● Teaching ideas ● Resources for teaching
- 36. For example, section 2 ● The notation f:x↦ 2x-1 is called “arrow notation” or more precisely “barred arrow notation” and its advantage is that, by using the arrow, it emphasizes that a function is a mapping. ● f:x↦ 2x-1 can be read “f is a function that maps x to 2x-1.” ● The notation f: ℝ →ℝ can be read as “f is a function that maps from the set of real numbers to the set of real numbers.” This notation (without the bar on the arrow) is used only when mapping set to set, such as domain to range. ● If the domain is not stated, students should assume that the domain is ℝ, or the largest possible subset of ℝ
- 37. For example, section 2 ● Domain and range should be emphasized in discussing logarithmic and exponential functions as inverse functions. Requiring the students to graph log and exponential functions with different bases is a good idea. ● Students should know the definition of a function from previous years. A function is a mapping of every element in one set (the domain) to exactly one element in another set (the range). ● Students need to be aware that functions can be many-to-one but not one-to-many. The words “relation” and “co-domain” do not appear on the syllabus -- it’s best to leave them out.
- 38. For example, section 2 ● Establishing domain and range with and without the use of a GDC is an important skill here. ● Past paper questions can be given on this topic and can be quite challenging for the students. ● Students need lots of practice about when to use a calculator and when not to use a calculator on Paper 2 Questions. They find Paer 1 Questions difficult, especially when graphing transformations involving absolute value.
- 39. Which Sections of the Guide are Important to Teachers but Probably not to Students? pp 60 - 67 and p 58 Assessment Explanations: we will discuss pp 11 - 16 notes, ATLs, and Prior Learning: for a Category 2 Workshop pp 1 - 7 Learner Profile & Nature of Subject: put it near your bed for insomnia
- 40. Which Sections of the Guide are Critically Important? pp 17 - 36 Core Syllabus Details pp 37 - 41? Option you will use pp 73 - 75 Notation List pp 68 - 70 Internal Assessment Criteria pp 71 - 72 Command terms P 58 Assessment Outline
- 41. Which Sections of the Guide are Absolutely Useless? pp 55 - 56 Discrete Maths Terminology pp 42 - 54? Options you will not use
- 42. Session 3: Course Guide Activity It is important to go through the Course Guide. In particular, let’s go through the Syllabus Content: pp 15 - 36 and 47 - 50 (for Calculus Option) I could lead it, such as: Section 1.1
- 43. Which Sections of the Guide are Critically Important? pp 17 - 36 Core Syllabus Details pp 37 - 41? Option you will use pp 73 - 75 Notation List pp 68 - 70 Internal Assessment Criteria pp 71 - 72 Command terms P 58 Assessment Outline