IB DP Higher Level Mathematics Cat. 1

Mick Purcell

Agenda1. Understanding the Course Guide2. Assessment3. Syllabus Details -- Core4. Syllabus Details -- Options5. The Burden of Proof6. Exploration7. Technology8. Writing Tests9. Classroom Practices

10. Relationship to Other Parts of IB11. Writing Unit Plans

Session 0: wifi OK?

Everybody will need internet access to participate effectively

SSID, username, and password are written on the whiteboard.

Session 1: Introductions and the Course Guide1. Introductions and Learning Objectives, 15 - 20 minutes2. Activity 1.1: Natural Numbers, 10 - 15 minutes3. Activity 1.2: Communicating with each other, 10 - 15 minutes4. Activity 1.3: Tangents, 10 - 15 minutes

About me: @mickpurcell

1. Gmail: mickpurcell@gmail.com2. Twitter: https://twitter.com/mickpurcell3. LinkedIn: https://www.linkedin.com/in/mickpurcell4. Facebook: https://www.facebook.com/mick.purcell5. Slideshare: http://www.slideshare.net/mickpurcell6. 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.

Session 1: Introductions

1. Introductionsa. About meb. Line up by date you taught your first math class (name, year, school, # of years)c. Learning Objectivesd. Essential Agreementse. What I know about you

Mick Hashtag #IBHLMathThe 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

Basic PlanDay 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

Essential AgreementsTo 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

Mick Code #IBHLMathKey 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

What I know about youInformation 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)

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

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.

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?

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.

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!

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

Communicating with each othera. Todaysmeet: https://todaysmeet.com/ibhlmathb. Slideshare: http://www.slideshare.net/mickpurcellc. Use the OCC: occ.ibo.org

Please make sure you have access to:

1. OCC2. Course Guide3. Formula Booklet4. Email5. Geogebra6. Any Social media you want to use7. A Folder of Bookmarks dedicated to Mathematics Teaching

Communicating with each other

a. Go to: https://todaysmeet.com/ibhlmathb. Join, and talk: just write which Option you teach or plan to teach:

i. Sets, Relations, and Groupsii. Statistics and Probabilityiii. Calculusiv. Discrete Mathematicsv. I don’t know

∃ 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

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.

A relatively simple problem

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.

Session 2: Introductions and the Course Guide1. Activity 2.1: Functions: 40 minutes2. Activity 2.2: Purists vs. Pragmatists 10 - 15 minutes3. Activity 2.3: Rating the Course Guide: 10 - 15 minutes4. 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.”

Mick Code #IBHLMathActivity 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?

Mick Code #IBHLMathActivity 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

24 = 12 + 12 minutes . . . . . HAVE FUN!

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

COMMAND TERMS

Mick Code #IBHLMathActivity 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.

20 = 10 + 10 minutes . . . . . HAVE FUN!

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” L4. “ToK links are important, especially axiomatic thinking and proof”R5. “Practicing old papers must be done early and often” L6. “Students benefit from metacognitive skills, such as learning how to learn” R7. “My students want top universities -- the grade is what matters.” L8. “Regardless of career, clear mathematical thinking is always beneficial.” R

Session 3: Assessing the Course Guide1. Activity 3.1: Assessing the Course Guide2. Activity 3.2: Rating the Course Guide: 10 - 15 minutes3. Activity 3.2: Detailed Examination of the Course Guide 50 minutes4. Activity 3.4: Reflection: what Have I learned? 10 minutes

Which Sections of the Guide are Critically Important?

Rank them.

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

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

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.

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.

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

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

Which Sections of the Guide are Absolutely Useless?

pp 55 - 56 Discrete Maths Terminology

pp 42 - 54? Options you will not use

Session 3: Course Guide ActivityIt 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

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