IB Update - Welcome to IBSCA | IBSCA · 2018-11-30 · The binomial theorem Applications SL Approximation, upper and lower bounds, percentage errors Financial applications of geometric

© International Baccalaureate Organization 2015

International Baccalaureate® | Baccalauréat International® | Bachillerato Internacional®

IB Update

IBSCA CP Conference

29th November 2018

Peter Fidczuk

Development and Recognition

Manager, UK & Ireland

[email protected]


International Baccalaureate® | Baccalauréat International® | Bachillerato Internacional®


IB Programmes are

globally recognizedTHE BIG

NUMBERS

5270Authorized IB World

Schools

around the world

2893Number of State

funded schools

1,500,000Number of students

with access to the

four IB programmes

1,745Programmes

1,544Programmes

3419Programmes

214Programmes

IB schools in 153 countries


CP news 1

• Stay up to date with developments in the CP and the Diploma

Programme courses through the CP Co-ordinators, and DP Co-

ordinators notes published quarterly on the PRC (latest issue Oct 2018).

• Stay up to date on Programme Standards & Practices by visiting the

PRC preview of the revised programme standards and practices

framework, prior to its full release in late 2020.

• Curriculum review of the core components has begun. If you are

interested in taking part in discussions and meetings for: language

development, reflective project, service learning and personal and

professional skills contact [email protected]

• Coordinators will be receiving email invites, to ask CP educators to

complete a language development survey by end of January 2019.

11/28/2018 4

mailto:[email protected]


CP news 2

• Reflective project subject report will be available by the end of the year.

Read through to find more information on: moving from descriptive to

interrogative reflective projects; improving theoretical dimensions of

research through source selection; conducting valid quantitative research;

maximising the usefulness of the RPPF (reflections on planning and

progress form).

• Join the CP Twitter network @ib_c_p. Twitter automatically sends you

news and updates. It also connects you to CP teachers from around the

world to share experiences, questions, ideas and resources. It is the best

place to keep up to date with CP news, updates, articles, educational

quotes, latest research, upcoming workshops and webinars.

11/28/2018 5


CP reminders

• Have you read through the IB’s publications on inclusive education?

Find out more about planning for learning diversity in classrooms

and how to ensure candidates with access requirements are

supported throughout their CP journey.

11/28/2018 6


IB DP curriculum review: 7 year cycle


Revised Diploma Courses

First teaching September 2019

• All Language A courses (except Literature &

Performance)

• All Mathematics courses


• Economics

• Music

• Theory of Knowledge

11/28/2018 8


Revised Diploma Courses


• Literature & Performance

• Classical languages

• Business management

• ITGS (as digital society)

• Biology

• Chemistry

• Computer Science

• Physics

• Dance

• Theatre

11/28/2018 9


Mathematics

Revised from September 2019

11/28/2018 10


Current mathematics offer

4 independent courses

• Mathematical Studies SL (DfE accepts this as a core

mathematics qualification)

• Mathematics SL (originally called Mathematical

Methods)

• Mathematics HL

• Further Mathematics HL

Summaries are found in our Diploma subject briefs

All courses are linear, 20% coursework, exam of a

problem solving & synoptic nature

No mechanics – this is delivered through Physics

11/28/2018 11


May 2017 Entries

Total number of Diploma Programme candidates:

157488

Entries and Grade distribution:

11/28/2018 12

Entries 7 6 5 4 3

MS SL 35919 6.4 14.9 25.6 24.8 15.6

SL 46659 8.2 16.8 22.6 22.8 15.6

HL 13981 13.0 21.8 22.2 20.4 14.1

FM HL 216 26.0 21.6 13.7 11.3 14.2


Mathematics comparability research

• Comparison of IB mathematics courses with A Level

carried out by Ofqual, ICOSSA report 2012

• In 2016 IB commissioned NARIC to compare

international Maths qualifications -

http://www.ibo.org/news/news-about-the-

ib/comparing-dp-mathematics-with-other-curricula-

around-the-world/

• Report extends Ofqual’s findings

http://www.ibo.org/news/news-about-the-ib/comparing-dp-mathematics-with-other-curricula-around-the-world/


NARIC findings

Maths courses ordered by conceptual difficulty

• Alberta Mathematics 30-2

• Alberta Mathematics 30-1

• IB Mathematical Studies SL

• Singapore H1 Mathematics

• IB SL Mathematics

• A Level Mathematics

• IB HL Mathematics

• Singapore H2 Mathematics

• Singapore H3 mathematics

• A Level Further Mathematics

• IB Further Mathematics


Reasons for changing the IB

mathematics offer• 4 separate courses are difficult for schools to implement.

• Prevents students easily moving between courses as

there is no common core content, common assessments

• Wide misconceptions about the content and demand of

Mathematical Studies SL – it has always been a course

following on from (i)GCSE and is level 3. The content and

approach is to relate mathematics to solving real world

problems, so has significant statistics.

• Out of step with all our other subjects where we have

integrated SL/HL

11/28/2018 15


Starting premises for the new courses• Mathematics is a compulsory requirement of the IB

diploma. We design courses that are appropriate for all

our students who will come to us with a variety of

interests, abilities and previous experience of

mathematics.

• We have a requirement to bring everyone up to an

acceptable standard to fulfil the diverse requirements of

universities around the world.

• Data and anecdotal evidence suggest that we have many

students taking mathematics as part of their diploma

who are able mathematicians but have no motivation

towards “pure” mathematics. So we have developed two

complementary routes

11/28/2018 16


Revised DP Mathematics

In development for first teaching September 2019, first examination May

2021:

Mathematics: Analysis and approaches HL and SL

Analytic methods with an emphasis on calculus – appropriate for pure

mathematicians, and those with an interest in analytic methods – current

calculus option content will form part of the HL course.

Mathematics: Applications and interpretation HL and SL

Applications and interpretation with an emphasis on statistics and use of

technology during assessment – appropriate for social scientists, biomedical

scientists, those with an interest in the applications of mathematics and how

technology can support this – SL will be appropriate for students who would

previously have taken Mathematical Studies SL – current HL content from

the statistics and discrete options will form part of the HL course.

11/28/2018 17


DP Mathematics

• Each subject will be available at SL and HL, with the SL course being a complete subset of the HL course

• There will be approximately 60 hours allocated to common material across both SL courses

• 30 hours will be allocated to the development of investigational and problem solving skills, collaboration, modelling skills, and completion of the internal assessment (IA) component

• The IA is an independent exploration of an area of mathematics chosen by the student. It is internally assessed by the teacher and externally moderated by the IB, contributing 20% to the overall level

11/28/2018 18


SL Common Core 60 hours

5 key areas of Maths

•Number & Algebra

•Functions

•Geometry & Trigonometry

•Statistics and Probability

•Calculus

Mathematics: analysis and approaches

Mathematics: applications and interpretation

Inquiry

Investigation

and

Modelling 30

hours

A & A SL/HL

Common

Content 60

hours

A & I SL/HL

Common

Content 60

hours

A & A AHL

90 hours

A & I AHL

90 hours

Inquiry

Investigation

and

Modelling 30

hours


Time allocations SL

11/28/2018 20

Syllabus component

SL Teaching Hours

Analysis ApplicationsNumber & Algebra 19 16Functions 21 31Geometry & Trigonometry 25 18Statistics & Probability 27 36Calculus 28 19IA and ‘toolkit’ 30 30TOTAL 150 150


Time allocations HL

11/28/2018 21

Syllabus component

HL Teaching Hours

Analysis ApplicationsNumber & Algebra 39 29Functions 32 42Geometry & Trigonometry 51 46Statistics & Probability 33 52Calculus 55 41IA and ‘toolkit’ 30 30TOTAL 240 240


Number and Algebra

11/28/2018 22

Core

Operations with numbers in standard form

Arithmetic and geometric sequences and series

Applications of arithmetic and geometric sequences and series including compound interest and annual depreciation

Simplifying numerical expressions with integer exponents

Introduction to logarithms and natural logarithms

Analysis SL

Simple deductive proof

Laws of exponents with rational exponents

Laws of logarithms

Change of base of a logarithm

Solving exponential equations

Sum of infinite geometric sequences

The binomial theorem

Applications SL

Approximation, upper and lower bounds, percentage

errors

Financial applications of geometric series: amortization

and annuities

Solving systems of linear and polynomial equations

Analysis HL

Permutations and combinations

Binomial theorem with negative indices

Partial fractions

Complex numbers – Cartesian, modulus-argument and

Euler form

Complex conjugate roots of quadratic and polynomial

equations

De Moivre’s theorem

Powers and roots of complex numbers

Proof by induction, contradiction and counter-exampleSolving systems of linear equations

Applications HL

Laws of logarithms

Expressions with rational exponents

Sum of infinite geometric sequences

Complex numbers – Cartesian, modulus-argument and

Euler form

Phase shift and voltage as complex quantities

Matrices: algebra and properties

Matrices applications to solving systems of equations,

and coding and decoding messagesEigenvalues and eigenvectors


Functions

11/28/2018 23

Core

Different forms of equations of straight lines, including parallel and perpendicular lines

Functions and inverse functions

Graphing skills and determining key features of graphs including horizontal and vertical asymptotes

Finding the point of intersection of lines and curves using technology

Analysis SL

Composite, identity and inverse functions

The quadratic function – factorisation and completing

the square

Solution of quadratic equations and inequalities

The quadratic formula and the nature of the roots

Reciprocal, rational (linear/linear), exponential and

logarithmic functions

Equations of horizontal and vertical asymptotes

Solving equations graphically and analytically

Graph transformations, including composite

transformations

Applications SL

Modelling skills and the modelling process

Modelling in contexts with linear, quadratic, exponential

growth and decay, direct and inverse variation, cubic,

and sinusoidal behaviours.

Analysis HL

Polynomial functions, factor and remainder theorems

Viete’s formula (sum and product of roots of polynomial

equations)

Rational functions of the form linear/quadratic and

quadratic/linear

Odd, even and self-inverse functions

Inverse functions requiring a domain restriction

Graphing and solution of modulus equations and

inequalities

Applications HL

Composite functions used in context

Inverse functions with domain restrictions

Transformations of functions

Modelling with exponential models with half-life,

complex sinusoidal models, logistic models and

piecewise models

Linearizing data

Log-log and log-linear graphs


Geometry and Trigonometry

11/28/2018 24

Core

Distance between points in 2d and 3d space

Midpoints of two points in 2d and 3d space

Volume, surface area and angles in 3d solids

Non-right-angled trigonometry, including area of a triangle, angles of elevation and depression

Three figure bearings

Analysis SL

Circles – length of arc and area of sector in radians

The unit circle – exact trigonometric ratios and their multiples

Ambiguous case of the sine rule

Pythagorean identity

Double angle identities for sine and cosine

Behaviour of circular functions

Composite functions of the form .

Transformations and real-life contexts

Solving trigonometric equations, including quadratic

trigonometric equations, in a finite interval

Applications SL

The circle – length of arc and area of sector

Equations of perpendicular bisectors

Voronoi diagrams – nearest neighbour interpolation and

toxic waste dump problems

Analysis HL

Reciprocal trig ratios, Pythagorean identities involving tan,

cot, sec and cosec

Inverse trig functions

Double angle identity for tan

Compound angle identities

Relationships between trig functions and their symmetry

properties

Vectors – algebraic and geometric approaches, dot and cross

products, angle between 2 vectors, vector algebra

Vector equation of a line in 2d and 3d space

Angle between 2 lines

Simple applications of vectors to kinematics

Coincident, parallel, intersecting and skew lines in 2d and 3d

space and their points of intersection

Vector product, properties and applications

Vector equations of a planeIntersections of lines and planes and angles

Applications HL

Radian measure

The unit circle and the Pythagorean identity

Solving trigonometric equations

Inverse trigonometric functions

Geometric transformation in 2d using matrices

Vectors – geometric approaches, dot and cross products,

angle between 2 vectors

Vector equation of a line in 2d and 3d space

Angle between 2 lines

Vector applications to kinematics, linear motion with

constant and variable velocity

Graph theory

Adjacency and transition matrices

Tree and cycle algorithms including Kruskal’s and Prim’s, Chinese postman and Travelling Salesman


Statistics and Probability - 1

11/28/2018 25

Core

Concept of population, sample, outliers, discrete and continuous data

Reliability of data sources

Interpretation of outliers

Sampling techniques – simple random, convenience, systematic, quota and stratified sampling methods

Presentation of discrete and continuous data in frequency tables, histograms, cumulative frequency graphs and

box plots

Measures of central tendency and dispersion for discrete and continuous data including the effect of

multiplication by or addition of a constant

Linear correlation – equation of regression line y on x including piecewise linear models, Pearson’s product-

moment correlation coefficient

Introduction to probability – independent events, mutually exclusive events, combined events, conditional

probabilities and probabilities with and without replacement

Use of Venn diagrams, tree diagrams, sample space diagrams and tables of outcomes

Probability distributions of discrete random variables, expected values and applications

The normal distribution – its properties, diagrammatic representation, expected values, probability and inverse

normal calculations

The binomial distribution

Analysis SL

The regression line x on y

Formal treatment of conditional and

independent probability formulae

Testing for independence

Standardization of normal variables

Inverse normal calculations

Applications SL

Spearman’s rank correlation coefficient

Appropriateness and limitations of different correlation

coefficients

Hypothesis testing

Significance levels

Chi squared test for independence and goodness of fit

T-test

One-tailed and two-tailed testing


Statistics and Probability - 2

11/28/2018 26

Analysis HL

Bayes’ theorem

Formal treatment of discrete random

variables and their probability

distributions

Continuous random variables and their

probability density functionsExpectation algebra

Applications HL

Data collection techniques, survey and questionnaire

design

Reliability and validity tests

Non-linear regression, sum of squares, R2

Interpolation and extrapolation

Linear transformation of a single random variable,

expectation and variance

Unbiased estimate and estimators

Sample means and the central limit theorem

Confidence intervals

Testing for population mean for normal and Poisson

distributions, proportion for binomial distribution

Critical regions and values

Type I and II errors

Poisson distribution

Transition matrices including regular Markov chains


Calculus - 1

11/28/2018 27

Core

Introduction to limits, rate of change and gradient

Increasing and decreasing functions and the graphical interpretation of the gradient

Differentiation of polynomials

Equations of tangents and normals at a given point

Integration as anti-differentiation of polynomials

Definite integrals using technology to find areas under curvesAnti-differentiation with a boundary condition to determine the constant term

Analysis SL

Derivatives of sin x , cos x, e x , and ln x, including

their sums and multiples

The chain, product and quotient rules

The second derivative and the graphical

relationships between f, f’ and f”

Local maximum and minimum points, points of

inflexion

Testing for maximum and minimum points

Optimisation

Kinematics problems involving displacement,

velocity, acceleration and total distance travelled

Indefinite integration of sin x, cos, 1/x and ex

Integration by inspection and by substitution

Definite integrals

Analytic evaluation of the areas under curves

Applications SL

Local maximum and minimum points

Optimisation problems

Numerical integration - the trapezoidal rule


Calculus - 2

11/28/2018 28

Analysis HL

Informal treatment of continuity and differentiability at

a point

Understanding of limits (convergence and divergence)

Differentiation from first principles; higher order

derivatives

L’Hopital’s rule

Implicit differentiation

Related rates and optimisation

Derivatives and indefinite integrals of tan, reciprocal and

inverse trig functions, the identity function, exponential

and log functions, including the composites of these and

partial fractions

Integration by substitution and by parts, repeated

integration by parts

Volumes of revolution about the x and y axes

First order differential equations – using Euler’s method,

separation of variables and integrating factor

Maclaurin expansions of ex, sin x, cos x , ln(1+x), (1+x)p

and composites of these

Applications HL

Derivatives of sinx, cosx, tanx, ex, ln x, xn

Chain, product and quotient rules

Related rates of change

Second derivative testing for concavity

Integration of sinx, cosx, sec2x, ex

Integration by inspection and substitution

Volumes of revolution about the x and y axes

Kinematics – displacement, distance, velocity and

acceleration

Setting up and solving first order differential equations

Slope fields

Euler’s method for first and second order differential

equations

Phase portraits


Assessment Objectives – common to both programmes• Problem-solving is central to learning DP mathematics and involves the acquisition of mathematical

skills and concepts in a wide range of situations, including non-routine, open-ended and real-world

problems. Having followed a DP mathematics course, students will be expected to demonstrate the

following:

• Knowledge and understanding: Recall, select and use their knowledge of mathematical facts, concepts

and techniques in a variety of familiar and unfamiliar contexts.

• Problem-solving: recall, select and use their knowledge of mathematical skills, results and models in

both abstract and real world contexts to solve problems.

• Communication and interpretation: transform common realistic contexts into mathematics; comment

on the context; sketch or draw mathematical diagrams, graphs or constructions both on paper and

using technology; record methods, solutions and conclusions using standardized notation; use

appropriate notation and terminology.

• Technology: use technology, accurately, appropriately and efficiently both to explore new ideas and to

solve problems.

• Reasoning: construct mathematical arguments through use of precise statements, logical deduction

and inference and by the manipulation of mathematical expressions.

• Inquiry Approaches: investigate unfamiliar situations, both abstract and from the real-world, involving

organizing and analyzing information, making conjectures, drawing conclusions, and testing their

validity.

11/28/2018 29


Assessment Structure HL Analysis and

ApproachesAssessment component Weighting

External assessment (5 hours)

Paper 1 (120 minutes) No technology allowed (110 marks)

Section A

Compulsory short-response questions based on the syllabus.

Section B

Compulsory extended-response questions based on the syllabus.

80%

30%

Paper 2 (120 minutes) Technology required. (110 marks)

Section A

Compulsory short-response questions based on the syllabus.

Section B

Compulsory extended-response questions based on the syllabus.

Paper 3 (60 minutes) Technology required. (60 marks)

Two compulsory extended response problem-solving questions.

30%

20%

Internal assessment

This component is internally assessed by the teacher and externally moderated by the IB at the

end of the course.

Mathematical exploration

Internal assessment in mathematics is an individual exploration. This is a piece of written work

that involves investigating an area of mathematics. (20 marks)

20%

11/28/2018 30


Assessment Structure HL Applications

and InterpretationAssessment component Weighting

External assessment (5 hours)

Paper 1 (120 minutes) Technology required. (110 marks)Compulsory short-response questions based on the syllabus.

80%

30%

Paper 2 (120 minutes) Technology required. (110 marks)Compulsory extended-response questions based on the syllabus.

30%

Paper 3 (60 minutes) Technology required. (60 marks)Two extended response problem-solving questions.

20%

Internal assessment

This component is internally assessed by the teacher and externally moderated by the IB at the end of the course.

Mathematical explorationInternal assessment in mathematics is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. (20 marks)

20%

11/28/2018 31


Replacement for Mathematical Studies

Mathematics: Applications and Interpretation SL

replaces Mathematical Studies.

11/28/2018 32


HE Entry Requirements for IB

Mathematics

IB view is that either HL course will be suitable for

university courses which require A Level Maths as an entry

requirement. However some subjects may consider that

one or other of the two courses might be more suitable

because of the specific content.

Guiding principle is that students should not be

disadvantaged.

11/28/2018 33


Initial HE position

University College London

“UCL are aware of the changes to the International

Baccalaureate Mathematics modules. From 2021,

programmes requiring A-level Mathematics will

accept either Mathematics: Analysis and Approaches

or Mathematics: Applications and Interpretation at

higher level. Programmes requiring Further

Mathematics at A-level will accept higher level

Mathematics: Analysis and Approaches only.”

11/28/2018 34


Initial HE position

Imperial College London

Both HL courses will be accepted but some subjects will have a preference for

Mathematics: Analysis and Approaches, eg

Civil Engineering

Minimum entry standards

• Our minimum entry standard for 2019 entry is 39 points overall, to include:

• 7 in Mathematics at higher level

• 6 in Physics at higher level

• Typical offer range

• As a guide, the typical offer made in 2017 to at least 85% of applicants

studying IB was 39 points overall.

• Mathematics Higher Level for award in 2021

• For entry in 2021, the Mathematics Analysis and Approaches or the

Applications and Interpretation syllabi will be accepted at higher level with

no preference.

11/28/2018 35


English A

11/28/2018 36


Language A (English)

The current offer is:

• Language A: Literature SL & HL

• Language A: Language and Literature SL & HL

• English (and Spanish) Literature and Performance SL

The Literature and Language and Literature

specifications are common to all languages examined.

All three courses assume students are proficient in the

language studied.

11/28/2018 37


General Characteristics

All three courses are designed for students who have experience of

using the language of the course in an academic context. The

language background of such students, however, is likely to vary

considerably — from monolingual students to students with more

complex language profiles. The study of texts, both literary and non-

literary, provides a focus for developing an understanding of how

language works to create meanings in a culture, as well as in particular

texts. All texts may be understood according to their form, content,

purpose and audience, and through the social, historical, cultural and

workplace contexts that produce and value them. Responding to, and

producing, texts promotes an understanding of how language

sustains or challenges ways of thinking and being.

11/28/2018 38


Differences between the 3 courses

The main difference lies in the different areas of focus each takes.

• In the language A: literature course, focus is directed towards

developing an understanding of the techniques involved in literary

criticism and promoting the ability to form independent literary

judgments.

• The focus of the language A: language and literature course is

directed towards developing and understanding the constructed

nature of meanings generated by language and the function of

context in this process.

• Literature and performance allows students to combine literary

analysis with the investigation of the role of performance in our

understanding of dramatic literature.

11/28/2018 39


May 2017 English Entries

Total number of Diploma Programme candidates:

157488

Entries and Grade distribution:

11/28/2018 40

Entries 7 6 5 4 3

Lit SL 7227 5.5 27.9 38.3 23.8 4.3

Lit HL 42338 3.6 18.9 40.4 28.7 7.6

Lang &

Lit SL

13322 4.9 32.3 43.5 17.0 2.2

Lang &

Lit HL

21109 4.8 25.1 38.9 25.4 5.5

Lit &

Perf SL

572 3.8 16.6 34.2 31.9 13.0


A more integrated course

11/28/2018 41

There are seven central concepts in

the proposed syllabus which act as

structuring axes around which the

syllabus revolves. The parts of the

syllabus will no longer be isolated

from one another; instead, they will

become “areas of exploration” which

will include texts from different

genres, and written originally in the

language studied or read in

translation, in each one of them.

These areas of exploration should

not be seen as isolated individual

units, but rather as complementary

and at times overlapping approaches

to the study of literature.

© International Baccalaureate Organization 2017 11/28/2018 42







Assessment – The Key elements

• There is no one-to-one correspondence between

the parts of the syllabus and the assessment

components

• Greater freedom for teachers and students to decide

which works to use in which part and for which

assessment component

• Portfolio: structuring element

• Internal assessment: focus on connections between

texts and global matters

11/28/2018 48




Professional development for Maths

and English A

• IBEN being upskilled now

• Guides, TSMs, specimen assessments available Feb

2019

• Experienced teachers can upskill to the new courses

through CAT 3 ‘subject specific seminars’ (SSS)

• First SSS at Aston University, Birmingham 22-24 Feb

2019

• IBSCA CAT 1 workshops at University of Warwick 5-7

April

• IBSCA also planning to deliver subject seminar days

after April 2019, dates to be circulated.

11/28/2018 51

Documents

IB Update - Welcome to IBSCA | IBSCA · 2018-11-30 · The binomial theorem Applications SL Approximation, upper and lower bounds, percentage errors Financial applications of geometric