Introduction to Mathematics IA
The Exploration
Internal assessment in mathematics SL is an individual
exploration. This is a piece of written work that
involves investigating an area of mathematics. It is
marked according to five assessment criteria.
Internal assessment is an integral part of the mathematics SL
course, contributing 20% to the final assessment in the
course.
It is expected that a total of approximately 10 teaching hours
should be allocated to the work. This should include:
•
time for the teacher to explain to students the
requirements of the exploration
•
class time for students to work on the exploration
•
time for consultation between the teacher and each
student
•
time to review and monitor progress, and to check
authenticity.
The internally assessed component in this course is a mathematical exploration. This is
a short report written by the student based on a topic chosen by him or her, and it
should focus on the mathematics of that particular area. The emphasis is on
mathematical communication (including formulae, diagrams, graphs and so on), with
accompanying commentary, good mathematical writing and thoughtful reflection. A
student should develop his or her own focus, with the teacher providing feedback via,
for example, discussion and interview. This will allow the students to develop area(s)
of interest to them without a time constraint as in an examination, and allow all
students to experience a feeling of success.
The final report should be approximately 6 to 12 pages long. It can be either word
processed or handwritten.
Students should be able to explain all stages of their work in such a way that
demonstrates clear understanding.
While there is no requirement that students present their work in class, it should be
written in such a way that their peers would be able to follow it fairly easily. The
report should include a detailed bibliography, and sources need to be referenced in
line with the IB academic honesty policy. Direct quotes must be acknowledged
Requirements and recommendations
Students can choose from a wide variety of activities, for
example, modelling, investigations and applications of
mathematics. To assist teachers and students in the
choice of a topic, a list of stimuli is available in the
teacher support material. However, students are not
restricted to this list.
The exploration should not normally exceed 12 pages,
including diagrams and graphs, but excluding the
bibliography. However, it is the quality of the
mathematical writing that is important, not the length.
Requirements and recommendations
The teacher is expected to give appropriate guidance at
all stages of the exploration by, for example, directing
students into more productive routes of inquiry, making
suggestions for suitable sources of information, and
providing advice on the content and clarity of the
exploration in the writing-up stage.
Teachers are responsible for indicating to students the
existence of errors but should not explicitly correct these
errors. It must be emphasized that students are expected
to consult the teacher throughout the process.
Requirements and recommendations
All students should be familiar with the
requirements of the exploration and the criteria by
which it is assessed.
Students need to start planning their explorations
as early as possible in the course. Deadlines should
be firmly established. There should be a date for
submission of the exploration topic and a brief
outline description, a date for the submission of the
first draft and, of course, a date for completion
Requirements and recommendations
In developing their explorations, students should
aim to make use of mathematics learned as part of
the course.
The mathematics used should be commensurate
with the level of the course, that is, it should be
similar to that suggested by the syllabus. It is not
expected that students produce work that is
outside the mathematics SL syllabus—however, this
is not penalized
Developing The Exploration
 The topic is one that interests you. (It is easier
to stay motivated and work hard)
While deciding the topic of the exploration a
student should keep in mind that there is
enough scope of Mathematical analysis in the
topic.
Timeline – Developing The
Exploration
Process
Date
begun
Date
ended
Think about a stimuli
 Choose a topic
Oct 3rd
Oct 10th
Draft exploration
Nov 11th Nov 14th
 Introduction
o Outline the aim and purpose in a clear and
succinct manner.
o Justify the exploration choice
o Briefly discuss the area of mathematics
that will be used.
o Evidence of some research.
Progress
check
Timeline – Developing The
Exploration
 Body/Mathematical Exploration
o Describe the method, followed
by an investigation
o Record your results (tables, lists
etc)
o Analyse the results (graphs,
diagrams, calculations etc) and
form conjectures.
Timeline – Developing The
Exploration
 Conclusion and Bibliography
o Summarise your findings in response to your
aim. Restate any rules, conjectures or
models that you found.
o Comment on any limitations to your
approach, or to your findings.
o Comment on possible extensions and real
life connections. Relate it to your personal
knowledge and to your previous knowledge.
o Including a reflection on what you have
learned and what you have taken away from
this experience will reflect personal
engagement.
Timeline – Developing The
Exploration
 First Draft Due date
Nov 25th
Teacher to review & comment on draft
 Meet with teacher
Dec 1st
Final writing
 Revise draft
Dec 15th Dec 16th
Final version due date: Dec 18th
Dec 3rd
Planning – Mind Mapping
Stimuli
sport
algorithms
sine
e
space
volcanoes
games
codes
tiling
viruses
play
biology
physics
psychology
archaeology
cell phones
musical harmony
electricity
orbits
diet
symmetry
the internet
population
health
π
business
chemistry
computers
music
motion
water
food
Euler
architecture
communication
agriculture
dance
geography
economics
information technology
in a global society
Choose a stimulus and create your
own mind map here.
The Assessment Criteria
The Assessment Criteria
Your teacher expects these skills and strategies
from you:
Choosing a topic
 Identifying an appropriate topic
 Developing a topic
 Devising a focus that is well defined and
appropriate
 Ensuring that the topic lends itself to a concise
exploration
The Assessment Criteria
Communication
 Expressing ideas clearly
 Identifying a clear aim for the exploration
 Focusing on the aim and avoiding irrelevance
 Structuring ideas in a logical manner
 Including graphs, tables and diagrams at
appropriate places
 Editing the exploration so that it is easy to follow
 Citing references where appropriate
The Assessment Criteria
Mathematical presentation
 Using appropriate mathematical language and
representation
 Defining key terms, where required
 Selecting appropriate mathematical tools
(including information and communication
technology)
 Expressing results to an appropriate degree of
accuracy
The Assessment Criteria
Personal engagement
 Working independently
 Asking questions, making conjectures and
investigating mathematical ideas
 Reading about mathematics and researching
areas of interest
 Looking for and creating mathematical models
for real-world situations
 Considering historical and global perspectives
 Exploring unfamiliar mathematics
The Assessment Criteria
Reflection
 Discussing the implications of results
 Considering the significance of the
exploration
 Looking at possible limitations and/or
extensions
 Making links to different fields and/or
areas of mathematics
The Assessment Criteria
Use of mathematics
 Demonstrating knowledge and understanding
 Applying mathematics in different contexts
 Applying problem-solving techniques
 Recognizing and explaining patterns, where
appropriate
 Generalizing and justifying conclusions
The Assessment Criteria
The Assessment Criteria
The Assessment Criteria
The Assessment Criteria
As part of the learning process, teachers can
give advice to students on a first draft of the
exploration. This advice should be in terms of
the way the work could be improved, but this
first draft must not be heavily annotated or
edited by the teacher.
The next version handed to the teacher after the
first draft must be the final one.
Authenticity
Authenticity may be checked by discussion with the
student on the content of the work, and scrutiny of
one or
more of the following:
•
the student’s initial proposal
•
the first draft of the written work
•
the references cited
•
the style of writing compared with work
known to be that of the student
Self-Assessment
When completing your self assessment, use the
language of the rubrics and the teacher
expectations to comment on why you have
given yourself this particular grade. Set goals for
yourself for each criterion.
Checklist
Item
Is the work entirely yours?
Have you chosen a topic that you are interested in and
developed your own ideas? Is it evident in your
exploration?
Have you explained the reason why you have chosen your
topic in your exploration?
Is the aim of your exploration included in your
introduction?
Do you have an introduction and conclusion? Is your
exploration organized?
Have you defined key terms/variables?
Have you used appropriate mathematical language
(notation, symbols and terminology) consistently
throughout your exploration?
** Calculator/computer notation should not be used. **
Yes
Partially
No
Checklist
Have you used more than one form of mathematical
representation? Are all graphs, tables and diagrams
sufficiently described and labeled?
Are formulae, graphs, tables and diagrams in the main body
of the text? No full-page graphs and no separate appendices.
Have you used technology to enhance your exploration?
Have you explained what you are doing at all times?
Explanatory comments should be seen throughout your
exploration?
Have you used mathematics that is commensurate with the
Standard Level course (or beyond)?
Is the mathematics in your exploration correct?
Have you reflected on your finding at appropriate places in
your exploration, particularly in your conclusion?
Have you considered limitations and extensions in your
reflection?
Have you considered the assessment criteria when writing
your exploration? Have you self assessed your exploration?
Checklist
Is your exploration approximately 6 to 12 pages long?
Have you referenced your work in a bibliography?
Have you had someone else read your exploration to ensure
that the communication is good? Does it have flow and
coherence? Is it easily understandable? Does it read well?
Have you completed your self-assessment?
Have you submitted a first draft to your teacher and used the
feedback to improve your report?
Authenticity
Plagiarism
This includes copying quotes, information and ideas, directly or paraphrased,
from books and websites.
Collusion
This includes working closely with another student such that the work
between the two students is similar.
Ensuring academic honesty
To prevent plagiarism, you need to cite your sources correctly and include any
sources in your bibliography. If you have questions on how to properly cite
your sources, seek advice from your teacher or from the school librarian.
To prevent collusion, you should discuss ideas with other students, but you
should never giver another student your work, either in print or electronically.
Recommended Technology
Some examples of technology include:
•any kind of calculators, the internet, data logging devices
•word processing packages, spreadsheets, graphics packages
•statistics packages or computer algebra packages.
Great software for working with graphs, diagrams, functions,
spreadsheets, statistics, calculus and much, much more.
www.geogebra.org
A modern, easy-to-learn, programming language that is great for
writing simulations. There are loads of tutorials available: just
google “python tuts”.
www.python.org
An online graph plotter with graphing capabilities similar to those of your
graphical calculators.
www.fooplot.com
A really powerful search engine. (For example,
type “find antiderivative of f(x) = 3x” into the
search bar.)
www.wolframalpha.com