1. Mathematical Exploration
New Internal Assessment
SAIBSA - Jamnabai Narsee School
February 9, 2013

2. The Agenda- Session
Page 2
o Internal Assessment in Mathematics HL/SL
o The role of the teacher
o Keeping the topic focused
o The assessment criteria and expectations

3. Mathematical Exploration :
Page 3
 Written submission addressing group 5 aims
 A short report written by the student based on the
chosen topic
 It should focus on the mathematics of that particular
area
 Emphasis is on mathematical communication
(including formulae, diagrams, graphs and so on), with
accompanying commentary, good mathematical
writing and thoughtful reflection.

4. Mathematical Exploration cont……….
Page 4
 The final report should be approximately 6 to 12
pages long. It can be either word processed or
hand written.
 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.

5. Mathematical Exploration cont……….
Page 5
 Teachers can provide feedback
 Approximately 10 hours of class time and a further 10
hours outside of class.
 Intended audience is the mathematics class
 Students will not receive a grade for Mathematics HL or
SL if they don’t submit an exploration.

6. Role of the Teacher
Page 6

7. What is the teacher role?
Page 7
 Advise on choice of topic
 Assist in learning new skills
 Clarify assessment criteria
 Support students through process
 Provide feedback

8. The Exploration Process
Page 8
How do we put a process in place?
When
to start
How to
start
Setting
deadlines

9. The Exploration:
Page 9
 When do we start preparing students about it?
 What do we do before the formal process begins?
 How many explorations does the student actually write?
 How do we ensure that exploration is student‟s own work?
 Difference between IAs and EEs

10. Page 10
 What do we do before the formal process
begins?

11. What are stimuli and how could they be used?
Page 11
Students sometimes find it difficult to know
where to start with a task as open-ended as this.
While it is hoped that students will appreciate
the richness of opportunities for mathematical
exploration, it may sometimes be useful to
provide a stimulus as a means of helping them
to get started on their explorations.

12. Page 12

13. A possible mind map for the stimulus “water”
Page 13

14. Can you think of other branches?
Expand this mind-map
Page
14

15. Opening their minds…………..
Page 15
 mathmoments.swf

16. Page 16
Encourage students to look for ideas everywhere
and give access to such material
 NCTM – National Council of Teachers of Mathematics
- http://www.nctm.org/
 NRICH mathematics - http://nrich.maths.org/teacher-
secondary
 Mathscareers - http://www.mathscareers.org.uk

17. Page 17
Understanding Internal
Assessment criteria

18. Each exploration is marked using the following 5 criteria
Page 18
4 marks
3 marks
4 marks
3 marks
6 marks
Math HL Guide – pg 66

19. Criterion A – Communication (4 marks)
Page 19
This criterion assesses the overall organization and
coherence of the exploration.
 Clearly explain what is being done in a concise and focused manner so the
reader is not left guessing
 Avoid over describing mathematical expressions / methods using words –
mathematics is itself a language
 Avoid repeating yourself
 Explicitly write what your aims are
 Ensure your original aims are addressed / fulfilled

20. Criterion B – Mathematical presentation (3marks)
Page 20
This criterion assesses the appropriateness of
the mathematics, in particular, to what extent
the student is able to:
 use appropriate mathematical language (e.g mathematical
notation, symbols, terminology)
 define key terms, where required
 use multiple forms of mathematical representation, such as
formulae, diagrams, tables, charts, graphs and models, where
appropriate.

21. Page 21
 Use a variety of graphs, tables and diagrams that:
 accompany the work in the appropriate place and not be
attached to the end of the document
 be clear and correctly labelled
 enhance the clarity and improve the communication of
mathematical ideas
 Any “screen shots” from graphic calculators should be labelled by
hand if necessary
 Avoid using calculator notation when writing mathematical
expressions

22. Criterion C – Personal Engagement (4 marks)
Page 22
This criterion assesses “ownership of the exploration” or
the extent to which the student engages with the
exploration and makes it his or her own.
 Choose a topic that you are genuinely interested in
 Ensure you explicitly refer to such personal interest in the chosen topic
early on in your report
 Use your own examples, language, solutions, proofs and explanations…
etc. to illustrate ownership of the exploration
 If the exploration allows, show initiative and go beyond your original aim

23. Criterion D – Reflection (3 marks)
Page 23
This criterion assesses how the student reviews,
analyses and evaluates the exploration. Although
reflection may be seen in the conclusion to the
exploration, it may also be found throughout the
exploration. Reflection may be demonstrated by:
 consideration of limitations and/or extensions
 relating mathematical ideas to personal/previous knowledge
 raising questions such as „what is the significance of what I have
learnt?‟ or „how could my ideas be extended in this context?‟

24. Criterion E – Use of Mathematics - HL vs SL (6 marks)
Page 24
 Students are expected to produce work that is commensurate
with the level of the course.
 The mathematics explored should either be part of the
syllabus, or at a similar level or beyond.
 It should not be completely based on mathematics listed in the
prior learning.
 If the level of mathematics is not commensurate with the level
of the course, a maximum of two marks can be awarded for this
criterion.

25. Characteristics of Good Exploration
Page 25
 Introduction/ aim, rational
 A coherent argument is developed
 Easy to follow
 Mathematical presentation is strong
 Personal engagement and enthusiasm come through
 Analyses and evaluation is given by the student through out the
exploration
 Mathematics explored is precise

26. Back to our questions………….
Page 26
 How many explorations does the student
actually write?
 How do we ensure that exploration is student‟s
own work?
 Difference between IAs and EEs

27. Planning……………
Page 27
1. Ensure that students have time to explore the mathematics.
2. Give a realistic deadline for submission of a draft of the written
exploration.
3. Give a realistic deadline for feedback to the students.
4. Give a realistic deadline for final submission.
5. Be aware of students‟ mathematical experience in relation to
the exploration at the time of doing the exploration and record
this.

28. Record Keeping:
Page 28
 Exploration form - TSM

29. True or false?
The purpose of the mathematical exploration is …
Page 29
1. To give the SL/HL student the opportunity to produce a mathematical
report that focuses on the mathematics of a topic that interests him/her
2. To enable the student to demonstrate the application of their skills and
knowledge, and to pursue their personal interests, without the time
limitations and other constraints that are associated with written
examinations
3. To highlight the importance of mathematical communication (including
formulae, diagrams, graphs and so on), with accompanying commentary,
good mathematical writing and thoughtful reflection.
4. To give the SL/HL student the opportunity to produce mathematical
reports of similar quality to the old portfolio tasks

30. True or false?
The purpose of the mathematical exploration is …
Page 30
1. To give SL/HL student the opportunity to produce a mathematical report
that focuses on the mathematics of a topic that interests him/her (T)
2. To enable the student to demonstrate the application of their skills and
knowledge, and to pursue their personal interests, without the time
limitations and other constraints that are associated with written
examinations (T)
3. To highlight the importance of mathematical communication (including
formulae, diagrams, graphs and so on), with accompanying commentary,
good mathematical writing and thoughtful reflection. (T)
4. To give the SL/HL student the opportunity to produce mathematical reports
of similar quality to the old portfolio tasks (F)