saibsa mathematical exploration session - feb 2013
TRANSCRIPT
Mathematical Exploration New Internal Assessment
SAIBSA - Jamnabai Narsee School
February 9, 2013
The Agenda- SessionPage 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
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.
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.
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.
Role of the TeacherPage 6
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
The Exploration ProcessPage 8
How do we put a process in place?
Setting deadlines
How to start
When to start
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
Page 10
What do we do before the formal process
begins?
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.
Page 12
A possible mind map for the stimulus “water”Page 13
Page 14
Can you think of other branches?
Expand this mind-map
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
Page 17
Understanding Internal
Assessment criteria
Each exploration is marked using the following 5 criteriaPage 18
4 marks
3 marks
4 marks
3 marks
6 marks
Math HL Guide – pg 66
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
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.
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
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
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?‟
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.
Characteristics of Good ExplorationPage 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
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
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.
Record Keeping: Page 28
Exploration form - TSM
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
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)