TataKelola dan KamSiber Kecerdasan Buatan v022.pdf
kla_maths_pd_trw.ppt
1. MATHEMATICS
KLA Years 1 to 10
Thinking, reasoning and
working mathematically
MATHEMATICS
Years 1 to 10
2. Purpose of
presentation
to define thinking, reasoning and
working mathematically (t, r, w m)
to describe how t, r, w m enhances
mathematical learning
to promote and support t, r, w m through
investigations.
3. Thinking, reasoning and
working mathematically
involves making decisions about what
mathematical knowledge, procedures and
strategies are to be used in particular
situations
incorporates communication skills and ways
of thinking that are mathematical in nature
is promoted through engagement in
challenging mathematical investigations.
4. Thinking, reasoning and
working mathematically
also
promotes higher-order thinking
develops deep knowledge and
understanding
develops students’ confidence in their
ability ‘to do’ mathematics
connects learning to the students’ real
world.
5. What is thinking
mathematically?
making meaningful connections with prior
mathematical experiences and knowledge
including strategies and procedures
creating logical pathways to solutions
identifying what mathematics needs to be known
and what needs to be done to proceed with an
investigation
explaining mathematical ideas and workings.
6. What is reasoning
mathematically?
deciding on the mathematical knowledge,
procedures and strategies to use in a situation
developing logical pathways to solutions
reflecting on decisions and making appropriate
changes to thinking
making sense of the mathematics encountered
engaging in mathematical conversations.
7. What is working
mathematically?
sharing mathematical ideas
challenging and defending mathematical
thinking and reasoning
solving problems
using technologies appropriately to support
mathematical working
representing mathematical problems and
solutions in different ways.
8. How can t, r, w m be
promoted?
By providing learning opportunities that are:
relevant to the needs, interests and abilities of the
students
strongly connected to real-world situations
based on an investigative approach — a problem to
be solved, a question to be answered, a significant
task to be completed or an issue to be explored.
9. Planning for investigations
Identify how and when reporting of
student progress will occur
Identify how and when
judgments will be made about
students’ demonstrations of
learning
Identify how evidence of
demonstrations of learning will be
gathered and recorded
Select and
sequence learning
activities and
teaching strategies
Identify or design
assessment
opportunities
Select learning
outcomes on which
to focus
Select strategies to promote
consistency of teacher
judgments
Choose the context(s)
for learning
Make explicit what students
need to know and do to
demonstrate their learning
10. How do investigations
promote t, r, w m?
Sample investigations present the learning
sequence in three phases:
identifying and describing
understanding and applying
communicating and justifying.
Each phase promotes the development of
thinking, reasoning and working mathematically.
11. Identifying and
describing
Students:
identify the mathematics in the investigation
describe the investigation in their own words
describe the mathematics that may assist them in
finding solutions
identify and negotiate possible pathways through
the investigation
identify what they need to learn to progress.
Phase 1
12. Sample questions to
encourage t, r, w m in
phase 1
What mathematics can you see in this
situation?
Have you encountered a similar problem
before?
What mathematics do you already know that
will help you?
What procedures or strategies could you use to
find a solution?
What do you need to know more about to do
this investigation?
13. Understanding and
applying
Students:
acquire new understandings and knowledge
select strategies and procedures to apply to the
investigation
represent problems using objects, pictures,
symbols or mathematical models
apply mathematical knowledge to proceed through
the investigation
generate possible solutions
validate findings by observation, trial or
experimentation.
Phase 2
14. Sample questions to
encourage t, r, w m
in phase 2
What types of experiments could you do to
test your ideas?
Can you see a pattern in the mathematics?
How can you use the pattern to help you?
What other procedures and strategies could
you use?
What else do you need to know to resolve
the investigation?
Is your solution close to your prediction? If
not, why is it different?
15. Communicating and
justifying
Students:
communicate their solutions or conclusions
reflect on, and generalise about, their learning
justify or debate conclusions referring to
procedures and strategies used
listen to the perceptions of others and
challenge or support those ideas
pose similar investigations or problems.
Phase 3
16. Sample questions to
encourage t, r, w m in
phase 3
What is the same and what is different
about other students’ ideas?
Will the knowledge, procedures and
strategies that you used work in similar
situations?
What mathematics do you know now
that you didn’t know before?
17. Teachers can support t,
r, w m by:
guiding mathematical discussions
providing opportunities for students to develop the
knowledge, procedures and strategies required for
mathematical investigations
presenting challenges that require students to pose
problems
providing opportunities to reflect on new learning.
18. The syllabus
promotes
t, r, w m by:
describing the valued attributes of a lifelong learner
in terms of thinking, reasoning and working
mathematically
encouraging students to work through problems to
be solved, questions to be answered, significant
tasks to be completed or issues to be explored
advocating the use of a learner-centred,
investigative approach in a range of contexts
emphasising the connections between topics and
strands that are often required in dealing with
mathematics in ‘real-life’ situations.
19. Materials to support thinking,
reasoning and working
mathematically
How to think, reason and work mathematically (poster)
About thinking, reasoning and working mathematically
(information paper)
Prompting students to think, reason and work
mathematically (paper)
Thinking, reasoning and working mathematically in the
classroom (paper)
Papers described in the annotated bibliography in the
‘Additional information’ section of the support materials
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