Solve The ’Handshakes’ Problem .

Instructions:
This assignment requires you to administer a mathematical problem to a primary-aged student in either Stage 2 or
Stage 3 (i.e. Year 3 to Year 6), and collect work samples that will be annotated and analysed in relation to the NESA
Mathematics K-10 (2022) Syllabus (Years 3-6). As a result of your analysis you will make suggestions for future
directions for your student.
TASK A: Problem-solving by you (i.e. the Pre-service Teacher)
1. Solve The ’Handshakes’ Problem (detailed below) yourself.
2. Provide at least two solutions to the problem, and include both concrete and abstract representations. Make sure one is concrete and one is abstract. You need to show evidence for both your solution and the students.
3. Use photos, drawings or diagrams, and algorithms to illustrate your abstract and concrete solutions.
4. Include an explanation in words about how you solved both representations.
The ’Handshakes’ Problem– Seven TEAC3019 mathematicians met up one week.– The first TEAC3019 mathematician shook hands with all the others.– The second one shook hands with all the others apart from the first one, since they had already shaken hands.– The third one shook hands with all of the others apart from the first and the second mathematicians, and so
on, until everyone had shaken hands with everyone else.
How many handshakes were there altogether?

TASK B: Problem-solving completed by Stage 2 or 3 Primary student
Select ONE student from Year 3 to 6 and have him/her attempt The ’Handshakes’ Problem.
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Note: You should make available a range of materials such as paper, pens, pencils, rulers, or any other appropriate
concrete materials you think the student might use. ( You can make this up as if you did ask a student in year 4) But you need to provide pictures of how they worked it out.

– Interview the student to gather further information for your report.– Code the questions you ask the student and the student responses (SI, 01 etc.), so that this information can
be used in your analysis.– Submit a transcript of this interview as a part of the Appendix for the assignment.– During the activity, record any observations that would be relevant to assessing the student’s thinking and
achievement. The observations recorded must be submitted with the assessment. Code these observations
(OS1 etc.), so that they can be used to justify the achievement or non-achievement of the mathematical
outcomes addressed in the analysis.– Collect, organise, annotate and submit the student’s works samples that show their mathematical thinking as
they investigate the problem. Code these work samples (WS01 etc.), and submit these work samples in the
Appendix of the assignment.–

Using all of the evidence you have collected, write a report (approx. 800 – 1000 words) analysing the work
samples, your observations and interview notes to determine the student’s knowledge and thinking according
to the current Mathematics K-10 (2022) Syllabus (Years 3-6). Include direct links to the evidence by using
your coding of the interview transcript, student observations and work samples, as well as the NSW K-10
Mathematics Syllabus (Eg. MA2-AR-01), to indicate the multiple levels of achievement of this student.– Justify your analysis discussion with references from at least five relevant sources and includes current mathematics literature.

TASK C: Suggestions for Improvement (Approx. 400 words) – Describe three activities or pedagogical strategies that you would use to further develop your student’s mathe
matical thinking. Include a rationale, based on your reading, for the activities or strategies that you describe.– Ensure your recommendations address the issues reported in the analysis and clearly link to the identified
needs of your particular student.– If your suggestions are pedagogical strategies, please provide a brief example of an activity that
exemplifies how you would implement your recommendation/

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