REASONING AND CONNECTION ACROSS A-LEVEL MATHEMATICAL CONCEPTS. Dr Toh Tin Lam National Institute of Education. COMMUNICATION, REASONING & CONNECTION. Singapore Mathematics Framework Reasoning Connection Communication. Singapore Mathematics Framework. Beliefs Interest Appreciation
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REASONING AND CONNECTION ACROSS A-LEVEL MATHEMATICAL CONCEPTS
Dr Toh Tin Lam
National Institute of Education
Monitoring of one’s own thinking
Self-regulation of learning
Reasoning, communication and connections
Thinking skills and heuristics
Applications and modelling
Use of mathematical tools
(Selden, Selden, Hawk & Mason, 1999)
to build on making gazing and making conjectures...
deeper understanding of the proof itself...
The sequence u1,u2, ...... , un ,...is defined by
and u 1 =1, u2 = 1. Express un in terms of n and justify your answer.
By considering the expansion of
or otherwise, evaluate the n derivative of
when x = 0.
Solving the differential equation,
Does it make sense?
Find the number of ways to permute 6 “s”s and 4 “f”s in a row.
Is the answer or
If X Bin (n, p), then
If you suspect a statement is TRUE, try to prove it; if you think that it is FALSE, try to look for a counter-example to disprove the statement. Get students to think over the logical statement. Lead students to communicate in acceptable mathematical language