What is mathematics?
Who called mathematics the "queen of the sciences"?
Carl Frederich Gauss
Can you explain two different meanings of "count" (v.) ? (related to numbers)
1. Determine the total number of (a collection of items)
‘I started to count the stars I could see’
2. Recite numbers in ascending order.
‘hold the position as you count to five’
3. (count down)Recite or display numbers backwards to zero to indicate the time remaining before the launch of a rocket or the start of an operation.
(Longman dictionary)
Alfred North Whitehead (1956, p.402) suggests mathematics is the "most original creation of the _____ ______".
human spirit
Which one is more fundamental:
ordinality or cardinality?
uncertain
ordinality (序数) cardinality(基数)
There is considerable dispute among mathematicians as to whether ordinality or cardinality is the more fundamental concept, and whether either is more fundamental than the natural numbers.
To many students:
"a set of rigid rules, _____ of which you should learn by heart before the final examinations, and _____ of which you should forget afterwards."
(George Polya, 1954b, p.157)
some;
all;
What is the difference between "subitizing" and "counting"?
Subitizing means “instantly seeing how many.”
Math educators have discovered that the ability to see numbers in patterns is the foundation of strong number sense.
The ability to visualize and understand numbers and numeration supports operational fluency and the ability to add and subtract mentally, to see relationships between numbers, and to see patterns.