Saturday, September 14, 2013
I Teach K: EDU330 Elementary Mathematics 08/17/13 Session 6: Today, you had fun with Ms Peggy Foo on lesson study and solving a bunch of enrichment lessons as well as to learn about differentiated inst...
Sunday, August 18, 2013
Gelman’s Counting Principle
How do we know whether children can count ?
If knowing how to count just means reciting
the numbers (i.e., ‘‘one, two, three...”) up to “five” or
“ten,” perhaps pointing to one object with each numeral,
then many two-year-olds count very well.
Of course, counting only tells you number of things if you do it correctly,
following the three ‘how-to-count’ principles identified by Gelman and
Gallistel (1978). These are :
(1) The one-to-one principle, which says that ‘‘in
enumerating a set, one and only one [numeral] must
be assigned to each item in the set.”
counting must be used in the same order in any one
count as in any other count.” and
(3) The cardinal principle, which says that ‘‘the [numeral] applied to the
final item in the set represents the number of items in the set.”
As Gelman and Gallistel pointed out, so long as the
child’s counting obeys these three principles, the numeral
list (‘‘one,” ‘‘two,” ‘‘three,”... etc.) represents the cardinalities
1, 2, 3,... etc.
However, observations have shown that three-year-old
children often violate the one-to-one principle by skipping
or double-counting items, or by using the same numeral
twice in a count.
Children also violate the stable-order principle, by producing different
numeral lists at different times.
The cardinal principle can also be viewed as something more profound
– a principle stating that a numeral’s cardinal meaning is determined by
its ordinal position
in the list. This means, for example, that the fifth numeral in
any count list – spoken or written, in any language – must
mean five. And the third numeral must mean three..
If so, then knowing the cardinal principle means having
some implicit knowledge of the successor function – some
understanding that the cardinality for each numeral is generated by
adding one to the cardinality for the previous numeral.
Thus Gelman feels that preschoolers learn to count as a result of the
perfecting of counting procedures.
Do you agree ?
Saturday, August 17, 2013
The multiplication method my teachers never taught me. I wish I had learnt this way earlier. I was taught the top down method.
Friday, August 16, 2013
This formula was created by Georg Alexander Pick in 1899.
Using the Geoboard to Assist :
· Draw a polygon on the Geoboard
· Determine the number of boundary points and the number of interior points and calculate its area
· Repeat with different polygons
· Draw polygons without any interior points and find the area
· Draw polygons with one interior point and find the area
· Draw polygons with two interior points and find the area
· Prepare a table with number of boundary points, number of interior points, and area. Discover that the relationship between B the number of boundary points, i the number of internal points, and the area of the geoboard polygon is given by Pick's formula A = I + ½ B – 1
The diagram below explains this further.
I understand this better now! Wow :)
Wednesday, August 14, 2013
What is Subitizing ?
Perceptual subitizing is closest to the original definition of subitizing: recognizing a number without counting. For example, children might "see 3" without using any learned mathematical knowledge.
But how is it that people see an eight-dot domino and 'just know" the total number? This is Conceptual subitizing. They are able to see the relationship between numbers when dealing with different quantities. These people are capable of viewing number and number patterns as units of units (Steffe and Cobb 1988).
Spatial patterns, such as those on dominoes, are one kind.
Subitizing and counting
Young children may use perceptual subitizing to make units for counting and to build their initial ideas of cardinality.
By : Marina Ho - BSc08