7 Jan 2014: Interview with Marian Lee

I Teach K: EDU330 Elementary Mathematics 08/17/13 Session 6

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...

Gelman's Counting Principle

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.”

 

(2) The stable-order principle, which says that ‘‘[Numerals] used in

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 ?

 

Marina Ho-BSc08

Fast Math Tricks - How to multiply 2 digit numbers up to 100 - the fast ...

The multiplication method my teachers never taught me. I wish I had learnt this way earlier. I was taught the top down method.

Pick’s Theorem

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 :)

Marina Ho
BSc08

 

 

By The Numbers - Subitizing

Watch this video on what subitizing means.

Elementary Math - Day 3 Blog

What is Subitizing ?

 

Perceptual 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.

 

Conceptual subitizing

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

Seed Institute