Saturday, September 14, 2013
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...
Sunday, August 18, 2013
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
twoyearolds count very well.
Of course, counting
only tells you number of things if you do it correctly,
following the three
‘howtocount’ principles identified by Gelman and
Gallistel (1978). These are :
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 threeyearold
children often
violate the onetoone principle by skipping
or doublecounting
items, or by using the same numeral
twice in a count.
Children also violate
the stableorder 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 HoBSc08
Saturday, August 17, 2013
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.
Friday, August 16, 2013
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
Wednesday, August 14, 2013
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 eightdot 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
Tuesday, August 13, 2013
Elementary Math  BSc08
What are Nominal Numbers ?Numbers used to name something eg. Blk 543, a bus number 963 or your IC No. 7612345B.
How we have often mistaken the bus numbers to be nine hundred and sixty three, instead of "9" "6" "3".
What are Ordinal Numbers ?
Ordinal numbers are used very often to label the position of children lined up in a row, eg. 1st, 2nd, 3rd, 4th, 5th etc.
In the picture below children can also learn to count from the 2nd person (Sam) and also backwards in position, to determine how many children are before Sam. Thus ordinal numbers can be used children a different way of understanding number counting.
Marina Ho  BSc08
Seed Institute
Elementary Math  Daily Blogs
Learning About Numbers for Children
Children have to learn about counting in 2 different ways; Rote counting and Rational Counting.When children learn rote counting they are counting in sequence without knowledge of quantity. However, when children learn rational counting, they learn how to count wth knowledge and understanding. They count with cardinality in mind.
The above video show rational counting, where children have to learn 1 to 1 correspondence in counting different objects.
This shows how children need to be shown concrete objects or have a pictorial representation to have a realtionship about what a number quantity means.
Sunday, August 4, 2013
Understanding Mathematics
well planned should examine whether 6 areas are present.
These
are; high standards and strong support
for students,
curriculum that is focused and coherent, teaching that
challenge
and support students. Next would be learning with
understanding from prior
knowledge, assessment for
students to find new information, and lastly
technology like calculators and computers are
used to enhance learning.
The Math classroom should also have 6 components
:

an environment that gives students an equal
opportunity to learn

teaching that has a balance of both conceptual
understanding and procedural fluency

ensures active student participation in problem
solving, reasoning, communications, connections and representation

use of technology to improve understanding

emphasis on reasoning of math
Parents also need to know what it means to
understand math in today’s classroom. Relational understanding means knowing
what to do and why, while the opposite is instrumental understanding (just
doing without understanding). Thus students who have proficiency in math would
have mastery in 5 areas :

conceptual understanding : knowledge about the
relationship between ideas in a topic.

Procedural fluency : able to use rules and procedures
in carrying out math processes.

Strategic competence : able to use different methods
to eventually solve a problem.

Adaptive reasoning : able to reflect, evaluate and
adapt or use different methods.

Productive disposition : when solving a problem you
should rely on a how to and applying your knowledge rather than a recall method
of how you can solve it.
I trust these
points in mind would make parents see Math in a different light.. Math is not
to be approached through rote drilling and countless worksheets but with
crystal clear thought and understanding.
By : Marina Ho Mee Lin
SEED  BSC08
By : Marina Ho Mee Lin
SEED  BSC08
Wednesday, July 31, 2013
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