Saturday, February 5, 2011

Better Spatial Sense as basis to strong Geometric Reasoning Power!

Young children at preschool age who are introduced to explore and experience Spatial Sense Concept is said to have a better reasoning in Geometric Thinking. Spatial Sense is defined as an intuition about shapes and the relationships among shapes. Spatial Sense includes the ability to mentally visualize objects and spatial relationships - to toggle things and objects around one's mind. It includes a comfort with Geometric descriptions of objects and position.
I began to realise the truth in the statement from the textbook, 
Elementary & Middle School Mathematics - Teaching Developmentally, which states that ;
" People with well developed spatial sense appreciate geometric form in art, nature and architecture. They are able to use geometric ideas to describe and analyze their world.
Some people say they are not good with shape or rather having poor spatial sense.The typical belief is that
some people either are or are not born with spatial sense. The writer simply disagree! The truth is
rich experiences with shapes and spatial relationships, when provided consistently over time, can and do develop spatial sense.

Where do you PLACE the numbers to gain VALUES??

When we discuss about PLACE VALUES, we are referring to the prior knowledge of the basic concept of 'Count by Ones' integrated to the Base-Ten concept. Dienes encouraged the use of variation in Mathematics Education.With Procedural knowledge, we are taught how to group the recorded place-value scheme, how numbers are written and how to say them.
According to NTCM Standard, "Making a transition from viewing 'ten' as simply the accumulation of 10 ones to seeing it both as 10 ones and as 1 ten is an important first step for students toward understanding the structure of base-ten number system".
  • The conceptual knowledge of place value consists of the base-ten grouping ideas.
  • When a collection of objects is grouped in sets of ten and some leftover singles, counting the groups of ten and adding the singles tells how many are in the collection.
  • There can be equivalent representations with fewer than the maximum groupings.
  • The base-ten grouping ideas must be integrated with oral and written names for numbers.
  • In addition to counting by ones, children may use two other ways of counting ; by groups and by singles separately and by terns and ones.All three methods of counting are coordinated as the principal method of integrating the concepts, written the names, and the oral names.

Monday, November 1, 2010

Mathematics and Environment?? How and How much are they connected!!

Day in day out, whether or not, are we aware that Mathematics and Environment are inseparable! True enough, I used to take the MRT to SEED Institute, and am not aware that there are lots of Mathematical concepts, we can catch the children's attention to tie with the Concepts learnt in class.
Children learnt to read maps in the MRT routes to enhance their Topological Skills. There is Sequencing in the Map too, like after one station, what is the next station.They will be introduced to terms like'before' and 
'in between'. They learn Ordinal Numbers of 1st,2nd,3rd,4th...
Taking a ride in the MRT, requires the passenger to make some payments. Through MRT fares, children learn Multiplication. They can make predictions of how much money is going to be deducted
from their MRT pre-paid cards. Children will problem solve and started to think, how much is the fare going to be.
Another pointer to take note is learning about directions and locations like right, left,North, South, East and West. These are concepts of Spatial awareness. Children will gain an understanding of positional Language.
Other concepts e.g Distance, Money and Time gives an insight that Mathematics is a Fun-Learning subject ever.....
Distance from Tampines MRT to Tanah Merah MRT, the concepts of _________km away.

Thursday, October 14, 2010

A: Lesson 1 Reflection: TRICKY TRICKS

   During the first lesson, we were given the opportunity to problem solve using cards. Interesting! Very Interesting and FUN!!  Children used to memorize o.n..e.. as 1, 2..Ooops not anymore. This game will get the children to spell, and play with cards with TRICKS.Our group did trial and error arranging the cards and ensure that as we spell o..n..e...the card card with '1' MUST appear right after and nothing else.Too many trials and too many errors!! That is how problem solving in Mathematics should be.We will learn better when we make mistakes.Allow our children to make mistakes during Problem Solving, only then they are learning 'What NEVER GIVE UP!' is all about. Isn't that GREAT, Maths teach you such good values like PERSEVERANCE!!
   I began to realize that in Mathematics, there are methods called heuristic which need us to guess and check through trial and error, in trying to find the principle of the whole thing, we are actually generalizing it. When we are acting it out as an idea, we are actually making or testing a conjecture. These are the examples of thinking skills in problem solving.

Monday, October 4, 2010

More Blogs still under constructions....

Dear Dr Yeap,

The blogs are still under construction and will be sent once done..

Warmest regards.

Sunday, September 19, 2010

MATH! Wow... not only 1...2,,,3.....( chapters 1 &2)

Teaching Math is FUN when Educators are clear What is it? Why teach MAth, the HOW TO teach in FUN, enjoying and that has enhanced learning .."Students must learn mathematics with understanding, active building new knowledge from experience and prior knowledge." (NCTM, 2000,p.20).

Children of today not only require computational skills, they are required to acquire problem solving skills and to be able to think critically so that they may reason out their findings. Another challenge is, for them to be able to make reflection on both their ideas and others' ideas as well.

To allow young children to develop the understanding of the Mathematical Concepts in a FUN way, early childhood educators need to

  • provide the conducive classroom environment.
  • give equal exposure to conceptual understanding and procedural fluency vice-versa
  • encourage their children to actively participate in problem solving, and be fully engaged to communicate their ideas, reasoning out and make connections.
  • use technology as a tool to enhance their understanding.
  • incorporate  multiple assessments aligned with instructional goals and practices.
  • Mathematics authority that lies within the power of sound reasoning and mathematical integrity(NTCM,2007,p.7)

We were reminded of some verbs that require higher level of thinking, and encompass"making sense" and "figuring out". Some examples are explore, investigate,, justify, construct, formulate etc.