Summary of learning for EDU 330

The five and a half day lessons were really fruitful and lot of learning taking place.  My brain cells were working actively and at some point seeing stars floating in the air.  The last time I have such serious learning about mathematics was more than thirty years ago... wah really back to school.

Three things I have learnt are:-

1)  Concrete, Pictorial and Abstract (CPA) by J. Bruner

When teaching mathematics to young children, we must begin with concrete materials to let children to have hands-on experiences and understand the concept.  Next, children understand by pictorial and diagram, that need a little more effort on learning as children solve problem through visualisation.  Finally, abstract, where more critical thinking require and that involve gaining intellectual competency.

2)  Four criteria questions in planning lesson

a) What is it the teacher want the child to learn?
    >> set teaching goals.

b) How does the teacher know the child has learn it?
    >>constant observation by asking questions and interaction.

c) What if the child cannot understand the concept?
    >> go back to basic and simplify the question or teaching methods.

d) What if the child feels that the activity is too simple?
    >> prepare more challenging task for the child to do.

All lessons planned must be of age appropriate.

3) Story books that teach mathematical concept

I enjoyed the two stories shared in the class, "Spaghetti and Meet Balls" and "How Big is a Foot".  During my Certificate and Diploma Preschool teaching, none of the lecturer had demonstrated teaching mathematical concept by story telling.  After the first book shared by Dr Yeap, I went to the library and I discovered that there are many literature materials teaching different mathematical concepts.  Children love listening to story, hence, teaching mathematics concept through story telling will be very interesting; children can make connections and at the same time improve their literacy skills too.

Two questions that I have:-

I)  Differentiated Lessons

I have spoken with my customers from the preschool sectors and few of my fellow course-mates about differentiated lessons written in the lesson plan; everyone tells me that they do not  have that written in the lesson plan.  Most of the time, they would just carry on the lesson.  Some of them said that though they do not write the differentiated activities in their lesson plan but they would reinforce activities or teaching the concept to the struggle learner whenever time permitted.  As for the advance children, teacher would give them other activities to occupy them.  (as I am not an in-service teacher, so I gathered information by asking friends who are in the industry).

I seriously think that have differentiated activities written in the lesson plan is vital.  It helps the teacher to be more efficient when carrying out the lesson; meanwhile, knowing what to scaffold and action to be taken.

II) Usage of language and explicit instructions

I have learnt so much about being careful on the usage of language and explicit explanation on teaching concepts and asking questions.  Many a times we have used wrong words or phrases, such as "take away", "what is your weight", etc.  I am sure  neither the in-service teacher or non in-service are aware about the mistake and have been teaching our children.  I seriously think that mathematical jargon, rules and instructions should be taught at the Elementary level if not at lease Diploma level. 

Technology in teaching Mathematics

In this 21st Century, technology has become part of our life.  The sophicated tools no longer mend for the coporate world and they are just as important for classroom teaching; hence, teachers must adjust their teaching style to keep up with the growing trend. 

The common technology tools are caculators, mathematics software (games and assessment sums). online research (children can get many sample working sums, formulas, definitions, video clips on instructions learning), interactive board with camera (that able to capture all working sums written on the board, record and save in the computer) and engaging software engineer to write mathematical programme to enhance mathematics learning in the classroom.

Advantages of using technology in Mathematics
~teachers can save all sums written on the interaction board into the computer and retrieve the data for revision (only school have the board).

~through interactive animation and games will capture the children attention to make learning more fun.

~children can understand concepts better and become fluency with constant revision and viewing.

~children are more motivated towards learning.

~students can enjoy hands-on activities while solving maths problems by drawing models, diagrams or dragging the pictures on the interactive board.

I have a few strong thoughts:-

~ when using technology to teach children, it is very important teachers select the right material and the age appropriate programme.

~ teachers must be able to control the time spend on computer and facilitate learning processing.

~ currently no technology can replace the teaching on full conceptual understanding of mathematical concepts and teachers are the best model for learning.





Mass and Weight

Something interesting (discovery)

In my first lesson, I have learnt that my mass is 48 instead of my weight is 48??????? That's so funny and interesting discovery.

My google findings

Mass - (noun) a large body of matter with no definite shape.

Cranfield University's Website, wrote that Mass is how heavy something without gravity. (http://www.racemath.info/matterandmolecules/what_is_a_mass.htm)


Weight - (noun) a body's relative mass, giving rise to downward force, the heavier of a person or thing.

Wikipedia
In science and engineering, the weight of an object is the force on the object due to gravity.  ^{http://en.wikipedia.org/wiki/Weight}

How are Weight and Mass different

1) Mass is a measurement of the amount of matter something contains, while Weight is the measurement of the pull of gravity on an object.

2) Mass is measured by using a balance comparing a known amount of matter to an unknown amount of matter. Weight is measured on a scale.

3) The Mass of an object doesn't change when an object's location changes. Weight, on the other hand does change with location.

How I know how to ask when I wish to know how heavy is the person.:)

Reading on Chapter 8
In this chapter, I have read about two interesting areas about how children learn mathematics and recommendations to help teachers develop high-quality activities for children preschool age.

How children learn mathematics

Children level of thinking increase gradually.  First, they learn number by route counting, i.e.  1,2,3...... (chanting).  In the beginning, they may skip 1 to 2 number in between but will perfect it as time goes by through continuous repetition.  Next, they are able to make connection to one-to-one correspondence by counting and matching; follow-by group blocks and counters of the same attributes and lastly they can count and understand that last count word indicates the amount.

Recommendations strategies on developing activities

~ enhance children's interest in mathematics
~ build on children's experiences and prior knowledge
~ plan developmentally age appropriate activities
~ use formal and informal experiences in the curriculum to extend practises
~ provide opportunity for exploration, reasoning and allow mistakes
~support children's learning by constant observation and assessment very proper guidance.


All students must be given the opportunity and adequate support to learn mathematics.

First Lesson of EDU 330

I never expected the lesson could be so fun and it really keep me awake.  Besides learning the following key points:

1) How do children learn Mathematics?
(by CPA approach ~ concrete, pictorial and abstract)
(by variability ~ appropriate material, tasks and conducive environment)

2) What are big ideas in Mathematics?
(patterns and problem solving)

3) Mathematical terms
(cardinal number ~ number denoting quantity, e.g. 1,2,3....)
(ordinal number ~ number defining in position / space, e.g. first, second, third)
(nominal number ~ number use as name, e.g. bus no. 14)
(measurement number ~ number use for purpose of measurement)

4) Using of Mathematical language and differentiated instructions

Interesting Learning Activities

>> finding our which letter in our name is at 99?  (to my surprise from this activity, we learn about patterns, various ways of counting and methods to derive an answer.)

>>the cards activity is really fun.  Beside demonstrating magic, we learn about counting, spelling number words, position, mathematical language.

1st Post by Dr Yeap

Students made mural using square sheets of paper

As not sure where you want us to post the answer, so I have made two posts; one directly to your blog and the other in mine.  Will clarify by tomorrow.


Ans to ~ How many sheets of square paper are needed to make this mural?  The Answer is 160 pieces of square paper.

First way of getting the answer:
by pasting the square paper horizontally and vertically.  Then count the number of paper used across and down and multiple the number.

Second way of getting the answer:
find out the area of the board, then find the area of the square paper (to find area we need to measure the length and breath and multiply it). The area of the board divide the area of the square will give tell us the number of square paper require.

To further extend the the task, we can ask children how many pieces of green, pink, yellow, blue and orange square paper are required to fill the mural and the number must be the same for all mentioned colours.

Pre-course reading - Chapter 2 (Exploring What It Means to Know & Do Mathematics

On page 13 of the text book Elementary and Middle School Mathematics Teaching Developmentally (8th Edition), the authors mentioned that when an odd number multiply with an odd number, would always generates an odd answer; when an even number multiply with an even number, would always generates an even answer; when an odd number multiply with an even number, would always generates an odd answer but why I always have an even answer?  Can clarify?  Thanks you.

In the text book, I enjoy solving the problem sums from page 15 to page 18, though I did not get 100% right for my answer.  The Star and Jump Numbers: Searching for Patterns and One Up, One Down really interesting.  Now I know why people can do their mental sum so quick.

On page 14, I total agreed with the authors that having a conducive environment for learning Maths will enhance children's learning.  During Maths lesson, teachers must provide adequate materials and engaging manipulative for children to learn through hands-ion; allow children to share their leads and encourage them to listen to their peers and learning from others; make a list of solution and brainstorm the possible answer; allow mistakes, as children can learn from mistakes, hence, it create opportunity in learning.

In this chapter I read about Jean Piaget, the constructivism theory and Les Vygotsky, the social-cultural theory, whom talk about children learn through the process of assimilation and accommodation, and zone of proximal development respectively.  Additional, I have learnt a new concept, i.e.  semiotic mediation; which is using diagram, pictorials and visuals to exchange information of one's beliefs.

The below diagram is found in page 24 of the text book; which I agreed that Maths should be taught through the 5 representation.