What I have learnt and questions...

Waaaaah....
Finally I have completed the EDU 330 Elementary Mathematics!! Wohoo!!!! Eh wait... Not yet.. I need to submit my final individual and group assignments.
Anyway, throughout the course, I have learnt:


1. Differentiated instructions - 
When you plan a lesson, prepare some activities for advance learners and struggling learners. According to Tomlinson,  The idea of differentiating instruction to accommodate the different ways that students learn involves a hefty dose of common sense, as well as sturdy support in the theory and research of education (Tomlinson & Allan, 2000). It is an approach to teaching that advocates active planning for student differences in classrooms. You can find out more about differentiated instruction at  http://www.caroltomlinson.com/


2. CPA - Concrete, Pictorial and Abstract. 
"When using the CPA approach, the sequencing of activities is critical. Activities with concrete materials should come first to impress on students that mathematical operations can be used to solve real-world problems. Pictured relationships show visual representations of the concrete manipulative and help students visualize mathematical operations during problem solving. It is important here that the teacher explain how the pictorial examples relate to the concrete examples. Finally, formal work with symbols is used to demonstrate how symbols provide a shorter and efficient way to represent numerical operations. Ultimately, students need to reach that final abstract level by using symbols proficiently with many of the mathematical skills they master. However, the meaning of those symbols must be firmly rooted in experiences with real objects. Otherwise, their performance of the symbolic operations will simply be rote repetitions of meaningless memorized procedures".  http://www.loganschools.org/mathframework/CPA.pdf
1st phase - real life objects
2nd phase - from authentic objects, slowly replace with generic objects
3rd phase - photographs (pictorial based)
4th phase - abstract pictorial such as dots


3. Using proper language and mathematical terms

2 is less than 3

not

2 is lesser than 3

The table has a rectangle

not

The table is a rectangle

The length of the phone is about 5 paper clips

not

The length of the phone is the same as 5 paper clips

subtract or minus

not 

take away

Questions:

I have two autistic children (4 years old) with different interest and learning needs in my class.

Child A is able to identify numbers up to 100, identify number names up to 10, do counting on, and understand the concept of less and more. He learn these skills from the computer software. He spends less time when playing with concrete objects.

Q1: Besides letting him to practice and learn mathematical skills from the computer software, are there any ways to keep him on task without using the computer?

Child B is able to identify up to 10. However, I realised that his mother use drilling method by asking him to practice writing number 1 to 10 daily. When I asked him to take 2 pencils, he took a pencil and write number 2 instead of giving me 2 pencils. I realised that he can recognise the numbers very well but he doesn't know the quantity yet.

Q2: Besides using counting and one to one correspondence, are there any activities that I can help Child B to link number with quantity?

Do we depend too much on technology? The importance of CPA approach

Are we too dependant on technology? In my opinion, its no. Why? As a teacher, you should identify where your children's level are at. I have encountered some children who can't do simple addition because they do not have prior knowledge on counting on. Dr Yeap shared with us how important to teach children starting by using concrete objects, then  pictorial and later abstract (CPA approach).


Jerome Bruner believes that it is important to start of with concrete objects. In this case, the child should have given some concrete objects to learn counting on and adding. Concrete objects can be cars, apples, pencils, etc. However, the concrete objects must be the same to avoid confusion (Hiele's theory).


Basically, we can let the children to be exposed with technology but not straight away letting them use the calculators to find the answers for them. Technology can be used in many different ways. For example, in this website the children can practice addition.
http://www.ezschool.com/Games/Addition.html


Mr Donald Sinclair shared some tips on how to let children practice addition. However, I find that the acitivities suggested by him may not be appropriate for children whom just learn addition.
http://www.videojug.com/film/how-to-teach-addition


That's all for today...

Day 3 of mathematics module with Dr Yeap

We had a quiz today and to get the answers required us to search for the real thing of the statues, objects and buildings. One of the questions is: How high is the church from the ground level?
The church is located just opposite of Singapore Art Museum at 8Q.

Nurul suggested to get someone to stand near to the church and we forced Sarah (as the rest of us are Muslims) to go near to the church and stand there. We estimated how many of her to reach to the building just by using our fingers. I'm not sure this is a good way to teach the kids but we would like to try out new method of estimating the height of the church by using real person.. Haha.. not a good example though.. but we can't stop laughing coz a few passersby took photos of her standing straight outside the door of the church while we use our fingers to estimate the number of Sarah to reach the highest part of the church.

Ouh yea.. another question is to calculate how much material needed to create the yellow and blue flower.
First, we counted the number of flowers. Sarah and Nurul counted the number of yellow flowers. While Huda and myself counted the blue flowers. Well, there are two ways of counting it. Sarah and Nurul counted the yellow flowers one by one meanwhile Huda and myself realised that there are patterns.
e.g.
x   x   x   x   x   x   x   x   x
  x   x   x   x   x   x   x   x
x   x   x   x   x   x   x   x   x
  x   x   x   x   x   x   x   x
It's an AB pattern! So we count the first two rows and multiplied by the number of sets to get the total number of blue flowers.
That's all for today!

More than... Less than.. Equal to...

Hi peeps... 
Would like to share some information about the relations core : more than, less than, and equal to. It is important for teachers to take note that children need to know the number concept very well before they are able to identify what is more and what is less. This topic can be found in page 134 from the book Elementary and Middle school mathematics: teaching developmentally by John A. Van de Walle, Karen S. Karp and Jennifer M. Bay-Williams.

Do you know that children have difficulties to understand the concept less as they have more opportunities to use the word more but have limited exposure to the word less?
I had the same experience too.. When I was in kindergarten, my grandmother scooped 2 scoops of rice, thinking that her granddaughter is hungry. In my mind, I wanted to say less but I do not know the word and instead and said more but my hand showing the action of putting the rice back into the rice cooker. My grandmother then realized what I want as she keep scooping and I keep pouring back. That's when I learnt the word 'less'.

Thus, to help children with the concept of less, frequently pair it with more so that the children can understand the concept clearly. 

Last night, Dr Yeap, our lecturer for Maths module showed us a sample activity of how to teach more than and less than by listening to the sound of coins in different bottles. One bottle is labelled 3 as there are 3 coins in it while the rest are labelled in letters. Each bottle has different amount of coins and the children are supposed to shake the bottle and identify which bottle has more than 3 coins and which bottle has less than 3 coins. The activity covers other skills such as identifying which is more by listening, by weighing, by counting, etc.
That's all for today...

I'm off to class now!

Integrating mathematics with technology

As I was searching for whole group reading, I came across a link at youtube about Kindergarten Tech Integration. I thought that it would be good to share the video in this blog.

The video was uploaded by Mrs. Kimballs, a teacher who conducted math lessons integrating technology. My first impression.. WOW! The school provides iPads, Mac computer and smartboards. All of the activities are play based. I know some schools do provide smartboards and computers in classes but do they integrate math lessons with technology?
I like the way the teacher use the art software (kidpix) to create a simple patterning game instead of just exploring the art tools only. You can also print out once the child has completed the activity and this can be added in the child's portfolio. This activity can also be applied using common software that can be found in your computer.

Reflection on chapter 1 & 2





Sometimes teachers are afraid to let children explore with mathematics. as shown in the picture above, the teacher is afraid of letting children explore and finding different ways and approach to get the same answer which is to create a bird. How will you react if you are in her place?

I remembered during my primary school years, I just need to memorise and follow whatever is in my notebook as my Math teacher will use the exact questions in the exam. most of us will pass with flying colours but we had a lot of problem in our 'O' level maths. Why? Because I do not learn that mathematics in classroom can be applied in the real world.

From chapter 1 and 2, I have learnt about the standards and principles for school mathematics and what are the teacher's roles in making children know and do mathematics. I agreed with what was mentioned in page 22, "Teaching should provide opportunities for students to build connections between what they know and what they are learning". This reflects back on constructivist theory on assimilation and accommodation. Thus, it is important for teachers to understand mathematics very well before creating an environment where children can try out different ways or approaches to solve the questions. Hope to learn more about teaching mathematics to young children this coming week!