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?