The Role of Technology in Math Education

In this 21st century, technologies has been integrated into our lifestyle. Hence,  we should make use of these technologies as an integrated part of our instructional tool to help in deepening children's understanding in mathematical concepts.  For example, the use of interactive whiteboard will increase children's chances in making sense of new information by interpreting concepts, exploring concepts in a totally new ways.

The following video gives a view on the Role of Technology in Math education and how it can be used to engage children in the process of thinking and applying mathematical concepts and how differentiated instructions can be incorporated to challenge the advance.

Finale

First and foremost, a very big thank you to Dr Yeap Ban Har. His excellent planning on activities that kept us thrilled throughout the module and the way he deliberately build up our understanding on concepts through his careful observation and picks on our answers has simply modelled to me that a teacher needs to be very observant, flexible, mindful with his/her choice of words and actions, know the class developmental progress and definitely a need to formulate your lesson with a purpose in mind.

There are four critical questions to follow when planning for lessons and activities. Firstly, you need to know what is it that you want the child to learn or make? Secondly, how do you know if they have learnt it? Thirdly, what if the child cannot even make one? Lastly, what if you have advance learner? These questions will guide you into a more focus objective while delivering your lesson and one that enable you to assess on the child's ability as well as how differentiated instructions can be used to scaffold learning.

Differentiated instructions are strategies in a lesson plan that support the range of different learning backgrounds found in classrooms. It can be in the content, the process of engaging thinking about that content, the product to show what they have learned on the content and even in the adaptation of the physical learning environment. It is important to incorporate differentated instructions because every child is unique and differed in learning abilities.

The above are just three of my learning points in this module, of course, there are many, many more.

However, there are two questions that ponder upon my head.
Firstly, due to globalisation, we are facing lots of cultural diversity in classroom. How than can we modify or plan our math lessons to include culturally relevant mathematics instruction?
Secondly, can assessment be done only by the observational method? Can the observation be concluded without a pencil and paper task?

Lesson 4

MULTIPLICATION

I used to dislike multiplication. Still remember the times when my knuckles were red due to my inability to memorize those multiplication tables. But hey, look here, it seems not to be my fault but rather the lack of proper delivering on the concept of multiplication to me.

Multiplication are SIMPLY repeated addition. When you know 2 x 5, you can simply add on another 5 to make 3 x 5, or another 10 to make 4 x 5.
It also involves number bonds. For example, 10 x 5, can be 4 x 5 and 6 x 5. Isn't it easy now? You don't have to worry that you will forget the tables.

That's not the only takings from last night lecture, I was pretty shock to find out that 'A SQUARE IS A RECTANGLE, A RECTANGLE IS NOT A SQUARE'. I am still in shock because I have been planting the wrong thoughts into our little ones.

Lesson 2 & 3

LEARNING TRAJECTORY FOR COUNTING

I was glad to stumble upon this research,

Learning and Teaching Early Math: The Learning Trajectories Approach
By Douglas H. Clements, Julie Sarama

This research talks about the three parts of the learning trajectories; The mathematical goal which is the Big Ideas of Mathematics basing on concepts and skills consistent with children's thinking; The path of learning by developmental progression which consist of level of thinking which lead to mathematical goals and the path of teaching using instructional task to match the level of thinking in development progression. And how it helps teachers like us to deliver mathematics effectively.

Children follow natural developmental progression in learning, even in Mathematics. Hence, as a teacher, we need to know these progression in order to develop their Mathematical goals for the the children and create task, activities and environment that are effective and developmental appropriate to help them reach these developmental goals.

Hence, I believe the learning trajectories approach serves as a very good guide for teachers to set goals and activities that are within developmental capacities of the children which in turn provide an environment that caters each level with natural developmental progression to the next.

Do take time to read this research. It will be of great help to all.

Lesson 1

Gosh!Mathematics was never so interesting in my life. Today's lesson was fun and it gave me a different perspective on how I view Mathematics. Thanks Dr Yeap for planning such interesting hands-on experiences for us. Well, I guess that is already an answer as to how children learn mathematics ....hands-on experiences, concrete materials, purposeful play and at the end abstract thinking together with a supportive and appropriate environment.

Tonight, I am pretty fascinated with what a simple instruction can lead to so many findings, for example, activity 1, what is the 99th alphabets in your name in a certain counting sequence. We came up with so many ideas to get the correct answers and each of us has our own preferences in ways to find the answer. I think this has to do with our prior knowledge and experiences in doing Mathematics. I believe it will be the same for the children when they solved their problems, they will exercise their prior knowledge too. Besides, this activity allowed me to see beyond just solving the question. It actually make me realised that there are mathematical 'rules' in it, for example, patterning.

I too learned that there are many big ideas in mathematics. For example, just numbers alone can be viewed in four different ways;Nominal, ordinal, cardinal and measurement. And there are patternings, differentiated instructions and the cpa approaches.... and I'm sure by the end of this module, the list might just be as long as the river nile.

Chapter 1 & 2

Mathematics surrounds us daily.  In the market, you see hawkers sorting their fishes, weighing their vegetables, counting the numbers of apples, counting money. In the city, you see patterns, shapes from flats, pavements, roads, ……  I can go on and  on and it is a never ending list.  And I believe it is important to create children’s awareness that their daily life function around many mathematics concepts. I, as early childhood educator, need to acknowledge that mathematics is not just about numbers, addition and subtraction but a vehicle to create intellectual competency in children’s development.

These are the few takings which I identified in chapter 1.  Firstly, the five process standards.  I notice that the five processes emphasize a lot on expressing and communicating mathematical ideas. I think this is one area which is lacking in our culture as well as in my teaching and the curriculum.  Our curriculum focus seems only to deliver the concepts across, very structured. Another is on reflecting, understanding and interconnecting the mathematical ideas with the children.  Most of the time, whenever a lesson is completed, children are expected to continue their learning in the learning corners.  However, from my observations, activities at the mathematics learning corners are pretty much goals orientated, such as having counting work sheets or charts to fill up.  It is not so much of extended learning by having opportunities for children to learn from each other through reflection or interconnecting their mathematics ideas.  Hence, it is time for me to rethink on the activities at the learning corners and include more “open-ended” activities that enhance these opportunities.

Secondly, on the becoming of a teacher of mathematics, I think these are important practises that a responsible teacher should exercise.  And that goes for me too.

As for chapter 2, I identified with Jean Piaget’s constructivism and Vygotsky‘s sociocultural theory.  Children learn best through constructing their own knowledge and of course, learning from the social learning settings which allow learners to move their ideas into their own psychological realm.  I am a believer in hands-on approach and peers learning. And of course, these implicate my teaching, whether in mathematics or others.

Next, after trying out the problems in the text, I realised that I began to think out of the box. I began to see beyond a simple problem. I began to understand interconnecting ideas, extending knowledge, how prior knowledge helps and how important it is to have fun with mathematics. I felt mathematics should not be viewed as “a problem” but “a challenge” for one to reflect and use that knowledge to acquire higher-level thinking.  Hence, it is important that we impart this thinking to our children so that they can be the creator of their own knowledge.

Lastly, Piaget, Vygotsky, Bruner and Dienes, the four famous cognitive psychologists, have formed basis for constructivism theory that a child creates knowledge by acting on experience gained from the world and then finding meaning in it.  Children recreate or reinvent mathematics as they interact with concrete materials, math symbols and story problems. Therefore, it is important that early childhood educators expose children to environments that maximize potential and opportunities for them to construct their own ideas.