Day 4 26 Sept 2013 Further concepts in learning mathematics

In class today, I was again baffled by the way Doctor Yeap showed us the concept of division and fraction. Recalling from my school days, division and fraction were taught as a matter of fact, no visual and/or concrete manipulation of materials. It was quite a trying time as I recalled to my early days of learning mathematics. In my view, I support the stance that we must build a belief system in the minds of the young learners. They must be given the opportunity to test it out themselves, allowed to play and come to the conclusion to the problems. Mathematics is important as it helps in the development and improvement of young learners. Why so, as one may ask. Looking at the subject of mathematics, it is time and again grounded in numerical logic. The concepts in mathematics can be applied to our everyday lives, the probability of an incident taking place, the calculation In the fraction and also a division exercise, Doctor Yeap showed us that in fraction, for example 1/3 should not be said as one upon three or one out of three. It should be be said as a third or one third. I noticed that learning of mathematics has changed much and for the better of the young learners in comprehending the subject.

I discovered through this problem with Doctor Yeap that there are many ways to derive the answer, for example, in the above problem of sharing the 4 pizzas equally, the solution can also be derived as follows: METHOD 2

In the above method, we will divide the four pizzas into 12 thirds and from there we will divide by three pigs giving each pig 4 thirds or 1 1/3 f from the exercises above,mathematics seem a fun way to learn!

Day 3.....25 Sept 2013.....Addition, Enrichment and Acceleration

In our experience as teachers, we will undoubtedly encounter children with difficulty in counting from 1 to 10. As teachers or for that matter, as parents, we should not be unduly worried for children not able to count because counting is not a cognitive process. It is a rote learning process and it comes with practice coupled with memory work in a sense. With exposure and practice, any child will be able to count after sometime.

Learning a different way to add digits was a fun way. Unlike the method learned in my school days where digits are added the vertical way the lateral way seems easier as it involves breaking the digits into tens and one. Conceptually, addition by this way seems easier as one count the number of tens and the number of ones. Take a look at the picture above and see how easy it was to count! Today parents send their children to many enrichment programs for mathematics. This is a indeed in the right direction for little minds to acquire mathematical skills, However, parents are at times guilty of exposing these little minds to acceleration program in mathematics which may not be conducive to young children acquiring greater skills but may deter them from liking the subject of mathematics as they find great difficulties in managing the problems far above their level. The learning of mathematical subjects should be one of scaffolding past experiences to the new ones.

28 Sept 2013 ................Farewell, Good Bye as we always say but it was a GREAT week of mental gymnastics & learning

Today is the last lesson for our mathematics module with Doctor Yeap Ban Har........... It had been a great time of learning mathematics, the problems we were given to do were simple but mentally challenging at time as we had to find different ways to solving the problems. The problem on the Magic Card tricks needed some mental thinking as my mind shuffled with the cards and the order they needed to be. To do the order in my mind was difficult but by placing them on the table and manipulate them and ordering them was the best way to tackle the problem. Again, the theory of Jerome Bruner emphasizing the importance of using "concrete material" with active play were obvious in the card game as its seemed magical The lesson ended with A QUIZZ, it was fun running through it, a recall of the things I had learned in the last six days, the importance of teaching mathematics in a way to the young learners, in short the "play of mathematics" rather than the horrifying moments of seeing the terrors of numbers that would stifle the "Love for Figures" as the learning of Mathematics should be enjoyable and the greatest achievement for any teacher of mathematics would surely be when their students said: "Teacher, I LIKE MATHEMATICS" MATHEMATICS SHOULD NEVER BE LIKE THIS FOR ANY LEARNER OF THIS BEAUTIFUL SCIENCE!!!

Day 5 27 Sep 2013 - Make Squares

Today we use tangram to make squares. Tangram consists of 7 pieces: 2 big triangles, 1 medium triangle, 2 small right angle triangles, 1 square and 1 parallelogram. I enjoyed exploring the many ways to find out: 1. How many different sizes? 2. How many ways to create the shape of one size? 3. How many pieces can you use to make a bigger square? 4. Are there squares of other sizes? 5. The more pieces you use, the larger other square. Is it true? Take a look:

The answer is: It is not true that the more pieces you use, the larger is the square. It's a surprise, isn't it? How many different sets of squares did we make in total?

Point to ponder: Learning is not knowing more information but to think more deeply.

Day 2 an approach to the teaching of Mathematics and concept of whole numbers

In teaching early learners to count, when we encounter problems in teaching, it would be good to examine the background of the child. It is sometimes not just the cognitive or the psychomotor development of the child. Reflecting to my early years of learning mathematics in school, I remembered the way of teaching it was so much filled with explanation upon explanation and rote learning on the process of solving mathematical problems was the mode of instruction. It is rather comforting to see the learning of mathematics in a different light from our class lecturer, Doctor Yeap. I do totally agree that teaching mathematics by way of explanation is not a good instructional approach as the tendency to veer into a rote style of instruction is highly probable. I see the powerful application of “concrete experiences” in teaching the learners the concepts and application of mathematics. A major theme in the theoretical framework of Jerome Bruner is that learning is an active process in which learners construct new ideas or concepts based upon their current/past knowledge. The learner selects and transforms information, constructs hypotheses, and makes decisions, relying on a cognitive structure to do so. In the Beans game, we see the application of concrete experience, that is, the nature of using beans giving “a feel and touch” stimulating the cognitive process as the players engage in the play and at the same time learning subtraction when they draw their beans in one or two number. This exercise also emphasizes the learning of “Whole Numbers” denoting that we only can subtract from things of a common noun, in this case, the beans.

Day 1 Reflection - My experience with today's activities

Wow! Today's activities are a revelation to me that maths is so fun and interesting. In Playing the game in problem 1, we found that there are many methods to find the solution of which letter in our name is counted number ninety nine. Through exploring the many methods to derive the solution we learnt rote counting, rational counting, patterning and multiples of certain numbers.

When teaching children how to do something, one of the successful ways to do is by using games. Games allow children to learn while they are having fun. They don't even realise that they are learning as children play spontaneously. With tasks such as counting that are learned from repetition, different games allow children to continuously having fun in the learning process. It also helps them to cultivate a thinking mind and understanding of numerical logic as they play the game.

Pre-course readng - Elementary and Middle School Mathematics

Pre-Course Reading

Teaching mathematics has always been a challenging task for all mathematics teachers as the subject fundamental basis is on numerical logic. Thus in expounding this intricate subject to the very young pre-schoolers, primary, secondary, junior college and tertiary level have undergone much study and research to make teaching of this subject systematic and comprehensible even in the  teaching of complex mathematical theories.

One of the most important features of principles and standards for school mathematics is the articulation of six principles fundamental to high-quality mathematics education:

·         Equity

·         Curriculum

·         Teaching

·         Learning

·         Assessment

·         Technology

The equity principle is that all students must have the opportunity and adequate support to learn mathematics regardless of background, physical challenges or characteristics.

The curriculum should be more than just a collection of activities, it must be coherent and focused on important mathematics and well articulate to the students. It may not be far from the truth that one can study to be a mathematics genius but one may not be a genius in teaching mathematics. In summary, not all mathematics teachers make good teachers. 

To provide high quality mathematics teaching, teachers must deeply understand the content they are teaching; understand how students learn mathematics and the awareness each student’s mathematical development; select meaningful instructional and strategies that will enhance learning.

The learning principle is that students must learn with understanding and be able to build knowledge from experience and prior knowledge. Students must be taught to think and reason mathematically to solve new problem as “scaffolding of mathematical knowledge” can be said to be the a good measure of successful teaching.

Assessment is an important tool in the teaching of mathematics as from the data collected, teachers are able to have solid gauge of the students’ progress and to make decisions and necessary strategic changes to support learning.

The application of mathematics can be seen where the generating of strategies for solving problems in the classroom can be translated to the application to real life situations.

Two theories, namely constructivism and sociocultural theory are most commonly used by researchers in mathematics education to understand how students learn. The aforementioned learning theories are not teaching tools in the education of mathematics but rather they provide an understanding on how learning takes place and this form a reliable framework for the teaching of mathematics. For example, constructivism might explain explicitly how a student internalize an idea while sociocultural theory would be a better tool for analyzing influence of the social/cultural aspects of the classroom.