I have earned myself four cookies!!
                       



Entry 8: My reflection on the whole course

I think everyone has to agree with me that Dr Yeap has totally changed our perception towards Math. Never has learning Math been this interesting and fun before. I was full of apprehension at the beginning of the course on how I will ride through the whole six sessions; given my strong incompetence in this subject area. With the technique and skills taught in teaching Math, I marvelled at how learning Math can be translated into something more fun!


Within a short period of time, we were brought back into the journey of learning Math all over again except that now it was done in a very tasteful manner. So much has been taught and covered. The various games that we've had; the dice, the paper clips, the cards, the tangrams, the cubes, to name but a few. Never have I came across Math lessons with so much life, zest, and excitement in it.

I see the great importance of learning Math as it is not only an examinable subject per se, but more of its application in our daily lives in terms of problem-solving, analysing and being able to think out of the box and to come out with different possibilities and solutions. These have to be instilled and inculcated since young. It is all about how learning can be imparted to entice young children to get engage and enjoy learning Math so that they can develop a strong foundation in it, have a strong liking and to apply it in their daily lives. It is important for me as the educator to have the right mindset and to think creatively with the interest of the children in mind                                     .

Thank you Dr Yeap for your sharing of those great ideas! We really wish to have more fun learning with you! 

Entry 7: Geometric thinking

One of the easiest concepts to teach to preschoolers are learning about shapes. This is one which children can connect very well as shapes are just about anywhere and everywhere! By providing the children with creative activities on shapes and getting them immersed in the activities, they will develop into observant individuals who will make intelligent observations to whatever that they can see in the environment. They will notice the circle on the lid of the dustbin, the rectangles on the false ceilings, the hexagons on the bee hives and so on.

I was challenged during the last lesson by counting the angles of the polygons. I could not even remember when was the last time I attempted to do so! It was rather enlightening to see how we strive to produce the correct answer helped by some smart alecks who have provided us with tips on solving the problems. Well, even though I did not derive with the correct answer for some of them, most importantly, I thought I have tried hard enough to come quite close to it.

I particularly enjoyed the actiivity where we had to come up with different designs on the dotted paper to form the four-sided shapes given the particular square area. That was really interesting and fun! I gained the most cookies based on what I have collected so far during the last lesson for participating actively. That was indeed a very good  closure towards a six sessions of fun and interactive learning on Math!

Entry 6: Whole Numbers and Common Practices.

Often times I heard parents sharing and comparing among themselves how much their child knows about numbers. Some even went to the extend of telling the other, "Oh, I am so amazed! My child already knows how to count up to 100! And he is only 3!" This will create unnecessary stress to the other parents whose child is only able to count up to 10. But how much does the former child know about numbers? By being able to count up to 100, does that make a child understands the underlying concepts of numbers up to 100?

What happened above is that some parents are unaware of the underlying and important concepts which come along with the numbers 1-10. That is the basic foundation before a child can even progress to bigger numbers. Of course, there is no harm if the child is able to rote-count of up to 100, but strictly speaking, there is nothing to be proud of. The child who is able to count up to 100 is basically practising his rote- counting skills; probably given the frequent exposure that he or she has received from adults in the environment. More importantly is how to equip the child with the knowledge of associating his or her rote-counting skills to serial counting and later to make relationship to its representation of symbols. 

On top of these, besides teaching concept of ordinal numbers, others include numbers which come before, after and in between, odd and even numbers and numbers more or less; all within 10. Once a child can master these concepts, then it is considered that he or she has a stable foundation for early Math.

From here, then the child is able to move on to place value, grouping of base ten and so on.

These are the common practices that has been implemented in my centre:-

Numbers up to 10: To associate symbols and their quantities.

Number concepts of 1-10: More /less, Numbers which comes before/after/between, odd/even numbers, and ordinal numbers.

Numbers up to 100: Grouping of base 10, associating symbols to quantities, place value

Concepts of money, length, time and mass.

Concepts of addition and subtraction

Story sums.

The non-common practices are:

Concepts of multiplication and division.

                                       
 

Entry 5: Reflection on using Technology in Math.

Coming from an era where I was introduced to technology at a much later age, at a much slower pace and people were not highly-strung with technology, that has resulted in a 'not IT-savvy me.' It is rather heartening as well as disheartening to see how the younger generations are so well-versed in it. Just pick any gaming activity using one of the hand-held machines and they will be well on their way to a world of fun and  excitement. Unlike me, I will still grapple with the functions of the keys and to apply them all the same.

How time has changed. The use of calculators in school gets more pronounced and children are getting exposed to its usage even as early as at primary level. As convenient as it may seems as compared to my time where I was expected to do my calculations manually, the standard of education now has definitely increased by leaps and bounds, that time spent for manual calculation is immaterial albeit they are allowed to use it for certain sections only. Rather, they are expected to spent more of their time solving complex problem-sums that the calculator has been used to aid them in speeding up their time in providing the solutions.

There are also many mathematical software applications that can be bought off the shelves which contribute to children being exposed to computers at a tender young age. This will definitely serve as a challenge especially for educators like me to equip myself with the necessary knowledge so as to keep up with the changes and challenges around me. I stand firmly on the ultimate importance of preschoolers being immersed with concrete experiences in learning Math. I must say that involving technology in Math is more applicable and approriate to the older children, probably a basic introduction at the beginning of K2 level before they progress to their primary schooling years.   

Entry 4: Place values

Being trained in Montessori Method of teaching and having taught in a Montessori setting for a good 7 years, I realised the importance of relaying the right concept of place values in preschoolers as early as at Nursery level. This foundation is critical as they will be able to see the relationship between numbers in relation to their place values.

We all know that very young children need to be exposed to concrete materials in order to make sense of what they are doing and learning. They need to experience the process of working through the specific tasks before they could acquire the concept. As with a Montessori setting, the children are taught this concept using the 'Golden Beads' using sets of units, tens, hundreds and thousands. However, in a different setting, this can always be substituted with other manipulative and the closest to it will be the unifix cubes.

Once the child is able to quantify the sequence of numbers 1-10 correctly, he or she can then be taught to do grouping of sets of 10. As in the case of the place value of 34, children will be given the understanding that '4' stands for ones or units,  and the '3' refers to the tens. Therefore, 34 is the same as 3 tens and 4 ones or units. And when it comes to writing it in symbols, they will be able to see that the number on the right represents the smallest set of values up to 9. If one more is added to it, it will become 10 which requires a different placeing. The same goes for hundreds and thousands (for example having sets of 9 tens and if 1 ten being added to the set, a 100 will be formed and so on)

This concept proved very essential and helpful in preparing children for futher mathematical functions in their later years. It really makes a difference whether a child is equipped or not equipped with this concept for their understanding number concepts and values to be challenged further.

Entry 3. Problem solving in relation to environment-based task.

Our group has chosen the topic on 'Money' for the environment-based task. We have chosen that topic as it is something which is very practical in our daily lives especially when the target group are the K2s. They need to be equipped with the concept and skills of handling money before they progress further to Primary 1.

We have understood the requirements of the task but thought that it would be more appropriate for such lessons to be translated and conducted in a classroom setting. At first, we decided to have Coffee Bean as our main setting, then MacDonald's, but in the end, we settled for the Marketplace at Raffles Shopping Centre.  We wanted to adopt the concept and have planned for a supermarket corner to be set up for the children where they will do pretend shopping of buying and selling of items using real money. Besides providing them with the right kind of language to use, it will definitely be a fun learning experience for them being given the liberty to consider and decide on what to buy for themselves given the limited amount of money that they have.

The extension for the planned activity would be to get the children to create a pictograph on the items purchased and to make their own comparisons. Besides, they can also create their own addition and substraction story sums given the prior knowledge of those concepts that they have earlier on. This is in line with what has been shared by Dr Yeap, that we should provide children with concrete experiences before moving on to pictographs and later on, the abstracts.

Entry 2: Reflection on my first lesson.

It was an enlightening experience that I have had on my first lesson. It was very different from what I have expected. On my way to class, I was pondering to myself, "How am I going to survive sitting down for four hours learning Math?" It was something which was unthinkable! My perception towards Math soon changed as I stepped into the classroom and being faced with our lecturer Dr Yeap. I could feel and hear voices of excitement buzzing in the air.

We were first introduced to the number sequence game. It was a struggle at first when my partner and myself tried to work on a trial and error method. We only managed to do up till '3.'It was much later when I actually thought of a faster solution; with the help of paper and pencil, I drew out ten squares and started to spell and fit in the corresponding numbers accordingly into the square I stopped at. It was truly a new discovery!

I enjoyed the video on 'Dice,' too. It is something which I have never thought of before though I have tried using a die for some movement games with my children as they count and move to the number of dots on the die. As I am working with the Nursery 2s, it is difficult for them to grasp the dice concept of the linear counting whichs adds up to 14 each time. Back in class the next day, I decided to simplify things to their level. I demonstrated how they can perform addition games or exercises with it. They were first being introduced to the sign '+' and '=' and I explained to them the meaning of both. I then showed them how to toss the dice and count the dots on one and then to add with the other. I got them to extend their learning and understanding by recording the responses in their journal. It was an effective and meaningful lesson for them all.

I also enjoyed the paper clips game of 'take one or take two.' After a few rounds of playing with my partner, we came to the conclusion that after the fifth paperclip, the next player who picked whether it is one or two will lose in the end. That is one strategy that we've found out in winning the game before the others shared theirs, too. Learning Math has never been this fun. Too bad we can't turn back the clock!  

Blog entries for chapters 1 and 2 of math module

Upon completion of reading only the first chapter of the textbook, I could envisage the amount of information that I will be gettting by internalizing the contents of the book. I see the importance of being in the right mindset before I could ever attempt to teach mathematics to my student because, my attitude and perception towards math will affect my method and teaching strategies, which will then leave an impact on how my children will perceive math as a learning subject.

I have learnt that there are two important tools that can be acquired in order to be an effective teacher; my knowledge of mathematics and how students learn mathematics. I feel that more importantly is not for the children to derive at the correct answer, but to be involved in the process of thinking or to problem-solve in finding the answers.  

I see the need to be aware of the six principles and standards for school mathematics which explains the underlying principles governing the teaching of mathematics. What I find truly enlightening is 'The teaching Principle' which states that 'what students learn about mathematics almost entirely depends on the experiences that teachers provide everyday in the classroom.' This means to say that the teacher needs to have a prior knowledge and a certain level of interests deemed necessary before he or she could impart learning to children.

Chapter One also explains the differences between 'Traditional Curricula' and 'Standards-Based Curricula.' It is mentioned that students for the latter perform much better on problem-solving measures and at least as well on traditional skills as compared to students in the former.

I really liked the quote written by Schifter and Fosnot at the beginning of Chapter Two which states, "No matter how lucidly and patiently teachers explain to their students, they cannot understand for their students." This is indeed so true and it does not only apply to the teaching of mathematics but in other areas of learning too. It is also important to note that mathematics is more than completing sets of exercises or following the processes the teacher explains. It is also means generating strategies for solving problems, applying those approaches and see if they lead to solutions and making connections to what is happening in the real world even within the confinement of the classroom situation. 

I liked the fact that this chapter uses colourful picture representations and illustrations to demonstrate explanations on a problem situation. It makes it clearer for the readers to understand the intended message brought forth. I have gathered the importance of the teacher's role in setting the right kind of mood and environment for  the students so as to make teaching and learning more effective.

Chapter two also touches on the two theories; Constructivist and Sociocultural. The former focuses on the cognitive schemas of assimilation and accomodation and also the process of reflective thought. Though learning is constructed within the self, the classroom culture contributes to learning while the learner contributes to the culture of the classroom. These two factors are influencing one another. Siciocultural theory touches on ZPD, also known as 'zone of proximal development.' Another major concept regarding this theory is semiotic mediation, which is a term used to describe how information moves from the social plane to the individual plane. It involves interaction not only through language but also through diagrams, pictures, and actions.

I see the importance of getting children engaged, involved and interacting actively among peers and their teacher in the process of solving mathematical problems. This involves active learning and thinking and teachers must be mindful not to feed students with too much info and explanation. It is also important to allow room for making errors and for them to learn from it.

I have learnt that mathematics proficiency encompasses two areas; conceptual and procedural. The former refers to knowledge about the relationships or foundational ideas of a topic and the latter refers to knowledge of the rules and procedures used in carrying out mathematical processes and also the symbolism used to represent mathematics. These two therefore, work hand in hand and the absence of conceptual understanding will lead to errors and a dislike of mathematics.

The two chapters above have proven to be comprehensive and have provided me with a clear understanding on the aspects and requirements of learning and teaching mathematics. I will revisit the mathematical problems posed in these chapters to test myself on my capability to solve them. What is most important for me is to come into the classroom with a proper mindset regarding mathematics and prove to the children that learning mathematics is so much fun!