Session Six

          Session six marked the end of EDU 330 Elementary Mathematics module. Six fun-filled days of math activities. Did I just write that down? I find it hard to believe it myself but yes, it's true. Mathematics was never my forte as a student but the pass six days under Dr Yeap's tutelage, I have found renewed interest in it.

One of the many things that will remain with me after today will be Jerome Bruner's Concrete Pictorial Abstract approach. The importance of this approach in helping children learn not only mathematics but for the learning of anything abstract is crucial.


          The second thing that I will take away from this module is the four questions teachers have to ask themselves when planning a lesson. 

1.  What do I want the students to learn?
2.  How do I know if they have learnt?
3.  What if the are unable to learnt it?
4.  What if they already can?

          Following the four questions are the stages of teaching that every teacher should follow:

1. Modelling
2. Scaffolding
3. Exploration
4. Enrichment

Of all the things that Dr Yeap taught.......this I will not forget

 The Importance of Using the Correct Language 

The use of language to connect math concepts and children's understanding of those concepts is a significant aspect that I must take into consideration from the initial moment children begin to acquire skills and mathematical knowledge.

Thank You Dr Yeap for making Mathematics fun and enjoyable and making me believe in myself that I need not be a mathematician to teach mathematics. All I need is to know the techniques of teaching mathematics.

Session Five

         

          We learnt how to find the area of a shape on a geoboard. Dr Yeap asked us to draw as many polygons as we possibly could by connecting only four dots. It was challenging yet interesting. He indirectly showed us how we could challenge young children in thinking of the various possibilities of drawing a four-dot polygon.We came up with a few shapes. Then he asked us to find the area of the polygon. I found cutting and pasting to find an area was easy to do but it can also be done by finding half of a rectangle and subtracting. Again we discovered that there was no one right way. This was a fun and an engaging activity. Definitely a very concrete way for children to learn the concept of area. Click here for more geoboard fun.

Creating 4-dot polygons 

          I am convinced that as teachers, it is important to always consider the process of thinking and finding an answer instead of insisting that students follow only one way of solving a problem.
          Dr Yeap always goes, "Is that so?" or "Do you think so?". I could never understand why he never gave an answer but having come to the end of the fifth session, I realised that Dr Yeap was modelling to us how to question children even though they had the right answer. This was how children can be given opportunities to rationalize their answers and understand how they came about in deriving the answers or solving a problem. I learnt that it is essential to not only question children when they have made a mistake but also when they have the right answer.

          Thank You Dr Yeap, for enlightening us with this undeniable fact.

Session Four

          Bruner's Concrete-Pictorial-Abstract (CPA) approach is undeniably a basis that all early childhood educators follow. The concept of using concrete materials to build concrete experiences, is a long established  approach in working with young children. Today Dr Yeap covered the concepts of area, division and multiplication. The division activity was a challenge as I had forgotten how to do division with fractions. But as always I recollected what I had learnt when I was in school through the hands-on activity and explanation given by Dr Yeap.
          I enjoyed trying to figure out how shapes fit together to form larger shapes and how larger shapes are made of smaller shapes using the mosaic puzzle. The use of mosaic puzzle is very concrete and it allows for students to visualize the concept of area without even having to talk about area.

          As an adult, we often tend to overlook the fact that 'spoon-feeding' can be a stumbling block in a child's learning process. When everything is given to a child without an opportunity for exploration, the child will not be able to form modify an existing schema or form new schemas. Intelligence is defined by refined schema or schema creation.          Another thing Dr Yeap brought to my attention was the importance of Jean Piaget's theory on assimilation and accommodation. As physical experience accumulates, accommodation is increased. A child will begin to think abstractly and conceptualize, creating logical structures that are meaningful to his or her experiences.



7 piece mosaic puzzle

Can you tell if shape 1 and shape 2 are equal in size?
What about shape 3? How many of shape 2 will fit into shape 3?
Try and find out how many pieces of shape 1 and shape 2 fit into shape 7.

I learnt of Van Hiele' s theory of geometric thought. Each level describes the thinking processes used in geometric contexts. Need to read up more to understand more about Van Hiele's theory.

Session Three

          Today I learnt an interesting way to teach fractions. Fractions is not an easy concept to comprehend, yet Dr Yeap demonstrated how easy it was to explain to children the concept of fractions.

          Just by folding a rectangular piece of paper into four equal parts, and finding out if it was equal made a lot of sense. Folding the paper seemed like play but it was truly purposeful play. Folding the paper or cutting it and placing it on each other to find out if they were equal in size embodied the idea of equals. 

          Dr Yeap made it clear through this activity that it is important to remember that the mere use of objects or manipulatives does not teach a certain concept. Children must be given concrete objects that help them encounter the concept.

          In learning about numerators and denominators, I was intrigued about how reading them correctly actually made a great difference in understanding the fraction. E.g.  3/4 is read as three fourths and not as three over four. The three in 3/4 is the number and the four in 3/4 is the noun. The four is not a cardinal number.

          Another thing I will take away with me is that when partitioning a whole into fractional parts, children need to be made aware that the fractional parts have to be the same size but not necessarily the same shape. 

          I learnt that as an Early Childhood teacher, I must be careful with the Mathematics language I use. It greatly affects how children perceive and understand a concept.

Session Two

          Today I was reminded of an important point in teaching preschoolers. Something that is not new but often forgotten in rat-race Singapore.
          The preschool years of a child are the foundation (preparatory) years for learning. As a teacher I should not be too concerned about what to teach but rather I should be giving careful thought to the way I teach. I will have to consider four critical aspects before I plan for activities that will promote the learning of mathematics. The four aspects are:

1. What is the objective behind a certain activity and what is it
     that I want the children to learn. 

2. How would I know if the child has learnt it?

3. What do I do for a child who is struggling with it?

4. What if the child has learnt it?

          To achieve the desired outcome in any lesson, I will have to use multiple assessment approaches to determine each child's mathematical understanding level and at the same time carry out observations in assessing their strengths and weakness in mathematical concepts. I must also bear in mind that a struggling child will eventually understand a concept if opportunities for more practice is given. A positive approach is also important in motivating a child to stay on the task until the child understands and achieves the desired outcome. I must also plan and carry out activities that will promote higher order thinking for the child who has learnt a concept or mastered a task. 
          Lesson plans should emphasize the task at hand rather than on logistics. Using differentiated instructions is important in catering for children with different learning needs.

Session One

          The first day of lecture, was a day of discoveries...I was amazed at how fast the time flew by during lecture because I never liked Mathematics especially if it had to do with solving 'complicated' problems. But to my surprise I thoroughly enjoyed today's session. It was FUN trying to solve the problems.
          The first problem Dr Yeap posed to us challenged my problem solving abilities. He asked us, which letter in his name was counted 99th. I tried solving it but it took me a long time but I eventually got the answer. While working on it, I noticed a pattern forming in the sequence of numbers. I discovered that it was the 3rd letter in Dr Yeap's name.

          At finding out the answer, Dr Yeap  challenged us to do the same with our names. I tried the same method I used earlier but could not see any pattern while I could hear some classmates saying that they could see a pattern. I persisted until I got to the number ninety-nine. It may not have been the most effective method but it helped me discover that it was the the 3rd letter.
          I learnt a few things today but I will surely remember the following three things from today's lecture...

1. There are many methods to solving a problem - no one way is the right way

2. In teaching there are four levels; by modelling, scaffolding, giving opportunities and explaining

3. Students may use less efficient approaches but they will acquire more strategies during the lesson through other students' sharing their approaches and the teacher's effective questioning.

          I will continue asking, "I wonder why?" to get my students thinking and going in the direction I want them to go in solving a problem.
                                      

  It was all about
          learning mathematics
                      by doing mathematics.

Reflections on Readings - Chapter Two

          "Doing mathematics begins with posing worthwhile tasks and then creating an environment where students take risks and share and defend mathematical ideas." (Van De Walle, Karp, Bay-Williams, 2013, p. 14). As a teacher I find this to be an important statement. I  need to create an environment that stimulates children's learning and provides challenges for them. An environment in which they can be actively thinking mathematical ideas while trying to solve the problems. A place where they can be engaged in sharing their ideas and reflecting on their mistakes as well as make connections between different strategies in solving a problem.
          In the learning process, both the Constructivist and Sociocultural theories should be applied to enhance the learning journey as both these theories emphasize the learner using their own knowledge and experience to solve problems through social interactions and reflections (Van De Walle, Karp, Bay-Williams, 2013, p. 29). As a teacher, I need to know the prior knowledge of my students in order to provide them with appropriate challenges in making the connections and bringing them to the next level. I need to apply the following strategies when considering practices that maximize learning:

• Build new knowledge from prior knowledge - through inquiry based approach.
• Provide opportunities for talk about Mathematics - through interaction with peers and teacher.
• Build in opportunities for reflective thought - by engaging students in interesting problems in which they use their prior knowledge to search for solutions and create new ideas.
• Encourage multiple approaches - by sharing ideas.
• Engage students in productive struggle - not by showing them but by asking probing questions until they reach a solution.
• Treat errors as opportunities for learning - by addressing student misconception.
• Scaffold new content - by giving more structure, and 
• Honour diversity - by including student's ideas for classroom discussion

Reflections on Readings - Chapter One

          In this chapter, I have come to understand the different principles and standards for the instruction of Mathematics in schools. This comes to show that Mathematics is definitely an essential aspect of education. All these frameworks have one thing in common. They all focus on the need to make it possible for all students to have the opportunity and the support necessary to learn significant mathematics with depth and understanding. It is evident that the long-term goal is for all students to develop lifelong problem solving skills. Mathematics ability is not inherited as anyone can learn mathematics.
          Mathematics was never my forte as a student, so I was a little apprehensive when I read that I would need to have a profound, flexible, and adaptive knowledge of mathematics content to be a teacher of Mathematics. I realized the important role a teacher plays in the teaching of Mathematics. The fact that student's learning of Mathematics may come only from the teacher, puts an enormous responsibility on the teacher. I totally agree that a teacher has to demonstrate persistence, have a positive attitude towards mathematics, be prepared for change, and always make time to be self-conscious and reflective (Van De Walle, Karp, Bay-Williams, 2013, p. 10).
          I need to change my attitude towards mathematics and be receptive to the joy that can be found in solving mathematical problems. This is important to me not only as an individual but more so as a teacher so that I can be a positive role model to my students. Only then can I nurture in my students a positive attitude and a life-long passion for mathematics.