Final Final words....

Solve:

Dr. Yeap gave 10 cookies to Hannah. Cookie Monster came along and ate 8 of Hannah's cookies. Hannah now has one-fifth of her cookies left. How many cookies exactly does she have now?

10 – 8 = 2 !!

Dr. Yeap, thanks for all.. Many apologies for my late submission of the last few entries.. L

Right or Wrong angle?

h) Geometric Thinking

Geometry relates to spatial sense in recognition to shapes and structures found in the environment. Young children learn about and use their knowledge of two and three-dimensional shapes when given the opportunity to create designs with pattern blocks; draw, paint and cut shapes for their artwork; organize blocks by sorting them; and locate shapes in outdoor settings.

By kindergarten age, children identify, classify, compare and analyze characteristics, properties and relationships of one-, two- and three-dimensional geometric figures and objects. Kindergarteners use spatial reasoning, properties of geometric objects and transformations to analyze mathematical situations and solve problems.

In van Hiele’s levels of geometric thought, early learners belong to the Visualisation Level (Level 0). As they are concrete learners, they engage in observing, feeling, building, taking apart, or working with shapes. Though they may be able to identify some properties of shapes at this level, it is only in an informal, observational manner.

I liked geometry in school, and I can reminisce the times where I would score on that topic as compared to others. Unfortunately that wasn’t the case during Dr. Yeap’s session on geometry.. I realized I lost touch completely! I couldn’t recall the total angles within a pentagon, and kept thinking it was 360º. Another way taught was also to see the triangles within the pentagon, which I don’t know if my eyes were wearing down on me (excuses..) or my memory is failing (ok, it’s the latter..). But still, it was amazing to see that we can actually come up with the formula once we can see the pattern!

Count on Me....

f) Developing Number Sense

One of the basis of mathematics is an understanding of number relationships. Children need to make sense of the ways numbers are used in their everyday world. Number senses and concepts develop gradually over time as young children explore, manipulate and organize materials and as they communicate their mathematical thinking. One of the earliest number concepts is counting. It begins with developing oral counting skills or rote counting. Following this is one-to-one correspondence, where only one number is linked with each item in a set of objects.

I have classified the activities from the text basing on my thoughts of practices in local preschools, as follows:

Commonly practiced:

J  Relationships of More, Less, and Same

J  Early Counting

J  Numeral Writing and Recognition

J  Counting On and Counting Back

J  Estimation and Measurement

J  Data Collection and Analysis

Not Commonly practiced:

L  Anchoring Numbers to 5 and 10

L  Doubles and Near-Doubles

Problem Solving

c) Chapter 3

All young children are problem solvers. As they explore and examine their world, they are attempting to find out how things work. When children involve themselves with various learning opportunities, real problems are posed, and children are guided to use the mathematical processes of reasoning, communicating, representing and connecting to solve them.

To promote problem solving, there must be provision of the environment, materials and experiences for solving problems. Early childhood educators should design the learning environment so it offers interesting problems and an array of materials for children to use in solving them.

It is interesting to read from this chapter that teachers may face the dilemma of how much to tell, when teaching problem solving. I have been caught in situations alike before when engaging children to problem solve, as I was then concerned with the time factor and only wanted to abide by the lesson duration. I was guilty at times then, for providing more information than I should as I was hoping that it would so much help them in deriving to a solution. And yes, I should be convicted for killing their rights to learning to problem solve..

Instead of offering solutions, teachers can help children state problems, provide time to listen and talk about the problems, and connect some of the problems occurring in their lives to mathematics learning. Of equal importance, young children learn powerful lessons when teachers model problem-solving strategies, convey the joys of finding solutions and acknowledge the frustrations during challenging moments (Copley, 2000).

Environment-based Task  < To the Outdoors We Go! >

We brainstormed many ideas on math lessons we can plan for environmental learning, but decided on a measurement activity for Kindergarten 2 level. Here’s what we did at the Burger King fast food outlet at Raffles City Shopping Centre:

 

We planned for children to measure using different given items, compare the data collected, and involve themselves in teamwork. Children will engage in the process of observing, prediction and logical thinking.

Task:

Children are grouped into groups of four. Each group will be given one type of item as a measurement tool. Children will measure selected objects / furniture at Burger King. Record the data collected on a chart. The groups will compare their data collected.

A follow-up activity may include predicting the measurement of a longer or shorter similar object / furniture.

Putting Learning into Practice....

Six sessions have passed in what seemed to be one of my most meaningful learning to date..

h) Reflection of the Course

Before the start of the course, I was asking one of my coursemates why this Elementary Mathematics module is required of us. The word “elementary” seems more suited towards primary schoolers and furthermore we have had math modules when we attended the Diploma level. She couldn’t answer, but now after undergoing the sessions I think I have found it.

Though of a little more complex level as compared to the math content learned at the Diploma level, it provided expansion in the degree of math concepts to be taught to young learners. I enjoyed hearing great-grandfather theories from Dr. Yeap’s friends of theorists! I also learnt a lot of math tricks which kept me very engaged and not ‘switch off’ like I normally do. Most importantly, I learnt to believe that my students would be able to involve themselves in these tricks too, as I initially thought that it would be a tad complex for them.

Now I hope I can make a difference.. It is my responsibility to ensure that knowledge is put into action. I am determined to share what I have learnt with my team of teachers and improvise on our math curriculum.

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Thanks Dr. Yeap, for making us see mathematics in a whole new light. And please, do send my regards to your good friends, if you can!    =)

HIGH-TECH(nology)

High-tech. That is how I would describe our nation and especially so the new-age kid. Technology is everywhere these days that you will have to travel to the Sahara Desert to evade this powerful tool.

e) Chapter 7

Calculators were a great help to me back in school days. I had a good trust in calculators and relied on them to provide me with the exact computation. I also liked calculators because it ended the nagging routine of school and tuition teachers who kept saying that I was guilty of making careless mistakes in my calculation.

In this chapter, we can read about the benefits of the use calculators that contribute to the learning of mathematics. I was amazed with what calculators can do in a child’s learning! Though calculators are commonly used in society, I assume that early childhood educators have never really brought it into their classrooms. After reading this chapter, I am convinced that it is a good tool to introduce at preschool level. While experiences with concrete materials are primary for young learners, calculators can also serve to be concrete as a tool that can enhance conceptual understanding, strategic competence, and disposition toward mathematics. I also agree with the authors that effective use of calculators is an important skill that is best learned by using them regularly in meaningful problem-solving activities.

For one of my assignments for the IT module back in poly days, I had to design a software for preschoolers. I recall designing an interactive math game, where I ensured that it incorporates math concepts, problem solving, and other skills (eye-hand coordination, etc) catering to a selected age group. As much considerations and thought goes into designing such software for preschoolers, I think the same applies for selecting them for application. There are numerous software and internet resources available, but it is the responsibility of educators to ensure that those selected are challenging, age and level appropriate, and meet the objectives of the lesson.

Teacher Resources

I especially liked the following websites:

1.     NCTM Illuminations

There are some really cool activities that anyone young and old can try. So I indulged myself with those activities…. I thought that this proved very well that such mathematics games will allow children to engage in resolving, concentration, the use of a variety of strategies, imagination, and creativity. This website did not disappoint.

2.     The Math Forum

Various activities catering to different age and complexity levels. Very useful for teachers' resource in designing their lesson plans too!

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My centre very recently purchased this thing called the “Portable Interactive White Board” that enables interactive teaching from anywhere in the classroom. It is to be used with an electronic pen (e-Pen), and interact with software applications simultaneously. My objective in making this purchase was so that my teachers can bring technology closer to our students, and of course, to make learning much more fun. However, I can foresee that I may have difficulty in getting teachers of the mature age to embrace this new technology. As it is, they are trying to cope with the conventional use of IT in children’s learning. It will take a lot from this self-declared “IT-idiot” to make this change.

Qsn: How do I change the mindset of early childhood educators who are afraid or not very willing to embrace new technology?

Sequencing Learning Task

d) Place Value (34)

1.            Number in numerals

2.            Place value chart

3.            Number in tens and ones

4.            Expanded notation

5.            Number in words

My rationale:

Bruner recommends using the CPA approach, where young children should start learning with concrete representation first. Moving on from concrete experiences, the next step is teaching children numerals. I think numerals are very straightforward digits. I find that children can actually identify numerals faster than they can as compared to learning it through the other longer routes first. Do they understand it?.. Yes. From the numeral 34, introduce the place value chart. From prior concrete experiences, children should be able to represent with placement of 3 tens and 4 ones. Then, as children have learnt that the number 34 is made up of 3 tens and 4 ones through the place value chart, they can now learn the number words form. After which, the expanded notation is introduced, where children then go in depth into how many tens and ones individually make up 34. Addition comes into place here. The last stage is teaching the number in words. This should be the last step as children must possess the ability to convert the mathematical symbols into letter symbols.

More blog posts coming your way this month-end....

Hi Dr. Yeap,

Blog's not ready for assessment  =)    Please check this month-end, thanks!

1st Session

b) Reflection on Session 1

     Talk it Out!

OK, honestly I didn’t really dread the thought of attending class on Teacher’s Day, as I was happy I had the whole morning and noon for “me” time anyway. But.. why math? I thought.. I may have liked the subject, but after leaving school for sooo long, do I need to learn all those math formulas again? Should I bring a calculator?....

Well Dr. Yeap proved to be in a different league from almost all my former math teachers. Not for the sake of saying it or to obtain good credits, but he really did make me view the subject in a new perspective. Let me share why..

When the three games were introduced, I doubted if my students would be able to engage in them based on level appropriateness. I know I shouldn’t undermine their abilities, but I wondered if they will be able to play with perfect understanding of the concepts or to even generate the desired response, for that matter. And then Dr. Yeap clarified my thoughts. It’s not about them getting the right answers; it’s all about them being able to talk about the process of how they derive to such an answer. There’s no right or wrong, really. If the child can clearly explain his or her thoughts in arriving to a particular answer, assumption or idea, it will reflect the level of understanding acquired. To relate my assessment practices at my centre, I normally do it the conventional way. If I don’t see the correct answers in place, I may allow the child to try a second time, and probably let him explain himself once or twice. But to what extent do I respect the child’s answers or ideas? How far do I facilitate in making the child speak about it?

It’s time for me to reflect on my existing assessment practices and make positive changes….

If children are excited, curious, resourceful and

confident about their ability to figure things out

and eager to exchange opinions with other

adults and children, they are bound to go on

learning, particularly when they are out of the

classroom and throughout the rest of their lives.

– Constance Kamii, 1990

Math & Me

My relationship with math is a complex one - Hated it in preschool, loved it in primary school, kind of liked it in secondary school, mad-liked about it when I taught it to preschoolers. Actually, mathematics was never listed on my Subjects-I-Hate list. I don’t have fantastic memory skills and therefore liked subjects which do not require much memorizing of facts and theories. That may explain why I actually liked mathematics back then in school (and hated History), as I know that I only need to remember the formula, have some level of “mathematical intelligence”, apply the formula accordingly to every question, and heed my teacher’s advice to practice(x10). I managed to obtain a credit (C6; nothing to boast about) in E Math for my ‘O’ Levels, but I did ask myself: Why didn’t I score better given that I did generally have a liking for math then? Perhaps the fault lies with my mathematics teacher back then in secondary school whom I feel did not contribute much to providing the maximum knowledge we needed to equip ourselves for the big exams. Or to point my finger back at me, I could have done more practice. Anyway, I think I have the “formula” to my relationship with mathematics….

Practice + Success (correct answers)  =  Happy  ;)

Practice + Failure (wrong answers)      =  Frustration :X

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a) Reflection on Chapters 1 & 2

After reading the initial chapters from the text, I realized that mathematics may not always mean practicing it to death. There is so much more to mathematics than what teachers back then told us: Practice (x100).

Chapter 1

Basing on the six principles in Chapter 1, it is clear that these principles contribute to excellence in mathematics education. For instance, early childhood educators would have learnt during their course of study that assessment is essential to find out child’s strengths and needs. The Assessment Principle quoted the author that “Assessment should not merely be done to students; rather, it should be done for students, to guide and enhance their learning”. I agree with the author that it is important for educators to ensure that assessment through student interaction shall encourage students to communicate and clarify their ideas. I also agree with the author that teachers must have a good idea of how their students may be thinking about or misunderstanding the mathematics that is being developed. It is important for teachers to understand their students’ mathematical abilities well to determine their competency level. Through personal experiences in school, I feel that teachers who can detect students’ misunderstanding of mathematical concepts at an early stage can help to render support accordingly, and administer more appropriate assessments to follow up.

Chapter 2
Halfway through reading Chapter 2, I digressed a little to actually engage myself with the math problems. Having left secondary school a little more than a decade ago, I got into “brain freeze” moments, but despite all that I wanted to get through the challenges. I recall the good old days where I got all hyped up upon solving mathematics problems and would be hungry for more. Then there’s some of the not-so-good old days where I couldn’t problem solve and would start pulling my hair. But I guess it all boils down to how well one understands mathematics and apply appropriate strategies. I feel that the Strategic competence is one of the most crucial out of the five strands of mathematical proficiency. Personally, I sometimes feel an adrenaline rush (in a good way) when I need to find different strategies to solve math problems.