The Most Significant Impact

The course module 'Elementary Mathematics' first felt like a horrible nightmare before it began and slowly drew me in as each lesson went by. By the end of the 2nd lesson, I felt drawn to math and realized how fun it could be to be actually physically in a mathematics class. Frankly, I have never felt that way in a math class. It always bore me to tears when I was a student in my younger days.

Dr. Yeap has demonstrated the 'magic' of math and uncovered the fun side of problem sums in this module. I came to realize the importance of math lesson is also to inculcate the love of mathematics in the young learner (so they will never end up with how I was before)! 

I learned that it doesn't always have to lead to the right answer during your first few attempts; it was really enjoyable to come up with conjunctions and discussing them with my course mates, and eventually coming up with a deeper understanding. That was so unlike the "Don't ask me why, but this is how you do it!" that my math tutor would always say when I raised a question. =( 

All in all, it was a very pleasant time, much to my surprise! Kudos to you, Dr. Yeap!

Whole Numbers/Numeracy

It is recommended by the authors in chapter 8 that abundant activities should be included to support a variety of experiences for young learners to acquire a full understanding of the concepts. 

Some of the common numeracy activities found in preschools are listed below:

• Counting

 

 

• Recognizing and Writing Numbers

I feel that the relationships of more than and less than, estimation and measurement, and part-part-whole relationships are uncommon teaching approaches adopted by teachers in preschool settings. To my dismay, we may have been teaching students too little of what they ought to or deserve to know.

Geometric Thinking

In chapter 20, the authors asserted that, "A rich understanding of geometry has clear and important implications for other areas of the curriculum." I remember being very interested in the topic of geometry when I was in secondary school. Hence, when Dr. Yeap challenged us with the pentagon problem in class, I have to say that I felt a leap in my heartbeat. I was excited! =) 

Although I didn't mange to solve the problem almost immediately, I was still relatively pleased when I did manage to figure it out. I guess my spatial sense was quite keen (haha!). Some people may feel that they are not born with spatial sense but the authors tell us in chapter 20 that that typical belief is simply untrue! A better competence in geometric thinking requires having an increased emphasis on geometric reasoning provided consistently over time. So fret not, for all those who think that they naturally have no 'talent' in geometric thinking, for persistence and focus helps!!

Tangrams... It's not the first time I played with them and through the lesson, I finally came to know its real name! It wasn't easy for me to construct the shape with all 7 pieces (I stayed during the break and kept trying)... I guess my spatial sense and geometric reasoning somehow 'weaken' at that period of time. Nevertheless, it was really rather fun! 

No wonder I get so tired after each lesson... I must have exercised too much of my brain cells! =P

Sequencing Learning Tasks

If it is likely that a teacher will start the lesson using the sticks, I would sequence the 5 steps as follows:

1. Number in Numeral

The first step I would do is to show the students the number in numerals. They would be invited to count the sticks and I would show the numerals to them. It is a concept that the students would be fairly familiar with.

3 Tens 2 Ones = 32                        2 Tens 3 Ones = 23

2. Numbers in tens and ones

The second step would be to show the students numbers in tens and ones. In this case, sticks can be bundled up in tens to demonstrate that the total number can be separated into tens and ones.

3. Place Value Chart

Right after showing the students the number in tens and ones, it seems natural to me that the place value chart could be used to show the students that the number could be placed in a chart. This third step demonstrates to them that the number could be shown in a slight different variation.

4. Expanded Notation

After reviewing the number in tens and ones as well as the place value chart, it seem appropriate to me that the expanded notation should be shown to the stu

5. Number in Words

The last step would be to show the number in words. Due to the age group of the students, I feel that the students should only be exposed to the number in words in the last step.

Problem Solving

Reminiscing my elementary days, I don't recall doing much problem solving during mathematics lessons. It was mainly teacher-directed activities. My math teacher would normally provide the solutions as well as the answers to the problems encountered. To a very large extent, I suspect that is the reason why I can't seem to retain many of the mathematical concepts I have learned.

In the three ways that problem solving might be incorporated into mathematics instruction, teaching through problem solving literally means that students learn math through real contexts, situations, problems, and models. Personally I vouch for the importance of integrating the real environment for teaching through problem solving. It was a first-hand experience for me as my group members and I walked right into Plaza Singapura (a shopping center). We took a walk around the shops and explored many possibilities for implementing a math activity with young children. 

Finally, we went into Daiso Singapore, where all the items were sold at $2 each. The shop had a wide variety of items such as gardening equipment, to food and drink items originating from Japan. We felt that it would be a very enriching experience for K1 or K2 students to plan and discuss constructing a present for their parents by purchasing materials from Daiso to make them. The plan is to give the students a meaningful reason to make real purchases from a real context by collaborating, discussing, and planning. They would also have the opportunity to count the money and plan what to spend on.

Technology and Mathematics

Using Technology to Teach Mathematics

As quoted from Walle, Karp, and Williams (2010), p.111, "Thinking of technology as an "extra" added on to the list of things you are trying to accomplish in your classroom is not an effective approach."

That statement struck me as 'out of the ordinary', at least in my personal world. I always had this misconception that too much usage of technology would probably hinder the development of mathematics concepts and skills. Hence, once again, I am rather taken aback to realize that technology should be not seen as an "extra" but rather as an essential tool! 

Moving on to the next page, the authors spoke of using calculators in Mathematics instruction. According to my knowledge, Dr. Yeap has mentioned that calculators were permitted during both papers of elementary mathematics paper. That certainly was different to the era that I was in! I now know that calculators are not to be seen as a 'hindrance' but more of a tool to help develop concepts, enhance problem solving, and improve attitudes and motivation of math learners. 

As I was browsing the website, "NCTM Illuminations" recommended on p.124 of the textbook, I came across this activity of "Investigating Shapes (Triangles)". I liked the way the planner organize the lesson into 4 sequential activities beginning with using blocks, continued by drawing and tracing, as well as geoboards, and making virtual triangles on the computers.

Click here for a link to the activity, "Invsetigating Shapes - Triangles"

Click here for the link to the activity "Investigating Shapes (Triangles)"

My Learning in the 1st Session

Skeptical I was, and yet I was proven wrong immediately. Being invited to the 'new era' of teaching Math, I was exposed to a new generation of teachers who no longer taught concepts and skills with repetitive and boring activities.

Instead, the 'Magic Poker Game' caught my immediate attention. It was absolutely a refreshing introduction to the supposedly 'lifeless' subject I had mistakenly assumed before!

"Math is magic!"

Click here for a link to Singapore's Primary Mathematics Syllabus

The emphasis on mathematics proficiency in the rationale statement to ensure a highly competitive workforce to meet the demands and challenges of today's modern society. In retrospective to my 1st blog entry, I fully felt the impact of that statement in the course of my own life.

Therefore, I am very much motivated by the 1st session to become a teacher of mathematics in a more authentic, fun, and innovative way!

Click here for an article that talks about "Living & Loving Math"

My Reflections on Chapter 1 & 2

I literally rolled my eyes at the sight of "EDU330 Elementary Mathematics" module on my course schedule outline and cringed when I received the textbook 'Elementary & Middle School Mathematics" by A. V. Walle, K. S. Karp, and J. M. B. Williams.

"Math was my least favorite subject."

But was I wrong! My biased assumption of 'another boring mathematics textbook' soon became an eye-opener into a new era of mathematics teaching and learning. As the opening paragraph of Chapter 1 dictates, in this fast-moving and modern world we live in, mathematical competency translates directly into better opportunities to a 'brighter future'.

As quoted from Walle, Karp, and Williams (2010) p.1, "Ultimately, it is you, the teacher, who will shape mathematics for the children you teach."

As opposed to what I have personally experienced as a mathematics learner, the 6 principles listed under the Principles and Standards for School Mathematics provided many liberating insights. Gone were the days where learners were only expected to 'memorize' the 'correct steps' to obtain the right answers. In this changing era, students are encouraged to learn mathematics with understanding; to think and reason mathematically to solve the problems and generate new ideas. 

At this point, it is almost 'tragic' to recall how tough it was for me to do mathematics without actually understanding what I was doing!

The authors suggested that at least 60% of all new jobs in our modern society today will require mathematical and logical skills that are possessed by merely 20% of the workforce in the United States (Walle, Karp & Williams, 2010).

Although the statistics shown referred to the population from the US, I felt it first-hand when I was still a student pursuing my Diploma in Early Childhood education just last year. Being born in a low-middle income family, I had wanted to take on part-time jobs to be more financially independent. Then came an opportunity to be a tutor (well-paid) but alas! The job offered was to be a P5 Math teacher. I squirmed from the insides (although I got an A2 for my O'levels math paper). The problem was I only knew the procedural process and did not have sufficient conceptual knowledge to be able to teach another.

Walle, Karp, and Williams (2010) also argued that the language of doing mathematics has to be dealt with accordingly to promote meaningful learning. Reading the terms 'reducing' and 'plussing' made me fall off my chair laughing. It is ironic that I came to realize the contradictions of these terms only now. Hence, it reminds me once again of the significance of what a teacher says in class. 

Even theorists like Jean Piaget and Lev Vygotsky promotes optimum learning to involve making connections among new and existing ideas (Walle, Karp & Williams, 2010). Learning mathematics means having both conceptual and procedural understanding.

A link that addresses how to teach math:

http://www.wikihow.com/Teach-Math

Being a new graduate, I have little experience in teaching. However, I think that my disadvantage is an advantage at the same time. Not yet tainted by the possible repetitive and monotonous feelings resulting from many years of teaching, I am very much open to new ideas. Hence, the implications mentioned in both chapters enlightened my perceptions of teaching particularly math. Although aiming for students to achieve relational understanding may be a demanding process, students eventually benefit to a great extent!

At this point with least malice, I wished from the bottom of my heart that I had learned math in times alike the above-mentioned new era of teaching and learning mathematics.

A link that addresses meaning of math for a new era:

http://www.massey.ac.nz/massey/about-massey/news/article.cfm?mnarticle=researchers-address-meaning-of-maths-for-new-era-03-07-2009