Of magic tricks, paper art and story time…

We had a very interesting and engaging session with the very energetic Peggy this morning. There were many hands on activities that we had. My favourite activity was the paper art activity. It was an activity that encourages us to think and predict. We used the 3-column method to present out ideas on the outcome of four fold triangle. We wrote down what we see, think and wonder.

One of my biggest takeaways from this lesson was the ‘using stories to teach mathematics’. I learn new activities that could be included in the before reading activity. For example, we could make word cards of the different characters from the story book and get the children to predict the story. The children can create a story by taking turns to come out with a sentence using the character word card. After telling the story, they can also tell the retell the story using the word cards.

From the story, we design a mathematics task. This was when we talked about differentiation. Many times, we always forget the importance of differentiating our lessons for young children. There are three ways in which we can differentiate lessons – by content, by process and by product.

The session ended with Peggy talking about lesson study – professional development process/tool that teachers engage in to systematically examine their processes. I think that this is very important to have in every school. For this to happen successfully, it needs to be teacher-driven/initiated, job-embedded and collaborative learning.

I truly enjoyed all my 6 sessions of elementary mathematics. And like I mentioned in my first session, my entire perspective of mathematics has changed. The sessions reminded me of the implications of the approaches I adopt when teaching mathematics to young children. Out with the old and in with the new! 

Angles, I love you still!

This used to be one of my favourite topics and I must say that I was rather good at it. I always enjoyed trying to figure out the unknown angle. I was pretty much gamed for any kind of problems related to angles that was thrown at me. The keywords here are ‘used to’, ‘enjoyed’ and ‘gamed’. After Friday’s session, I realized that I no longer enjoyed doing the problems on geometry. Dr Yeap gave us a geometry problem based on a parallelogram and an isosceles triangle. I struggled with it. I tried and tried but I was unable to solve it.

This really got me thinking. What went wrong? I wondered whether it was because I haven’t been practicing. After attending the fifth session of Dr Yeap’s classes, I know very well that practicing the way I did was not the way to learn math. The problem I faced was the fact that I was not able to visualize – to be able to see what is not obvious. I had trouble seeing what others saw.

Mathematics is not about knowing the formulas, the properties of geometrical shapes and practicing. It is a lot more than that. It is about having enough concrete and then pictorial experiences. Young children will need to have a variety of hands on experiences. As educators, it is important for us to realize the importance of developing the five competencies:

1. number sense
2. looking for patterns and generalizing
3. visualization
4. metacognition
5. communication

Therefore, I am glad that we are moving along with time. There is no use blaming our past experience with math. It is time now we adopt MOE’s new mathematical problem solving framework. And let’s remember as early childhood educators, we play a vital role in providing these experiences for children.

“Mathematics an excellent vehicle for the development and improvement of a person’s intellectual ability in logical reasoning, spatial viasualization, analysis and abstract thought.” (CPDD, MOE)

Measurement and Geometry

As defined in the required textbook, geometry is a “network of concepts, ways of reasoning and representation system” use to explore and analyze shape and space. Acquiring geometric thinking and understanding geometric concepts are essential for better understanding of algebra, proportional reasoning, measurement and integers.

What are geometry goals for children?

1. spatial sense and geometric reasoning: children think and reason about shape and space.
2. the specific geometric content objectives: shapes & properties, transformation, location, visualization

In class, we were given square tiles to explore. We were asked to make different shapes using 3, 4 and 5 pieces of squares. We then looked at the number of different shapes we can make. It was then that we learn that making the odd shape using the 5 squares is pentomino. It is just like the shapes we see in a traditional game of Tetris. We learnt that all the pentominoes have the same area but different perimeter.

                        

We then explore the geoboard in a pictorial form. We were asked to draw out any shape leaving only one dot in the middle. This was an interesting activity. We then had to find the area of these shapes. We look at very interest shapes. It was easy to find the area of the odd shapes when we find other shapes within that odd shape. For example, different size triangles within that odd shape and square too. We also used addition and subtraction when looking for the area of the shape.

It is through this activity, that we discovered a pattern that allowed would help us find the area of the odd shape easily. As long as there is one dot in the middle, we only needed to count the number of dots in the perimeter and divide it by two. This is incidentally a simplified version Pick’s theorem. I thought that was really interesting. It also reinforces the importance of looking for patterns.

OUT with the OLD and IN with the NEW. It’s time for FRACTIONS!

Today’s lesson caused quite a stir. People were debating over how fractions were taught eons ago and how it is being taught now or rather how we should be teaching it now. It is no secret that I struggled A LOT with mathematics. Needless to say, the topic on fractions was one of my least favourite things on the mathematics list. However, I came out of class today with a new perspective. Everything goes back to Jerome Bruner’s theory of concrete, pictorial and abstract. But first, before anything teaching and learning can be done, as educators, we need to let go of the following:

1. torturing ourselves with memorizing everything
2. following pre-set procedures
3. doing tedious calculations

Once, we are able to let this go, especially the fact that we have to memorize the one billion formulas to solve equations, we can move on with time.

Fractions can be challenging for anyone especially a young learner. Therefore, as educators, it is our responsibility to ease children into understanding this “complex” concept. It is essential to know that children need to experience fractions across any construct. They need many experiences in estimating fractions. Teachers need help children see how fractions are like and different from whole number. Concrete experiences are important. Thus, the use of manipulatives to explore fractions is critical. It is also important that during this time to provide and encourage children to come up with a variety of ways to solve fractions.

I am thankful that the use of “formulas” to solve fraction has somewhat become obsolete. It was painful to have to remember all those “formulas” back in school. After participating in today’s activities using concrete and pictorial approach as well as coming up with different variation to solve a fraction problem, my fear of fractions is beginning to fade. I feel a lot more confident in doing fractions by myself and also have a better idea on how I can teach fractions.

With that, I would like to urge my fellow colleagues to leave our “formulas” behind and adopt this method of learning and teaching. Trust me, subtracting and multiplying fractions have never seems so manageable until today.

WHOLE NUMBERS

Oh wow! Whole numbers - I thought I had this one in the back. Came into class thinking I already know everything there is to know about whole numbers. Boy, was I wrong. The minute the first problem was presented I had that ‘deer in the headlights’ look. The same look I had back in school at almost every math lesson. However, having adopted a new attitude towards mathematics, I felt a little less anxious and a little more excited.

My new favourite thing from learning about whole numbers would be using the 10-frame to teach the concept. Having my love for children’s literature already embedded in me, it was no surprise that I love how a story (Jack and the Beanstalk) is being used at the beginning of the math lesson. I learnt how to use the 10-frame to find the sum of three different numbers. It reinforced the importance of the use of concrete materials when working with addition of whole numbers. My big takeaway here was that there were many ways that were discuss on solving that one problem. Just by using the 10-frame alone, we came up with at least 7 different ways of adding together 5, 6 and 7. Truly amazing!

Here are some advantages of using the 10-frame:

• teaching counting
• teaching number bonds
• understanding number conservation
• understanding one-to-one correspondence
• cultivate place values (tens and ones)

 

The big emphasis in today’s lessons – the importance of allowing children to as many concrete experiences and then pictorial before attaining the abstract. Ways children learn:

1. Looking for patterns
2. Visualization
3. Number sense
4. Metacognition
5. ??? (Be on the lookout for this in the next few blog entries)

It is time we all move away from the convention way of learning and teaching mathematics. The new era of teaching mathematics begins now.

Wise words:

“Children learn by manipulation of concrete materials.”

“You cannot imagine well what you have never experience.”

How children learn mathematics? What are the big ideas?

Today we got an opportunity to become learners in the class. We had the chance to experience what our children go through. It is something that I believe every teacher knows but sometimes I feel we need a little reminder. It is the importance of learning through exploration.

We were given a set of Chinese tangrams and told to use the shapes and form a rectangle. Sound pretty simple? Well, maybe to some. The challenge was finding different ways to form a rectangle and also to use different number of shapes to create a rectangle. It is through the freedom of exploration that along with my partner, we were able to come out with different ways of creating a rectangle.

  

This simple activity allowed me to see the importance of exploration and also the role the teacher plays in children’s learning. Here are some of the roles a teacher plays in this activity:

-         knowing the child’s prior knowledge and tapping on that

-         allowing room and ample time for exploration

-         role-modeling and creating a sense of wonderment

-         challenging the child to the next level

-         Scaffolding the child’s learning

My other big takeaway from today’s session was learning about Jerome Bruner’s Learning Theory. The theory talks about concrete, pictorial and abstract (CPA). It emphasizes on the importance of first having concrete experiences then moving onto pictorial (visualizing) and then going into abstract. Each stage is essential in learning.

 

I hope to be able to explore more on this CPA approach and also how looking at and understanding patterns will lead to visualization. More on this and the importance of problem solving in the entries to come. 

Exploring What It Means to Know and Do Mathematics

“Mathematics is more than completing sets of exercises or mimicking processes. Doing mathematics means generating strategies for solving problems, applying those approaches and checking to see if the answers make sense.”

Mathematics and Science go hand-in-hand. While Science is a process of figuring out or making sense, mathematics is the science of concepts and processes that have a pattern of regularity and logical order. It is about finding and exploring the regularity or order and making sense of it.

As an educator of young children, I live by the theories of Jean Piaget and Lev Vygotsky. Both constructivism and sociocultural theories are essential tools when teaching young children. With the theories locked in, another important factor to consider will be ‘The Classroom Environment for Doing Mathematics.’ It is important to note that creating this classroom takes a conscious effort and it is also my personal belief that it comes with experience. With that said, the classroom should provide for:

-         persistence, effort and concentration

-         a place where students can share their ideas

-         a place where students listen to each other

-         a place where errors or strategies that did not work are opportunities for learning

-         a place for students to  look for and discuss connections.

I am really excited to start this module and learn more about how I can teach mathematics and make it fun and meaningful for children. See you in the next entry!