Tag Archives: elementary mathematics

Reflection: tangram activity PLUS! an idea for a class project using tangram pictures!

Tangram (Image: Wikimedia)

I loved working with the tangram! I loved the challenge that Dr. Yeap posed- such as “I wonder if we can make a rectangle with three pieces” and “Did anyone manage to make a rectangle with five pieces?”

The way the questions were posed hinted at the possibility of the task- at the back of my mind I was thinking “OOOOOOH it can be done and I must try!” Soon, I was trying to make rectangles using all the pieces and was well pleased with myself for being able to make a rectangle using all seven pieces!

Making pictures using pieces of a tangram (Image: http://www.clccharter.org)

What made this particular activity with the tangram great is the use of

  1. the CPA approach: it is a concrete activity- you get to move the pieces around and discover different ways
  2. SCAFFOLDING: the teacher asked questions that set students thinking about the next step ie. help in the student’s learning process
  3. MODELLING: teacher and classmates demonstrated how certain shapes were achieved

Dr. Yeap asked if we knew any books featuring tangrams and he introduced us to Grandfather Tang’s Story, which is based on a Chinese folktale. I learnt that the tangram was traditionally used by Chinese storytellers as visual aid! You can expect tangrams at my next storytelling session :D

When I did a Google search, I found another book featuring the tangram.

You know what I think will be an interesting class activity using the tangram? (What what what?) Get each child to create a character or feature using different pieces, and incorporate these elements in a story. Publish the class story ala Writer’s Workshop!

The Concrete-Pictorial-Abstract Approach: An Acronym is born

Wah! FREE!
Really, internet? Where do I queue?!?!

If yesterday’s entry mentioned Piaget’s Constructivism and Vygotsky’s Social-Cultural theory, let’s now talk about Jerome Bruner, who suggests that there are three steps (or representations) necessary for pupils to develop understanding of a concept

The three steps are:- 

  1. Concrete representation
    This means using real objects such as cookies, unifix cubes, counters, beads, and blocks, to solve problems. 
  2. Pictorial representation
    Putting the concrete into pictures- using shapes for example, to represent the objects. 
  3. Abstract representation (sometimes called Symbolic representation)
    No concrete material or picture representation is used- instead, use numbers and math symbols. 

The goal of mathematics is the ability to handle abstraction. To achieve this, students must be able to do math in concrete, then pictorial representations before being able to do the abstract. In fact, the CPA approach does not just apply to mathematics but to other areas of learning as well. 

Jussssssssssst in case you think the CPA approach ends in preschool, NOPE! It is also used in Primary schools around Singapore


Let’s talk about math!

Over the next few days, this blog will feature posts on teaching and learning mathematics. If you have been a long-time reader of this blog (ie. hello mama, papa, and self!), you will know that my inclination has always been towards language and literacy. You will also know that I am new to preschool teaching, and math is a subject never-before-mentioned on my blog save for this picture. This is also the first time blog entries account for grading! 

My math is bad but not this bad, hokay?
What a steal, guys!

A tired refrain from my days in secondary school math class was ‘Will I ever need to do this in real life?’ In my case, almost never (logarithms, anyone?). I admit, the lack of application put me off some branches of mathematics then. Thankfully I can still do the kind of math that count- you know, calculating the bill at the end of a meal, adding in service and government taxes, making sure everyone pays their share and not a cent less (or more). I can also convert SGD to IDR pretty quickly.

My biggest takeaway from reading chapters 1 & 2 of Elementary and Middle-School Mathematics: Teaching Developmentally (8th Ed.) is that I have much to learn! It reads like a to-do list-

  1. I need to grow my knowledge of mathematics to become a teacher of mathematics
  2. I need to understand how children learn mathematics 
    Two guiding theories here: constructivism (Piaget) and social-cultural theory (Vygotsky). I already know from experience that meaningful, real-life application is important in helping children make sense of their learning. Knowledge about how children learn mathematics provide us with suggestions for teaching mathematics. This include building from children’s prior knowledge, building in opportunities for reflective thought, engaging children in productive struggle*, and treating errors as opportunities for learning. And let it never be said that I never invoke the names of theorists :p
  3. These will guide me in selecting tasks and activities for children
    A-HA! This is what it all boils down to, ladies and gents. Selecting meaningful activities that will enhance each child’s learning. In other words, I shouldn’t be fielding questions such as ‘Will I ever need to do this in real life, Ms. Harlina?’ from my class of three year olds, EVARRRRRR.

Incidentally, these points make up the teaching principle, one of six principles fundamental to high-quality mathematics education. The other five are equity, curriculum, learning, assessment and technology. I expect Dr. Yeap will employ all six principles in the classroom. See, he already got the technology bit covered by maintaining his own blog and setting us this task!

It was a wise old owl (high on diet Pepsi, Satay-flavoured broad beans, and international travel) who first told us ‘We teach how we were taught’. I am so glad I have a second chance at learning mathematics!

*as opposed to unproductive struggle, which happens from time to time in preschool settings, sometimes resulting in tantrums, usually thrown by children and rarely by teachers. There is a venn diagram in there somewhere just begging to be drawn!