6th Session – The Last Math Session & More Encounters with Math

At the start of the session, Dr Yeap stated the fact that we should not name a Math problem a problem sum (oxymoron). Instead Math problem should be called story problem or simply, word problem.

We revised doing a word problem with 4 ÷ ²/₃. An example of a word problem of this equation is:

If Jane shared 4 cakes with her friends and each of her friends received ²/₃ of the cakes, how many friends did Jane share the cakes with?

4 ÷ ²/_{3 =} 6

Jane shared the cakes with 6 friends.

Next, we went into assessments (which will form the essential part of our final assignment). Assessments are done to evaluate children’s understanding of Math concepts. Paper and pencil test is often the common method of assessment. Another method of assessment is oral test (interview); in which can be used as simply to assess if children understand the concept of time – instead of drawing the hands of the clock in worksheets. One should always remember that assessment should be valid or in line with the objective of the activity.

The story How Big is a Foot? By Rolf Myller is a simple story that can be introduced to children for the concept of measurement.

Tip of the day: If you want to lose weight, go to the moon.

With this, when teaching preschoolers on weight (focusing on non-standard measurement), teachers are encouraged to question children in this way:

How heavy is the teddy bear? (avoid any mention of weight – kg or mass)

We went to Bras Basah MRT to measure the height of from Ground floor to the basement, just by using a ruler.

** Solution to the MRT steps

16 steps X 4 sections X 13.5cm = 864cm (possibly incorrect!)

Dr Yeap emphasized on Bruner’s theory in teaching Math:

- concrete / enactive representative

- abstract

We did an activity to make a paper container to hold 15 beans to illustrate capacity. We thought our container could fit the 15 beans; however a group did the container so accurately that the container could exactly fit 15 beans. Hence, we should never underestimate the size of a container, especially when it contains water as there could be a large amount of water in one small container.

MATHEMATICS IS:

            Visualization               Number Sense             Looking for patterns

                         Communication                      Metacognition

To conclude this Math module, Dr Yeap read to us the story of a cocoon turning into a butterfly, as a representation on how we should allow children to fix their own Math problem and not spoon-feeding them as this will deter any future development in their growth.

Lastly, thank you Dr Yeap for making complicated MATH simpler!

5th Session…Bloom & Pick, Pick & Bloom

Fractions…again?!?! Now in problem sum…Didn’t we had enough yesterday???

Anyway, fractions continued and in conclusion I found out that fraction is:

- measurement number (quantity)

- represent proportion

We also learnt about Bloom’s Taxonomy.  Out of the six levels in Bloom’s Taxonomy, three levels were used in mathematics and they are knowledge, comprehension and application levels.

So enough on fractions and Bloom…we had better things to do visually.

Making shapes on dots! Really cracked the brain and came up with various shapes on the dots (including rhombus – which is NOT a triangle, heart & circle – which are INVALID as the shapes should all have straight lines). As we tried to figure out the area of the shapes on the dots, we come to understand Pick’s Theorem.

Based on Pick’s Theorem (area of figure drawn related to dots), the formula is as such:

Area (Area of figure) = i (dots inside) + p (dots in perimeter)

With that, the concept of tessellation was recalled. What is a tessellation? Tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps. Another word for a tessellation is a tiling. Referring to the dictionary, it tells that "tessellate" means to form or arrange small squares in a checkered or mosaic pattern. Anyhow, there are five ideas of tessellation:

-         rotate

-         reflect

-         translate

-         stretch

-         shear

I noted the importance of NOT sending out artificial signals to children as these may lead to future confusion and insecurities. As children do things tight or wrong in life, always question them and get them to justify their answer. That is, I suppose, the best way for children not only to learn, but think out of the box too!

4th Session with Dienes (and his idea on Variations)

The first activity of the day was an interesting one where we had to think of 2 digits, put them together and subtract from the addition of the two digits. It is amazing how Dr Yeap was able to find out our answers just by knowing one number that we thought of. Well, at the end of it, I come to realize that there are indeed many connections between numbers and its pattern.

It is useful to note that things like money and kilograms are called continuous quantity and things like marbles and monsters are called discreet quantity as they are counted as a whole.

Zoltan Dienes stressed the importance of variations, where children learnt better with a variant of ideas on a topic. In this way, children get to explore the multiple ways of solving a problem; there will be no standardization (just like how we taught in school – don’t ask me why, it’s always like this!).

There are two types of division: sharing and grouping.

An example of division in sharing meaning is:

Three boys shared 12 cookies equally. How many cookies did each boy get?

An example of division in grouping meaning is:

12 cookies are put in groups of threes. How many groups of cookies are there?

From this session, there is one vivid idea that was stuck in this brain in relation to fraction: Being equal does not mean identical…(surely something that one should always ponder upon when encountering with shapes; or even other objects in this world, perhaps!)