Conclusion (Part 2)

My Maths Metaphors

In Week 2, I mentioned about some metaphors that were given by the lecturer which I can relate to my maths learning experience. Having had to attend this unit for 12 weeks, I am now able to think of my own maths metaphors.

• Learning maths is like solving a puzzle. Be it a jigsaw puzzle or any other kinds of puzzles, in order to be able solve it, we need to gather the pieces of information and clues that we have.

• Learning maths is like participating in a treasure hunt where solving a problem depends on understanding the clues given.

• Learning maths is like going on a journey. Any journey has its starting point as well as its ending point. It goes the same in solving with any mathematical problems, if we try our very best to solve it, we will get the answer, it's only a matter of right or wrong.

My Personal Teaching Philosophy


Teaching Early Childhood Mathematics is not an easy task. One needs to have patience as well as passion in order to make the learning fun and meaningful. I realize that young learners should not be underestimated and lessons need to be interactive and expose them to language that is a step ahead of what they have already learnt.

After 12 weeks of workshops , I have begun to see that there are three main elements in teaching early childhood maths. The three main elements are:

• Literature That Teaches -This includes books or story books designed to teach maths to young learners

• Games That Teach -This includes hand-on activities as well as computer games

• Songs That Teach -This includes any songs and chants created to teach maths to the young learners

In order to cater for students' different learning preferences, I believe that these three elements should be included in teaching mathematics to early childhood students. Furthermore, with variety of teaching styles, learning can be maximized.

Week 12

Patterns & Algebra

Do early childhood learners learn about algebra? I would not have said yes, until I attended today’s workshop. Yes, they do! Taylor-Cox (2003) claims that it is never too early for young children to start thinking in terms of algebra. Instead, we do need to offer young children a solid foundation of algebraic thinking. Algebra has long served both as a gate and a barrier for students (Lott 2000). Therefore, we can prepare students to be successful in algebra if we begin teaching them to think algebraically in the early years.

The central ideas promoted in the national algebra standard for young children are (1) patterns, (2) mathematical situations and structures, (3) models of quantitative relationships, and (4) change (NCTM 2000, as cited in Taylor-Cox, 2003).

From the workshop activities that we have done, it could be seen that Algebra in the Early Childhood focuses more on patterns; recognizing, describing, extending, and translating patterns. Working with patterns invites young children to identify relationships and form generalizations (NCTM 2000, as cited in Taylor-Cox, 2003).

One of the activities that we did in the workshop was creating patterns. The purpose of this activity was to engage students in focusing on ‘What comes next after the pattern?’. Being able to describe these regular relationships leads to predicting how the pattern will continue. In my opinion, for young children, recognizing that patterns are predictable is an important Mathematical idea. In addition, having students to explain why that pattern comes after the next pattern is a good way to encourage students to interact as well as to think critically as it will enhance their prior Mathematical knowledge.

Creating patterns

Having to do this 'creating patterns' activity brought me back to the first few weeks of the semester where we learned about the beginning processes where students sort the objects according to their attributes and making pattern like 'repeating patterns' and 'growing patterns'.

Growing patterns

Reference:

Taylor-Cox, J. (2003). Algebra in the early years? Yes!. Young Children, 58(1), 14-21.

Week 11

Chance & Data

According to Geist (2001) every day children in the classroom actively work with raw data. They generate, organize and interpret data and they draw conclusions or make predictions on the basis of the data they have collected. Hence it is important to expose and teach the young learners about organizing and interpreting data.

In the workshop, we did sorting smarties according to their colour and comparing the amount of smarties between peers. We also get to predict the number of times the spinner (clips) land on the colour.

Making the smarties into a bar chart

Data collected when predicting the number of times the clips fall on a colour

The idea of using smarties to teach the young learners about data makes me realise that that I need to be more creative in my teaching and maximize the use of materials and resources in the classroom so that I will be able to get the students interested in what they are learning. This workshop has also proved to me that learning Mathematics can be really fun if we could incorporate good resources, materials and fun into the lesson.

Reference:

Geist, E. (2001). Children are born Mathematicians. Young Children, 56, 12-19.

Week 10

Measurement

As an adult, if we were asked a question on ‘how long is one minute?’ our answer would typically and certainly be ’60 seconds’. But what if we ask this question to the young learners in their early childhood, would they be able to give the same answer as us? Looking at a learning Mathematics in early childhood, what are other possible answers for this question? One of this week’s workshop activities is ‘Perceiving One minute’. We explored many possible ways for the young learners to perceive time.

In my opinion, it would be appropriate for young children to be introduced to non-standard units of time before they proceed to the standard units of time. It is because the idea of learning itself, where it should move from a lesser complexity of ideas to a more complex one. Hence in an early childhood classroom, perceiving one minute could be done with variety of simple variables like:

• No of beads can be threaded in one minute
• No of unifix cubes can be stacked in one minute
• No of pendulum swings in one minute
• No of marching steps in one minute

Another activity could be done with young learners to perceive time is looking at how a pendulum swings. Strings with different length are used in this activity. You can ask children to roughly create a data table as below:



When all the data is collected, let the students investigate the relationships between the length of the pendulum and the number of swings made. (e.g. the shorter the length of the pendulum, the greater the number of the swings made).

* In order to get a more accurate result of the number of swings, students could be asked to record them twice and then find the average.




One-Handed Demonstration Clock

Krech (2000) in his article, It’s time! talks about the use of one-handed demonstration clock to help students learn what ‘the space in between the numbers’ all about. This clock focuses merely on the hour hand in time-telling. The language used with this one-handed demonstration clock is an easy language such as:

• About nine o'clock
• A little past nine o'clock
• Halfway past nine o'clock

A one-handed demonstration clock

The minute hand can later be added to the one-handed demonstration clock, after the students have had plenty of practice with the hour hand. Krech (2000) believes that focusing on the hour hand on its own helps the students gain stronger overall understanding of how the minutes hand functions.





Literature That Teaches

This week’s workshop captured my attention as I got to know a few story books that are meant to teach Mathematics to young children. One of the books is:

The Bad Tempered Ladybird


The topics focused in this book are time and size. It uses non-standard units to measure the size (the size of the ladybird is used to compare the sizes of other animals. The terms used are like big and bigger.)

The fist time that we read the book, we asked the children to listen carefully and to focus on what the ladybug might have learned through its adventures. For the second reading, we asked them to listen and watch for patterns. On a chart paper, we recorded each pattern that the children identified (Kelly & Burke, 1998).

Back in Malaysia, during my time as an early childhood learner, I was not exposed to this kind of book. Even nowadays, the use of story books to teach Mathematics is still not very significant. As a future teacher, I'll take the challenge to promote this kind of literature to the Malaysian classroom.





References:

Kelly, M. G., & Burke, K.(1998). A matter of grouchy time. Teaching Children Mathematics, 4(7), 404-407.

Krech, B. (2000). It's time!. Instructor, 109(5), 16-17.

ExtraS

• Songs That Teach

This site contains a collection of songs and chants for teaching young learners Mathematics for various topics. Each song listed is included with its lyric and a preview of the song. To listen to the full version of the song listed, users need to buy the CD from the online store on the website. However, being able to listen to the song preview is already an advantage because the rest of the melody for the song can be created by the user itself (be creative!). Just a word of caution, do acknowledge the source if a lyric of song from this site is used in a lesson because it involves copyrights. (I myself would not like if my ideas get stolen!). Have fun!

*Other than the songs listed in the above website, I also found songs that teach from youtube. The first one is The Shape Song. It talks about the attributes of each basic shapes; a circle, square, rectangle and triangle. There are also visual representations for each shape. In my opinion, this song could be very useful in teaching young learners the properties of basic shapes because while recognizing shapes, children learn about the attributes of each shape.

*Another song Ifound on youtube is the Malaysian version song, entitled '10 Budak Hitam' (10 Black Kids). The original version of this song was not meant for educational purposes, but it has been modified to be one. This modified version of '10 budak Hitam' talks about 10 black kids who were playing together as big group at the beginning but later one by one get parted from the group. Basically, the song teaches students about subtraction. In between the subtraction processes, there are some moral values added to it.

• Games that teach

Below is one example of interactive flash games that could be found from the link above. This game help student further learning and understanding about angles in a circle. It may or may not be appropriate for the early childhood learners, it is all depend on the learners proficiency levels. The game is certainly appropriate for primary school children.

Week 9

Shape (Part 2)

I find that today’s session is the most interesting session so far. Why? Because today I have been introduced to a very useful Mathematics teaching instrument, which is a set of tangram. The tangram is an ancient Chinese geometric puzzle with seven pieces: 2 large mangles, 1 medium triangle, 2 small triangles, 1 square and 1 rhomboid (Bohning, 1997).

A set of tangram

I was amazed with the fact that this set of seven pieces of shape is a very powerful Mathematical instrument to teach geometry, especially to young children. When I was a kid, I remember to having had to do the puzzle using these seven pieces but I was not being explained about the relationships that these seven pieces of shape have. Back then, my focused was only to solve the puzzle. However, unlike a jigsaw puzzle where a piece must fit in only one way to complete a picture, the geometric tangram pieces can be arranged in many different ways to make figures of; a watchful cat, a soaring bird, a bubbling teapot and children who run and play (Bohning, 1997).

A figure of a watchful cat

Experiences with tangrams actively involve children as they develop the skills of a geometry vocabulary, shape identification, classification (Bohning, 1997). Clements and Sarama (2000) add that identifying shapes is important but the focus on the properties and the relationship should be strong. Children's reaction to tangramming is one of surprise and amazement, surprise that manipulating the geometric shapes can be so much fun and amazement that the seven pieces can be arranged to make so many different figures (Bohning, 1997).

After further investigation on the tangram set, we have also discovered that the seven pieces can be used to teach children about fraction (based on area of the shapes). For example,

• The area of 1 little triangle is equal = ½ the area of the square = ½ the area of the rhomboid.

Other than that, children could also be asked to create a rectangle using only 3, 4 or 5 pieces from a set of tangram.

A square with 3 pieces of a tangram set

A square with 4 pieces of a tangram set

A square with 5 pieces of a tangram set

As they are manipulating the shapes in the tangram set, children will develop a positive attitude toward geometry, furthering their spatial sense, and developing a basic understanding of geometric concepts and relationships (Bohning, 1997).

Reflection

It could be observed that young children learn Mathematics mostly through experiential learning. They observe, question and make mistakes. Hands-on activity like tangramming therefore gives children to solve puzzles and manipulate shapes without the restriction of one single right answer.

References:

Bohning, G., & Althouse, J. K. (1997). Using tangrams to teach geometry to young children. Early Childhood Education Journal, 24(4), 239-242.

Clements, D.H. & Sarama, J. (2000). Engaging young children in mathematics: Standards for Early Childhood Mathematics Education. London: Lawrence Erlbum Associates.

Week 8

Shape (Part 1)

This week’s lesson started off with classifying the 2D shapes (quadrilaterals). As we all have learnt, a trapezium, rhombus, rectangle and kite are all quadrilaterals. Some of them (e.g. rectangle and rhombus) can be classified in many categories under quadrilaterals. A rectangle for example is also known as a ‘square’ and a ‘paralellogram’ and can be classified as a trapezium because it has two pairs of parallel sides. Hence it is learned that any shapes should be classified according to its attributes/properties for example the number of sides it has. If shapes are classified by labeling, it will certainly confuse the students.

One of the activities that could be done to introduce young learners to 2D shapes is to get them each to cut out various shapes from a piece of paper and then sort the shapes according to its attributes/properties. Then have students to describe how they sort the shapes.

Have the students to sort the shapes and ask them how they would sort it.

Instead of cutting shapes out of papers, the teacher could also get the students to draw 2D shapes that they could find in their surroundings and then sort the shapes according to its attributes.

Further discussion about the shapes created by the students could be held in order to get students to recognize and notice the critical attributes of each shape. Question like ‘tell me more about the shape’ could be asked to stimulate students’ critical thinking.

Reflection

While discussing about the properties of quadrilaterals, we have come to realization that the US definition of a 'trapezium' is different from other countries. This might cause learners, especially the young ones confusion. The issue raised was 'could we have one standard definition of a trapezium?'.

*If we can have the standard measurement units for all over the world, why not?*