Measurement
“A four year old boy was rolling out a piece of clay into the familiar snake form. As he finished, he repeatedly moved his hands from the centre toward the ends on the rolled-out clay object. He was quietly saying in a measured tone, “Long. Lo-o-ong. L-o-o-o-ng”.
Schwartz (1995)
This is just one of the scenes that is played out again and again in pre-kindergartens and kindergartens across the world. Indeed, I also experienced the same when I was in kindergarten. As far as I can remember, once I was required to make a long snake, I tried my best to make it longer than before. In addition I was using my thumb and my index finger to measure it. However, when I tried to use a ruler to measure it, I was told that a ruler can measure length, but I can not measure ‘my snake’ with it! It was hard and I got confused. Eventually, I used my preferred unit; my thumb and my index finger. After reading Schwartz (1995) article, I realized that I am not the only one. It is amazingly common! Young children in kindergartens use repeated units and both standard and nonstandard unit as I used. They also spontaneously solve measurement problems emerging from their ongoing activities and eagerly discover measurement relationships as they construct the materials (Schwartz, 1995). This situation also related with five stages of development advanced by Piaget (Charlesworth & Kind, 2007): at the preoperational stage; children develop the measurement stage of making comparisons and in transitional to concrete operational, they tend to use arbitrary units.
Interestingly, Board of Studies NSW (2002) mentioned that students develop the key understandings of the measurement process using repeated informal units through these five principles:
1. The need for repeated units that do not change
2. The appropriateness of a selected unit
3. The need for the same unit to be used to compare two or more objects
4. The relationship between the size of the unit and the number required to measure, and
5. The structure of the repeated units.
Teaching that builds on students’ intuitive understanding and informal experiences helps them understand the attributes to be measured as well as what it means to measure (NCTM, 2000)
I agreed with NCTM (2000); learning about measuring in this week’s workshop put me in a comfort zone as I have some prior and background knowledge of some aspects of measurement: capacity, volume, area, length, height, mass and temperature. Not only that, the beginning process advocated by Irons (1999): identifying, simulating, comparing, sorting and ordering are still used as a teaching sequence. In the three hours workshop, I learnt many new aspects of measurement.
Length
In everyday life, children measure the length of everyday objects such as books, boxes, toys and pencils with non-standard units (Smith, 2001). Indeed, they measure things for their own purposes, which most often include using the information to make comparisons, to describe their constructions, and to make objects fit or align. If the child is not interested in why he or she is being asked to find out the length of an object, the task lacks purpose and fails to engage the child meaningfully (Schwartz, 1995). In this workshop, we were required to measure height using the non-standard units. Interestingly, my friends and I used the methods for measuring for physical quantities that agreed with most professionals (Smith, 2001). They are:
1. Choose the appropriate unit
2. Use the unit to cover object with no spaces or gaps
3. Count the units
4. Decide on what to do with leftover parts
For the non-standard units, we decided to use unifix cubes instead of paper clips, streamer and paddle pop sticks. We preferred to use colourful unifix cubes as we can combine it while measuring and it was fascinating and colourful.
Before measuring, we estimated and chose the highest person to be our ‘guideline’. While measuring, we made sure that it was end on end with no overlap. Then, we counted the unifix cubes, and we used the highest person’s height as a ‘standard’ unit. Then, while measuring others, we put aside the leftover parts and documented our heights.
After finishing recording our height, I found that this activity was a new and challenging activity for me. As an adult, I myself felt quite ‘unsatisfied’ with the result and the process of measuring. It was challenging and involved lots of processes.
So how will young kids cope? Curry, Mitchelmore and Outhred’s (2006) article really gave me new insight. They stated that there is strong evidence that, in the early stages of learning about measurement, children do not see the need for congruent units when measuring individual objects (Bragg & Outhred, 2001; Outhred & Mitchelmore, 2000). Several studies have revealed students’ difficulties with the principle that the object being measured must be covered with no gaps or overlaps (Bragg & Outhred, 2001; Curry, Mitchelmore, & Outhred, 2006; Outhred & Mitchelmore, 2000). Another issue arose from the activity; the accuracy of the units used.
If we were to compare the accuracy of using paddle pop sticks and unifix cubes, I found that using unifix cubes was more accurate. It is because, unifix cubes have smaller components and the probability of an error occurring was small as we used different cubes. But, with paddle pop sticks, normally we used the same stick and it has quite a long ‘standard’ per stick.
Time
Scott (1998): time= space, time as a domain is also measurable
I agreed with Scott (1998) that time equals to space. According to Heirdsfield (2007) and Smith (2001), the concept of time involves time sequence of events, duration of events and duration of various units of time. Everyday classroom activities provide opportunities to estimate time. In this workshop, I experienced measuring time by estimating how long a pendulum swings to construct a unifix tower of 10 cubes. 
After measuring the time for 10 unifix cubes, we added the number of unifix cubes with 12 and 15. From the table, I found that there was no change in the time in constructing the 10 and 12 unifix cubes. One of us suggested that it just involved the addition of 2 cubes, so it wasn’t so much. But, it changed with 2 or 3 swings when they were required to construct a unif
ix cube of 15 cubes! It made me think of the reason. I believed that something was missing or maybe some mistakes had occurred. My hypotheses was that my friend had miscalculated the unifix cubes or she may have been having difficulty with it at that time. I agreed with Kribes-Zaleta and Bradshaw (2003) that children actually have clear ideas about what it means to use units in measuring length, but the incompleteness of their understanding of the formal properties of measurement units makes this exploration interesting.
Mass
Another interesting and educational activity in this workshop was using paddle pop sticks to estimate the mass of a variety of objects. We used a balance scale and paddle pop sticks to measure the mass. Personally, I felt very excited to know how paddle pop sticks can be used as a non-standard unit and estimate the mass of other objects. Here is 
the result of mass of a variety of objects . 
I think this activity was a good idea for teaching young kids as mentioned by Smith (2001) that measurement activities must involve ideas that they can enjoy and that have significance for their lives. Not only that, a foundation in measurement concepts enables students to use measurement systems, tools, and techniques should be established through direct experiences with comparing objects, counting units, and making connections between spatial concepts and numbers (Wall & Posamentier, 2007).
Final thought and my personal philosophy
In short, as a future teacher, I found a useful reminder from Wall and Posamentier (2007):
[the] teacher can guide young children’s exploration and understanding of measurement concepts and relationships by making resources for measuring available, planning opportunity to measure, and encouraging children to explain the results of their actions.
This strong reminder also constructs my personal philosophy in teaching Mathematics. I should not merely depend on drilling and memorization as to ensure my students learn Maths and pass the exams. I should use myriad of resources, as I used in this workshop to help them build their understanding and knowledge of Mathematics. I also should give my students chance to measure things in their environment and therefore relate it to meet the needs of curriculum. I also should not ignore their ideas and thinking of measurement. “The best time to learn mathematics is when it is first taught; the best way to teach mathematics is to teach it well the first time” (National Research Council 1989, as seen in Cockcroft and Marshall, 1999:p. 329).
References
References for picture
http://www.chadiscrafts.com/fun/Claysnakes.jpg
Suggested website
>> Heaps of resources that can be used to teach measurement for young kids. Interestingly, it has been divided into aspects of measurement such as length, time and so on. It's also easy to access in any formats such as powerpoint presentation, flash player, or pdf files.
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