Measurement

The concept of measurement covers a variety of attributes including, length, mass, area, volume, time, temperature, weight and capacity. The following reflection will discuss important principles and common misconceptions held by young children (and some adults) in relation to the attributes covered in the early years of mathematical learning, these are – length, area, volume, mass, and time; key concepts/misconceptions regarding the relationships between perimeter and area, volume and mass, as well as length and volume as well as suggest the general sequence of learning in regards to principles of measurement.

Length, Area and Volume

According to Currie, Mitchelmore and Outhred (2006), five important principles in measuring length, area, or volume are:

1. Congruent units must be used when measuring an individual object


2. The attribute of the measuring object has to be the same as the attribute of the object being measured to have


3. The transitivity principle – the units used to measure two different objects need to be the same (or converted to being the same)in order to compare the two objects


4. There is a relationship between the size of the units used to measure length, area and the number of units required to make the measurement (i.e. the smaller the unit, the more of that unit is needed to make the measurement. And in reverse, the bigger the unit, the less of that unit is needed)
   
5. Iteration principle –there is to be no gaps and no overlaps between each unit used to measure an object

The result of a study conducted by Currie, Mitchelmore and Outhred (2006) highlight some misconceptions held by the participants of this study in relation to the measurement of length, area and volume, in that “young children appear to have a much poorer understanding of the need for identical units that leave no gaps and no overlaps than teachers often presume and they may indeed have no clear concept of what they are actually measuring” (Currie, Mitchelmore and Outhred, 2006, p. 383). This is why it is important to begin learning of measurement by identifying attributes for measurement, e.g. by discussing what is meant by the attributes of length, perimeter, area and so forth (see the sequence of learning).

Currie, Mitchelmore and Outhred (2006) suggests that mathematical learning experiences being implemented in early years classrooms should focus on helping children develop the skills to justify reasons for adhering to measurement principles, (e.g. no gaps no overlaps) as well as make children aware of errors that can possibly result from misapplying measurement principles. An idea I have to facilitate this is to give children opportunities to choose the appropriate instruments to use to take different measurements, rather than always being told what to use.

Furthermore, Kribes-Zaleta and D’Lynn (2003) shows how everyday play situations often give rise to measurement-related problem posing by the children or teacher. In the vignette of children discussing how long their snake was, Kribes-Zaleta and D’Lynn described how the children identified a problem in how they were comparing the lengths of two snakes drawn by different children in that although one snake was clearly longer, it was only “25-long”, whereas a snake drawn by another girl was “28-long” but was clearly shorter. The author highlighted that although the children were not yet aware of the reason why their data is the way it was (the fact that they had used different units to measure length) the fact that they recognised that a problem existed created a context for learning. To me, this reminds me to observe not only the misconceptions that the children hold when attempting measuring tasks, but also what they can and do notice when provided with a little scaffolding. It also reminds me to seize opportunities for learning that arises from play because they can and do occur all the time.

Time

Something else which the workshop activities reminded me of the how abstract the concept of time is. No wonder young children sometimes have trouble understanding some of the words used to describe time. When you have only been alive for three, it is difficult to contemplate how long a year is, as it is one third of your whole life so far. What would be even more difficult is appreciating how long a decade is, as it is a period of time which is just outside your experience. Nevertheless most children have some understanding of concepts of time even prior to starting school. It is important to help children clarify the relationships between the different words used to describe different periods of time. It is important to discuss concepts such as, the smaller the units of time, the more of that unit is needed to measure a period of time; whereas the larger the unit, the less number of units is needed to measure that same period of time, just like measuring other attributes such as length, area, volume or mass. The activity of The Time Clothes-Line can be helpful in discussing the relationships that exist between different words used to signify different periods of time.

Another aspect of time is related to how to tell what time it is on a watch or clock, which is something that affects our everyday lives. According to Krech (2000) the one-handed clock is a useful resource for addressing the problem that many children face in not being able to tell the time on an analogue clock when the minute hand is pointing to anything other than 12 or 6.

Sequence of learning:
The general sequence of learning in regards to developing understanding of measurement concepts specific to each of these attributes are: