THE BIG IDEAS
The teaching sequence for measurement involves four steps that is based off the language model.
In the first step, the attribute (or concept) is identified. It is a teacher's first duty to ensure that the students understand the attribute they are measuring. The students experiences will help develop this understanding by creating a mental picture for each of the concepts.
The next step involves choosing an appropriate standard of measurement. This begins with arbitrary units such as blocks, paddle pop sticks, pens, shoes, etc. Once the students have recognised that arbitrary units such as the ones mentioned do not provide us with a universal answer, standardised units using measurement technology (such as a ruler or tape measure) can be introduced.
Thirdly, the object is measured in the chosen units (arbitrary or standardised). In this stage number concepts such as counting, comparing, ordering and sequencing is used to distinguish between objects using descriptions such as taller, smaller, thinner and wider.
The final step is to record the number of units. In accordance to the Australian curriculum, this data should be represented with numbers, pictures and graphs.
As a teacher, this means that I must use this sequence when introducing each measurement concept to ensure the students have a deep understanding of the concept, the skills and materials that can be used to find the measurement - both standardised and arbitrary.
In the first step, the attribute (or concept) is identified. It is a teacher's first duty to ensure that the students understand the attribute they are measuring. The students experiences will help develop this understanding by creating a mental picture for each of the concepts.
The next step involves choosing an appropriate standard of measurement. This begins with arbitrary units such as blocks, paddle pop sticks, pens, shoes, etc. Once the students have recognised that arbitrary units such as the ones mentioned do not provide us with a universal answer, standardised units using measurement technology (such as a ruler or tape measure) can be introduced.
Thirdly, the object is measured in the chosen units (arbitrary or standardised). In this stage number concepts such as counting, comparing, ordering and sequencing is used to distinguish between objects using descriptions such as taller, smaller, thinner and wider.
The final step is to record the number of units. In accordance to the Australian curriculum, this data should be represented with numbers, pictures and graphs.
As a teacher, this means that I must use this sequence when introducing each measurement concept to ensure the students have a deep understanding of the concept, the skills and materials that can be used to find the measurement - both standardised and arbitrary.
THE CONCEPT, SKILL, STRATEGIES AND SUPPORTING RESOURCES
There are 6 concepts that fall under measurement. These concepts include:
Link: Measuring Length PDF
- 1. Length
- 2. Perimeter
- 3. Area (involves geometry)
- 4. Mass
- 5. Capacity/Volume
- 6. Time
Link: Measuring Length PDF
Concept
The general concept for measurement is counting units. This concept can be introduced through a story, Maths for Kids: Measurement "How do you measure up?" is an interactive story that explores all the things you can measure. This story also introduces measurement technologies such as scales, stop watches, tape measures, thermometers, etc and the real world situations where these technologies would be used.
Video: Maths for Kids: Measurement "How do you measure up?"
The skill for measurement is the ability to count the appropriate number of units in order to find a measurement. For length, this may be finding how many paperclips long a pencil is (such as in the video below).
Strategies
Strategies involved with length is understanding how to find the length with different units - both arbitrary and standardised. This will develop as the skills develop.
THE LANGUAGE MODEL
The language model is used to display the relationship between the visual, verbal and symbolic elements of mathematics and forms 'stages' of learning.
Student language - During student language, all language used should be familiar to the child and accompanied with familiar objects.
Materials language - At this stage, there is still no introduction of mathematical terms. The language is very similar to student language however the visuals used have become more abstract.
Mathematics language - Moving away from 'stories', this stage introduces mathematical terms.
Symbolic language - This stage introduces symbols.
THE LANGUAGE MODEL FOR PLACE VALUE
THE MISCONCEPTION
One misconception students may have is understanding that to find the length of an object, they need to use the same units. Particularly with arbitrary units, students may think that as long as it is the same 'kind' of unit, it is ok rather than the same sized unit. for example, a student might measure a pencil with paper clips, however not all the paperclips are the same size.
To remedy this situation, I would have a "competition". For the competition, I would split the class up into small teams and encourage team work by allowing the students to choose their team name. I would then provide each team with a pencil and some paper clips (Each team will have the same size pencil but there will be two sizes of paper clips, some teams will get all large paperclips, some teams will get all small paperclips and some teams will get a random combination of large and small paperclips). The students will be told that the competition is to find out how many paperclips long the pencil is. Once each team has their answer, all results are written on the board. This then give the class opportunities to explore why some teams had the same result and why others had different results. This could turn into an investigation.
To remedy this situation, I would have a "competition". For the competition, I would split the class up into small teams and encourage team work by allowing the students to choose their team name. I would then provide each team with a pencil and some paper clips (Each team will have the same size pencil but there will be two sizes of paper clips, some teams will get all large paperclips, some teams will get all small paperclips and some teams will get a random combination of large and small paperclips). The students will be told that the competition is to find out how many paperclips long the pencil is. Once each team has their answer, all results are written on the board. This then give the class opportunities to explore why some teams had the same result and why others had different results. This could turn into an investigation.
THE ACARA LINK
Measurement is first introduced in the foundation year.
Strand: Measurement and Geometry
Substrand: Using units of measurement
Content descriptions: Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language
Elaborations:
- comparing objects directly, by placing one object against another to determine which is longer or by pouring from one container into the other to see which one holds more
- using suitable language associated with measurement attributes, such as ‘tall’ and ‘taller’, ‘heavy’ and ‘heavier’, ‘holds more’ and ‘holds less’
Scootle resource ideas:
- Which container holds more magic rocks? is a short video on capacity.
- What can be measured? is a video that talks about all the things that can be measured using arbitrary measurements.
- .Who is taller? Which is longer? is a short video that talks about length and the key descriptions: taller, shorter and longer.
THE RESOURCES AND IDEAS
- Sid the Science Kid - Measurement is a video that discusses measuring with a ruler.
- Sesame Street - Measure That Animal is an online game that measures animals in a zoo using familiar, arbitrary units such as hats or crayons.
THE TEXTBOOK SUMMARY
- Measurement starts in the foundation year
- Measurement is the topic from the primary mathematics curriculum that is used the most directly in students' daily lives
- Measurement, together with geometry, is one of the three content strands in the Australian curriculum
- Measurement is one of the ten standards in the Principles and standards for school mathematics
- Measurement can also assist students with other areas of mathematics, for example, the number line is based on length
- Measurement is also used in other subjects such as art, music, science, history, geography and the language arts
- Wilson and Osborne gave the following recommendations in 1988:
- Children must measure frequently and often, preferably on real problems rather than on textbook exercises
- Children must develop estimation skills with measurement in order to to develop common referents and as an early application of number sense
- Children should encounter activity-orientated measurement situations by doing and experimenting rather than by passively observing. The activities should encourage discussion to stimulate the refinement and testing of ideas and concepts
- Instructional planning should emphasise the important ideas of measurement that transfer or work across measurement systems
- The measure with understanding, children should know what attribute they are measuring
- Formulae for perimeter, area, volume and surface area are usually introduced in the upper primary years. Although formulae are necessary in many measurement situations, they should not take the place of careful development of measurement attributes and the measuring process. The skill of formulae should be developed, but not at the expense of helping students build meaning for the formulae.
- Esitmating is very important in the development of measurment - it helps to reinforce the size of units and the relationship between units as well as being a practical application
- Activities involving two attributes can help children see how the attributes are related or how one attribute does not depend on another (Reys, Lindquist, Lambdin, Smith, Rogers, & Falle, et al., 2012)
THE REFERENCES
ACU,. (2016). Learning Environment Online. Leo.acu.edu.au. Retrieved 3 March 2016, from http://leo.acu.edu.au/course/view.php?id=18458
Australia, E. (2016). Home - Scootle. Scootle.edu.au. Retrieved 3 April 2016, from https://www.scootle.edu.au/ec/p/home
Australian government,. (2016). Home - The Australian Curriculum v8.1.Australiancurriculum.edu.au. Retrieved 3 April 2016, from http://www.australiancurriculum.edu.au/
Reys, Lindquist, Lambdin, Smith, Rogers, & Falle, et al. (2012). Helping children learn mathematics. Milton, QLD: John Wiley & Sons.
YouTube. (2016). Youtube.com. Retrieved 3 April 2016, from https://www.youtube.com/
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