Teaching of linear measurements to middle level requires the pupil to had extensive knowledge on numbers. Linear measurements are first learnt in elementally mathematics. Children begin to learn linear abstractions at fourth grade. Although majority will be able to measure without problems, they are not able to conserve the measurements. The learners should have had learnt observation skills and shape vocabulary this includes circles, rectangles, triangles, square etc. Children tent to learn progressively from concrete experiences to abstract ones (Van Hiele 1986), i.e. they make connections from known to unknown and from simple to complex. The expectations are by the end of the topic or chapter the learner should be able to recognize and describe the meaning of length, breadth/width, height, depth, thickness and be able to apply the measurements to calculate perimeter and circumference. The learner should also learn how to problems that concerns mass by use of grams, kilograms and tonnes and also be able to know which type of units of measurements is used where and how. All the linear measurements integrate completely with geometry of space and location.
The teacher should have the following instruments in readiness to teach linear measurements.
- Pieces of wood ( of equal and varying lengths)
- Pieces of treads/string( of equal and varying length)
- Rulers ( one each student)
- Tape measures
- Pair of scissors( to cut the stings in to various lengths as may be required during the lesson)
- Jug and cups of various sizes
- Water in a larger container( this should be handle with care to avoid spiling over )
Activities of the learning process
The following are the activities made for children of age 8 -12 years. The teacher should let the learners match equal lengths i.e. the teacher can provide pieces of wood or thread/ string of equal length and let the learners match them. Can also let them to identify and match containers of equal height or plants of equal height, filling containers of equal volume etc. Such an experience make the learners to develop a general idea in measurements is further refined. Counting abilities of the learners can also be sharpened further. These activities promote the ability of the child to reason and also conserve measurements. Since conservation is a problem to young children, the teacher should direct the learner appropriately to achieve this. For example most learners find it difficult to realise or comprehend a cup p of water transferred to a bigger container the volume doesn’t change or when a folded string is stretched the total length does not change (Piaget 1968).
The teacher may then progress by letting the learners to use unit blocks to measure the sizes of a bigger block. A good example is the use of a toot pick as a unit to measure the length of a desk or a seat. A cup can also be used to fill a larger container (a jug or a flask). This type of an activity will help the leaner to develop measurements in relative aspect i.e. relationship in measurement e.g. a jug is filled by four cups. Since children make comparison using an arbitrary measure use same object to measure other objects e.g. use the same cup to fill a different jug (different in size) in this case the cup is used as a standard measure. These activities sharpen the learners’ creativity in that the child/learner is able to us available tools to measure objects around. The activities also help in boasting the learners’ ability to reason in relative aspects and logically.
The teacher should then direct the learners to approximate/estimate several measurements in the environment. Let the measure the lengths of the desks, books, wall, body parts etc. May also direct them to estimate masses of several object using a weighing tool like beam balance.
The units of measurements can then be introduced. These should include millimetres, centimetres, metres and kilometres for lengths. Grams and kilograms should be introduced for the measurement of mass and millilitres and litres can be introduced for the measurement of capacity.
Let the learners identify measuring tools. This will include the rulers, tape measure etc. At this point prior knowledge on instruments will be useful. The teacher may enquire where the instruments are used.
The teacher should then introduce concrete measuring instruments/tools each by name and the type of measurements and units. For length, the teacher introduces a ruler, describes the ruler in terms of graduations i.e. millimetre and centimetres. The relationship between the units of measurements (mm and cm) should also be drawn at this stage. The teacher should then demonstrate how measurements are obtained using the ruler and recorded. At this stage the teacher leads the learners to measure lengths of various objects. For example;
With each student having a piece of thread/string and a ruler or a tape measure, guide them on how to place the thread or string along the edge of the ruler, take the reading and record it. It is after this that the teacher leads the learners to obtain various measures of a variety of the objects in the environment and record them in different units. This could be done in groups. This enhances the creativity of the learners and logical reasoning.
The teacher should then proceed to discus with the learners the results obtained in the measurements. This should be done in the following procedure
- Let the groups summit their measurements
- Record all the measurements on the board
- Compare the measurements of the same/similar objects obtained by each group.
- If differences occur ( this is a must in any practical session),
- Ask the learners the reasons for the differences
- How could the measurements be corrected
- Then the teacher should explain in details the reasons for such occurrences and also the means of correcting them
Learners should consolidate their comprehension of measurements in relation to real life situations. During the teaching of linear measurements, the teacher needs to present to the students a number or real measuring equipments. For any given measurement, the right equipment needs to be used correctly in that the real and correct measurement is obtained in the right units.
The activities above lead to a comprehensive understanding of the whole concept of linear measurement. This is because by the end of the lesson, the learner should have learnt the following: to,
- Compare objects of same shape
- Identify the objects of the same size.
- Compare the lengths of different objects
- Estimate measurements
Applications of measurements to real life situations.
To prepare the learner for the next level, operations on conversion from one unit to another is necessary. Three dimensional thinking is also required therefore the learner should be exposed to shapes and area. This could include calculation of areas of different shapes like squares, rectangles and triangles.
Indiana Undergraduate Journal of Cognitive Science 2 (2007) 28-32
Jeremy Kilpatrick, Jane Swafford, Bradford Findell, National Research Council (U.S.). Mathematics Learning Study Committee - 2001 - 454 pages