Table of Contents

Title Page

1. Introduction ………………………………………………………………………………...1

2. The Meaning of Volume of Liquid…………………………………………………………4

3. Process of Teaching…………………………………………………………………………8

4. Teaching Activity 1………………………………………………………………………..10

5. Teaching Activity 2………………………………………………………………………..13

6. Conclusion………………………………………………………………………………....15

7. Bibliography……………………………………………………………………………….16

Introduction

In this video titled “Child Conservation”, a child is shown two identical glasses which

contain the same amount of milk. When asked whether the glasses have the same amount or

is one more, the child put the glass side by side and seeing that the milk in both glasses were

at the same level, answered that both glasses had the same amount.

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When the milk in one of the glasses was poured into another glass which was taller and

thinner, the child was asked which glass had more milk or did both have the same amount of

milk.

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Upon seeing that the milk in the taller glass was at a higher level than the milk in the other

glass, the child concluded that the taller glass had more milk.

According to Piaget's theory of cognitive development, children around the age of 8 are at the

concrete operational stage, which is the third of four stages of cognitive development in

Piaget's theory. This stage is characterized by the appropriate use of logic wherein one of the

important processes during this stage is conservation, ie. understanding that quantity, length

or number of items is unrelated to the arrangement or appearance of the object or items.

In Piaget's most famous task, a child is presented with two identical beakers containing the

same amount of liquid. The child usually notes that the beakers have the same amount of

liquid. When one of the beakers is poured into a taller and thinner container, children who are

around 7 or 8 years old say that the two beakers now contain a different amount of liquid.

The child simply focuses on the height and width of the container compared to the general

concept. Piaget believes that if a child fails the conservation-of-liquid task, it is a sign that

they are at the preoperational stage of cognitive development. The child also fails to show

conservation of number, matter, length, volume, and area as well. Simply put, children at this

stage are unaware of conservation.

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The Meaning of Volume of Liquid

Volume of liquid refers to how much three-dimensional space a liquid occupies or

contains, that is, the capacity of liquid held in a container.

Capacity can be measured by using non-standard units or standard units. The former

refers to the utilization of non-standard volume units such as “cups”, “spoons” and “bottles”

in measuring capacity while the latter involves the usage of the metric system in calculating

capacity using units such as millimeters (ml) and liters (l).

The exploration of capacity or volume of liquid involves the manipulation of

containers of various shapes and sizes. However, Year Two students while learning volume

of liquid often confuse the height of the container with its capacity. As such, they mistakenly

believe that the volume of liquid depends on its height when it is held in a container rather

than its capacity.

To clear up students' misconception on capacity, teachers while teaching volume of

liquid may show students a video which demonstrates clearly how volume of liquid is

measured. Such an audio and visual presentation will enable students to understand better the

concept of volume of liquid and the correct method to measure volume of liquid.

Additionally, teachers may also conduct teaching activities on the topic which are

appropriate for both high achiever and low achiever students using teaching aids such as

water, graduated cylinders and containers of various shapes and sizes which may be collected

or purchased.

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This video titled “Using a Graduated Cylinder” introduces the graduated cylinder as a tool

used to measure the volume of liquid. It is thus called because it is cylinder in shape and has

gradations or a set of marks showing units of measurement on it.

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The liquid the volume of which is to be measured is poured into the graduated cylinder and a

reading is taken.

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The reading is taken at the bottom of the curved surface of the water, which is called the

meniscus. The water in the graduated cylinder has a slightly curved surface due to the

tendency of the water to cling to the graduated cylinder hence pulling the edges of the water

slightly upwards.

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Process of Teaching

The process of teaching and learning Mathematics is different from that which is

required in other subjects. Other than counting skills which involve high levels of thinking

and creativity, it also requires a precise and thorough understanding of concepts (Cockroft,

1986). Every Mathematics teacher has the responsibility to carry out the process of teaching

and learning with competence while taking into account the needs and levels of achievement

of students. A teacher must be sensitive to the needs of their students and dedicate themselves

to improve students’ learning, which ought to be their primary professional objective

(NCTM, 1980).

Several skills are essential to teach Mathematics effectively and the skill to evaluate

the comprehension of concepts and mastering of skills is one of them (D’Augustine, 1973).

Upon determining the topic and related concepts to be taught, teachers need to list

down the objective of behaviour that would be displayed by each student when he or she has

really understood or mastered the content that has been taught (Sobel, M.A. & Maletsky,

E.M. (1972). Such displayed behaviour tends to show the student’s level of understanding.

An objective is usually established for a certain period of teaching depending on the

teaching content and the time allocated to teach. Establishing an objective determines not

only the level of understanding of a student but also the appropriate methods and tools to be

used. As such, while teaching the topic of volume of liquid, teachers will need to list down

the teaching objective or learning outcome being that by the end of the lesson, students will

be able to measure and compare volume of liquids by using non-standard units and standard

units correctly.

Having identified the teaching and learning objective, teachers need to list down the

knowledge and skills that need to be mastered by students which in this case would be the

knowledge that the volume of liquid depends on its capacity while being held in a container

rather than the height of it and the skills of being able to measure volume of liquid using non-

standard units such as “cups” and standard units such as millimeters (ml) and liters (l).

The next step would be to determine the most appropriate technique or method to be

utilised in the teaching and learning process. According to Shaharir, an appropriate technique

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or method would be one which is able to assist students to achieve the teaching and learning

objective.

Teaching styles, technique and ability differ from teacher to teacher depending on the

teacher’s personality, experience and the training received. Despite the difference in methods

of conveying knowledge and implementing teaching and learning activities, the general

approach used in the process of teaching and learning is similar (Tg. Zawawi, 1997b). One of

these general approaches that teachers can use is audio and/or visual presentation via video

clips. Teachers can first show students a video on how such misconception on capacity is

common among their peers followed by a video which demonstrates how volume of liquid is

measured to give them an idea of the difference between the capacity and the height of liquid

while being held in a container.

Another approach is the method of experiment or practical work where students are

trained to use teaching aids to understand mathematical concepts and master mathematical

skills. Teachers can create teaching activities that entail the method of experiment to help

students in understanding the concept of volume of liquid and to clarify any misconception

regarding the concept.

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Teaching Activity 1

For the topic titled “Measuring and Comparing Volume of Liquid Using Non-

standard Units”, the learning outcome would be students being able to measure and compare

volume of liquid by using non-standard units correctly by the end of the lesson. The teaching

activity can be conducted using teaching aids such as:

a small paper cup;

a large water jug;

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a large pail; and

a tea pot.

Teachers can divide the class into groups of four and have them work in their

cooperative groups. After appointing one student in the group to record the findings, teachers

can give each group a paper cup, a large water jug, a large pail and a tea pot and have

students fill the jug, pail and tea pot with water.

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Subsequently, students are to estimate the number of paper cups needed to contain all

the water in the jug, pail and tea pot respectively. Then, students should fill the paper cup

with water from the jug, pail and tea pot to check their respective estimates.

Students should record their findings in the following table:

Container Water jug Pail Tea pot

Estimate

Measurement

Have students write their findings in the statements below:

The water in the water jug can fill ______ paper cups.

The water in the pail can fill ______ paper cups.

The water in the tea pot can fill ______ paper cups.

Then, have them discuss which of the three (water jug, pail and tea pot) has the

smallest capacity. Instruct the students to arrange the three containers in descending order of

their capacities and ascending order of their capacities.

Through this experiment, students will be able to measure and compare volume of

liquid by using non-standard units correctly and understand that the volume of liquid depends

on the capacity of the container in which it is held.

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Teaching Activity 2

For the topic titled “Measuring and Comparing Volume of Liquid Using Non-

standard Units”, the learning outcome would be students being able to measure and compare

volume of liquid by using standard units correctly by the end of the lesson. The teaching

activity can be conducted using teaching aids such as:

5 containers of different sizes among which 2 have the same capacity; and

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a graduated cylinder measuring millimeters.

Teachers can divide the class into groups of four and have them work in their

cooperative groups. After appointing one student in the group to record the findings, teachers

can give each group 5 containers of different sizes among which 2 have the same capacity, a

large pail and a graduated cylinder measuring millimeters and have students fill the

containers with water.

Subsequently, students are to measure the volume of the water in the containers by

pouring it into the graduated cylinder. The appointed student records the reading for each

container.

Through this experiment, students will be able to measure and compare volume of

liquid by using standard units correctly and understand that the volume of liquid depends on

the capacity of the container in which it is held rather than the height of the liquid while being

held in the container.

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Conclusion

According to Piaget's theory of cognitive development, Year Two students who are

around the age of 8 are at the preoperational stage of cognitive development. As their

cognitive development is still incomplete, they are unaware that altering a substance's

appearance does not change its basic properties hence their misconception on capacity.

To rectify such a misconception, several approaches generally used in the process of

teaching and learning are available to teachers. The approach of audio and/or visual

presentation via video clips will engage students’ interest in the subject and enhance their

learning experience as the conveyance of information through both audio and visual means

will enable them to absorb the concept of volume of liquid more easily.

Teaching activities which include the method of experiment or practical work can also

be conducted to help students understand the concept of volume of liquid and clarify any

misconception about the concept. This approach is undoubtedly very useful in helping

students grasp the concept of capacity as their active involvement in such teaching activities

will give them hands-on experience related to the concept as opposed to a mere theoretical

understanding through having the concept dictated to them.

Note: Link to my blogger at http://lausiehming.blogspot.com

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Bibliography

Books and Research Papers

Cockroft, W. H. (1986). Mathematics Counts. London: HMSO.

D’ Augustine, C.H. (1973). Multiple Methods of Teaching Mathematics in the

Elementary School. New York: Harper & Row Publisher.

NCTM (1989). Curriculum and Evaluation Standards for School Mathematics. New

York.

Newman, M. A. (1997). “An Analysis of 6th Grade Pupil’s Error on Written

Mathematical Task”. Research in Mathematical Education in Australia. Vol 5: 239-

258.

Shaharir Mohammad Zain (1982). “Pengajaran dan Pembelajaran Matematik

Universiti di Malaysia”. Kertas kerja yang dibentangkan dalam Simposium

Kebangsaan Matematik: UKM.

Sobel, M.A. & Maletsky, E.M. (1972). Teaching Mathematics: A Sourcebook of

Aids, Activities, and Strategies. Prentice Hall: New Jersey.

Tengku Zawiwi b Tengku Zainal (1997b). “Peranan Komputer dalam Pendidikan

Matematik”. Buletin Jabatan Sains (JASA). Jilid 1(1):1-6.

Websites

“Piaget's theory of cognitive development”, http://en.wikipedia.org/wiki/Piaget

%27s_theory_of_cognitive_development. (11.11.10)

Video titled “Child Conservation”, http://www.youtube.com/watch?v=qYtNhNP69lk.

(11.11.10)

Video titled “Using a Graduated Cylinder”, http://www.youtube.com/watch?

v=JRcWj3mfJEw. (11.11.10)

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