This study analyzed common errors made by primary students when interpreting and drawing column graphs. The researcher designed a question paper and interviewed students who made errors. Several types of errors were identified: 1) Students did not start the vertical axis scale at zero. 2) Students numbered the spaces on the vertical axis instead of using a number line. 3) Students used inconsistent scales or incorrect labeling on the horizontal and vertical axes. The interviews found students struggled with starting the vertical scale at zero instead of one, and were more familiar with number tracks than the number line concept. Understanding column graphs is important for students and the public to interpret data representations.

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A study on primary students’ errors on column graph
T.Mukunthan
Department of Early Childhood and Primary Education, The Open University of Sri Lanka
Introduction Results and Discussion  Inconsistent scale used on horizontal axis. (Students Conclusion
have used different widths for their column).
Sri Lankan Primary Mathematics syllabi consist of six main Interpret and draw the column graph is essential not only
topics: When marking the answer scripts, following types of
errors were identified: to the students but also to the general public. Because
 Numbers there are many information given in the column graph
 Mathematical Operations  Scale used on vertical axis does not begin at zero
(Students have labelled the vertical axis starting at format in the newspapers and television programmes. But
 Measurement many people does not understand the information from
 Money one)
the graph. This study is find the students errors on column
 Space and Shapes and graph. The question paper was designed by the
 Data Handling. researcher. After marking the answer scripts, the students
who had made errors were interviewed to identify the
From these topics handling data consists of following sub . reasons for making such errors. The data collected from
topics: the interviewee were further analysed to categorise errors.
1. Collect data and represent in a graph When marking the answer scripts, the following types of
2. Read timetables and graphs logically. errors were identified:
 Scale used on vertical axis does not begin at zero
The concept of column graph is introduced to the
Sri Lankan children in grade three (at the age of 8 years). It
Reasons for errors  Number track used on vertical axis
 Incorrect labelling of horizontal axes
is then developed up to grade 5 in the primary circle. The  Inconsistent scale used on vertical axis
column graphs could be defined as a ‘type of graphic  Scale used on vertical axis does not begin at zero  Inconsistent scale used on horizontal axis.
presentation in which numerical values are represented by The students did not understand that the vertical
vertical columns’. Column graphs are particularly effective  Number track used on vertical axis (Students have
scale should start at zero and not at one. The reason The knowledge of above identified errors is useful to
for showing values that are categorized by two separate numbered the spaces on vertical axis of a column
for this is that the students usually start counting at primary mathematics curriculum developers, educators,
characteristics, such as year and sector. Column graphs are chart).
one and they are confused when labelling the teacher trainers and teachers.
similar to bar graphs and line graphs. All three have vertical axis, which should start at zero as the origin.
gridlines going horizontally and vertically. Therefore, it is very important that the primary
teachers have to explain the axis of scale Literature cited
Collecting data and representing in a graph is one of the measurement to the students very carefully.
competencies that has to be developed in grade 5 students.
However, the grade 5 scholarship examiners’ reports  Number track used on vertical axis Circa, (1997). Pictures from data. Circa: The
highlighted that the students’ performance in column graph Mathematical Magazine. Volume 6.
is poor. It was evident from the interview with the students
that the primary students are familiar with number Surtees, L. (2009). Handling data, Children’s Errors in
tracks and do not have the knowledge of number Mathematics understanding common
Methods line. Because, students learned pictogram in grade
3. In the pictogram the students marked the pictures
misconceptions in Primary Schools
as 1. 2. 3 etc. indicating each picture. Number line is
 Incorrect labelling of horizontal axes (Students have
labelled the items represented on the horizontal
introduced in secondary level. Therefore the Acknowledgments
Objective curriculum developers have to consider the
axis).
introduction of number line in the primary level with I thank Principal, teachers and students of
Identify the errors in representing data on column graph. the positive numbers. C/Ramakrisna Vidyalam, Pamankadai, Wellawatte,
Colombo-6
Sample  Incorrect labelling of horizontal axis
The sample for the study consist of Grade 5 students from Students do not know the importance of labelling the
four 1 AB type Tamil medium schools in Colombo
Education Zone. 108 boys and 117 girls considered as the
axis. The teachers have to explain to the students
about the importance of labelling.
For further information
 Inconsistent scale used on vertical axis. (Students
sample of this study from the four schools.
have labelled the vertical axis using an inconsistent Please contact:
 Inconsistent scale used on vertical axis
scale). tmuku@ou.ac.lk
Research Instrument Students do not understand how a scale has to be
A question paper included 5 problems on the concept decided. The teachers have to explain the important 0773732652
data handling. The question paper was designed by the of use the proper scales in the graphs to the
researcher. students.
Data collection  Inconsistent scale used on horizontal axis
After marking the answer scripts, the students who have Students do not understand the convention. The
made errors were interviewed to identify the reasons for teachers have to explain the important of use the
making such errors. The data collected from the interview proper scales in the graphs to the students.
were further analysed to categorise the errors.