Errors in Rational Number Operations: A Case of DEBESMSCAT Preservice Teachers
1. Errors in Rational
Number Operations:
A Case of Preservice
Teachers
Presented by:
SHERWIN E. BALBUENA
Dr. Emilio B. Espinosa Sr. Memorial State College of Agriculture
and Technology (DEBESMSCAT), Masbate, Philippines
2. Contents
Rationale
Statement of the Problem
Objectives
Significance of the Study
Methods
Results and Discussions
Conclusions
Recommendations
3. Rationale
Rational numbers – fractions, mixed
numbers, integers
Rational numbers have different constructs
(Behr, Lesh, Post, & Silver ,1983)
Taught as early as Grade III
Low mastery level of high school graduates,
college entrants
Preservice teachers’ understanding of
fraction content knowledge is weak (Behr,
Khoury, Harel, Post, & Lesh, 1997; Cramer,
Post, & del Mas, 2002).
4. Rationale
Preservice teachers find it difficult to
conceptualize fractions (Ball, 1990)
Can hardly explain fractions to children
and why computation procedures work
(Chinnappan, 2000)
Cannot operate fractions correctly, even
if they have chosen the correct answer
(Becker & Lin, 2005).
Future problems posed by this difficulty
Diagnosis of procedural errors is
imperative
5. Statement of the Problem
DEBESMSCAT two teacher education programs
Bachelor in Secondary Education (BSEd)
Bachelor in Elementary Education (BEEd).
Admission process
Enrollees are required to pass the college entrance test
and screenings to ensure that students are highly qualified
to undergo teacher education trainings for four years.
However, diversity implies that certain learning
difficulties exist among entrants.
This study is interested about the learning difficulties
exhibited by preservice teachers in understanding
rational numbers.
6. Objectives
What is the level of performance of
DEBESMSCAT preservice teachers in
operating rational numbers?
Which of the errors exhibited by
preservice teachers in dealing with
rational number operations are
more prevalent?
What are the implications for
teaching and learning rational
numbers?
7. Significance of the Study
Information dissemination of
results to the basic education
teachers
Diagnosis of the learning
difficulties and research
opportunities for tertiary
educators
Basis for enhancing preservice
teachers’ procedural skills
8. Methods
Participants
38 preservice teachers enrolled in their first of
four-year BEEd program in DEBESMSCAT
Sampling
Systematic Random Sampling
Profile of Participants
97% are younger than age 25
76% were female, 24% male
87% graduated from secondary schools in the
2nd district of Masbate
9. Methods
Instrument
Diagnostic pretest with 8 multiple-choice items on
adding and multiplying rational numbers
Item 1 for identifying errors in adding dissimilar and common
fractions,
Item 2 in adding dissimilar and uncommon fractions,
Item 3 in adding a mixed number and a fraction which are
similar and common,
Item 4 in adding similar fractions,
Item 5 in adding a mixed number and a fraction which are
dissimilar and uncommon,
Item 6 in multiplying common fractions,
Item 7 in multiplying a whole number by a fraction, and
Item 8 in multiplying a mixed number by a fraction which are
common.
10. Methods
Instrument (cont’d)
Example of an item
1/2 + 3/4=
A. 4/6
B. 2/3
C. 10/8
D. 5/4
Each distracter has some diagnostic designs to
identify student’s error
13. Results and Discussions
Total % of errors > Total % of
correct responses
Only 21.05% of the
participants obtained at least
4 marks (50%)
Very low performance of the
participants in operating rational
numbers
14. Correct vs. Wrong Answers
0
10
20
30
40
50
60
70
80
90
1 2 3 4 5 6 7 8
Item Number
Percentage
of correct
responses
Percentage
of the more
prevalent
wrong answer
20. Conclusions
Preservice teachers’ knowledge of
rational number operations is very weak
More prevalent errors were observed in
adding dissimilar fractions and in
multiplying a mixed number by a fraction
Preservice teachers tend to mix up
memorized fraction rules
Good at adding similar fractions and
reducing answers to the lowest terms
21. Conclusions
Lack of sufficient knowledge of equivalence of
mixed numbers and improper fractions
Confirms that preservice teachers’ procedural
knowledge predominates over their conceptual
knowledge (Forrester & Chinnappan, 2011)
There is a need for students to gain mastery of
the processes involved in performing operations
on dissimilar fractions
Preservice teachers are not ready to learn more
advanced topics in mathematics
22. Recommendations
Improve the quality of teaching and learning
fractions in the elementary and secondary levels
Enhance students’ retention and conceptual
understanding of fractions
Give preservice teachers more curative
interventions and trainings in mathematics
Further studies
Limitations:
Small number of participants
Use of “fixed” questions
Emphasis on the procedural knowledge
