Errors in Rational Number Operations: A Case of Preservice TeachersPresented by:

SHERWIN E. BALBUENA

Dr. Emilio B. Espinosa Sr. Memorial State College of Agriculture and Technology (DEBESMSCAT), Masbate, Philippines

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Contents

Rationale Statement of the Problem Objectives Significance of the Study Methods Results and Discussions Conclusions Recommendations

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).

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

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.

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?

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

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

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.

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

Results and Discussions

Results and Discussions

1 2 3 4 5 6 7 80

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Percentages of Occurences of Responses in the Item Choices

A B C D

D A A C B B C D

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

Correct vs. Wrong Answers

1 2 3 4 5 6 7 80

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Percentage of cor-rect responses

Percentage of the more prevalent wrong answer

Item Number

More Prevalent Errors

Procedural Errors Item 1

1/2+3/4 =4 /6

= 2/3

Numerator plus numerator

Denominator plus denominator

Reducing to the lowest term

Procedural Errors Item 2

1/3+3/5 =4 /8

= 1/2

Procedural Errors Item 5

2 1/3+2/7 = 3/102

Copying the whole part

Procedural Errors Item 8

1 1/4 x 1/2= 1/81

Copying the whole part

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

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

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

Thank you very much!Madamo nga salamat!