VALIDITY AND RELIABILITY OF PATTERN TEST

Dilek TANISLIAynur OZDAS

Anadolu University Faculty of Education

Eskisehir/Turkey

INTRODUCTION

Mathematics covers the subject fields like, numbers, measurement, plane shapes, space and data. Out of these, algebra is one of the most important fields of math. Algebra requires the skill to be able to consider abstractly.

Therefore, the teaching of algebra starts at the second year of primary school education since children start to think abstractly at this time.

Introduction 2

However, although algebra is a word that has not commonly been heard in grades 3-5 classrooms, the mathematical investigations and conversations of students in these grades frequently include elements of algebraic reasoning.

These experiences and conversations provide rich contexts for advancing mathematical understanding and also an important precursor to the more formalized study of algebra in the middle and secondary grades.

Introduction 3

Algebraic thinking has broader and different connotation than the term algebra.

Kieran (1996) defined the term algebraic thinking as “the use of any of a variety of representations that handle quantitative situations in a relational way”.

Driscoll (1999) said that algebraic thinking could be considered to be the “capacity to represent quantitative situations so that relations among variables become apparent”.

Introduction 4

Smith (2003) believed that for students to think algebraically they must be able to identify, extend, and generalize patterns in order to understand quantitative relationships.

By combining these views of algebraic thinking, includes the ability to analyze and recognize patterns, to represent the quantitative relationships between the patterns, and to generalize these quantitative relationships.

Introduction 5

Relating patterns in numbers, geometry and measurement helps pupils understand connections among mathematical topics. Such connections foster the kind of mathematical thinking that serves as a foundation for more abstract ideas studied in later grades.

Introduction 6

As can be understood from the definitions, looking for pattern and making generalization lie at the base of algebraic thinking.

Patterns are the heart and soul of mathematics. Algebra and indeed all of mathematics is about generalizing patterns.

Introduction 7

Also, students’ thinking about patterns can help them develop a better understanding of mathematical concepts and the representations that reflect those concepts.

Introduction 8

NCTM (2000) suggests using the patterns for the purpose of developing the skill for algebraic consideration and the math understanding. According to NTCM, the pattern studies guide the development of logical thinking, which is an important case in algebraic consideration and of making the generalization related to the relationships in patterns.

Introduction 9

A pattern is a systematic configuration of geometric figures, sounds, symbols, or actions.

Mathematics has been described as the study of patterns. Little children discover patterns through their experiences. For them, the classification and enumerating of the objects is a natural and also an interesting experience.

Introduction 10

Initially, students may describe the regularity in patterns verbally rather than with mathematical symbols.

In grades 3-5, they can begin to use variables and algebraic expressions as they describe and extend patterns.

By the end of secondary school, they should be comfortable using the notation of functions to describe relationships.

Introduction 11

However, many studies carried out in the field indicated that many students at different schools and different grades have problems in understanding patterns, have mistakes in common and misconceptions.

Introduction 12

In the study which was carried out in National Assessment of Educational Progress’(NAEP) to examine the math performance of students, it was found that students at fourth grade had some misconceptions related to patterns and also students had great difficulty in explaining the patterns even when they seemed to have understood a certain pattern.

Introduction 13

Similarly, the results of national testing in USA, points out that although most students could recognize a simple pattern in a table of ordered pairs connected by a simple relationship, the majority were unable to generate the corresponding algebraic rule. Other studies have also shown that generating algebraic rules from patterns and tables is difficult.

Introduction 14

According to the results of the study which was carried out by The Assessment and Performance Unit’ (APU) for the purpose of determining the math performance of the students, including number patterns, aged between 11 and 15, the following results were obtained:

– Pupils found explaining patterns more difficult than continuing them;

– Few 11-year-olds were successful in continuing patterns which did not have a constant difference;

Introduction 15

– Few pupils knew the names of sequences such as ‘square’ or ‘triangular numbers’;

– A significant number of pupils made generalizations using only partial information and this occurred more frequently with difficult sequences.

Introduction 16

For the first time in Math curriculum which was renewed in 2004-2005 education term in Turkey, the patterns subject was included.

Therefore, there has been no similar research

in Turkey to the one mentioned and summarized above, which was carried out to measure the skills of the students like defining patterns and constructing them, determining the relationship among patterns and explaining it verbally, indicating the pattern in shapes, expand the pattern in a finite step.

Introduction 17

There is a serious shortage of research which aims to measure the understanding of patterns related to algebra at the first grade of primary school.

Introduction 18

Therefore, a new pattern test was prepared to measure their competence like, the strategies that they employ, expand the pattern in a finite step, indicating the pattern in shapes, determining the relationship among the patterns and explaining it verbally and defining the numerical and geometric patterns of the students at the fifth grade of primary school in Turkey.

With this study, the reliability and validity of the pattern test was confirmed.

METHOD

Sampling

The reliability and validity of the pattern test was done on 14 female and 17 male fifth grade students attending a primary school in 2005-2006 education term. The school which is in middle socio economic group was chosen randomly.

Method 2

Instrument

The items in the test were developed through the review of the related literature, the review of the gains stated in the math curriculum and through the interviews conducted with the field experts. At the same time, students’ books were also used in the preparation of the items in the test. The duration of the test is 60 minutes.

Validity of the Test.

The validity of the test is confirmed through the content validity. The content validity is used, as a whole, to mean to what extent the test itself and each of the item in the test serve the intended purpose of the researcher. Content validity can be determined with logical or rational approach, and also statistical approach can also be used in determining it.

Method 3

In this study, logical approach has been adapted. In testing the content validity logically, we try to confirm if each of the items in the test and the distribution of the items in the test as a whole cover the subjects and the gains that the test intends to measure.

Method 4

For this purpose, the gains related to each of the items in the test were determined. Then, to confirm whether the items in the test match with the gains with regards to measuring these gains, the test was submitted to a group of instructors from Education Faculty, Primary School Teacher Training Department and some teachers teaching at some local Primary schools and they were asked for their opinions related to the test. Considering the feedback taken from the experts, some items of the test were revised.

Method 5

Reliability of the Test

To confirm the reliability of the test, some possible responses to the items were listed in the test and each of the listed response was graded. After that, the grades were distributed depending on the criteria which was prepared for each of the items in the test. The test was submitted to the sampling group and the criteria and the grades were revised again depending on the responses taken from the sampling group.

Method 6

Next, three field experts submitted their evaluation related to the test considering the already prepared criteria and grades.

In the investigation of the relationship among the three evaluations, alpha reliability coefficient and the match among the independent observers were investigated. The match among the independent observers is a kind of measurement criteria employed in the cases when more than one observers attempt to measure the same thing at the same time, independently from one another.

Method 7

When the other measurement criteria is especially not practical, this criteria is known to be the best method in testing the reliability of a certain test.

In such measurements, the mean scores of the measurements that independent observers carried out independently are taken and a certain value is found and this value is true for every case. The most significant one here is that this value should be reliable.The closer the findings of the seperate observers are, the higher the reliability of the mean score obtained in the end is.

Method 8

The SPSS package programme was used in testing the reliability of the test. In the evaluation of the alpha coefficient, the following criteria was used:

If 0.00 α<0.40, the test is not reliable If 0.40 α<0.60, the test has weak reliability. If 0.60 α<0.80, the test is quite reliable. If 0.80 α<1.00, the test has quite high

reliability.

Method 9

Examples of questions

FINDINGS

The validity of the test. The pattern test was primarily prepared with

the use of 21 items and the gains of every item was determined. The distribution of the items in the test as a whole and each item in the test were submitted to the expert in the field to see if the prepared test covers the subjects and gains which the test attempts to measure. The experts submitted their opininions suggesting that some of the items should be shortened to make the meaning clearer.

One of the experts suggested that the numbers in the fibonacci pattern item should be smaller numbers and two of the items may be too difficult for the 5th grade primary school students.

Considering the feedbacks taken from the experts, necessary revision was done on the test, one of the items was removed from the test, some expressions were modified.

Finding 2

Some of the items which seem to express more than one gains were divided into new items, and thus the number of the items in the test was increased. This also helped the items to be more comprehensible for the participants. The test, in the end, consisted of 26 items including the sub-items.

Finding 3

The reliability of the test.

To confirm the reliability of the pattern test, the alpha reliability coefficient α=0.98 and the mean of the match among the independent observers was found to be α=0.94. As these results obtained in the study were found to be between 0.80 α<1.00, the pattern test was considered to be highly reliable.

Finding 4

DISCUSSION AND CONCLUSION

As conclusion, the findings obtained relatedly to the reliability and validity of the test showed that the pattern test could be used as a reliable instrument to extend the pattern to determine the relationship in the pattern and express it orally, to define the geometric and numerical patterns for the 5th grade students at primary schools. In other words, when we consider the findings above, it can be stated here that the pattern test has high reliability and validity.

Discussion and Conclusion 2

For the first time in the primary school math curriculum, the subject of patterns was included in the curriculum in 2004-2005 education year at every grade. Therefore, no instrument to measure the performans of the primary school students related to this subject has been detected yet in Turkey. With the help of this study, it is expected that this pattern test, the reliability and validity of which has been confirmed, can be used on the Turkish 5th grade primary school students by teachers after finishing of my dissertation.