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المستخلص
Title Of The Study :
Assessing the Effectiveness of a Training Program for Developing Mathematics self-Efficacy and its Effect on Mathematics Achievement of Primary School Students Using Item Response Theory.
Aim Of The Study :
The current study aims at constructing a training program for improving Mathematics self-Efficacy and Mathematics Achievement for fifth grade students and assessing its effect on the independent variables of the study using a group of equated and equivalent scales in case of each variable.
Importance Of The Study :
A-Theoritical Importance :
-This study enriches the scope of psychological research in the Arab world by introducing a new research trial in self-Efficacy and draws a spot of light on the important role self-Efficacy can play in enhancing mathematics achievement and improving mathematics learning .
-This study provides the Arabic library of psychological tests with a new scale of Mathematics self-Efficacy calibrated by Item Response Theory. Such a scale is claimed to provide objectivity & accuracy in the measurement of this variable .
-This study may provide a group of research suggestions & recommendations that help enriching the movement of scientific research .
B-Practical Importance :
-The training program designed in this study for developing Math Self-Efficacy may help students improve their achievement & performance in mathematics and its related activities .
-Mathematics teachers and advisors may make use of the results of this study while they are setting or implementing their instruction policies and strategies for enhancing the achievement level of their students .
-The advantage of linearity offered by Rasch measurement sets the opportunity for realizing accuracy and objectivity in measuring the variables of the current study .
-The advantage of parameter invariance ( item parameter invariance / person parameter invariance ) offered by Rasch measurement sets the opportunity for :
a)Withdrawing equated versions from the calibrated scale , that can be used in different measurement situations ( pre-test , after-test , and monitoring ) while overcoming the problem of test familiarity
bHolding various invariant comparisons across different groups of examinees & items .
Problem Of The Study : The problem of the current study can be confined to the following questions :
1)Is it possible to obtain equivalent and equated versions of the mathematics self efficacy scale using Rasch model ?
2)Is it possible to obtain equivalent and equated versions of the mathematics achievement test using Rasch model ?
3)How much is the proposed traing program effective in developing Math Self-Efficacy of the examinees ?
This question involves the following two subsequent questions :
a)Does the test group outweigh the control group in the magnitude of improvement in the level of Math Self-Efficacy shortly after applying the training program ?
b)Are there relative differences among the components of Math Self-Efficacy in the magnitude of improvement as a result of self-efficacy training ?
c)Will the test group maintain the level of improvement in Math Self-Efficacy after ending the training applications ?
4)How much is the training program effective in improving the level of Math Achievement for the examinees ?
This question involves the following two subsequent questions :
a)Does the experimental group outweigh the control group in the magnitude of improvement in the level of Math Achievement shortly after applying the training program ?
b)Are there relative differences among the topics of interest of the math curriculum in the magnitude of improvement as a result of self-efficacy training ?
c)Will the experimental group maintain the level of improvement in Math Achievement after ending the training applications ?
Terms Of The Study :
•Item Response Theory : It is a contemporary approach in psychological measurement that addresses objectivity. It has managed to provide solutions to many practical testing problems as well as offered several advantages over classical measurement methods. This theory depends on a number of mathematical probabilistic models that predict the responses of the examinees to test items from the characteristics of the examinee (person parameters) and those of the individual test item (item parameters).
•Calibrating the scale by Rasch model : calibrating a scale used to assess a certain trait by Rasch model refers to the process of constructing a linear metric on which the items of that scale are scaled according to their difficulties.
•Equated tests : they are tests whose items are all calibrated on a common linear metric, where the estimated measure for a given individual will not vary whatever test is used.
•Math self-Efficacy : the researcher could define math self-efficacy as the individual’s confidence in his/her ability to learn mathematics and fulfils its related tasks . In the current study it represents in the scores of the examinees on the Math self-efficacy scale used in the study.
•The Training Program : In the current research , the training program can be executively defined as a group of procedures , activities , and practices intended to improve the levels of math self-efficacy and math achievement in the context of the mathematics curriculum for the fifth-grade students .
•Rasch Model: It is the simplest and most familiar logistic model of Item Response Theory , It assumes that the items of a given scale don’t allow guessing responses , have the same discrimination power , and vary only in difficulty . In this model the test items are calibrated according to the parameter of difficulty on one linear metric along with the examinees that are calibrated according to the parameter of ability.
Theoritical Framework Of The Study :
It included :
1-Self-Efficacy ( concept , sources , effects , related consructs , traits of self-efficacious individuals , and measurement of self-efficacy ).
2-Methods of behavior measurement ( classical theory of measurement and its deficits , Item Response Theory and its models ).
Previous Studies :
These have been categorized into the following divisions :
1.Previous studies that investigated the effect of Mathematics Self-Efficacy on Mathematics Achievement.
2.Previous studies that investigated the effectiveness of different training interventions in improving Mathematics Self-Efficacy.
3.Previous studies that used the Rasch model for calibrating and/or validating scales of Mathematics Self-Efficacy.
Hypotheses Of The Study :
1)It is possible to obtain equivalnt and equated versions of the mathematics self efficacy scale using the Rasch model.
2)It is possible to obtain equivalent and equated versions of the mathematics achievement test using the Rasch model.
3)It is possible to improve the levels of mathematics self efficacy and mathematics achievement of the examinees by the proposed program.
The training program will prove effective if :
a)The experimental group outweighs the control group in the magnitude of improvement in the levels of Math Self-Efficacy and Math Achievement shortly after applying the training program.
b)The experimental group maintains the levels of improvement in Math Self-Efficacy and Math Achievement after ending the training applications.
c)There are relative differences among the components of each of the two dependent variables of the study (Math Self-Efficacy and Math Achievement) in the magnitude of improvement as a result of self-efficacy training.
Plan Of The Study:
I- Variables Of The Study :
The variables of the current study include :
1)Independent variable : this represents in the training program used for developing Mathematics Self-Efficacy in the current study.
2)Dependent variables : these represent in :
•Mathematics Self-Efficacy .
•Mathematics Achievement .
3)Control variables : these are the variables that are held under control while collecting the sample of the study so as to secure the equivalence of the control and the test groups before treatment . They include : Age , Socio-economic level of the examinees , and mathematical ability.
II- Methodology of the Study :The current study has employed the experimental methodology through a design of equivalent groups that involves :
-An experimental group : submitted to the independent variable.
-A Control group : not submitted to the independent variable.
III- Sample Of The Study :
The sample of the current study involves :
1)the calibration sample : that is used to calibrate the items of the Mathematics Self-Efficacy Scale and those of the Mathematics Achievement Test in the current study according to Rasch model using the Winsteps computer program .
2the experimental sample : that is useo test the hypotheses of the study . It consists of a suitable number of the fifth grade students . This sample is partitioned into a control group and a test group . IV- Tools Of The Study :
The instrument of the current study involves the following :
•The Mathematics Self-Efficacy Scale : designed in the current study.
•Mathematics Achievement Scale for the fifth grade students : constructed by the researcher in the current study .
•A training program for the development of Math self-Efficacy : designed by the researcher in the current study .
V -Procedures of the study:
The researcher followed the following procedures for testing the hypotheses of the study :
1) Reading the literature and previous studies on self efficacy carefully for analyzing this construct , wording the hypotheses of the study , and building the tools of the study .
2) Surveying the scales of MSE for finding out and defining the most frequent aspects and dimensions of this variable
3) Constucting the tools of the study which involve:
-The MSE scale
-The Math achievement test for fifth grade students.
-The training program for improving MSE.
4) Applying the scales of the two independent variables of the study to the calibration sample , followed by calibration the two scales according to Rash Model using the winsteps statistical program , then withdrawing 3 equated and equivalent short versions of each scale to be used in the different measurement stages (pre-, post-) for testing the hypotheses of the study .
5) Conducting pre-test for both of the control and experimental groups of examinees on self-Efficacy , Math achievement & Math ability followed by verifying the equivalence of the control and experimental groups on the two independent variables of the study .
6) Applying the training program to the experimental group of examinees.
7)Conducting Post-test for both of the control and experimental groups of examinees on self-Efficacy & Math . performance.
8)Conducting the monitoring test for the members of experimental group one month and half after ending the training procedures.
9) Manipulating the results of the study statistically in order to assess the effectiveness of the training program.
VI- The Statistical Manipulation Plan :
The Following Statistical Manipulation has been made for calibrating the tools of the study and testing its hypotheses:
-Entering and grading the test data using the SPSS computer program .
- Analyzing the data according to Rasch mdel using the Winsteps computer program .
-Calculating the descriptive statistical measures ( mean , median , standard deviation & skewing coefficient ) for the variables of the study in pre- , post- , monitoring tests.
-Using the T-test for two independent samples to test the statistical significance of :
A.the difference between the mediums of Rasch measures of the control and expreimental groups for each of the two dependent variables of the study .
B.The difference between the mediums of change in Rasch measures of the control and expreimental groups after applying the program for each of the two dependent variables of the study .
-Using the T-test for two dependent samples to test the statistical significance of :
A.The difference between the mediums of Rasch measures of the control and expreimental groups separately in pre- and post- testes for each of the two dependent variables of the study.
B.The difference between the mediums of Rasch measures of the expreimental group in post- and monitoring tests for each of the two dependent variables of the study.
-Setting up graphical plots for comparing :
a)The mediums of Rasch measures of the control and expreimental groups
b)The mediums of change in the measures of the two groups as a result of applying the program both for the two dependent variables of the study.
c)The gain ratios for the components of each of the two dependent variables of the study .
-Using the Effect Size test to investigate the effect of the independent variable of the study ( The training program) on the two dependent variables ( M.S.E. & M.A. ).
-Using the McGuigan equation of Gain Ratio to assess the effect of the training program on the components of each of the two dependent variables of the study for the experimental group .
The Results Of The Study :
The results of the study involved the following :
•The performance of the experimental group on both the Math Self-Efficacy scale and the Math Achievement scale exhibited significant improvement shortly after applying the program.
•The performance of the control group on either of the independent variables’ scales showed no significant change shortly after applying the program.
•The experimental group has significantly outweighed the control group in the magnitude of improvement in both of the levels of the independent variables shortly after applying the program.
•The MSE component of ” Planning and organization of learning ” offered the greatest magnitude of improvement as a result of self-efficacy training in the current study ( Gain Ratio = 0.53), succeeded by the component of ” Confidence in the ability to learn and study mathematics’’ which offered a gain ratio of (0.48), and finally the component of ”Perseverance and willingness to make an effort’’ that offered the smallest gain ratio (0.18).
•The topic of ”Multiplying decimal numbers and fractions” offered the greatest magnitude of improvement as a result of self-efficacy training in the current study ( Gain Ratio = 0.19 ), succeeded by the topic of ”Dividing decimal numbers and fractions” which offered a gain ratio of (0.18), then the topic of ”Comparing fractions” which offered a gain ratio of (0.15), and finally the topic of ”Approximation’’ that offered the smallest gain ratio (0.14).
• The experimental group has maintained the improvement in both Math Self-Efficacy and Math Achievement one and half months after applying the program.
Title Of The Study :
Assessing the Effectiveness of a Training Program for Developing Mathematics self-Efficacy and its Effect on Mathematics Achievement of Primary School Students Using Item Response Theory.
Aim Of The Study :
The current study aims at constructing a training program for improving Mathematics self-Efficacy and Mathematics Achievement for fifth grade students and assessing its effect on the independent variables of the study using a group of equated and equivalent scales in case of each variable.
Importance Of The Study :
A- Theoritical Importance :
- This study enriches the scope of psychological research in the Arab world by introducing a new research trial in self-Efficacy and draws a spot of light on the important role self-Efficacy can play in enhancing mathematics achievement and improving mathematics learning .
- This study provides the Arabic library of psychological tests with a new scale of Mathematics self-Efficacy calibrated by Item Response Theory. Such a scale is claimed to provide objectivity & accuracy in the measurement of this variable .
- This study may provide a group of research suggestions & recommendations that help enriching the movement of scientific research .
B- Practical Importance :
- The training program designed in this study for developing Math Self-Efficacy may help students improve their achievement & performance in mathematics and its related activities .
- Mathematics teachers and advisors may make use of the results of this study while they are setting or implementing their instruction policies and strategies for enhancing the achievement level of their students .
- The advantage of linearity offered by Rasch measurement sets the opportunity for realizing accuracy and objectivity in measuring the variables of the current study .
- The advantage of parameter invariance ( item parameter invariance / person parameter invariance ) offered by Rasch measurement sets the opportunity for :
a) Withdrawing equated versions from the calibrated scale , that can be used in different measurement situations ( pre-test , after-test , and monitoring ) while overcoming the problem of test familiarity
b) Holding various invariant comparisons across different groups of examinees & items .
Problem Of The Study :
The problem of the current study can be confined to the following questions :
1) Is it possible to obtain equivalent and equated versions of the mathematics self efficacy scale using Rasch model ?
2) Is it possible to obtain equivalent and equated versions of the mathematics achievement test using Rasch model ?
3) How much is the proposed training program effective in developing Math Self-Efficacy of the examinees ?
This question involves the following two subsequent questions :
a) Does the test group outweigh the control group in the magnitude of improvement in the level of Math Self-Efficacy shortly after applying the training program ?
b) Are there relative differences among the components of Math Self-Efficacy in the magnitude of improvement as a result of self-efficacy training ?
c) Will the test group maintain the level of improvement in Math Self-Efficacy after ending the training applications ?
4) How much is the training program effective in improving the level of Math Achievement for the examinees ?
This question involves the following two subsequent questions :
a) Does the experimental group outweigh the control group in the magnitude of improvement in the level of Math Achievement shortly after applying the training program ?
b) Are there relative differences among the topics of interest of the math curriculum in the magnitude of improvement as a result of self-efficacy training ?
c) Will the experimental group maintain the level of improvement in Math Achievement after ending the training applications ?
Terms Of The Study :
• Item Response Theory : It is a contemporary approach in psychological measurement that addresses objectivity. It has managed to provide solutions to many practical testing problems as well as offered several advantages over classical measurement methods. This theory depends on a number of mathematical probabilistic models that predict the responses of the examinees to test items from the characteristics of the examinee (person parameters) and those of the individual test item (item parameters).
• Calibrating the scale by Rasch model : calibrating a scale used to assess a certain trait by Rasch model refers to the process of constructing a linear metric on which the items of that scale are scaled according to their difficulties.
• Equated tests : they are tests whose items are all calibrated on a common linear metric, where the estimated measure for a given individual will not vary whatever test is used.
• Math self-Efficacy : the researcher could define math self-efficacy as the individual’s confidence in his/her ability to learn mathematics and fulfils its related tasks . In the current study it represents in the scores of the examinees on the Math self-efficacy scale used in the study.
• The Training Program : In the current research , the training program can be executively defined as a group of procedures , activities , and practices intended to improve the levels of math self-efficacy and math achievement in the context of the mathematics curriculum for the fifth-grade students .
• Rasch Model: It is the simplest and most familiar logistic model of Item Response Theory , It assumes that the items of a given scale don’t allow guessing responses , have the same discrimination power , and vary only in difficulty . In this model the test items are calibrated according to the parameter of difficulty on one linear metric along with the examinees that are calibrated according to the parameter of ability.
Theoritical Framework Of The Study :
It included :
1- Self-Efficacy ( concept , sources , effects , related consructs , traits of self-efficacious individuals , and measurement of self-efficacy ).
2- Methods of behavior measurement ( classical theory of measurement and its deficits , Item Response Theory and its models ).
Previous Studies :
These have been categorized into the following divisions :
1. Previous studies that investigated the effect of Mathematics Self-Efficacy on Mathematics Achievement.
2. Previous studies that investigated the effectiveness of different training interventions in improving Mathematics Self-Efficacy.
3. Previous studies that used the Rasch model for calibrating and/or validating scales of Mathematics Self-Efficacy.
Hypotheses Of The Study :
1) It is possible to obtain equivalent and equated versions of the mathematics self efficacy scale using the Rasch model.
2) It is possible to obtain equivalent and equated versions of the mathematics achievement test using the Rasch model.
3) It is possible to improve the levels of mathematics self efficacy and mathematics achievement of the examinees by the proposed program.
The training program will prove effective if :
a) The experimental group outweighs the control group in the magnitude of improvement in the levels of Math Self-Efficacy and Math Achievement shortly after applying the training program.
b) The experimental group maintains the levels of improvement in Math Self-Efficacy and Math Achievement after ending the training applications.
c) There are relative differences among the components of each of the two dependent variables of the study (Math Self-Efficacy and Math Achievement) in the magnitude of improvement as a result of self-efficacy training.
Plan Of The Study:
I- Variables Of The Study :
The variables of the current study include :
1) Independent variable : this represents in the training program used for developing Mathematics Self-Efficacy in the current study.
2) Dependent variables : these represent in :
• Mathematics Self-Efficacy .
• Mathematics Achievement .
3) Control variables : these are the variables that are held under control while collecting the sample of the study so as to secure the equivalence of the control and the test groups before treatment . They include : Age , Socio-economic level of the examinees , and mathematical ability.
II- Methodology of the Study :
The current study has employed the experimental methodology through a design of equivalent groups that involves :
- An experimental group : submitted to the independent variable.
- A Control group : not submitted to the independent variable.
III- Sample Of The Study :
The sample of the current study involves :
1) the calibration sample : that is used to calibrate the items of the Mathematics Self-Efficacy Scale and those of the Mathematics Achievement Test in the current study according to Rasch model using the Winsteps computer program .
2) the experimental sample : that is used to test the hypotheses of the study . It consists of a suitable number of the fifth grade students . This sample is partitioned into a control group and a test group .
IV- Tools Of The Study :
The instrument of the current study involves the following :
• The Mathematics Self-Efficacy Scale : designed in the current study.
• Mathematics Achievement Scale for the fifth grade students : constructed by the researcher in the current study .
• A training program for the development of Math self-Efficacy : designed by the researcher in the current study .
V -Procedures of the study:
The researcher followed the following procedures for testing the hypotheses of the study :
1) Reading the literature and previous studies on self efficacy carefully for analyzing this construct , wording the hypotheses of the study , and building the tools of the study .
2) Surveying the scales of MSE for finding out and defining the most frequent aspects and dimensions of this variable
3) Constucting the tools of the study which involve:
-The MSE scale
-The Math achievement test for fifth grade students.
-The training program for improving MSE.
4) Applying the scales of the two independent variables of the study to the calibration sample , followed by calibration the two scales according to Rash Model using the winsteps statistical program , then withdrawing 3 equated and equivalent short versions of each scale to be used in the different measurement stages (pre-, post-) for testing the hypotheses of the study .
5) Conducting pre-test for both of the control and experimental groups of examinees on self-Efficacy , Math achievement & Math ability followed by verifying the equivalence of the control and experimental groups on the two independent variables of the study .
6) Applying the training program to the experimental group of examinees.
7)Conducting Post-test for both of the control and experimental groups of examinees on self-Efficacy & Math . performance.
8)Conducting the monitoring test for the members of experimental group one month and half after ending the training procedures.
9) Manipulating the results of the study statistically in order to assess the effectiveness of the training program.
VI- The Statistical Manipulation Plan :
The Following Statistical Manipulation has been made for calibrating the tools of the study and testing its hypotheses:
- Entering and grading the test data using the SPSS computer program .
- Analyzing the data according to Rasch model using the Winsteps computer program .
- Calculating the descriptive statistical measures ( mean , median , standard deviation & skewing coefficient ) for the variables of the study in pre- , post- , monitoring tests.
- Using the T-test for two independent samples to test the statistical significance of :
A. The difference between the mediums of Rasch measures of the control and expreimental groups for each of the two dependent variables of the study .
B. The difference between the mediums of change in Rasch measures of the control and expreimental groups after applying the program for each of the two dependent variables of the study .
- Using the T-test for two dependent samples to test the statistical significance of :
A. The difference between the mediums of Rasch measures of the control and expreimental groups separately in pre- and post- testes for each of the two dependent variables of the study.
B. The difference between the mediums of Rasch measures of the expreimental group in post- and monitoring tests for each of the two dependent variables of the study.
- Setting up graphical plots for comparing :
a) The mediums of Rasch measures of the control and expreimental groups
b) The mediums of change in the measures of the two groups as a result of applying the program both for the two dependent variables of the study.
c) The gain ratios for the components of each of the two dependent variables of the study .
- Using the Effect Size test to investigate the effect of the independent variable of the study ( The training program) on the two dependent variables ( M.S.E. & M.A. ).
- Using the McGuigan equation of Gain Ratio to assess the effect of the training program on the components of each of the two dependent variables of the study for the experimental group .
The Results Of The Study :
The results of the study involved the following :
• The performance of the experimental group on both the Math Self-Efficacy scale and the Math Achievement scale exhibited significant improvement shortly after applying the program.
• The performance of the control group on either of the independent variables’ scales showed no significant change shortly after applying the program.
• The experimental group has significantly outweighed the control group in the magnitude of improvement in both of the levels of the independent variables shortly after applying the program.
• The MSE component of ” Planning and organization of learning ” offered the greatest magnitude of improvement as a result of self-efficacy training in the current study ( Gain Ratio = 0.53), succeeded by the component of ” Confidence in the ability to learn and study mathematics’’ which offered a gain ratio of (0.48), and finally the component of ”Perseverance and willingness to make an effort’’ that offered the smallest gain ratio (0.18).
• The topic of ”Multiplying decimal numbers and fractions” offered the greatest magnitude of improvement as a result of self-efficacy training in the current study ( Gain Ratio = 0.19 ), succeeded by the topic of ”Dividing decimal numbers and fractions” which offered a gain ratio of (0.18), then the topic of ”Comparing fractions” which offered a gain ratio of (0.15), and finally the topic of ”Approximation’’ that offered the smallest gain ratio (0.14).
• The experimental group has maintained the improvement in both Math Self-Efficacy and Math Achievement one and half months after applying the program.
Title Of The Study :
Assessing the Effectiveness of a Training Program for Developing Mathematics self-Efficacy and its Effect on Mathematics Achievement of Primary School Students Using Item Response Theory.
Aim Of The Study :
The current study aims at constructing a training program for improving Mathematics self-Efficacy and Mathematics Achievement for fifth grade students and assessing its effect on the independent variables of the study using a group of equated and equivalent scales in case of each variable.
Importance Of The Study :
A- Theoritical Importance :
- This study enriches the scope of psychological research in the Arab world by introducing a new research trial in self-Efficacy and draws a spot of light on the important role self-Efficacy can play in enhancing mathematics achievement and improving mathematics learning .
- This study provides the Arabic library of psychological tests with a new scale of Mathematics self-Efficacy calibrated by Item Response Theory. Such a scale is claimed to provide objectivity & accuracy in the measurement of this variable .
- This study may provide a group of research suggestions & recommendations that help enriching the movement of scientific research .
B- Practical Importance :
- The training program designed in this study for developing Math Self-Efficacy may help students improve their achievement & performance in mathematics and its related activities .
- Mathematics teachers and advisors may make use of the results of this study while they are setting or implementing their instruction policies and strategies for enhancing the achievement level of their students .
- The advantage of linearity offered by Rasch measurement sets the opportunity for realizing accuracy and objectivity in measuring the variables of the current study .
- The advantage of parameter invariance ( item parameter invariance / person parameter invariance ) offered by Rasch measurement sets the opportunity for :
a) Withdrawing equated versions from the calibrated scale , that can be used in different measurement situations ( pre-test , after-test , and monitoring ) while overcoming the problem of test familiarity
b) Holding various invariant comparisons across different groups of examinees & items .
Problem Of The Study :
The problem of the current study can be confined to the following questions :
1) Is it possible to obtain equivalent and equated versions of the mathematics self efficacy scale using Rasch model ?
2) Is it possible to obtain equivalent and equated versions of the mathematics achievement test using Rasch model ?
3) How much is the proposed training program effective in developing Math Self-Efficacy of the examinees ?
This question involves the following two subsequent questions :
a) Does the test group outweigh the control group in the magnitude of improvement in the level of Math Self-Efficacy shortly after applying the training program ?
b) Are there relative differences among the components of Math Self-Efficacy in the magnitude of improvement as a result of self-efficacy training ?
c) Will the test group maintain the level of improvement in Math Self-Efficacy after ending the training applications ?
4) How much is the training program effective in improving the level of Math Achievement for the examinees ?
This question involves the following two subsequent questions :
a) Does the experimental group outweigh the control group in the magnitude of improvement in the level of Math Achievement shortly after applying the training program ?
b) Are there relative differences among the topics of interest of the math curriculum in the magnitude of improvement as a result of self-efficacy training ?
c) Will the experimental group maintain the level of improvement in Math Achievement after ending the training applications ?
Terms Of The Study :
• Item Response Theory : It is a contemporary approach in psychological measurement that addresses objectivity. It has managed to provide solutions to many practical testing problems as well as offered several advantages over classical measurement methods. This theory depends on a number of mathematical probabilistic models that predict the responses of the examinees to test items from the characteristics of the examinee (person parameters) and those of the individual test item (item parameters).
• Calibrating the scale by Rasch model : calibrating a scale used to assess a certain trait by Rasch model refers to the process of constructing a linear metric on which the items of that scale are scaled according to their difficulties.
• Equated tests : they are tests whose items are all calibrated on a common linear metric, where the estimated measure for a given individual will not vary whatever test is used.
• Math self-Efficacy : the researcher could define math self-efficacy as the individual’s confidence in his/her ability to learn mathematics and fulfils its related tasks . In the current study it represents in the scores of the examinees on the Math self-efficacy scale used in the study.
• The Training Program : In the current research , the training program can be executively defined as a group of procedures , activities , and practices intended to improve the levels of math self-efficacy and math achievement in the context of the mathematics curriculum for the fifth-grade students .
• Rasch Model: It is the simplest and most familiar logistic model of Item Response Theory , It assumes that the items of a given scale don’t allow guessing responses , have the same discrimination power , and vary only in difficulty . In this model the test items are calibrated according to the parameter of difficulty on one linear metric along with the examinees that are calibrated according to the parameter of ability.
Theoritical Framework Of The Study :
It included :
1- Self-Efficacy ( concept , sources , effects , related consructs , traits of self-efficacious individuals , and measurement of self-efficacy ).
2- Methods of behavior measurement ( classical theory of measurement and its deficits , Item Response Theory and its models ).
Previous Studies :
These have been categorized into the following divisions :
1. Previous studies that investigated the effect of Mathematics Self-Efficacy on Mathematics Achievement.
2. Previous studies that investigated the effectiveness of different training interventions in improving Mathematics Self-Efficacy.
3. Previous studies that used the Rasch model for calibrating and/or validating scales of Mathematics Self-Efficacy.
Hypotheses Of The Study :
1) It is possible to obtain equivalent and equated versions of the mathematics self efficacy scale using the Rasch model.
2) It is possible to obtain equivalent and equated versions of the mathematics achievement test using the Rasch model.
3) It is possible to improve the levels of mathematics self efficacy and mathematics achievement of the examinees by the proposed program.
The training program will prove effective if :
a) The experimental group outweighs the control group in the magnitude of improvement in the levels of Math Self-Efficacy and Math Achievement shortly after applying the training program.
b) The experimental group maintains the levels of improvement in Math Self-Efficacy and Math Achievement after ending the training applications.
c) There are relative differences among the components of each of the two dependent variables of the study (Math Self-Efficacy and Math Achievement) in the magnitude of improvement as a result of self-efficacy training.
Plan Of The Study:
I- Variables Of The Study :
The variables of the current study include :
1) Independent variable : this represents in the training program used for developing Mathematics Self-Efficacy in the current study.
2) Dependent variables : these represent in :
• Mathematics Self-Efficacy .
• Mathematics Achievement .
3) Control variables : these are the variables that are held under control while collecting the sample of the study so as to secure the equivalence of the control and the test groups before treatment . They include : Age , Socio-economic level of the examinees , and mathematical ability.
II- Methodology of the Study :
The current study has employed the experimental methodology through a design of equivalent groups that involves :
- An experimental group : submitted to the independent variable.
- A Control group : not submitted to the independent variable.
III- Sample Of The Study :
The sample of the current study involves :
1) the calibration sample : that is used to calibrate the items of the Mathematics Self-Efficacy Scale and those of the Mathematics Achievement Test in the current study according to Rasch model using the Winsteps computer program .
2) the experimental sample : that is used to test the hypotheses of the study . It consists of a suitable number of the fifth grade students . This sample is partitioned into a control group and a test group .
IV- Tools Of The Study :
The instrument of the current study involves the following :
• The Mathematics Self-Efficacy Scale : designed in the current study.
• Mathematics Achievement Scale for the fifth grade students : constructed by the researcher in the current study .
• A training program for the development of Math self-Efficacy : designed by the researcher in the current study .
V -Procedures of the study:
The researcher followed the following procedures for testing the hypotheses of the study :
1) Reading the literature and previous studies on self efficacy carefully for analyzing this construct , wording the hypotheses of the study , and building the tools of the study .
2) Surveying the scales of MSE for finding out and defining the most frequent aspects and dimensions of this variable
3) Constucting the tools of the study which involve:
-The MSE scale
-The Math achievement test for fifth grade students.
-The training program for improving MSE.
4) Applying the scales of the two independent variables of the study to the calibration sample , followed by calibration the two scales according to Rash Model using the winsteps statistical program , then withdrawing 3 equated and equivalent short versions of each scale to be used in the different measurement stages (pre-, post-) for testing the hypotheses of the study .
5) Conducting pre-test for both of the control and experimental groups of examinees on self-Efficacy , Math achievement & Math ability followed by verifying the equivalence of the control and experimental groups on the two independent variables of the study .
6) Applying the training program to the experimental group of examinees.
7)Conducting Post-test for both of the control and experimental groups of examinees on self-Efficacy & Math . performance.
8)Conducting the monitoring test for the members of experimental group one month and half after ending the training procedures.
9) Manipulating the results of the study statistically in order to assess the effectiveness of the training program.
VI- The Statistical Manipulation Plan :
The Following Statistical Manipulation has been made for calibrating the tools of the study and testing its hypotheses:
- Entering and grading the test data using the SPSS computer program .
- Analyzing the data according to Rasch model using the Winsteps computer program .
- Calculating the descriptive statistical measures ( mean , median , standard deviation & skewing coefficient ) for the variables of the study in pre- , post- , monitoring tests.
- Using the T-test for two independent samples to test the statistical significance of :
A. The difference between the mediums of Rasch measures of the control and expreimental groups for each of the two dependent variables of the study .
B. The difference between the mediums of change in Rasch measures of the control and expreimental groups after applying the program for each of the two dependent variables of the study .
- Using the T-test for two dependent samples to test the statistical significance of :
A. The difference between the mediums of Rasch measures of the control and expreimental groups separately in pre- and post- testes for each of the two dependent variables of the study.
B. The difference between the mediums of Rasch measures of the expreimental group in post- and monitoring tests for each of the two dependent variables of the study.
- Setting up graphical plots for comparing :
a) The mediums of Rasch measures of the control and expreimental groups
b) The mediums of change in the measures of the two groups as a result of applying the program both for the two dependent variables of the study.
c) The gain ratios for the components of each of the two dependent variables of the study .
- Using the Effect Size test to investigate the effect of the independent variable of the study ( The training program) on the two dependent variables ( M.S.E. & M.A. ).
- Using the McGuigan equation of Gain Ratio to assess the effect of the training program on the components of each of the two dependent variables of the study for the experimental group .
The Results Of The Study :
The results of the study involved the following :
• The performance of the experimental group on both the Math Self-Efficacy scale and the Math Achievement scale exhibited significant improvement shortly after applying the program.
• The performance of the control group on either of the independent variables’ scales showed no significant change shortly after applying the program.
• The experimental group has significantly outweighed the control group in the magnitude of improvement in both of the levels of the independent variables shortly after applying the program.
• The MSE component of ” Planning and organization of learning ” offered the greatest magnitude of improvement as a result of self-efficacy training in the current study ( Gain Ratio = 0.53), succeeded by the component of ” Confidence in the ability to learn and study mathematics’’ which offered a gain ratio of (0.48), and finally the component of ”Perseverance and willingness to make an effort’’ that offered the smallest gain ratio (0.18).
• The topic of ”Multiplying decimal numbers and fractions” offered the greatest magnitude of improvement as a result of self-efficacy training in the current study ( Gain Ratio = 0.19 ), succeeded by the topic of ”Dividing decimal numbers and fractions” which offered a gain ratio of (0.18), then the topic of ”Comparing fractions” which offered a gain ratio of (0.15), and finally the topic of ”Approximation’’ that offered the smallest gain ratio (0.14).
• The experimental group has maintained the improvement in both Math Self-Efficacy and Math Achievement one and half months after applying the program.