Vijayalakshmi, Prof Ch. (2011). DEVELOPMENT OF A TRAINING PACKAGE IN SCHOOL MATHEMATICS (DTPSM) FOR PRE-SERVICE AND IN-SERVICE TEACHERS. Unpublished. ERIC, Education

Objectives of the study

• To identify the difficult units/ concepts for teachers to teach in secondary school mathematics.

• To identify the difficult units/concepts for students to learn in secondary school mathematics.

• To develop Instructional strategies for teaching the selected basic mathematical concepts, useful for pre-service and in-service teachers to improve the quality of mathematics education at school level.

• To validate the effectiveness of the developed Instructional Strategies.

Sample selected for the study

• To find out the difficult units and the most difficult unit in each of the classes VIII, IX and X, to teach in mathematics, opinionnaire was given to 90 mathematics teachers.

• To find out the difficult units and the most difficult unit in each of the classes VIII, IX and X, for the pupils to learn in secondary school mathematics, opinionnaire was given to 90 students in each of the three classes namely VIII, IX and X, arriving to a total of 270 students from the same schools where the sample of teachers is drawn.

• It was difficult to get two equivalent groups as experimental and control groups for the experiment, the PI used two intact class groups in the study. One intact class group was selected randomly as experimental group and the other as control group. This process was repeated for the standards VIII, IX and X.

Tools used for the Study
The Pl used the following materials and tools for the study.

• Identifying the most difficult Units/Concepts to teach/learn
  Using three opinionnaires, the difficult Units/Concepts to teach for teachers and to learn for students were identified at the Standards VIII, IX and X. Out of them the most difficult unit/concept at each of the Standards VIII, IX and X were identified as 'Polynomials, 'Motion Geometry and 'Lnear Programming respectively.

• Instructional Strategies
  Three Instructional Strategies for teaching the identified most difficult basic mathematical concepts 'Polynomials, 'Motion Geometry' and Linear Programming were constructed and validated by the experimental method. The experiments were conducted at standards VIII, IX and X. The Instructional Strategies were used as treatment to the experimental
  groups.

• Achievement Test for the Concept 'Polynomials'
  The Pl constructed and standardized an Achievement test for the concept 'Polynomials'. This test was treated as the pre test and post test in the experimental design selected for the validation of the Instructional Strategy for the concept 'Polynomials.

• Achievement Test for the Concept 'Motion Geometry'
  An Achievement test for the concept Motion Geometry' was constructed and standardized. This test was used as pre test and post test in the experimental design for the validation of the Instructional Strategy of the concept 'Motion Geometry.

• Achievement Test for the Concept 'Linear Programming'
  The PI constructed and standardized an Achievement test for the concept 'Linear Programming'. This test was treated as the pre test and post test in the experimental design selected for the validation of the Instructional Strategy for the concept 'Linear Programming’

Method of the study.

Experimental design was selected for the study. The Quasi Experimental design with pre test-post test Non equivalent group was used as the experimental design. The experimental groups was used as the experimental design. The experimental groups were taught by the newly developed Instructional strategy and the control groups were taught by the Conventional Method of teaching mathematics. The experiment was conducted at three standards VIII, IX and X.

Statistical Techniques used in the Study
The major statistical techniques used in the study were Preliminary Analysis and Comparison of Means (Effect Size and Test of Significance of Difference between Means).

• Preliminary Analysis
  The important statistical constants of the variables in the study arithmetic mean, median, mode, Standard deviation, Skewness and Kurtosis - were estimated for standards VII, IX and X.
  
  

• Comparison of Means
  The comparison of the mean Achievement scores in the basic mathematical concepts obtained in the pre test and post test of the experimental and control groups were done by the statistical techniques Effect Size' and Test of Significance of Difference between Means in three standards VIII, IX and X

Findings of the study

The major findings of the study are given below

• Comparison of Means
  The comparison of the mean Achievement scores in the basic mathematical concepts obtained in the pre test and post test of the experimental and control groups were done by the statistical techniques Effect Size' and Test of Significance of Difference between Means in three standards VIII, IX and X.

• Effect size

The comparison of Achievement Score means by using the statistical technique ‘Effect size’ was done for three standards VIII, IX and X.

It was found that the new Instructional strategies of the concepts, Polynomials, Motion Geometry and Linear Programming improved the performance of students significantly.

The mean achievement scores obtained in the post test of the experimental and control groups were compared using effect size in standards VIII, IX and X.

The obtained values of Effect Size indicate that an average student in the experimental group of these standards had an Achievement significantly greater than that of the control group

• Test of Significance of Difference between Means

The comparison of means of Achievement scores using the statistical technique Test of Significance in Difference between means' was done. The pre test scores of the experimental and control groups of standards VII, IX and X were compared.

The obtained ‘t' values indicate that in standards VIII and X there is no significant difference between the mean pre test scores of the experimental and control groups. That is both the groups were equivalent in terms of the pre test scores. But in standard IX no significant difference between the mean pre test scores of the experimental and control group was noticed. That is the experimental

and control groups of standard IX were not equivalent in terms of pre test scores.

The comparison of Mean post test Achievement scores of the experimental and control groups of Standards VIII, IX and X were done by the test of significance of difference between means.

It was found that there is significant difference between the Mean post scores of the experimental and control groups of standards VIII, IX and X. The significant values of 't indicate the better performance of students of the experimental groups in the post test. This is due to the effect of the treatment (teaching the concerned mathematical concepts by the newly developed Instructional Strategies) given to the experimental groups.

Educational Implications

The present study revealed that the newly developed Instructional strategies based on Piaget and Vygotsky’s theories prepared for teaching the three selected basic mathematical concepts each from standards VIII, IX and X are very effective than the existing conventional method of teaching mathematics.

Following the structure of the developed Instructional strategies, for teaching any mathematical concept, Instructional Strategies can be developed by a mathematics teacher for the clear concept formation and attainment and also to prevent the students in committing mistakes by their students in secondary school mathematics.

The existing system of mathematics teaching considers mathematics teaching considers mathematics learning as mastering a predetermined body of knowledge and procedures. The teachers job is presenting the subject matter in small, easily manageable pieces and demonstrating correct procedures. Then students individually practice exercises. But this approach alone is

not found to be educationally and psychologically sound. This is one of the major reasons for the students, committing mistakes, becoming slow in learning and ultimately ending in either 'drop out' or stagnation.

The Pl found that the newly developed instructional Strategy enables the students to learn to think mathematically and make sense in mathematics. It also develops collaborative learning and communication skills (mathematical as well as language) in students Students develop problem solving capacities and experiences of the actual mathematical process.

This approach reduces the gap between the teacher and students as they work together in discussions, in joint activities academic conversations, exchange ideas and so on. This gives ample opportunities for the teacher to understand the level of attainability of each student.

Adopting this newly developed instructional Strategy in the secondary school mathematics education, students can acquire the basic mathematical concepts, which is essential for the content mastery in mathematics. This approach reduces committing mistakes and most of the other problems related to teaching learning of mathematics at secondary school mathematics education.

Keyword(s): In-service teachers, Pre-service teachers, Instructional Strategy, Training Package ,