The Student Initial Survey

 

ABOUT THE PROJECT

THE EFFECT OF STUDENTS' AFFORDABLE AND COGNITIVE CHARACTERISTICS ON MATHEMATICS SUCCESS

 

 

 

PREPARED BY Ali PANAL

 

Summary

The education received by the International Organization for Economic Cooperation and Development-OECD in the fields of mathematics, science and reading skills of 15-year-old students who regularly receive formal education every three years in member and partner countries; In the International Student Assessment Program (PISA) study, which is organized to measure the skills of use in their daily lives, each semester is focused on a different field. In the study, in which our country has been participating regularly since 2003, the 2003 and 2012 cycles were mainly carried out on the field of mathematics. In this study, in the PISA 2012 application, the effect of the affective characteristics of our country students on learning mathematics is examined based on the results of the application. In the realization of the study, the results obtained from other researches in this field, mathematics teaching programs prepared by the Ministry of National Education and academic articles in the press were used. As can be understood from our study, which is a literature review; Self-efficacy and self-confidence, which are the affective characteristics of students, have an impact on learning in the field of mathematics. In other words, although the explanatory power of students' affective characteristics and mathematics performance in Turkey is significant, the relationship between them is very low. While it is seen that students with high self-efficacy in mathematics have higher academic achievement due to their greater effort towards the field; In general, it has been determined that although the students have a positive attitude towards mathematics, their success rates in mathematics lessons remain low. This result shows that there is a moderately significant relationship between students' attitudes towards mathematics and their mathematics achievement scores. As a result; In the case of providing environments that will keep our students' anxiety levels low and their self-efficacy levels high, the PISA mathematical literacy scores of our country will increase even more.

 

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Many factors affect learning at school. Some of these are factors that cannot be developed directly through the teaching-learning process, such as the student's maturity level, general ability, teacher's personality traits, and the socio-economic status of the family. These are factors that can be changed through the teaching-learning process in schools, such as interest, attitude, belief that one can be successful, and the quality of the teaching service. The first element of the mastery learning model is the student-qualified feature (Bloom). This feature is considered in two groups as cognitive entry behaviors and affective entry features. Affective input characteristics are the set of features consisting of the interests, attitudes, and the degree of belief and confidence that students will be successful in such a process as they enter a certain learning process, and it has the power to explain 25% of the variability in learning products. In other words, by making students' affective input characteristics positive, the differences between students' success can be reduced by 25%. This is possible by providing the student with the opportunity to be successful. Affective features, which are the determining factors of affective input characteristics, are examined in three groups: school-related, a certain course-related and academic self-concept. Students' attitudes towards school in general, their interest and desire to go to school show their affective characteristics about school. The affective characteristics of students emerge as a product of their school experiences.Failures in school cause new failures, and successes cause new successes. Although students develop different feelings towards some of the courses they take at school, very few of them develop negative feelings towards the whole school. In order for a student to learn a certain unit well, this student must be open to the new unit to be learned; he/she should have a desire to learn that unit and believe that he/she will make enough effort to overcome these difficulties if he/she encounters difficulties, and he/she should be confident in this regard. Academic self-concept, which is defined as the degree of belief and confidence that the student will be successful in a job with a dominant academic aspect, is defined as the attitude of the individual towards himself and is affected by the academic self-perception style and the judgments of those around him.

 

The Effect of Students' Affective Characteristics on Mathematics Achievement

The affective characteristics of students towards mathematics were defined by the Program for International Student Assessment (PISA) in 2012 with eight variables observed. These; (1) interest in mathematics, (2) instrumental motivation towards mathematics, (3) mathematical self-perception, (4) mathematical behavior, (5) mathematics work ethic, (6) self-efficacy perception towards mathematics, (7) problem solving determination, and (8) is listed as openness to problem solving. These and similar features, which are measured with a limited number of items in PISA studies, are naturally defined as students report themselves. According to the estimations obtained with the structural model, the variable with the highest explanatory power on students' affective characteristics towards mathematics and therefore on student performance is interest towards mathematics. When we look at the results of PISA 2012 in our country, it is seen that a 1-unit increase in our students' interest in mathematics provides an increase of 0.94 units in their affective characteristics towards mathematics and an increase of 0.11 units in student performance (PISA 2012). In other words, the interest in the course causes a certain increase in both the affective characteristics of the student and the success of that course.Perseverance to solve problems and openness to problem solving are seen as the affective features with the lowest explanatory power on student performance. It is seen that it causes an increase of 0.46 and 0.48 units, respectively, and an increase of 0.06 units in student performance. According to the structural model, when the lower, middle and upper proficiency levels are examined separately, there is no significant difference in terms of mathematical behavior and mathematical work ethic among the eight variables that define the affective characteristics of students towards mathematics. In terms of the other six variables, a significant difference was determined between the proficiency levels. When the significant differences are evaluated, it has been seen that the degree of having affective characteristics is higher in the higher ability levels. When the structural model was examined separately for each of the three levels, it was observed that the students' affective characteristics towards mathematics were not a significant explanatory factor in student performance at any proficiency level. As can be understood from the findings of the PISA 2012 application, it is unlikely that a positive change in the affective characteristics of students towards mathematics in Turkey will bring a solution to the problem, that is, lead to an increase in students' mathematical literacy performance. In other words, these affective characteristics of students and their explanatory power on student performance are significant but very low.Based on the results of the PISA 2003 study and published in the Journal of Eurasian Educational Research, in the academic study titled "Affective Characteristics of Students in the Program for International Student Assessment (PISA 2003) and Their Relationship with Mathematics Literacy", the students in the International Student Assessment Program (PISA 2003) Affective factors associated with their literacy are evaluated. In the study, which aimed to examine the affective variables associated with the PISA 2003 mathematical literacy of 15-year-old Turkish students using the Structural Equation Model, the affective variables expected to be related to the PISA 2003 mathematical literacy were analyzed, and the PISA Turkey data were analyzed within the framework of structural equation modeling. In the study, implicit variables examined in relation to mathematical literacy; interest in mathematics, motivation towards mathematics, anxiety about mathematics, self-efficacy in mathematics, self-confidence in mathematics, sense of belonging to school and classroom discipline and environment in mathematics lessons.The implicit variable that gives the greatest relationship with mathematical literacy is self-efficacy in mathematics. Other implicit variables that have a statistically significant relationship with mathematics literacy are observed as interest in mathematics, anxiety about mathematics, and classroom discipline and environment in mathematics lessons. In the study, in which the mathematical literacy performance of students who indicated a high interest in mathematics was found to be lower, it was also observed that the interest in mathematics variable had a small but positive indirect relationship to mathematics literacy over the variable of classroom environment in mathematics lessons. In the study, 42% of the mathematical literacy variance is explained by the structural equation model. The amount of variance explained also reveals how important affective characteristics are in explaining students' academic performance. As a result, it is seen that Turkish students generally have positive attitudes towards mathematics, but their self-confidence level in mathematics is low and their anxiety level about mathematics is high. These positive attitudes of students cannot be directed to bring higher academic success within the education system.

 

The research also provides findings related to the fact that the increase in anxiety and self-confidence levels negatively affects the classroom environment. This result can also be interpreted as a finding that some classroom management problems are experienced in classrooms. In the academic study titled "Determination of the Relationships between Academic Achievement-Self-Efficacy and Attitudes Regarding Mathematics", in which the role of affective factors on mathematics student performance of students studying in the fifth grade of primary schools was investigated, results similar to the findings obtained from the PISA study are striking. In the aforementioned study, the results of the students' attitudes towards mathematics were obtained by using the data collected by the "Math Attitude Scale" and "Mathematics Self-Efficacy Scale" developed by the researcher. In the study; students have positive attitudes towards mathematics, attitudes towards mathematics do not differ according to gender and mathematics exam score averages. When the results of the study regarding the mathematics self-efficacy levels of the fifth grade students are examined, it is seen that this level is high, it differs in favor of female students and changes depending on the scores the students get from the mathematics exams.The results of the study on the level of predicting academic achievement of mathematics self-efficacy and attitude; revealed that the scores of the students studying in the fifth grade in the mathematics exams, the scores they got from the Mathematics Attitude Scale and the scores they got from the Mathematics Self-Efficacy Scale were positively related. Also in the study; It is also among the results obtained that while the self-efficacy variable related to mathematics is a significant predictor of academic achievement, the variable of attitude towards mathematics is not a significant predictor of academic achievement. In the study, in which students' self-efficacy and attitudes towards mathematics lesson predict their mean scores in mathematics exams, it was also found that fifth grade students' scores in mathematics exams, the scores they got from the Mathematics Attitude Scale and the scores they got from the Mathematics Self-Efficacy Scale were found to be positively related. The result that there is a positive relationship between the mathematics achievement of the fifth grade students and their mathematics self-efficacy levels; When evaluated together with the results of the related research, it is revealed that the mathematics achievement of the students who see themselves as competent in mathematics, that is, with a high level of mathematics self-efficacy, may be positively affected.Therefore; School life has a very important place in students' positive attitudes and high self-efficacy perceptions in the field of mathematics. This positive relationship between attitude and self-efficacy obtained from the study; reveals that attitude and self-efficacy are affected by the same situations. Another result obtained from the study is; reveals that while the variable of self-efficacy regarding mathematics is a significant predictor of academic achievement, the variable of attitude towards mathematics is not a significant predictor of academic achievement. Considering that self-efficacy is related to coping with the difficulties encountered in a field, participating actively in the learning-teaching process, being more patient in spending more effort and time to be successful in the given task; It is expected that students will be successful in the field that they strive to learn and achieve. Based on the results obtained from the study; Since individuals with high mathematics self-efficacy put more effort into the field; academic achievement may also be higher. And also; It is not possible to say that every child who is successful in mathematics loves mathematics. Because although children do not like, they can be successful to prove themselves to their friends and teachers or to get the appreciation of their parents-teacher; Although they love / have fun and believe in its necessity, their academic success may be low because they do not make much effort.In another academic study titled "The Relationship Between Second Year High School Students' Attitudes Towards Mathematics Lesson and Achievement", which supports the results regarding the effect of students' affective characteristics on mathematics performance in the PISA 2012 results, it was determined that the attitudes of the second year students of public general high schools towards mathematics, their mathematics achievements and mathematics achievements. By examining the relationships between students' attitude scores and achievement scores, students' attitudes towards mathematics were determined by the mathematics attitude scale developed by Aşkar (1986). In the study in which the mathematics achievement of the students was determined by the mathematics achievement test prepared by the researcher, the scales were applied to 500 high school sophomore students in eight schools in Ankara. As a result of the analysis of the data related to the study, it was seen that more than half of the students had a positive attitude towards mathematics. Despite this, in the study in which more than three-fifths (68.4%) of the students were evaluated as unsuccessful according to the mathematics achievement test results, it was observed that there was a significant difference between the students' attitude scores and achievement scores. From the findings, it was seen that more than two-thirds (70%) of high school sophomore students had a positive attitude towards mathematics and were anxious about their success in mathematics. It is understood that the same students are right in their concerns, since 68.4% of the students are unsuccessful.As a result of the research, it was seen that although the students generally have a positive attitude towards mathematics, the success rate in mathematics is low, and there is a moderately significant relationship between students' attitudes towards mathematics and mathematics achievement scores. In line with these results; In the study, in which it was concluded that students' mathematics anxiety should be eliminated, it was stated that, in addition to the studies to increase the attitude towards the mathematics lesson, among the measures to be taken, it was stated that new studies could be made about the teaching situations, and the effect of the attitude on the success is explained with a percentage of 15%. It is a suggestion to determine what other 85% variables that affect mathematics achievement are. In addition, it is stated in the study that establishing a connection between the mathematics lesson and daily life will increase the success in the mathematics lesson. In addition, it is mentioned by the researchers that the factors affecting the mathematics achievement of Turkish students can be investigated and more concrete suggestions can be made to increase the mathematics achievement of the students.prof. Dr. In the article titled “Thinking Processes Achieved by Students in PISA” written by Giray Berberoğlu and published in the Hürriyet Newspaper, it was stated that students' mathematics anxiety in Turkey emerged more clearly with PISA tests, and that the models tested in PISA studies generally improved the mathematical literacy of reading skills at the student level. It is stated that it is an important variable for the students and when the mathematics self-efficacy perception, mathematics anxiety and classroom discipline variables are defined and analyzed at the school level, a significant part of the differences between schools in mathematics literacy scores is explained. reported to have positive relationships. In the article, in which it is stated that dividing students into ability groups in mathematics lessons in schools has negative relations with PISA mathematics scores, it is emphasized that students' mathematics anxiety is higher in Turkey than in OECD countries, but mathematics self-efficacy and classroom discipline seem lower than OECD countries.In the article, it was also stated that students do not feel confident in performing basic mathematical skills in situations that require using mathematics in their daily lives, and that their anxiety levels about learning mathematics and getting bad grades in mathematics lessons are quite high, according to PISA results. It is also stated that he does not listen to the lesson, there is noise in the classroom, the teachers expect the class to be silent, and the students do not study enough. It is also stated in the article that Turkish students appear better in PISA mathematical literacy scores when their anxiety level is low, self-efficacy level is high and classroom discipline is provided. In the detailed examination of the basic education and secondary education mathematics education programs revised by the Board of Education and Discipline in 2013, it was determined that the programs were generally used by the student to use technology as an effective tool, to be responsible for his/her own learning process, to make reasoning, to solve problems that he might need in daily life after this education. It is seen that it overlaps with the PISA study in terms of having skills such as constructing and evaluating.The aim of the curriculum is to enable the student to use high-level thinking skills such as estimating, analyzing, explaining, and problem solving about situations that may be encountered in daily life in a changing world. Tips on how to take this approach are also available in the programs. It is also emphasized in the programs that students should develop their affective characteristics.

 

In this sense, student behaviors that should be taken as a basis for the development of affective characteristics in secondary and high school students;

• Being aware of the contribution of mathematics to scientific and technological development

• Being aware of the importance of mathematics in real life and appreciating the benefits it provides

• Confident in mathematics and believing that you can learn mathematics

• Be patient while solving problems

• Willingness to learn mathematics and enjoying dealing with mathematics

• Believing that mathematics improves thinking skills

• Studying mathematics effectively

• Doing studies other than what needs to be done in the mathematics course

• Willingness to take part in mathematical studies

• Believing that mathematics improves one's creativity and aesthetic understanding

• Being aware of the aesthetic aspect of mathematics

• Being aware of the fun side of mathematics

• Being aware of the role of mathematics in making logical decisions (analytical thinking) Some indicators of high school students' self-regulation in mathematics are;

• Self-motivation in math-related subjects

• Guiding oneself to reach these goals by setting goals for the mathematics lesson.

• Doing what is requested in the mathematics lesson on time and regularly

• Self-questioning in mathematical studies

• Asking for help from family, friends and teachers (math-related issues) when needed

• Studying the math lesson efficiently

• Not being excited and panicky in math exams

• Being regular in the work done in the math class

• It is listed as taking care when using tools and materials in the mathematics lesson.

MEB TTKB a, S VI, MEB TTKB b, S IX-X). In addition, in order to develop students' skills in problem solving, which is a sub-field of application in PISA studies; In the programs in which the necessity and importance of understanding the problem, planning the solution, applying the plan, checking the correctness and validity of the solution, generalizing the solution and posing similar/original problem processes are emphasized, the development of students' affective skills, students' positive attitudes towards mathematics, their self-confidence, their understanding of mathematical values. It is important for them to have self-regulation skills and to use self-regulation skills. It is also important for teachers to consider that students' skills can develop in the process, both for the academic and emotional development of the student. In addition to the development of students' mathematical content and skills, importance should be given to the development of their productive tendencies. In other words, students should be made to see mathematics as a sensible, useful and worthwhile field. In this context, students' affective development, attitude, self-confidence and mathematics anxiety should also be taken into consideration. The most important feature of the mathematics curriculum is “Every child can learn mathematics.” is based on the principle. Although this principle is an extremely important and correct approach, it contradicts the way of thinking that believes that mathematics should be learned only by those who are interested and talented in the subject area. In fact, it should be aimed for every student to reach the achievements discussed in basic education.Another goal of the programs is to develop students' thinking about mathematics, understanding problem-solving strategies and appreciating mathematics as an important tool in real life, in addition to gaining basic concepts and skills. The role of the student in the activities is now to discover mathematics and to construct the knowledge by reasoning and reaching the result himself. At this point, the process to be put into practice is student-centered activities. The dimensions of the programs and the findings obtained as a result of scientific studies also give important clues about what should be done while teaching mathematics in schools. Since the achievements and higher-order thinking processes in mathematics programs are expanded and repeated at every grade level, they have a spiral structure. This allows for learning to be considered as a process and for the achievements to be developed at later grade levels. In addition, this structure shows that the perception of learning outcomes that can be achieved in a short time is unrealistic.Studies show that especially students need to have confidence in themselves in the field of mathematics. It is a known fact that there is a significant relationship between the feeling of being successful in mathematics and success in mathematics. This dimension is partially covered in the above statements. The use of tools is not a frequently observed method in mathematics lessons. Mathematics lesson takes place on the blackboard as a subject transfer to students in a very abstract scope. As a result, students do not participate in the lesson, in other words, the process is handled far from being student-centered. Especially, students who have developed the feeling of "I am successful in mathematics" have higher mathematics achievement. In other words, students need to feel that they are successful in mathematics. More importantly, it is easier to teach students who feel good at math. Concepts related to mathematics are abstract in nature. However, studies carried out abstractly and on the mental development of students seriously damage students' self-confidence in the field of mathematics, and the feeling of "I am not good at mathematics" becomes more and more permanent.Teachers do not focus on the thinking processes, since the learning outcomes are defined in a subject-dimensional way, the most difficult problems related to the subject are tried to be taught to the students for different reasons. In addition, it is observed that students who do not complete their mental development try to memorize the taught subjects at an algorithmic level, and this emerges as an important problem (CITO, 2010).

Conclusion: PROJECT PLANNING PHASE

 

 

As can be understood from the academic studies on the effect of students' affective characteristics on mathematics learning;

• Students' affective input characteristics can explain 25% of the variability in learning products. In other words, by making students' affective input characteristics positive, we can reduce the differences between students' achievements by 25%. This is possible by providing the student with the opportunity to be successful.

 

• According to the PISA results, our students do not feel confident in performing basic mathematical skills in situations that require using mathematics in their daily lives, and their anxiety levels about learning mathematics and getting bad grades in mathematics lessons are not seen as high. It is also stated that the classroom environment is generally in a structure where the students do not listen to the lesson, there is noise in the classroom, the teachers expect the class to be silent, and the students do not study enough. In cases where the level of anxiety is low, self-efficacy is high, and classroom discipline is provided, Turkish students' PISA mathematical literacy scores seem to be better.

• Mathematics should be taught in an environment where students actively participate in the process. Students should be individuals who participate in the lesson and show conceptual development as a result of this participation, not listening. This should be accomplished largely using tools and equipment.

• Mathematics should be taught in self-confident student groups. Especially, students who have developed the feeling of "I am successful in mathematics" have higher mathematics achievement. More importantly, it is easier to teach students who feel good at math. Students should be made to feel that they are successful in mathematics.

• Mathematics should be taught with concrete examples. Abstract lessons and studies on students' mental development seriously damage students' self-confidence in the field of mathematics, and the feeling of "I am not good at mathematics" becomes more and more permanent.

• The implicit variable that gives the greatest relationship with mathematical literacy is self-efficacy in mathematics. Other implicit variables that have a statistically significant relationship with mathematics literacy are observed as interest in mathematics, anxiety about mathematics, and classroom discipline and environment in mathematics lessons.

• Since individuals with high mathematics self-efficacy put more effort into the field; academic achievement may also be higher. And also; It is not possible to say that every child who is successful in mathematics loves mathematics.

• Although students in our country generally have a positive attitude towards mathematics, their success rates in mathematics lessons remain low. This shows that there is a moderately significant relationship between students' attitudes towards mathematics and their mathematics achievement scores.

Source:

1. Bloom, B. S. (1979). Human characteristics and school learning. trans. D. A. Ozcelik). Ankara: National Education Printing House. 2. National Final Report of PISA 2012 Research, S 143,144, ODSGM, MEB 3. “Affective Characteristics of Students in the Program for International Student Assessment (Pisa 2003) and Their Relationship with Mathematical Literacy” Eurasian Journal of Educational Research (EJER), . Jul2010, Issue 40, p93-113. 21p 4. “Determination of Relationships Between Academic Achievement-Self-Efficacy and Attitudes Regarding Mathematics”, The Journal of Academic Social Science Studies International Journal of Social Science Doi number:http://dx.doi.org/10.9761/JASSS2621, Number: 31 , p. 343-366, Winter II, 2015 5. “The Relationship Between Second Year High School Students' Attitudes Towards Mathematics Lesson and Their Success” Dr.Murat Peker, Prof. Dr. Şeref Mirasyedioğlu, Pamukkale University Faculty of Education Journal Year:2003 (2) Issue:14 6. “Thinking Processes Achieved by Students in PISA” Prof.Dr. Dr. Giray Berbereoğlu, METU Faculty of Education, Hürriyet Newspaper, 07.04.2014 7. “Developing High Level Thinking Skills in Mathematics Lesson”, CITO Magazine November-December 2010 8. TTKB, Secondary School 9-12 Mathematics Curriculum, TTKB, MEB 9 TTKB, Primary School 5-8 Grade Mathematics Curriculum, TTKB, MEB