The document summarizes a study that investigated the views of primary teachers and pre-service teachers on the misconceptions primary school students have about fractions. The teachers stated that students most often had difficulties representing fractions with models, understanding the concepts of the numerator and denominator, ranking fractions, solving problems, reading and writing fractions, distinguishing fraction types and converting between them, and placing fractions on a number line. They reported misconceptions with these concepts, such as thinking the numerator and denominator are separate numbers rather than parts of a whole. The study aimed to help teachers address common student misconceptions to improve fractional understanding.
The study aimed at investigating the levels of geometrical thinking among students receiving blended learning in Jordan. The study sample consisted of (104) students/teachers of open education systems in Jordan for the 2015-2016 academic year. In order to answer the questions of study, the researcher developed a scale of geometric thinking, it is validity and reliability has been verified. The results of the study showed a low level of geometrical thinking among students receiving blended learning. The percentage of students in the first level (visual) (51%), the percentage of students in the second level (descriptive) (15%), and the percentage of students in the third level (logical) (3%). Also it showed differences in the levels of geometric thinking between males and females in favor of males, as well as differences in the level of geometrical thinking between students from the scientific stream and students from the literary stream in favor of scientific stream. In the light of the results of the study, the researcher recommends that pre-service teachers should be trained on programs contains geometrical thinking at open learning universities.
The affective aspects must be owned by students in a lesson, where the
affective aspects will have a relationship with the cognitive aspects of a
student, therefore this study aimed to determine whether there is a
relationship between students 'mathematical dispositions and students'
mathematics learning outcomes. Using a mixed method and a sequential
explanatory plan, the research was undertaken by first collecting quantitative
data and then continuing to collect qualitative data. Where, the sample count
in this study was 413 students from junior secondary schools 18 in Jambi
City, Indonesia who used a total sampling technique. Data were then
analyzed with the help of SPSS 21 application to find descriptive statistics in
the form of mean, min, max, and category as well as inferential statistics
using Pearson Product Moment. The results obtained in this study dominate
both the mathematical disposition of pupils and the learning outcomes of
pupils in mathematics. This was reinforced by the existence of a relationship
between mathematical disposition and student learning outcomes in
mathematics which is indicated by the obtained sig <0.05. This means that
the mathematical disposition of students which includes the affective aspect
of students has a relationship with the cognitive aspect, by having a good
affective aspect, the cognitive aspects of the student are also good.
This study aims to produce a learning trajectory using the mathematical modeling in helping students to understand the concept of algebraic operations. Therefore, the design research was chosen to meet the research aims and to give in formulating and developing local instructional theory in learning algebraic operations.Learning trajectory designed in the early phases and tested on 34 seven-grade students in SMP N 10 Palembang. Data collection was conducted through observation by recording the learning process that occured in the classroom and students’ group work was evidenced by video and photos. Data was analyzed qualitatively by describing actual learning which happened in pilot experiment and teaching experiment. There are 3 learning activities in the design of this study. These 3 activities are designed based on the steps of the Mathematical Modeling, activity 1 meaning of algebraic expressions, activity 2 addition of algebraic and activity 3 subtraction of algebraic. Based on the result, it can be concluded that activity which has been designed can help the students in learning algebraic operations using mathematical modeling. Used mathematical modeling can help student solve the problems and understand concept are structured using the assumptions and model start they design so gradually developed into formal mathematics.
Analysis of Students in Difficulty Solve Problems TwoDimentional Figure Quadr...IOSRJM
This research is a descriptive study that aims to determine the difficulty of concepts, principles difficulty and skill difficulties experienced by students of SMPN 8 Makassar to solve problems, specifically about waking flat rectangle. The subject of this research was the seventh grade students of SMPN 8 Makassar in the academic year 2015/2016 consisting of 5 classes of 200 students, while research subjects were students of class VII SMPN 8 Makassar as many as 35 students. The data collection is done by providing an instrument in the form of a test which consists of 5 items essay in the classroom in order to obtain a score of each kind of level of difficulty with descriptive analysis. The results were obtained percentage score of the degree of difficulty concept was 71.43% categorized as moderate difficulty level, the difficulty level of the principles is 25.71% categorized as very low level of difficulty, the difficulty level of skill 20% categorized the degree of difficulty is very low.
The Application of Bruner’s Learning Theory on Teaching Geometric at Smp Nege...IJAEMSJORNAL
This study aimed to find out the activity and learning outcomes of the eight grade mathematics students at SMP N.2 Sipahutar in academic year 2017/2018 on the application of Bruner's theory on the subject of parallel lines. The subject of this research was the eight grade students of SMP N.2 Sipahutar in academic year 2017/2018, while the object of research was the result of learning and students’ activity while learning with the application of Bruner's theory on the subject of parallel line. This research was a descriptive research, and the instrument of data collection used was the test in the form of description and students’ activity observation sheet. Based on the result of data analysis, the results of the research are: (1) The average score of learning result obtained by students is 24.64 with the average grade 77.02 or with the percentage of mastery level of 77.02%. It shows that the students' level of mastery is still classified as moderate. (2) Student's learning completeness: a) Persuasion ability, many students who completed the study were 27 students, while the unfinished study was 4 students, b) Classical absorption, from 31 students there are 27 students or 93.55% completed the study, while the unfinished study is 4 students from 31 students or 6.45%. It shows that classically, the students' learning completeness is achieved; (3) Achievement of specific learning objectives was over 65.0%. (4) Students’ activity, activity level on first learning is equal to 75,71 and the mean of students’ activity reliability level is equal to 82,62%; students’ activity level on the second learning is equal to 88,82 and the mean of students’ activity reliability level is equal to 84,61%, it concluded that there is increase of students’ activity during learning.
The study aimed at investigating the levels of geometrical thinking among students receiving blended learning in Jordan. The study sample consisted of (104) students/teachers of open education systems in Jordan for the 2015-2016 academic year. In order to answer the questions of study, the researcher developed a scale of geometric thinking, it is validity and reliability has been verified. The results of the study showed a low level of geometrical thinking among students receiving blended learning. The percentage of students in the first level (visual) (51%), the percentage of students in the second level (descriptive) (15%), and the percentage of students in the third level (logical) (3%). Also it showed differences in the levels of geometric thinking between males and females in favor of males, as well as differences in the level of geometrical thinking between students from the scientific stream and students from the literary stream in favor of scientific stream. In the light of the results of the study, the researcher recommends that pre-service teachers should be trained on programs contains geometrical thinking at open learning universities.
The affective aspects must be owned by students in a lesson, where the
affective aspects will have a relationship with the cognitive aspects of a
student, therefore this study aimed to determine whether there is a
relationship between students 'mathematical dispositions and students'
mathematics learning outcomes. Using a mixed method and a sequential
explanatory plan, the research was undertaken by first collecting quantitative
data and then continuing to collect qualitative data. Where, the sample count
in this study was 413 students from junior secondary schools 18 in Jambi
City, Indonesia who used a total sampling technique. Data were then
analyzed with the help of SPSS 21 application to find descriptive statistics in
the form of mean, min, max, and category as well as inferential statistics
using Pearson Product Moment. The results obtained in this study dominate
both the mathematical disposition of pupils and the learning outcomes of
pupils in mathematics. This was reinforced by the existence of a relationship
between mathematical disposition and student learning outcomes in
mathematics which is indicated by the obtained sig <0.05. This means that
the mathematical disposition of students which includes the affective aspect
of students has a relationship with the cognitive aspect, by having a good
affective aspect, the cognitive aspects of the student are also good.
This study aims to produce a learning trajectory using the mathematical modeling in helping students to understand the concept of algebraic operations. Therefore, the design research was chosen to meet the research aims and to give in formulating and developing local instructional theory in learning algebraic operations.Learning trajectory designed in the early phases and tested on 34 seven-grade students in SMP N 10 Palembang. Data collection was conducted through observation by recording the learning process that occured in the classroom and students’ group work was evidenced by video and photos. Data was analyzed qualitatively by describing actual learning which happened in pilot experiment and teaching experiment. There are 3 learning activities in the design of this study. These 3 activities are designed based on the steps of the Mathematical Modeling, activity 1 meaning of algebraic expressions, activity 2 addition of algebraic and activity 3 subtraction of algebraic. Based on the result, it can be concluded that activity which has been designed can help the students in learning algebraic operations using mathematical modeling. Used mathematical modeling can help student solve the problems and understand concept are structured using the assumptions and model start they design so gradually developed into formal mathematics.
Analysis of Students in Difficulty Solve Problems TwoDimentional Figure Quadr...IOSRJM
This research is a descriptive study that aims to determine the difficulty of concepts, principles difficulty and skill difficulties experienced by students of SMPN 8 Makassar to solve problems, specifically about waking flat rectangle. The subject of this research was the seventh grade students of SMPN 8 Makassar in the academic year 2015/2016 consisting of 5 classes of 200 students, while research subjects were students of class VII SMPN 8 Makassar as many as 35 students. The data collection is done by providing an instrument in the form of a test which consists of 5 items essay in the classroom in order to obtain a score of each kind of level of difficulty with descriptive analysis. The results were obtained percentage score of the degree of difficulty concept was 71.43% categorized as moderate difficulty level, the difficulty level of the principles is 25.71% categorized as very low level of difficulty, the difficulty level of skill 20% categorized the degree of difficulty is very low.
The Application of Bruner’s Learning Theory on Teaching Geometric at Smp Nege...IJAEMSJORNAL
This study aimed to find out the activity and learning outcomes of the eight grade mathematics students at SMP N.2 Sipahutar in academic year 2017/2018 on the application of Bruner's theory on the subject of parallel lines. The subject of this research was the eight grade students of SMP N.2 Sipahutar in academic year 2017/2018, while the object of research was the result of learning and students’ activity while learning with the application of Bruner's theory on the subject of parallel line. This research was a descriptive research, and the instrument of data collection used was the test in the form of description and students’ activity observation sheet. Based on the result of data analysis, the results of the research are: (1) The average score of learning result obtained by students is 24.64 with the average grade 77.02 or with the percentage of mastery level of 77.02%. It shows that the students' level of mastery is still classified as moderate. (2) Student's learning completeness: a) Persuasion ability, many students who completed the study were 27 students, while the unfinished study was 4 students, b) Classical absorption, from 31 students there are 27 students or 93.55% completed the study, while the unfinished study is 4 students from 31 students or 6.45%. It shows that classically, the students' learning completeness is achieved; (3) Achievement of specific learning objectives was over 65.0%. (4) Students’ activity, activity level on first learning is equal to 75,71 and the mean of students’ activity reliability level is equal to 82,62%; students’ activity level on the second learning is equal to 88,82 and the mean of students’ activity reliability level is equal to 84,61%, it concluded that there is increase of students’ activity during learning.
Developing a Learning Trajectory on Fraction Topics by Using Realistic Mathem...iosrjce
This research and development was purposed at (1) developing a learning trajectory on fraction
topics by using Realistic Mathematics Education approach in Primary School; and (2) determining the validity,
practicality, and the effectiveness of the learning trajectory. The results of this research were (1) a learning
trajectory on fraction topics in the form of Teacher’s Guide Book and Student’s Book. (2) Teachers’ Guide Book
and the Student’s Book of learning trajectory were considered valid, practical and effective after being judged
by experts in Mathematics Educators, Language Educators, Experienced Teachers and an Educationalist.
Based on the research results, it can be concluded that the learning trajectory on Fraction Topics by using
Realistic Mathematics Education Approach can be effectively used to improve the learning effectiveness on
Fraction Topics in Primary School.
This research aimed to produce a learning trajectory which could help students to understand the concept of permutations through role-playing activity in the election of chairman and vice-chairman of Intra School Students Organization. This research was a design research method through three stage, 1) preliminary design/preparing for the experiment were used to design the Hypothetical Learning Trajectory, 2) design experiment was a Hypothetical Learning Trajectory test phase consisting of pilot and teaching experiment, 3) retrospective analysis. It was Indonesia’s Realistic Mathematics Education Approach at tenth grade of Senior High School No 15 Palembang. Data collecting technique were obtained from observations, recorded videos, photos, students’ sheet activities, and field documentation. The result of this research was a learning trajectory which has three activities that could help student to understand the concept of permutations, there are: 1) the students could determine the form of administrative committee and calculate the number of formed groups formation in the election from 2, 3, 4 and 5 nominated candidates, 2) Students could determine the number of groups’ formation convert into the closest form of the multiplication and the factorial, 3) by using the students understanding of factorial, students found the concept of permutations form: nPr
This research is aimed at finding out: 1) the influence of discovery learning model with RME approach on Mathematics learning achievement; 2) the influence of interpersonal intelligence on Mathematics learning achievement; 3) the interaction between discovery learning model with RME approach and interpersonal intelligence on Mathematics learning achievement. The research was conducted at one of the state Elementary Schools in Banjarsari sub-district, Surakarta. The method used in this research was quasiexperimental method with 2x3 factorial design. Hypothesis test was done by two-way variance ANOVA test with different cells. It can be concluded that the discovery learning model with RME approach gives better influence on the Mathematics learning achievement than the direct learning model. Students having high interpersonal intelligence category get better Mathematics learning achievement than those having medium and low category. The students having medium interpersonal intelligence get better Mathematics achievement than those having low category. There is no interaction between learning model and interpersonal intelligence on Mathematics learning achievement.
The study determined the arithmetic verbal problem solving skills of primary
school students and to examine them according to grade level and
mathematics achievement variables. The study was designed according to
the relational survey model, one of the quantitative research methods. The
population of the research consists of students studying in public primary
schools in the central districts of a large city in the south of Turkey. The
sample consisted of 1,865 students determined according to the
disproportionate stratified sampling method. The "arithmetic verbal problem
test for students" prepared by the researchers was used as a data collection
tool. As a result of the research, it was revealed that the students were most
successful in the problems of combining and separating with “consequence
unknown”, then “with change unknown” and “initial unknown”, but they
were less successful in part-whole type problems. Thus, it was concluded
that as the mathematics achievement and grade levels of the students
increased, their success in solving verbal problems also increased.
Purpose: This study aims to identify the problem solving abilities possessed by junior high school students. The type of research used is quantitative which uses a research design survey. The sample of this study is 98 students taken based on purposive sampling techniques. This study uses descriptive statistics to analyze the data generated. From the results of the analysis that has been done, it was found that there is a problem solving indicator by students in mathematics which is a indicated by the indicators of planning a solution which has a good category of a 56.1% (55 of 98) students, the indicator of problem solving has a good category of a 56.1% (55 out of 98) students, indicators of a problem solving planning had a good category of a 54.1% (53 of 98) students, and an indicator of understanding a problem had a good category of a 60.2% (59 of 98) students.
This study aimed to produce a learning path that can help students
understand the concept of percent using the context of an egg rack. This
study used a design research method through the Indonesian Realistic
Mathematics Education approach which was carried out at Elementary
School No. 2 Gumawang, Indonesia. Data were obtained through
observation, photos, video recordings, student activity sheets, and field
documentation. The result of the research was a learning trajectory
consisting of three activities; first, students explore their knowledge of egg
racks which are very close to students' self-life, secondly, students change
the problem into a bar form based on students' knowledge of egg racks, then
students change the problem into fractions and students change the fraction
with the denominator one hundred, third, students solve the percent problem
in a more complicated form. The activities that have been produced and
tested on percent learning using the context of an egg rack, can help students
to better understand the concept of percent.
The aim of the study is to develop an understanding of the kinds and sources errors and misconceptions that characterise students’ learning of school algebra. Systematic random sampling was used to draw sixty-five participants from a population of two hundred and twenty-three form three students. A cross sectional survey design was employed to collect data using written tests, a structured questionnaire and interviewing of the students from one high school in Zimbabwe. Content analysis technique was applied to textual data from three sources in order to determine the types of errors and misconceptions. The main findings are that both procedural and conceptual errors were prevalent that errors and misconceptions can be explained in terms of the students’ limited understanding of the nature of algebra; in particular their fragile grasp of the notion of a variable. Sources of misconceptions could be explained in terms of the abstract nature of algebra Mathematics educators should embrace errors and misconceptions in their teaching and should not regard them as obstacles to learning but rather engage with them for better understanding of algebraic concepts by students. Future studies can be carried on systematic errors as one of the ways of improving students’ understanding school mathematics.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
The purpose of this research is to analyze the improvement of students' mathematical literacy ability through the use of mathematics teaching materials with metacognitive approach guidance. This research will be held in the city of Kendari to the subject of this research target is students who are at grade 5 Land in Junior High VIIID Kendari years lessons 2017/2018 with many limited scale trial class is only required as much as 1 class. To know the significance of the increase in the literacy abilities of students using paired t-test. Data processing using the SPSS program with criteria if α=0,05 then there is an increased of student's mathematical literacy ability. The results of the analysis on the stages of the evaluation shows the learning materials with metacognitive approach guidance can provide better against an increase in student learning. The ability of the early mathematical literacy against students is very less because of learning during this time students have not been directed with the ability of mathematical literacy. After the students get learning by using learning materials through metacognitive approach guidance, the ability of mathematical literacy students’ level 3 and level 4 underwent significant improvement.
This quantitative descriptive study aims to describe the Mathematical Literacy of Grade 5 of Primary Students regarding their mathematical problem-solving abilities. The samples of this study were 35 5th-gradestudents at Muhammadiyah Condongcatur Elementary School in academic year 2017/2018. The data were collected through observations and tests with five questions containing indicators of mathematical literacy regarding mathematical problem-solving abilities; two experts have validated the test instruments. Moreover, the test estimated Cronbach's alpha of 0.749 proved reliability. The data analysis in this study was carried out descriptively based on the average score, the standard deviation, the maximum score, the minimum score, the total score, and the percentage correct answer. The results showed that the mathematical literacy of the 5th-grade students at SD Muhammadiyah Condongcatur was generally at the high category (indicated by the problem-solving abilities). Students have been able to understand a problem, to use logic to describe the solution to a problem, and to choose the most appropriate solution to solve a problem.
The Investigation of Primary School Students’ Ability to Identify Quadrilater...theijes
In Vietnamese mathematics curricula, primary school students explicitly learn the concept of quadrilaterals such as parallelogram, rhombus, rectangle, square and trapezoid in the Grades 3, 4 and 5. They are presented individually, and there is no comparison between their characteristics. Therefore, the students will be difficult to recognize the relationships among kinds of quadrilaterals. The results of an investigation of 186 primary school students revealed that most of them found it easy to identify squares and rectangles but many of them asserted that “a square is not a rectangle”
Mathematical problem solving was an crucial skill to be mastered by primary
school student so that will help student to unravel their problems encountered
in everyday life. By using the realistic mathematics approach, stundents learn
mathematical concept based on reality or scope around students. This study
aimed to develop an eligible learning materials and test the effectiveness of
learning materials based on realistic mathematics education to enhance the
problem solving skill of primary school students. This research and
development study was conducted in Sawangan Subdistrict, Magelang
Regency, Central Java, Indonesia. The testing subjects consisted of 12
students in the the preliminary field, there were 42 students in the main field,
and 90 students in the operational field that divided into experiment dan
control class. The data were collected by interviews, observation, and tests.
The analyzing N-gain score and t-test with a significant level of 0.05 done to
find out th effectiveness of the teaching materials. The developed of realistic
mathematics eduation learning materials is feasible and effective in
improving problem solving skill with significance value of 0.000 (p≤0.05). It
can enhance the problem solving skills of 4
th
grade elementary school.
Engineering Technology Students’ Perception towards Promoting Interaction for...iosrjce
Classroom social environment is very important in academic life because it can affect students’
lifestyle in terms of their studies. One of the important elements in getting positive classroom social environment
is interaction amongst the students. The objective of this study is to understand and examine the engineering
technology students’ perceptions towards promoting interaction for the classroom social environment at the
Faculty of Engineering Technology (FTK), Universiti Teknikal Malaysia Melaka. This study investigated the
perceptions of 177 second year students from four different departments taking mathematics subject. A set of
questionnaire that covers questions regarding students’ perceptions towards promoting interaction by
mathematics lecturers and also their classmates was distributed to the students. From the findings, a conclusion
was drawn regarding their perceptions towards promoting interaction for the classroom social environment.
The result shows that students have a very good perception in increasing a positive social environment where
both parties, which are lecturers and classmates, play an important role in promoting interaction
Developing a Learning Trajectory on Fraction Topics by Using Realistic Mathem...iosrjce
This research and development was purposed at (1) developing a learning trajectory on fraction
topics by using Realistic Mathematics Education approach in Primary School; and (2) determining the validity,
practicality, and the effectiveness of the learning trajectory. The results of this research were (1) a learning
trajectory on fraction topics in the form of Teacher’s Guide Book and Student’s Book. (2) Teachers’ Guide Book
and the Student’s Book of learning trajectory were considered valid, practical and effective after being judged
by experts in Mathematics Educators, Language Educators, Experienced Teachers and an Educationalist.
Based on the research results, it can be concluded that the learning trajectory on Fraction Topics by using
Realistic Mathematics Education Approach can be effectively used to improve the learning effectiveness on
Fraction Topics in Primary School.
This research aimed to produce a learning trajectory which could help students to understand the concept of permutations through role-playing activity in the election of chairman and vice-chairman of Intra School Students Organization. This research was a design research method through three stage, 1) preliminary design/preparing for the experiment were used to design the Hypothetical Learning Trajectory, 2) design experiment was a Hypothetical Learning Trajectory test phase consisting of pilot and teaching experiment, 3) retrospective analysis. It was Indonesia’s Realistic Mathematics Education Approach at tenth grade of Senior High School No 15 Palembang. Data collecting technique were obtained from observations, recorded videos, photos, students’ sheet activities, and field documentation. The result of this research was a learning trajectory which has three activities that could help student to understand the concept of permutations, there are: 1) the students could determine the form of administrative committee and calculate the number of formed groups formation in the election from 2, 3, 4 and 5 nominated candidates, 2) Students could determine the number of groups’ formation convert into the closest form of the multiplication and the factorial, 3) by using the students understanding of factorial, students found the concept of permutations form: nPr
This research is aimed at finding out: 1) the influence of discovery learning model with RME approach on Mathematics learning achievement; 2) the influence of interpersonal intelligence on Mathematics learning achievement; 3) the interaction between discovery learning model with RME approach and interpersonal intelligence on Mathematics learning achievement. The research was conducted at one of the state Elementary Schools in Banjarsari sub-district, Surakarta. The method used in this research was quasiexperimental method with 2x3 factorial design. Hypothesis test was done by two-way variance ANOVA test with different cells. It can be concluded that the discovery learning model with RME approach gives better influence on the Mathematics learning achievement than the direct learning model. Students having high interpersonal intelligence category get better Mathematics learning achievement than those having medium and low category. The students having medium interpersonal intelligence get better Mathematics achievement than those having low category. There is no interaction between learning model and interpersonal intelligence on Mathematics learning achievement.
The study determined the arithmetic verbal problem solving skills of primary
school students and to examine them according to grade level and
mathematics achievement variables. The study was designed according to
the relational survey model, one of the quantitative research methods. The
population of the research consists of students studying in public primary
schools in the central districts of a large city in the south of Turkey. The
sample consisted of 1,865 students determined according to the
disproportionate stratified sampling method. The "arithmetic verbal problem
test for students" prepared by the researchers was used as a data collection
tool. As a result of the research, it was revealed that the students were most
successful in the problems of combining and separating with “consequence
unknown”, then “with change unknown” and “initial unknown”, but they
were less successful in part-whole type problems. Thus, it was concluded
that as the mathematics achievement and grade levels of the students
increased, their success in solving verbal problems also increased.
Purpose: This study aims to identify the problem solving abilities possessed by junior high school students. The type of research used is quantitative which uses a research design survey. The sample of this study is 98 students taken based on purposive sampling techniques. This study uses descriptive statistics to analyze the data generated. From the results of the analysis that has been done, it was found that there is a problem solving indicator by students in mathematics which is a indicated by the indicators of planning a solution which has a good category of a 56.1% (55 of 98) students, the indicator of problem solving has a good category of a 56.1% (55 out of 98) students, indicators of a problem solving planning had a good category of a 54.1% (53 of 98) students, and an indicator of understanding a problem had a good category of a 60.2% (59 of 98) students.
This study aimed to produce a learning path that can help students
understand the concept of percent using the context of an egg rack. This
study used a design research method through the Indonesian Realistic
Mathematics Education approach which was carried out at Elementary
School No. 2 Gumawang, Indonesia. Data were obtained through
observation, photos, video recordings, student activity sheets, and field
documentation. The result of the research was a learning trajectory
consisting of three activities; first, students explore their knowledge of egg
racks which are very close to students' self-life, secondly, students change
the problem into a bar form based on students' knowledge of egg racks, then
students change the problem into fractions and students change the fraction
with the denominator one hundred, third, students solve the percent problem
in a more complicated form. The activities that have been produced and
tested on percent learning using the context of an egg rack, can help students
to better understand the concept of percent.
The aim of the study is to develop an understanding of the kinds and sources errors and misconceptions that characterise students’ learning of school algebra. Systematic random sampling was used to draw sixty-five participants from a population of two hundred and twenty-three form three students. A cross sectional survey design was employed to collect data using written tests, a structured questionnaire and interviewing of the students from one high school in Zimbabwe. Content analysis technique was applied to textual data from three sources in order to determine the types of errors and misconceptions. The main findings are that both procedural and conceptual errors were prevalent that errors and misconceptions can be explained in terms of the students’ limited understanding of the nature of algebra; in particular their fragile grasp of the notion of a variable. Sources of misconceptions could be explained in terms of the abstract nature of algebra Mathematics educators should embrace errors and misconceptions in their teaching and should not regard them as obstacles to learning but rather engage with them for better understanding of algebraic concepts by students. Future studies can be carried on systematic errors as one of the ways of improving students’ understanding school mathematics.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
The purpose of this research is to analyze the improvement of students' mathematical literacy ability through the use of mathematics teaching materials with metacognitive approach guidance. This research will be held in the city of Kendari to the subject of this research target is students who are at grade 5 Land in Junior High VIIID Kendari years lessons 2017/2018 with many limited scale trial class is only required as much as 1 class. To know the significance of the increase in the literacy abilities of students using paired t-test. Data processing using the SPSS program with criteria if α=0,05 then there is an increased of student's mathematical literacy ability. The results of the analysis on the stages of the evaluation shows the learning materials with metacognitive approach guidance can provide better against an increase in student learning. The ability of the early mathematical literacy against students is very less because of learning during this time students have not been directed with the ability of mathematical literacy. After the students get learning by using learning materials through metacognitive approach guidance, the ability of mathematical literacy students’ level 3 and level 4 underwent significant improvement.
This quantitative descriptive study aims to describe the Mathematical Literacy of Grade 5 of Primary Students regarding their mathematical problem-solving abilities. The samples of this study were 35 5th-gradestudents at Muhammadiyah Condongcatur Elementary School in academic year 2017/2018. The data were collected through observations and tests with five questions containing indicators of mathematical literacy regarding mathematical problem-solving abilities; two experts have validated the test instruments. Moreover, the test estimated Cronbach's alpha of 0.749 proved reliability. The data analysis in this study was carried out descriptively based on the average score, the standard deviation, the maximum score, the minimum score, the total score, and the percentage correct answer. The results showed that the mathematical literacy of the 5th-grade students at SD Muhammadiyah Condongcatur was generally at the high category (indicated by the problem-solving abilities). Students have been able to understand a problem, to use logic to describe the solution to a problem, and to choose the most appropriate solution to solve a problem.
The Investigation of Primary School Students’ Ability to Identify Quadrilater...theijes
In Vietnamese mathematics curricula, primary school students explicitly learn the concept of quadrilaterals such as parallelogram, rhombus, rectangle, square and trapezoid in the Grades 3, 4 and 5. They are presented individually, and there is no comparison between their characteristics. Therefore, the students will be difficult to recognize the relationships among kinds of quadrilaterals. The results of an investigation of 186 primary school students revealed that most of them found it easy to identify squares and rectangles but many of them asserted that “a square is not a rectangle”
Mathematical problem solving was an crucial skill to be mastered by primary
school student so that will help student to unravel their problems encountered
in everyday life. By using the realistic mathematics approach, stundents learn
mathematical concept based on reality or scope around students. This study
aimed to develop an eligible learning materials and test the effectiveness of
learning materials based on realistic mathematics education to enhance the
problem solving skill of primary school students. This research and
development study was conducted in Sawangan Subdistrict, Magelang
Regency, Central Java, Indonesia. The testing subjects consisted of 12
students in the the preliminary field, there were 42 students in the main field,
and 90 students in the operational field that divided into experiment dan
control class. The data were collected by interviews, observation, and tests.
The analyzing N-gain score and t-test with a significant level of 0.05 done to
find out th effectiveness of the teaching materials. The developed of realistic
mathematics eduation learning materials is feasible and effective in
improving problem solving skill with significance value of 0.000 (p≤0.05). It
can enhance the problem solving skills of 4
th
grade elementary school.
Engineering Technology Students’ Perception towards Promoting Interaction for...iosrjce
Classroom social environment is very important in academic life because it can affect students’
lifestyle in terms of their studies. One of the important elements in getting positive classroom social environment
is interaction amongst the students. The objective of this study is to understand and examine the engineering
technology students’ perceptions towards promoting interaction for the classroom social environment at the
Faculty of Engineering Technology (FTK), Universiti Teknikal Malaysia Melaka. This study investigated the
perceptions of 177 second year students from four different departments taking mathematics subject. A set of
questionnaire that covers questions regarding students’ perceptions towards promoting interaction by
mathematics lecturers and also their classmates was distributed to the students. From the findings, a conclusion
was drawn regarding their perceptions towards promoting interaction for the classroom social environment.
The result shows that students have a very good perception in increasing a positive social environment where
both parties, which are lecturers and classmates, play an important role in promoting interaction
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
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The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
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A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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incorrect rules and performing operations carelessly [7]. Misconceptions lead students to develop negative
attitudes towards mathematics [8].
Fractions and operations with fractions are among the top subjects in mathematics because of both
their structure and their relationship with other subjects [9]. The subject of fractions is highly important due
to its relationships to subjects like rational numbers, ratio and proportion, decimals, percentages and
probability [10], [11]. Fractions, which constitute one of the hardest topics for students and teachers, are
among difficult mathematical concepts children encounter in primary school [11]-[21]. One main reason that
students find fraction operations difficult is that they memorize formulae and algorithms instead of
understanding fractions, while another is that they perceive the denominator and the numerator in fraction as
two separate integers [22]. Each piece of information in mathematics generally have three different ways of
expression as verbal, numerical and visual. The ability of students to make transitions among these
expressions depends on their level of comprehension. Fractions have four different ways of expression as
verbal, symbolic, objective and model. It is important in the subject of fractions and operations with fractions
that students are able to make strong connections among these expressions. In this sense, it may be stated that
there are serious problems in the transition between visual expression and the other ways of expression [9].
In Turkey, the subject of fractions is introduced beginning with the first years of primary school.
The Primary School Mathematics Curriculum consists of four learning fields as ‘Numbers and Operations’,
‘Geometry’, ‘Measurement’ and ‘Data Processing’. While all fields of learning are included in all class
levels, some sub-fields are introduced after a certain grade. In the primary school mathematics curriculum
(1st
-4th
grades), the subject of fractions is discussed under the fractions sub-field within the field of ‘Numbers
and Operations’. The subject of fractions is distributed along the grades as the following: raising awareness
on whole and half fractions in the 1st grade; introducing the relationships of the whole and the half with the
quarter grade and introduction to division (grouping, dividing into pieces) in the 2nd
grade; introducing
fraction-related terms by emphasizing the whole-piece relationship and reinforcing the understanding on the
relationship between the numerator and the denominator by discussing the concept of unit fractions in the 3rd
grade; defining/using proper, compound and mixed fractions, performing addition and subtraction operations
on fractions and solving suitable problems [3]. Although these are not in the primary school curriculum,
students are expected to understand compound and mixed fractions and convert these to each other, rank
fractions, perform addition and subtraction operations with these fractions, make sense of these operations,
and at the same time, solve problems.
Several studies have reported that students have difficulty in learning the concept of fractions and
fraction-related operations [14], [17], [18], [23]-[32]. As students think the characteristics of fractions are the
same as those of other numbers, they try to apply the same rule, and this leads to the development of their
misconceptions [33], [34]. In the primary school mathematics curriculum, fractions are after the introduction
of integers. However, fractions have different characteristics. While operations with fractions conceptually
resemble those with integers, they are different to integer operations due to their numbers of operational
steps. Teaching fractions in mathematics classes requires care and attention because of their complexity and
conceptual richness. Understanding fractions and related concepts well in primary school and gaining skills
of performing operations with fractions fast by understanding them will not only make this enjoyable subject
of mathematics meaningful for students and contribute to their success in using fractions in other classes, but
it will only set a solid preliminary learning basis for advanced mathematics subjects [35].
Another reason for misconceptions in students is the instructional approach of their teachers [36],
[37]. Moreover, knowing about the misconceptions of students is very important also for teachers to diversify
and use their instruction techniques [38]. As a result of the interviews they held with teachers and students,
[39] reported two reasons for the very low accessibility levels of the targeted outcomes in the fractions unit as
the misconceptions of the students and the learning-teaching process that is carried out by the teachers
without taking the students’ preliminary knowledge into account. Hence, it is important for teachers to know
about misconceptions and take the precautions that are necessary to avoid them in students. This is because
teachers may prevent the likely mistakes or misconceptions of students if they know about misconceptions
and their reasons [40]. Likewise, if teachers determine the learning difficulties and misconceptions of
students in the subject of fractions and prefer an instruction strategy based on these, learning of fractions may
take place on a conceptual level [29]. Thus, it is important that teachers and prospective teachers know about
the misconceptions of students. When the literature on misconceptions was reviewed, no study was found to
investigate the views of both teachers and prospective teachers on the issue.
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2. RESEARCH METHOD
2.1. Design
This study, which aimed to reveal an existing situation, was in the form of a descriptive case study.
In this study, which was conducted with the aim of examining the current knowledge of primary teachers and
primary pre-service teachers on the misconceptions of primary school students in the subject of fractions, the
qualitative research method of multiple case study was used. The problem with the generalizability of case
studies may be overcome by carefully designed multiple case studies [41]. This study utilized open-ended
questions to collect the views of primary teachers and the primary prospective teachers on determining the
misconceptions in the subject of fractions.
2.1. Sample
The sample consisted of 26 primary teachers employed at three different primary schools in
Istanbul, Turkey and 73 3rd
and 4th
year primary pre-service teachers enrolled at a faculty of education in the
same province and were doing internship within the scope of the ‘Teaching Practice’ course. The
demographic information of the form teachers is provided below.
Among the primary teachers who participated in the study, 5 were 1st
grade, 2 were 2nd
grade, 10
were 3rd
grade and 9 were 4th
grade teachers. 15 of the teachers had 1-10 years, 5 had 11-20 years, 3 had 21-
30 years and another 3 had 31-40 years of professional experience shown in Table 1.
Table 1. Descriptive characteristics of the primary teachers
Grades f Years of professional experience f
1st
grade 5 1-10 Years 15
2nd
grade 2 11-20 Years 5
3rd
grade 10 21-30 Years 3
4th
grade 9 31-40 Years 3
Total 26 26
2.1. Data collection
The data were collected by two semi-structured forms that were prepared by the researcher as data
collection tools.
Teacher Form: This form is a measurement instrument that was prepared to learn about the
misconceptions of students determined by the teachers as a result of their experience. In this form, the
primary teachers were asked about their demographic information and to provide three situations under the
question ‘what are the misconceptions your students have about the subject of fractions based on your
experience?’ to reveal the misconceptions that they thought their students had.
Prospective Teacher Form: The prospective teacher form was adapted for the prospective teachers,
and the participants were asked to provide three situations under the question ‘what are the misconceptions
primary school students have about the subject of fractions based on your observations?
In order to achieve content validity for these forms that were developed by the researcher, as
reported by [42] opinions of three academics who are experts in the subject of mathematics and primary
education were received. The forms were organized by examination based on the expert opinions
and finalized.
2.1. Data analysis
The purpose of analysis in qualitative studies is to discover patterns, views, explanations and
meanings [43], [44]. The data about the misconceptions of primary school students that were obtained in the
study by the open-ended forms that were applied with both teachers and prospective teachers were analyzed
with the method of ‘descriptive analysis’ [41]. The written explanations provided to respond to the open-
ended questions were content-analyzed. The responses of the teachers and the prospective teachers were
interpreted with descriptions by the researchers, and similarities and difference in the comments were
revealed. The similarities and differences that were determined was named by various codes and tabulated
based on their frequency of occurrence. In order to increase the reliability of the study, the determined
categories and codes were separately examined by two experts experienced in qualitative research and a
mathematics educator other than the researcher, and the categories were given their final shape. Including
direct quotes from the views of participants and explaining the results based on these is also an important
issue for the reliability of a study [41]. This study used this strategy and included direct quotes from the
responses of the participants. The participants’ views were presented by assigning codes for the two types of
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participants as PT for the primary teachers and PPT for the primary pre-service teachers. The analysis of the
demographic information in the study was achieved by SPSS 16.0.
3. RESULT AND DISCUSSION
This section of the article presents the respective views of the primary teachers and the primary
prospective teachers on the misconceptions that they thought were present in primary school students in the
subject of fractions.The primary teachers were asked the question ‘what are the misconceptions your students
have about the subject of fractions based on your experience?’ and the responses are shown in Table 2.
Table 2. Primary teacher’s responses to the question ‘what are the misconceptions your students have about
the subject of fractions based on your experience?’
Categories f
Showing with models 14
Concepts of the numerator and the denominator 13
Ranking 13
Problem Solving 10
Concept of fractions and related reading and writing 8
Distinguishing types of fractions and conversion 8
Representation on the number line 7
Operations 5
Accordingly, the teachers stated that the students had difficulty mostly in showing with models, in
concepts of the numerator and the denominator, when they needed to rank, when they needed to solve
problems, in reading and writing at the same time in concepts that express fractions and in distinguishing
types of fractions and converting them to each other, and they had misconceptions in these issues (Table 2).
Some teacher views on these are listed below in the order from the most frequently stated misconception to
the least frequently stated one:
‘They make mistakes in showing with models’ (PT 3).
‘Students find it difficult to divide a whole into unit fraction pieces’ (PT 17).
‘They see the numerator and the denominator in the fraction as separate, and they cannot notice
that these numbers are related’ (PT 9).
‘They confuse the concepts of greatness-smallness. They cannot decide upon which fraction is
greater as they still cannot comprehend the natural number and piece-whole sub-titles’ (PT 13).
‘They fall into a misconception by considering the natural number values while ranking
fractions’ (PT 3).
‘As their conceptual knowledge about fractions are not internalized, students may experience
confusion in algorithmic operations or forget easily’ (PT 9).
‘While comparing two fractions, they say the one with larger numbers is greater’ (PT 7).
‘In the case that the greatness of the fraction is dependent on a whole, students are not aware
that the wholes will not have the same greatness, so they make mistakes in ranking’ (PT 12)
‘They do not understand specific problems’ (PT 12).
‘They perform operations from memory while solving problems’ (PT 14).
‘Not being able to notice fractions in different wholes may express different
greatness’ (PT 25).
‘They cannot conceive that the numerator and the denominator represent a whole
together’ (PT 6).
‘They might not comprehend the piece-whole relationship between the numerator and the
denominator’ (PT 24).
‘They cannot conceive that pieces constitute the whole and the numerator is a piece of the
whole, and they cannot realize that both are related’ (PT 3).
‘They have difficulty in understanding the concepts of piece-whole’ (PT 17).
‘Mistakes in showing the whole by dividing it into pieces and failure to draw each piece
identically’ (PT 6).
‘They cannot read fractions correctly as they do not fully understand the concepts of numerator
and denominator’ (PT 4).
‘They make mistakes while converting fractions into each other’ (PT 4).
‘Proper fractions are easier to understand than compound and mixed ones’ (PT 18).
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‘Failure to determine the intervals while showing on the number line’ (PT 18).
‘Failure to show compound or proper fractions on the number line’ (PT 21).
‘When they are asked to show a compound fraction on the number line, they do so by firstly
converting it to a mixed fraction’ (PT 20).
‘They might miss the integer part while showing mixed fractions on the number line’ (PT 12).
‘There are problems in addition and subtraction as they do not see fractions as an entirety or a
number and perform separate operations’ (PT 5).
‘Trying to perform operations as in natural numbers’ (PT 13).
‘Using the rules in natural numbers while performing operations’ (PT 11).
‘Thinking that addition is adding numerators and denominators separately’ (PT 1).
The primary prospective teachers were asked the question ‘what are the misconceptions primary
school students have about the subject of fractions based on your observations?’ and the responses are shown
in Table 3.
Table 3. Primary prospective teacher’s responses to the question ‘what are the misconceptions primary
school students have about the subject of fractions based on your observations?’
Categories f
Concept of fractions and related reading and writing 76
Ranking 40
Operations 35
Representation on the number line 25
Represent with models
Concepts of numerator and denominator
16
14
Distinguishing types of fractions and conversion 10
Problem solving 3
As a result of their teaching observations for three semesters, the primary prospective teachers stated
that primary school students had difficulty in the concept of fractions and related reading and writing,
ranking fractions, fraction operations, representation on the number line, when they need to represent
fractions with models, in the concepts of numerator and denominator, in distinguishing types of fractions and
conversion, and while solving problems, and they may have misconceptions on these issues (Table 3). Some
prospective teacher views on these are listed below in the order from the most frequently stated
misconception to the least frequently stated one:
‘Students treat fractions as integers, they consider the numerator and the denominator as
separate numbers (PPT 3).
‘While expressing fractions with shapes, they cannot draw identical lines or squares. This
shows that there is a problem in dividing the fraction into identical pieces in the subject of
piece-whole’ (PPT 16).
‘They cannot understand the concepts of whole and piece’ (PPT 3).
‘Students may reflect their generalizations on natural number onto fractions and consider the
numerator and the denominator as separate numbers’ (PPT 29).
‘Considering the numerator and the denominator as separate natural numbers’ (PPT 33).
‘They make mistakes while verbally expressing a fraction’ (PPT 46).
‘Students cannot conceive that identical pieces represent a whole, and thus, they cannot divide
whole into identical pieces’ (PPT 48).
‘While comparing fractions, students generalize their preliminary information on natural
numbers in fractions’ (PPT 7).
‘Assuming that the fraction with higher numbers is greater as in natural numbers’ (PPT 59).
‘While ranking fractions with equal numerators, they think the one with larger denominator is
greater’ (PPT 18).
‘They might not think of a fraction as pieces of a whole in comparisons’ (PPT 63).
‘They separately add numerators and denominators in addition operations’ (PPT 3).
‘In operations on fractions, they act like they are natural numbers’ (PPT 71).
‘In operations on fractions, they generalize operations in natural number to this
subject’ (PPT 43).
‘They make mistakes in representation on the number line, especially representing operations
like addition and subtraction’ (PPT 42).
‘They confuse the number of pieces to divide intervals while showing fractions on the number
line’ (PPT 17)
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‘They have difficulty in showing especially mixed fractions on the number line’ (PPT 72).
‘They have difficulty in showing compound and mixed fractions on the number line’ (PPT 58).
‘They make mistakes in representation by models, especially showing mixed
fractions’ (PPT 69).
‘Failing to divide into identical pieces while representing fractions with a model’ (PPT 5).
‘They can form inaccurate displays as they cannot convert compound fractions into mixed ones
while representing them with models’ (PPT 13).
‘They have difficulty in distinguishing the denominator and the numerator’ (PPT 72).
‘They make mistakes in converting a compound fraction into a mixed fraction’ (PPT 39).
‘They make mistakes in converting a mixed fraction into a compound fraction’ (PPT 3).
‘They have difficulty in reflecting problems on shapes for solution’ (PPT 62).
‘They cannot solve problems’ (PPT 1).
One result of the study was the statements that primary school students ‘confused fractions with
their knowledge on integers.’ It was found that a significant part of misconceptions in students were caused
by students’ generalization of observations that are valid in integers for fractions [35]. An attentive education
process may lead students to understand and learn fractions to the required depth and prevent misconceptions
caused by such generalizations. In fact, it was observed that most misconceptions were caused by inattentive
approaches to fraction instruction. There are findings that suggested that an early and hasty transition to
representation of fractions in the classroom with abstract symbols without dependence on student experience
and a basic conceptual framework leads to misconceptions (Bezuk & Bieck, 1993; cited in [35]).
According to the views of the primary teachers and the primary prospective teachers, another
situation among primary school students was that they had mistakes ‘while showing fractions with models’.
It is a known fact that visual representations or shapes affect comprehension of mathematical concepts
positively. Fractions and operations with fractions are a top subject among those where using shapes is the
most important [9]. Shapes that are drawn and models that are used in relation to a problem provides ease of
reaching the correct solution by making it easier to understand [45]. As using a set of models and
manipulative tools in introduction to fractions makes fractions tangible for primary and secondary school
students who are still in their tangible operation stage, it leads to easier learning of the concept of fractions
and students to perform fraction-related operations more easily [22]. Davis, Hunting and Pearn Vergnaud and
Kieren recommended the use of schemas that show the characteristics of rational numbers and fractions
(geometrical models) and emphasize that using especially schemas of dividing a whole into pieces is highly
important for establishment of knowledge on rational numbers [22]. In many studies, as in the case of this
study, students experienced difficulty in expressing the fractions on given models and reaching the correct
answer in problems of finding the model that is suitable for a given fraction [10], [46-48].
Based on their experiences and observations, the participants stated that students confused the
denominator and the numerator, the concept of fractions was not fully established and especially the whole-
piece relationship was not understood, and students had difficulty in writing and reading fractions. While
providing students with knowledge on expressing a fraction in writing, the questions of how many identical
pieces the whole is divided into and how many of these pieces are colored/selected should be answered, and
the answers these answers should be represented with symbols [49]. Students think the numerator and the
denominator are separate values. The main reason for this is that student use their knowledge on natural
numbers when they encounter fractions [2]. The reason for this misconception is that, while fractions are
taught, their representation with symbols is introduced without setting the conceptual basis for the symbols
[35]. This agrees with the result found by [26] that students find it difficult to solve some fraction problems
as they cannot fully understand piece-whole relationships. Although ‘piece-whole’ is the most basic concept
in fractions [37] and it is in the nature of fractions [11], some students experience difficulty in learning this
concept [51], [52] investigated the mistakes of fourth-and fifth-grade students in fractions and found that the
students had problems in the principle of identical pieces in the piece-whole relationship. In the qualitative
study by [53] with primary school students, the students thought of fractions like they are integers, expressed
the concepts of the numerator and the denominator as separate numbers, and confused these with each other.
Several studies reported findings that students confuse numerators and denominators [7], [26], [45]-[57]. In
order to overcome these difficulties, firstly the piece-whole relationship should be taught to students while
teaching fractions and a basis should be formed in students regarding the concept of fractions [50]. Baykul
argued that models should also be used in teaching fraction-related concepts [1]. Doğan-Temur emphasized
that for good development of a concept of fractions, education processes should be carried out by using real-
life situations, tangible tools and equipment and models, rather than teaching rules to students [58].
According to the experiences and observations of the primary teachers and the primary prospective
teachers, it is believed that the basis of the misconceptions on ranking fractions is that students think of
fractions as if they are integers. As the quantity represented by a number is proportional to its greatness in
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integers, this is mistakenly generalized for fractions, and some think that fractions with larger numbers are
greater [35], Doğan-Temur reported that students made mistakes in several subjects such as ranking fractions,
equivalency in fractions and mixing denominators and numerators [58]. Biber stated that, while ranking
fractions, students rank denominators amongst each other, rank numerators amongst each other, and then,
they apply these operations to the fractions [45]. Several other studies also reported that students had
misconceptions about ranking fractions [7], [31], [48], [55]-[61]. In order to prevent this misconception, it
should be shown that the quantities represented by equivalent fractions are the same by using tangible and
pictorial materials in the classroom [35].
The primary teachers and the primary prospective teachers stated that primary school students had
difficulty in fraction problems and made mistakes. They wrote that there were issues especially in the parts
while understanding the problems, students made mistake in the solutions of the problems. Soylu observed
that, in fraction problems, students experienced difficulty in understanding the problem, and therefore,
determining the operations and order of operations in the problems [29]. Başgün found that students made
mistakes in applying concepts about fractions in problems [62].
The statements of the participants suggested that students could not distinguish types of fractions
and had difficulty in converting them into each other. As in this study, the teachers who participated in the
study by Demiri reported that students had misconceptions about converting fractions into different types.
‘Representing fractions on the number line’ is one of the problems experienced by students [10]. In activities
of drawing a number line model that is used to express fractions, the necessity to divide the whole into
identical pieces should be emphasized with care. As in the case of the area model, showing fractions on the
number line also requires careful consideration of the number of pieces to be shown in a whole and the
number of pieces among these to be selected. There should be no hurry to transition to symbols so that the
shape-related meaning of fractions on the number line is not neglected [63], Doğan-Temur conducted
interviews with primary teachers, and the teachers stated that students made mistakes most frequently in
ranking fractions, showing fractions on the number line, problems, reading the fraction, fraction rules,
equivalency in fractions and confusing numerators and denominators [58]. Kutluca stated that it is important
to use transparent fraction cards, which are tangible materials, to provide students with skills of comparing
fractions, ranking, identification, addition and subtraction, multiplication and division operations [64]. Many
other studies also reported that students experienced problems while showing fractions on the number line
[6], [7], [57], [63], [65]-[67].
Finally, primary teachers and the primary prospective teachers stated that students made mistakes in
addition and subtraction operations. Schumacher and Malone prepared problems to determine the mistakes of
fourth-grade students in the subject of fractions, and it was found that the students performed addition
operations by adding the numerators and denominators separately [68]. The same mistake was also found in
the study by Okur and Çakmak-Güler that was carried out with fifth-grade students [69]. The study by Idrisand
Narayanan revealed that, while students could perform addition and subtraction operations with fractions that
had equal denominators, they had difficulty in operations with fractions that had different denominators [47].
Misconceptions of students in addition and subtraction operations have been reported by several other studies
[6], [10], [45], [55], [70], [71]. As addition and subtraction in fractions require a common denominator, it is
necessary to have comprehended basic fraction-related concepts in order to perform these operations by
understanding them. That is, it is highly difficult to learn and teach addition in fractions without
understanding what fractions mean and what equivalent fractions are [35]. Therefore, there is a need for a
common denominator to add fractions. If the denominators are not equal, the fractions should be converted
into equivalent fractions to make the denominators equal. This is how misconceptions in addition and
subtraction will not be encountered, or it will be to overcome misconceptions if they exist [2].
The study by Moss and Case that was conducted with the aim of determining whether or not
prospective primary and secondary school mathematics teachers are aware of the mistakes of students in the
subject of fractions revealed that most prospective teachers were aware of the mistakes of students [72].
While the prospective teachers were aware of the mistakes of the students, they could provide superficial
reasons for the mistakes. For solving the mistakes of students, they recommended strategies of verbal
explanations, area models, daily-life examples, repetition of preliminary knowledge, teaching standard
solutions, asking leading questions, using easy examples, using opposite examples, exercises and practices,
leading students to notice their mistakes and increasing students’ motivation.
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4. CONCLUSION
Consequently, this study showed that primary teachers and the primary prospective teachers did not
have much difficulty in identifying the misconceptions of students regarding operations in fractions. It is
believed that, in order to minimize misconceptions in students, the concept of fractions should be introduced
starting with identical piece problems and developing the concept with student-centered activities by using
various methods will be appropriate. It will also contribute greatly to the field to conduct qualitative studies
that involve the analysis of the mistakes primary school students make in the subject of fractions.
REFERENCES
[1] Baykul, Y., "Elementary Mathematics Teaching (6-8 classes)," Ankara: Pegem Publishing, 2009.
[2] Van de Walle, J. A, Karp, K. S, & Bay-Williams, J. W., "Elementary and Middle School Mathematics Teaching
Developmentally (Trans. Ed. S. Durmuş)," Ankara: Nobel Publishing, 2014.
[3] Mathematics Curriculum. "Millî Eğitim Bakanlığı," Ankara, Turkey, 2018.
[4] Sadi, A., "Minscoption in Numbers," UGRU Journal, vol. 5, pp. 1-7, 2007.
[5] Yılmaz, Z, and Yenilmez, K., "7 th and 8th Grades Students’Misconceptions About Decımal Numbers (The Case of
Uşak)," Afyon Kocatepe University Journal of Science, vol. 8(1), pp. 291-312, 2008.
[6] Önal, H, and Yorulmaz, A., "The Errors Made By Primary School Fourth Graders on Fractions," Journal of
Research in Education and Society, vol. 4(1), pp. 98-113, 2017.
[7] Ersoy, Y. and Ardahan, H., "Teaching of fractions in elementary schools II: Organizing events for diagnosis,"
[Online] [Available], http://www.matder.org.tr/index.php?option=com_content&view=article&catid=8:matematik-
kosesi-makaleleri&id=64:ilkogretim-okullarinda-kesirlerin-ogretimi-ii-taniya-yonelik-etkinlikler-
duzenleme&Itemid=38, 2003.
[8] Yenilmez, K, and Yaşa, E, "Primary School Students’ Misconceptions about Geometry," Journal of Uludağ
University Education Faculty, vol. 21(2), pp. 461-483, 2008.
[9] İpek, A. S, Işık, C, & Albayrak, M., "Conceptual Performances of Prospective Primary Teaehers on Operations
with Fraction," Journal of Kazım Karabekir Education Faculty, vol. 1, pp. 537-547, 2005.
[10] Demiri, L., "Researching Teachers and Pre-Service Teachers’knowledge of Students’ Misconceptions about
Fractions," Master's Thesis, Marmara University Institute of Educational Sciences, Istanbul, Turkey, 2013.
[11] Gabriel, F, Coché, F, Szucs, D, Carette, V, Rey, B, & Content, A., "A componential view of children's difficulties
in learning fractions," Developmental Psychology, vol. 715(4), 1-12, 2013.
[12] Anthony, G, and Ding, L.," Teaching and Learning Fractions: Lessons from Alternative Example Spaces,"
Curriculum Matters, vol. 7, pp. 159-174, 2011.
[13] Bottge B. A, Ma X, Gassaway L, Butler M, & Toland M. D., "Detecting and Correcting Fractions Computation
Error Patterns," Exceptional Children, vol. 80(2), pp. 37-255, 2014.
[14] Newstead, K, and Murray, R., "Young Student’s Construction of Fraction," Proceedings of the 2200 Conference of
The international Group for the Psychology of Mathematics Education, vol. 3, pp. 295-302, Stelllenbosh: South
Africa, 1998.
[15] Purnomol, Y. W, Widowati, C, Aziz, T. A, & Pramudiani, P., "Fractions Division Knowledge of Elementary
School Student: The Case of Lala," The 4th International Conference on Research, Implementation, and Education
of Mathematics and Science (4th ICRIEMS), pp. 1-8, 2017.
[16] Saxe, G. B, Taylor, E, V, McIntosh, C, & Geahart, M., "Re-Presenting Fractions with Standard Notations: A
Development Analysis," Journal for Research in Mathematics Education, vol. 36, pp. 137-157, 2005.
[17] Olkun, S, and Toluk-Ucar, Z., "Activity-Based Mathematics Teaching in Primary Education," Ankara: Anı
Publishing, 2012.
[18] Ünlü, M, and Ertekin, E., "Why do Pre-Service Teachers Pose Multiplication Problems Instead of Division
Problems in Fractions?," Procedia-Social and Behavioral Sciences, vol. 46, pp. 490-494, 2012.
[19] Tanner, K., "Working with Students to Help Them Understand Fractions," Australian Primary Mathematics
Classroom, vol. 13(3), pp. 28-31, 2008.
[20] Tzur, R., "An Integrated Study of Children’s Construction of Improper Fractions and the Teachers Role in
Promoting That Learning," Journal for Research in Mathematics Education, vol. 30, pp. 390-416, 1999.
[21] Young-Loveridge, J, Taylor, M., Häwera, N, & Sharma, S., "Year 7-8 Students’ Solution Strategies for A Task
İnvolving Addition of Unlike Fractions," In Findings from the Numeracy Development Projects: 2006 pp. 67-84,
Wellington: Ministry of Educatio, 2007.
[22] Şiap, İ, and Duru, A, "The Ability to Use Geometrical Models in Fractions," Kastamonu Education Journal,
vol. 12(1), pp. 89-96, 2004.
[23] Davis, E. G., "Teaching and Classroom Experiments Dealing with Fractions and Proportional Reasoning," Journal
of Mathematical Behavior, vol. 22, pp. 107-111. 2003.
[24] De Castro, B., "Cognitive Models: The Missing Link to Learning Fraction Multiplication and Division," Asia
Pacific Education Review, vol. 9(2), pp. 101-112, 2008.
[25] Işık, C, and Kar, T., "Analyzing Problems Posed by 7th Grade Students for Addition Operation with Fractions,"
Elementary Education Online, vol. 11(4), pp. 1021-1035, 2012.
[26] Kocaoğlu, T, and Yenilmez, K., "5 th Grade Students’ Mistakes and Misconceptions in Solving Problems about
Fractions," Journal of Dicle University Ziya Gökalp Education Faculty, vol. 14, pp. 71-85, 2010.
9. Int. J. Eval. & Res. Educ. ISSN: 2252-8822
Misconceptions of primary school students about the subject of fractions: views of ... (Yasemin Deringöl)
37
[27] Moss, J, and Case, R., "Developing Children’s Understanding of The Rational Numbers: A New Model and
Experimental Curriculum," Journal for Research in Mathematics Education, vol. 30(2), pp. 122-147, 1999.
[28] Olkun, S, and Toluk, Z., "Activity-Based Mathematics Teaching in Primary Education" Ankara:
Anı Publishing, 2003.
[29] Soylu, Y. and Soylu, C., "Learning Difficulties of 5th Class in Primary Education at Fraction: Ordering, Adding,
Subtraction, Multıiplication in Fraction and Problems Related to Fraction," Journal of Erzincan Education Faculty,
vol. 7(2), pp. 101-117, 2005.
[30] Soylu, Y., "Students Made Mistakes and Have Misunderstandings Related to The Fractions, and The Ability of
Teacher Candidates To Predict The Students’mistakes," Journal of Contemporary Education, vol. 33(356),
pp. 31-39, 2008.
[31] Stafylidou, S, and Vosniadou, S., "The Development of Students’understanding of the Numerical Value of
Fractions," Learning and Instruction, vol. 14, pp. 503-518, 2004.
[32] Tirosh, D., "Enhancing Prospective Teachers’ Knowledge of Children’s Conceptions: The Case of Division of
Fractions," Journal for Research in Mathematics Education, vol. 31(1), pp. 5-25, 2000.
[33] Bush, S. B, and Karp, K. S., "Prerequisite Algebra and Associated Misconceptions of Middle Grade Students: A
Review," The Journal of Mathematical Behavior, vol. 32, pp. 613-632, 2013.
[34] Siegler, R.S, Fazio, L.K, Bailey, D.H, & Zhou, X., "Fractions: The New Frontier for Theories of Numerical
Development," Trends in Cognitive Sciences, vol. 17(1), pp. 13-19, 2013.
[35] Alacacı, C., "Misconceptions of Students about Fractions," (Ed. Bingölbali, E. ve Özmantar M. F.), Mathematical
Challenges and Solution Suggestions, Ankara: PegemA Publishing, 2010.
[36] Aksu, M., "Student Performance in Dealing with Fractions," The Journal of Educational Research, vol. 90(6),
pp. 375-380, 1997.
[37] Charalambous C. Y, and Pitta-Pantazi, D., "Revisiting A Theoretical Model on Fractions: Implications for teaching
and Research," In Chick, H.L. & Vincent, J. L. (Eds.), Proceedings of the 29th Conference of the International
Group for the Psychology of Mathematics Education, vol. 2, pp. 233-240, 2005.
[38] Kilpatrick, J, Swafford, J, & Findell, B., "Adding it up: Helping children learn mathematics. National Academy of
Sciences," National Research Council, National Academy Press, Washington, DC, 2001.
[39] Hıdıroğlu, Ç. N., "Evaluation of Fractions Unit of Secondary School 5th Grades’ Mathematics Curriculum,"
Master's Thesis, Pamukkale University Institute of Educational Sciences, Denizli, Turkey, 2016.
[40] Özdemir, B, G, Bayraktar, R, & Yılmaz, M., "Explanations of Primary and Middle School Mathematics Teachers
on Misconception," Journal of Trakya University Education Faculty, vol. 7(2), pp. 284-305, 2017.
[41] Yıldırım, A. and Simşek, H., "Qualitative research methods in social sciences (5th Ed.)," Ankara Seckin
Publications, 2005.
[42] Balcı, A, "Research Methods, Techniques and Principles in Social Sciences," Ankara: PegemA Publishing, 2005.
[43] Büyüköztürk, Ş, Kılıç, Ç. E, Akgün, Ö. E, Karadeniz, Ş, & Demirel. F., "Scientific Research Methods," Ankara:
Pegem Publishing, 2012.
[44] Creswell, J. W., "Qualitative Research Methods (Trans. Eds: Bütün, M. & Demir, S. B)." Ankara:
Siyasal Book, 2014.
[45] Biber, A, Ç, Tuna, & Aktaş, O., "Students’ Misconceptions of Fractions and its Effect on Solving Fractions
Problems," Trakya University Journal of Education, vol. 3(2), pp. 152-162, 2013.
[46] Aksoy, N. C, and Yazlik, D. O., Student Errors in Fractions and Possible Causes of These Errors. Journal of
Education and Training Studies, vol. 11(5), pp. 219-233, 2017.
[47] Idris, N, and Narayanan, L. M., "Error Patterns in Addition and Subtraction of Fractions among Form Two
Students," Journal of Mathematics Education, vol. 4(2), pp. 35-54, 2011.
[48] Kurdal, C., "Student’s Errors on Ratı̇o and Proportı̇ons Done in Dynamic and Interractive Mathematics
Environments," Master's Thesis, Bayburt University, Bayburt, Turkey. 2016.
[49] Pesen, C., "Students’ Misconceptions about Fractions," Education and Science, vol. 143(32), pp. 79-88, 2007.
[50] Meert, G, Grégoire, J, &, & Noël, M. P., "Comparing the magnitude of two fractions with
commoncomponents: Which representations are used by 10-and 12-year-olds?," Journal of Experimental Child
Psychology, vol. 107, pp. 244-259, 2010.
[51] Chinnappan, M., "Children’s Mappings of Part-whole Construct of Fractions," In P. Clarkson et al. (Eds.),
Conference of the Mathematics Education Research Group of Australasia, Melbourne, pp. 241-248, Sydney:
Mathematics Education Research Group of Australia, Jul, 2005.
[52] Loc, N. P, Tong, D. H., & Chau, P. T., "Identifying the Concept “Fraction” of Primary School Students: The
İnvestigation in Vietnam," Educational Research and Review, vol. 12(8), pp. 531-539. 2017.
[53] Ndalichako, J. L., "Analysis of Pupils’ Difficulties in Solving Questions Related to Fractions: The Case of Primary
School Leaving Examination in Tanzania," Creative Education, vol. 4(9), pp. 69-73, 2013.
[54] Karaağaç, K. and Köse, L., "Examination of Pre-Service and In-Service Teachers’ Knowledge of Students’
Misconceptions on the Topic of Fractions," Journal of Sakarya University Education Faculty, vol. 30,
pp. 72-92, 2015.
[55] Mohyuddin, R. G, and Khalil, U., "Misconceptions of Students in Learning Mathematics at Primary Level,"
Bulletin of Education and Research, vol. 38(1), pp. 133-162, 2016.
[56] Wong, M, and Evans, D., "Students’ Conceptual Understanding of Equivalent Fractions," Proceedings of the 30th
annual conference of the Mathematics Education Research Group of Australasia J. Watson & K. Beswick (Eds).
Mathematics: Essential Research, Essential Practice-vol. 2, pp. 824-833, 2007
10. ISSN: 2252-8822
Int. J. Eval. & Res. Educ. Vol. 8, No. 1, March 2019: 29 - 38
38
[57] Yetim, S. and Alkan R., "Common Mistakes and Misconceptions of 7th Grade Students about the Rational
Numbers and Placement of the Rational Numbers on the Number Line," MANAS Journal of Science Researches,
vol. 11, pp. 87-109, 2010.
[58] Doğan-Temur, Ö., "Opinions of Teachers of Fourth and Fifth Grade About Teaching Fractions: A
Phenomenograhic Research," Dumlupınar University Journal of Social Sciences, vol. 29, pp, 203-212, 2015.
[59] Altıparmak, K, and Özüdoğru, M., "Error and Misconception: Relation of Fraction and Part-Whole," International
Journal of Human Sciences, vol. 12(2), pp. 1465-1483, 2015.
[60] Gökkurt, B, Şahin, Ö. Soylu, Y, & Soylu, C., "Examining Pre-Service Teachers' Pedagogical Content Knowledge
on Fractions in Terms of Students’Errors," International Online Journal of Educational Sciences, vol. 5(3),
pp. 719-735, 2013.
[61] Orhun, N., "A Cognitive Gap between Formal Arithmetic and Visual Representation in Fractional Operations,"
Journal of Inonu University Education Faculty, vol. 8(14), pp. 99-111, 2007.
[62] Başgün, M. and Ersoy, Y., "Numbers and Arithmetic I: Some Difficulties and Misconceptions in Teaching
Fractions and Decimal Numbers," IV. Science Education Congress Paper, pp. 604-608, Ankara:
MEB Publishing, 2000.
[63] Pesen, C., "Students’Learning Difficulties and Misconceptions in Pointing the Fractions on The Number Line,"
Journal of Inonu University Education Faculty, vol. 15(9), pp. 157-168, 2008.
[64] Kutluca, T, and Kutluca, S., "The use of concrete materials in the teaching of fractions," Oral presentation
presented in Turkish Computer and Mathematics Education Symposium, Karadeniz Technical University, 2013.
[65] Lemmo, A, Branchetti, L, Ferretti, F, Maffia, A, & Martignone, F., "Students’ Difficulties Dealing with Number
Line: A Qualitative Analysis of a Question from National Standardized Assessment," Quaderni di Ricerca in
Didattica (Mathematics), vol. 5(2), pp. 149-156, 2015.
[66] Okur, M, and Çakmak-Güler, Z," 6 th and 7th Grade Secondary School Students’ Misconceptions about Fractions,"
Erzincan University Journal of Education Faculty, vol. 18(2), pp. 922-952, 2016.
[67] Özcan, Z. Ç, Kılıç, Ç, and Obalar, S., "Worked-Out Questions Supported With Self-Explanatıon Prompts For
Determination And Elimination of Students Mistakes in Mathematics," Journal of Mehmet Akif Ersoy University
Education Faculty, vol. 45, pp. 1-22, 2018.
[68] Schumacher, R. F, and Malone, A. S., "Error Patterns with Fraction Calculations at Fourth Grade as a Function of
Students’Mathematics Achievement Status," Elementary School Journal, vol. 118(1), pp. 105-127. 2017.
[69] Trivena, V, Ningsih, A. R., & Jupri, A., "Misconception on Addition and Subtraction of Fraction at Primary School
Students in Fifth-Grade. International Conference on Mathematics and Science Education (ICMScE)," Journal of
Physics: Conference Series 895 (2017) 012139, 2017.
[70] Ojose, B., "Students’ Misconceptions in Mathematics: Analysis of Remedies and What Research Says," Ohio
Journal of School Mathematics, vol. 72, pp. 30-34, 2015.
[71] Rose, "M. B, Learners’errors and Misconceptions Associated with Common Fractions," Master’s Thesis,
University of Johannesburg, 2011.
[72] Eroğlu, D., "Examining Prospective Elementary Mathematics Teachers’Knowledge About Students’ Mistakes
Related to Fractions," Master's Thesis, Middle East Technical University, Ankara, Turkey, 2012.
BIOGRAPHY OF AUTHOR
In 2002 She graduated from Istanbul University Elementary Mathematics Department
and in 2003, she completed his undergraduate education at the same university.
Between 2003 and 2015, She worked as a research assistant at Istanbul University,
Hasan Ali Yücel Faculty of Education, Elementary Education Department. Since 2015,
she has been working as an Assistant Professor in the Department of Primary School
Teaching, teaching mathematics, classroom education, teacher training and higher-order
thinking skills.