In primary schools of Viet Nam, solving problems on percentages is a very important bit of knowledge because it not only provides a full range of knowledge of percentages but also a lot of practical applications and has a great effect in the development of thinking for students. However, it is a kind of new and difficult problem, so students often commit errors to solve problems on percentages. A survey of 149 primary school students was done. The students had to answer 7 questions about the problems on percentages. Results show that they suffer some errors such as: misunderstanding kinds of problems, doing wrong calculation, confusing the units of measurements. At the end of the paper, some suggestions in mathematics education are made to teachers to support students avoiding errors in solving problems on percentages
The document describes the Kagiso Learning Aid Project's approach to teaching, which centers around continuous assessment of student understanding through analysis of test and assignment responses. Key points:
- Teaching, learning, and practice form an interactive cycle with the Kagiso Analysis (assessment of student work) at the core to strengthen connections between these elements.
- Rather than just evaluating if students got the right answer, the Kagiso Analysis identifies specifically which questions students struggled with, through a template tracking mistakes by student and question.
- This detailed analysis guides the teacher's next steps, ensuring they address areas of weakness before misunderstandings solidify. It also helps design effective assessments.
- An example analysis
The Mistakes of Algebra made by the Prep-Year Students in Solving Inequalitiesiosrjce
The document summarizes a study examining the mistakes made by prep-year students in solving inequalities. An exam with 5 inequality questions was given. For question 1, 68% answered correctly, while 32% made mistakes like incorrect factorization. For question 2, 34% were correct, while others made mistakes like ignoring negative signs. For question 3, 52% were correct, while some confused positive and negative values. For question 4, 50% drew correct graphs while others made table errors. For question 5, 70% handled negatives correctly, while some changed inequality signs incorrectly. Overall, students struggled with conceptual understanding of inequalities rather than algebraic skills. Teachers should analyze student mistakes to help refine their understanding of challenging math concepts.
The document is a study on money management skills among students at Sultan Abdul Halim Mu'adzam Shah Polytechnic. It includes a questionnaire given to 50 respondents to understand their sources of income, spending habits, and savings. The results found that most students spend the majority of their budget on food and get their income from PTPTN loans. The study recommends students create spending plans, save for emergencies, set financial goals and say no to unnecessary spending to better manage their money.
This document provides information about mathematics assessment in PISA. It discusses three key dimensions that are assessed: content, processes, and situations. For content, it focuses on overarching ideas like quantity, space, change, and relationships. For processes, it evaluates skills like reproduction, connections, and reflection. For situations, it considers where math is used like personal, educational, public, or scientific settings. It also provides examples of math questions and explains how they are categorized based on these three dimensions.
Facilities provided at each department of seberang peraiNur Dalila Zamri
The document summarizes the results of a survey conducted with students from various departments at Polytecnic Seberang Perai regarding facilities on campus. The survey found that 72% of students feel the classroom sizes are standard, while 6% feel they are large. For specific departments like Commerce, 10 students agreed their classrooms had enough chairs and tables. However, 57% of overall respondents felt projectors in classrooms were often unavailable. Based on the results, the document recommends that the university add more classrooms, equip classrooms with more chairs and tables, improve maintenance and servicing of projectors, and add more projectors to better support student learning.
The document is a 12-page extended essay on Vedic mathematics and its methods for multiplication. It explores several Vedic multiplication techniques including vertically and crosswise, multiplying numbers above 10, multiplying by one more than the number before for squaring numbers ending in 5. The essay finds that Vedic multiplication can shorten and ease both basic and complex multiplication problems by using numerical patterns, though some problems require adapting the methods.
Use of Technology in Education, But at What Cost?IJITE
Use of technology in the field of education has been a blessing. Faster grading, quicker notes / media availability for students, interactive communication outside of classrooms with students and faculty, online courses etc. have added to the enhancement of our education system. But when technology is pushed in teaching without proper thought, it becomes a black box approach at the cost of intuition, commonsense, and overall understanding of the concepts. Instead of supplementing technology in the process of learning, it has been used in making the black box approach more common. When we can shift the question from “How to educate with technology?” to “How to teach people best, and how should we design learning experiences in light of existing technology?”, then learning becomes a way to quench curiosity, and passion for learning will become a never ending pursuit for students. Models and textbook theories can help build the knowledge base, but they miss the context [5,7]. Students take them at face value without thinking through the real world implications. This is a recipe for failure since the industry expects business school students to tell the story with a strong reference to the context. A simplistic understanding of the formulas is what students’ need instead of a plug and solve formula based teaching method.
The document describes the Kagiso Learning Aid Project's approach to teaching, which centers around continuous assessment of student understanding through analysis of test and assignment responses. Key points:
- Teaching, learning, and practice form an interactive cycle with the Kagiso Analysis (assessment of student work) at the core to strengthen connections between these elements.
- Rather than just evaluating if students got the right answer, the Kagiso Analysis identifies specifically which questions students struggled with, through a template tracking mistakes by student and question.
- This detailed analysis guides the teacher's next steps, ensuring they address areas of weakness before misunderstandings solidify. It also helps design effective assessments.
- An example analysis
The Mistakes of Algebra made by the Prep-Year Students in Solving Inequalitiesiosrjce
The document summarizes a study examining the mistakes made by prep-year students in solving inequalities. An exam with 5 inequality questions was given. For question 1, 68% answered correctly, while 32% made mistakes like incorrect factorization. For question 2, 34% were correct, while others made mistakes like ignoring negative signs. For question 3, 52% were correct, while some confused positive and negative values. For question 4, 50% drew correct graphs while others made table errors. For question 5, 70% handled negatives correctly, while some changed inequality signs incorrectly. Overall, students struggled with conceptual understanding of inequalities rather than algebraic skills. Teachers should analyze student mistakes to help refine their understanding of challenging math concepts.
The document is a study on money management skills among students at Sultan Abdul Halim Mu'adzam Shah Polytechnic. It includes a questionnaire given to 50 respondents to understand their sources of income, spending habits, and savings. The results found that most students spend the majority of their budget on food and get their income from PTPTN loans. The study recommends students create spending plans, save for emergencies, set financial goals and say no to unnecessary spending to better manage their money.
This document provides information about mathematics assessment in PISA. It discusses three key dimensions that are assessed: content, processes, and situations. For content, it focuses on overarching ideas like quantity, space, change, and relationships. For processes, it evaluates skills like reproduction, connections, and reflection. For situations, it considers where math is used like personal, educational, public, or scientific settings. It also provides examples of math questions and explains how they are categorized based on these three dimensions.
Facilities provided at each department of seberang peraiNur Dalila Zamri
The document summarizes the results of a survey conducted with students from various departments at Polytecnic Seberang Perai regarding facilities on campus. The survey found that 72% of students feel the classroom sizes are standard, while 6% feel they are large. For specific departments like Commerce, 10 students agreed their classrooms had enough chairs and tables. However, 57% of overall respondents felt projectors in classrooms were often unavailable. Based on the results, the document recommends that the university add more classrooms, equip classrooms with more chairs and tables, improve maintenance and servicing of projectors, and add more projectors to better support student learning.
The document is a 12-page extended essay on Vedic mathematics and its methods for multiplication. It explores several Vedic multiplication techniques including vertically and crosswise, multiplying numbers above 10, multiplying by one more than the number before for squaring numbers ending in 5. The essay finds that Vedic multiplication can shorten and ease both basic and complex multiplication problems by using numerical patterns, though some problems require adapting the methods.
Use of Technology in Education, But at What Cost?IJITE
Use of technology in the field of education has been a blessing. Faster grading, quicker notes / media availability for students, interactive communication outside of classrooms with students and faculty, online courses etc. have added to the enhancement of our education system. But when technology is pushed in teaching without proper thought, it becomes a black box approach at the cost of intuition, commonsense, and overall understanding of the concepts. Instead of supplementing technology in the process of learning, it has been used in making the black box approach more common. When we can shift the question from “How to educate with technology?” to “How to teach people best, and how should we design learning experiences in light of existing technology?”, then learning becomes a way to quench curiosity, and passion for learning will become a never ending pursuit for students. Models and textbook theories can help build the knowledge base, but they miss the context [5,7]. Students take them at face value without thinking through the real world implications. This is a recipe for failure since the industry expects business school students to tell the story with a strong reference to the context. A simplistic understanding of the formulas is what students’ need instead of a plug and solve formula based teaching method.
The document discusses using an empty number line as a mental math strategy for primary grade students. It explains that the empty number line allows students to create a mental image of math strategies and more easily make the leap to mental calculations without paper. Using the empty number line also increases students' number sense and flexibility with numbers. The document provides an example of how to introduce the empty number line technique to students and have them use it to solve math problems.
This is a presentation to help students who always become feared during Maths Exam. This presentation tells about what are the elements that initiates this phobia and what are the possible ways by both the teachers and the students to overcome such Phobia. This presentation also contains Vedic mathematics tricks that helps you to do calculations easily
The document describes the guess-and-check algorithm for division. It involves estimating how many times the divisor goes into the dividend and recording estimates in a side column. The estimates are then added to find the quotient. Even students with limited math facts knowledge can use this intuitive approach to find correct answers. The document also provides guidance for teachers to help students understand the process.
This document contains an initial report with responses from 21 faculty members at UNC regarding their teaching experience and needs. Some key findings include:
- Most respondents (38%) have taught at UNC for less than 1 year, while 19% have taught for over 10 years.
- Subjects taught include various disciplines like education, nursing, music, and Spanish.
- Respondents were most interested in receiving technology support and training.
- Most drive 10-50 miles per week for teaching and hold 1-2 classes this semester at 1-2 institutions.
- The majority (67%) of courses are primarily face-to-face.
- Respondents indicated their best availability for meetings as Monday,
This study assessed a multilingual education program in primary schools in Thailand's Deep South. Researchers compared learning achievement between experimental schools using multilingual education and comparison schools. Students in experimental schools performed significantly better across subjects in grades 1-3. The study also found higher learning development in grade 2 students but slightly lower development in science and social studies for grade 3 students in experimental schools. The researchers concluded that multilingual education benefits student learning and should be expanded to more schools, while also providing additional training for teachers in certain subjects.
The document discusses a study investigating 200 Malaysian secondary students' understanding of logarithms. There were two main findings: 1) Students made various common mistakes when working with logarithms, especially with the second and third laws of logarithms. 2) Students struggled most with questions requiring higher-order thinking beyond routine calculations. The researchers aim to identify errors to help teachers improve instruction on this challenging topic.
This document summarizes a daily lesson plan for a Grade 8 mathematics class on probability. The lesson plan covers key concepts of probability including calculating the probability of simple events and appreciating its importance in daily life. Example probability problems are provided to help students understand concepts like determining possible outcomes and calculating probabilities. A quiz is used to evaluate student learning, and additional activities are suggested for students requiring remediation.
Brainwonders | Career counselling centres in mumbai | iq testBrainwonders
Brainwonders offers IQ Test and Psychometric Test. An IQ test (intelligence quotient) is a total score derived from several standardised tests designed to assess human intelligence. Get Connected to the best Career Counselling Centres in Mumbai and get answers to all your queries.
This project analyzed the amount of time 13 grade 12 students spent studying for finals. It found that on average students spent 14.23 hours studying, with the most time spent on math (4.54 hours), natural sciences (4.23 hours), and English (2.85 hours). Less time was spent on social sciences (1.85 hours) and arts (0.77 hours). Charts clearly represented the individual and average study times and showed that students generally spent the most time preparing for math, science, and English finals.
Unit 6 presentation base ten equality form of a number with trainer notes 7.9.08jcsmathfoundations
The document discusses concepts related to base ten, equality, and forms of numbers. It defines these concepts, examines how students develop an understanding through research on cognitive development, and provides classroom applications and strategies for teaching these concepts effectively. Diagnostic questions are presented to assess student understanding, and examples show how to respond to common student errors or misconceptions in working with numbers.
This document provides a series of mathematics assessment tasks for kindergarten students addressing common core standards for counting, cardinality, operations and algebraic thinking. The tasks involve counting objects, comparing quantities, addition and subtraction word problems, and missing addend problems. Teachers are instructed to observe students' strategies and accuracy in completing the tasks. The tasks increase in difficulty level across the school year quarters.
This document summarizes research assessing the educational consequences of teacher deficits in content matter and language of instruction. Testing of 185 teacher trainees in Cameroon found low levels of English proficiency and math knowledge. On average, trainees scored below 50% on a reading comprehension test and 38% in math. Analysis suggests teachers' limited content mastery and language skills may negatively impact students' learning through a probabilistic model. The research highlights the need to better understand how to improve teacher competency to support quality instruction in diverse educational systems.
nsejs 2013 question paper fiitjee
nsejs 2014 question paper
nsejs question paper 2016
nsejs preparation books
nsejs syllabus
nsejs 2016 question paper pdf
nsejs 2013 question paper pdf
nsejs 2012 question paper
nsejs previous year papers
NSEJS Olympiad Sample & Previous Year Papers
SECTION 1A. Journal Week 2Chapter 4 in Affirming Diversity pag.docxkenjordan97598
SECTION 1
A. Journal Week 2
Chapter 4 in Affirming Diversity pages 65-91.
1. How might you make a convincing argument that all students should have equal access and opportunity to algebra or its integrated counterpart in grade 8 and advanced placement courses in high school?
Reflect upon the following curriculum questions:
· In what ways is the mathematics curriculum limiting or detrimental?
· In what ways is the mathematics curriculum beneficial?
· Does the classroom teacher make his/her own mathematics curriculum and if so how is it evaluated in terms of student achievement?
· Have you and/or your colleagues been involved in developing the curriculum or do you rely on the textbooks?
Reflect upon the following pedagogy questions:
· What might you look for in order to identify the philosophical framework of a practitioner's pedagogy?
· How can pedagogical strategies reflect or promote anti-bias, equity, or social justice?
· What do you need to know in order to identify and claim your own pedagogy?
Read the Case Study: Linda Howard. Chapter 4, pages 91-101.
Answer the following questions in your journals:
1. If you were one of Linda's teachers, how might you show her that you affirm her identity? Provide specific examples.
2. What kind of teachers have most impressed Linda? Why? What can you learn from this in our own teaching?
3. What skills do you think teachers need if they are to face the concerns of race and identity effectively?
B. Journal Week 3—ANSWER QUESTIONS & REFLECT
A group of students were asked to compare the following ratios which represent the amount of orange concentrate mixed with the amount of water. The students needed to determine which of the mixes was the most 'orangey." The students were also told they could not convert the ratios to decimals or percents, nor could they use calculators.
Orange Mix
Water
a.
1
to
3
b.
2
to
5
c.
3
to
7
d.
4
to
11
One student responded as follows:
What does the evidence in this work tell you about the student's understanding of comparing ratios? How would you respond to the student?
C. Journal week 7---REFLECTION ON ARTICLE
D. JOURNAL WEEK 8
"Each student, regardless of disability, difference, or diversity, needs access to the curriculum that is meaningful and that allows the student to use his or her strengths."
Earlier in this course we examined templates for multiple representations and for vocabulary development. Examine the following graphic organizer:
From Math for All: Differentiation Instruction, Grades 3 - 5, pg. 143.
Complete this graphic organizer or one of your choosing for the Speeding Ticket problem.
How do you think using a graphic organizer will help your students? Would you require all students to use a graphic organizer or only certain students? Explain your thinking.
SECTION 2
A. REPLIES
ELIZABETH:You cannot take a smaller number from a larger number.
I’m thinking this must be a typo. It should read you couldn’t take a larger number from a.
The document provides information about student work on a task involving analyzing data about duckling families. It includes the task rubric, examples of different student work showing understandings and misunderstandings, and discussion questions for teachers. Several students were able to correctly fill in a frequency table and find the median but struggled with conceptual understanding of the mean. Many students treated the frequency table as a numerical sequence instead of representing data. The document examines what students understood about measures of central tendency and areas of difficulty, and provides questions to help teachers reflect on supporting students' conceptual development.
Tailieu.vncty.com ielts general test 3Trần Đức Anh
- The document contains an IELTS practice reading test with multiple choice and short answer questions about three passages.
- The passages discuss topics like a health center policies, employee break policies, and library resources and policies.
- The questions test comprehension of details in the passages like services provided, policies, required actions, and headings that match paragraphs.
The document discusses a study examining the concurrent and predictive validity of two nonverbal tests (the Naglieri Nonverbal Ability Test and Raven's Colored Progressive Matrices) in relation to math and reading comprehension exam scores of Italian third- and fifth-grade students from diverse sociocultural backgrounds. A group of 253 students took the nonverbal tests at the start and end of the school year, and their exam scores were analyzed. The students were grouped by grade, gender, age, and family cultural status (low, moderate, high). The purpose of the study was to evaluate whether the nonverbal tests could accurately predict academic performance across sociocultural groups.
The document provides examples of student work and analysis on a 7th grade math assessment task involving mixing paints. It includes:
1) Examples of four student solutions, with some students accurately tracking amounts and percentages while others lost track of whole amounts.
2) Analysis of common student errors like providing fractions instead of amounts in quarts or incorrectly thinking the percentage was 66% instead of 33%.
3) A summary of what students understood, such as finding fractional amounts of paint, and areas of difficulty like using fractions versus amounts and tracking part-whole relationships.
Problem-Solving Capacity of Students: A Study of Solving Problems in Differen...theijes
Training towards the development of the capacity of learners has become an inevitable trend of world education. Vietnamese education also emphasizes the comprehensive development of the capacity and the quality of students. In mathematics teaching, there are some notable capacities such as problem-solving capacity, cooperation capacity, capacity for using mathematical language, computing capacity and so on. In particular, the problem-solving capacity is very important to students because it helps them to solve problems not only in mathematics but also in practice. In this paper, we want to investigate the problem-solving capacity of students in primary schools through a problem required to solve in different ways. The results of the study showed that students had enough the problem-solving capacity to find out various solutions to the given problem
The document discusses using an empty number line as a mental math strategy for primary grade students. It explains that the empty number line allows students to create a mental image of math strategies and more easily make the leap to mental calculations without paper. Using the empty number line also increases students' number sense and flexibility with numbers. The document provides an example of how to introduce the empty number line technique to students and have them use it to solve math problems.
This is a presentation to help students who always become feared during Maths Exam. This presentation tells about what are the elements that initiates this phobia and what are the possible ways by both the teachers and the students to overcome such Phobia. This presentation also contains Vedic mathematics tricks that helps you to do calculations easily
The document describes the guess-and-check algorithm for division. It involves estimating how many times the divisor goes into the dividend and recording estimates in a side column. The estimates are then added to find the quotient. Even students with limited math facts knowledge can use this intuitive approach to find correct answers. The document also provides guidance for teachers to help students understand the process.
This document contains an initial report with responses from 21 faculty members at UNC regarding their teaching experience and needs. Some key findings include:
- Most respondents (38%) have taught at UNC for less than 1 year, while 19% have taught for over 10 years.
- Subjects taught include various disciplines like education, nursing, music, and Spanish.
- Respondents were most interested in receiving technology support and training.
- Most drive 10-50 miles per week for teaching and hold 1-2 classes this semester at 1-2 institutions.
- The majority (67%) of courses are primarily face-to-face.
- Respondents indicated their best availability for meetings as Monday,
This study assessed a multilingual education program in primary schools in Thailand's Deep South. Researchers compared learning achievement between experimental schools using multilingual education and comparison schools. Students in experimental schools performed significantly better across subjects in grades 1-3. The study also found higher learning development in grade 2 students but slightly lower development in science and social studies for grade 3 students in experimental schools. The researchers concluded that multilingual education benefits student learning and should be expanded to more schools, while also providing additional training for teachers in certain subjects.
The document discusses a study investigating 200 Malaysian secondary students' understanding of logarithms. There were two main findings: 1) Students made various common mistakes when working with logarithms, especially with the second and third laws of logarithms. 2) Students struggled most with questions requiring higher-order thinking beyond routine calculations. The researchers aim to identify errors to help teachers improve instruction on this challenging topic.
This document summarizes a daily lesson plan for a Grade 8 mathematics class on probability. The lesson plan covers key concepts of probability including calculating the probability of simple events and appreciating its importance in daily life. Example probability problems are provided to help students understand concepts like determining possible outcomes and calculating probabilities. A quiz is used to evaluate student learning, and additional activities are suggested for students requiring remediation.
Brainwonders | Career counselling centres in mumbai | iq testBrainwonders
Brainwonders offers IQ Test and Psychometric Test. An IQ test (intelligence quotient) is a total score derived from several standardised tests designed to assess human intelligence. Get Connected to the best Career Counselling Centres in Mumbai and get answers to all your queries.
This project analyzed the amount of time 13 grade 12 students spent studying for finals. It found that on average students spent 14.23 hours studying, with the most time spent on math (4.54 hours), natural sciences (4.23 hours), and English (2.85 hours). Less time was spent on social sciences (1.85 hours) and arts (0.77 hours). Charts clearly represented the individual and average study times and showed that students generally spent the most time preparing for math, science, and English finals.
Unit 6 presentation base ten equality form of a number with trainer notes 7.9.08jcsmathfoundations
The document discusses concepts related to base ten, equality, and forms of numbers. It defines these concepts, examines how students develop an understanding through research on cognitive development, and provides classroom applications and strategies for teaching these concepts effectively. Diagnostic questions are presented to assess student understanding, and examples show how to respond to common student errors or misconceptions in working with numbers.
This document provides a series of mathematics assessment tasks for kindergarten students addressing common core standards for counting, cardinality, operations and algebraic thinking. The tasks involve counting objects, comparing quantities, addition and subtraction word problems, and missing addend problems. Teachers are instructed to observe students' strategies and accuracy in completing the tasks. The tasks increase in difficulty level across the school year quarters.
This document summarizes research assessing the educational consequences of teacher deficits in content matter and language of instruction. Testing of 185 teacher trainees in Cameroon found low levels of English proficiency and math knowledge. On average, trainees scored below 50% on a reading comprehension test and 38% in math. Analysis suggests teachers' limited content mastery and language skills may negatively impact students' learning through a probabilistic model. The research highlights the need to better understand how to improve teacher competency to support quality instruction in diverse educational systems.
nsejs 2013 question paper fiitjee
nsejs 2014 question paper
nsejs question paper 2016
nsejs preparation books
nsejs syllabus
nsejs 2016 question paper pdf
nsejs 2013 question paper pdf
nsejs 2012 question paper
nsejs previous year papers
NSEJS Olympiad Sample & Previous Year Papers
SECTION 1A. Journal Week 2Chapter 4 in Affirming Diversity pag.docxkenjordan97598
SECTION 1
A. Journal Week 2
Chapter 4 in Affirming Diversity pages 65-91.
1. How might you make a convincing argument that all students should have equal access and opportunity to algebra or its integrated counterpart in grade 8 and advanced placement courses in high school?
Reflect upon the following curriculum questions:
· In what ways is the mathematics curriculum limiting or detrimental?
· In what ways is the mathematics curriculum beneficial?
· Does the classroom teacher make his/her own mathematics curriculum and if so how is it evaluated in terms of student achievement?
· Have you and/or your colleagues been involved in developing the curriculum or do you rely on the textbooks?
Reflect upon the following pedagogy questions:
· What might you look for in order to identify the philosophical framework of a practitioner's pedagogy?
· How can pedagogical strategies reflect or promote anti-bias, equity, or social justice?
· What do you need to know in order to identify and claim your own pedagogy?
Read the Case Study: Linda Howard. Chapter 4, pages 91-101.
Answer the following questions in your journals:
1. If you were one of Linda's teachers, how might you show her that you affirm her identity? Provide specific examples.
2. What kind of teachers have most impressed Linda? Why? What can you learn from this in our own teaching?
3. What skills do you think teachers need if they are to face the concerns of race and identity effectively?
B. Journal Week 3—ANSWER QUESTIONS & REFLECT
A group of students were asked to compare the following ratios which represent the amount of orange concentrate mixed with the amount of water. The students needed to determine which of the mixes was the most 'orangey." The students were also told they could not convert the ratios to decimals or percents, nor could they use calculators.
Orange Mix
Water
a.
1
to
3
b.
2
to
5
c.
3
to
7
d.
4
to
11
One student responded as follows:
What does the evidence in this work tell you about the student's understanding of comparing ratios? How would you respond to the student?
C. Journal week 7---REFLECTION ON ARTICLE
D. JOURNAL WEEK 8
"Each student, regardless of disability, difference, or diversity, needs access to the curriculum that is meaningful and that allows the student to use his or her strengths."
Earlier in this course we examined templates for multiple representations and for vocabulary development. Examine the following graphic organizer:
From Math for All: Differentiation Instruction, Grades 3 - 5, pg. 143.
Complete this graphic organizer or one of your choosing for the Speeding Ticket problem.
How do you think using a graphic organizer will help your students? Would you require all students to use a graphic organizer or only certain students? Explain your thinking.
SECTION 2
A. REPLIES
ELIZABETH:You cannot take a smaller number from a larger number.
I’m thinking this must be a typo. It should read you couldn’t take a larger number from a.
The document provides information about student work on a task involving analyzing data about duckling families. It includes the task rubric, examples of different student work showing understandings and misunderstandings, and discussion questions for teachers. Several students were able to correctly fill in a frequency table and find the median but struggled with conceptual understanding of the mean. Many students treated the frequency table as a numerical sequence instead of representing data. The document examines what students understood about measures of central tendency and areas of difficulty, and provides questions to help teachers reflect on supporting students' conceptual development.
Tailieu.vncty.com ielts general test 3Trần Đức Anh
- The document contains an IELTS practice reading test with multiple choice and short answer questions about three passages.
- The passages discuss topics like a health center policies, employee break policies, and library resources and policies.
- The questions test comprehension of details in the passages like services provided, policies, required actions, and headings that match paragraphs.
The document discusses a study examining the concurrent and predictive validity of two nonverbal tests (the Naglieri Nonverbal Ability Test and Raven's Colored Progressive Matrices) in relation to math and reading comprehension exam scores of Italian third- and fifth-grade students from diverse sociocultural backgrounds. A group of 253 students took the nonverbal tests at the start and end of the school year, and their exam scores were analyzed. The students were grouped by grade, gender, age, and family cultural status (low, moderate, high). The purpose of the study was to evaluate whether the nonverbal tests could accurately predict academic performance across sociocultural groups.
The document provides examples of student work and analysis on a 7th grade math assessment task involving mixing paints. It includes:
1) Examples of four student solutions, with some students accurately tracking amounts and percentages while others lost track of whole amounts.
2) Analysis of common student errors like providing fractions instead of amounts in quarts or incorrectly thinking the percentage was 66% instead of 33%.
3) A summary of what students understood, such as finding fractional amounts of paint, and areas of difficulty like using fractions versus amounts and tracking part-whole relationships.
Problem-Solving Capacity of Students: A Study of Solving Problems in Differen...theijes
Training towards the development of the capacity of learners has become an inevitable trend of world education. Vietnamese education also emphasizes the comprehensive development of the capacity and the quality of students. In mathematics teaching, there are some notable capacities such as problem-solving capacity, cooperation capacity, capacity for using mathematical language, computing capacity and so on. In particular, the problem-solving capacity is very important to students because it helps them to solve problems not only in mathematics but also in practice. In this paper, we want to investigate the problem-solving capacity of students in primary schools through a problem required to solve in different ways. The results of the study showed that students had enough the problem-solving capacity to find out various solutions to the given problem
This document describes a study conducted to improve the mathematical skills of engineering students. It found three groups of students - high school, vocational training modules (VTM), and others - had different mathematical deficiencies. An online tool was developed to help VTM students, who had the lowest scores. Classroom sessions also aimed to address common errors. Results showed the online course improved exam scores and confidence for VTM students. Classroom work reduced errors in targeted areas but had less impact on untargeted concepts.
Analysis Of Students Errors On The Fraction Calculation Operations ProblemLisa Garcia
This document summarizes a study on students' errors in fraction calculation operations. The study analyzed test responses from 61 fifth grade students from two elementary schools in Banda Aceh, Indonesia. The majority of students made concept errors in problems involving converting mixed fractions to ordinary fractions, determining fraction values, and performing fraction addition and subtraction. Some students also made principle errors or careless mistakes. Interviews revealed that students struggled with understanding the concepts and procedures for fraction calculations. The study aims to help teachers identify common errors and address conceptual misunderstandings to improve the teaching and learning of fractions.
This document discusses different techniques for analyzing problems, including stratification of symptoms, Pareto analysis, and identifying the most frequent causes. It explains that Pareto analysis uses the 80/20 rule to identify the top 20% of causes that account for 80% of the problems. The document provides steps for performing a Pareto analysis, including arranging causes by frequency, adding a cumulative percentage column, plotting the data on a graph, and identifying the key causes above the 80% line. The learning from this technique is that it helps prioritize problems by focusing first on the most impactful few causes.
This document discusses bunking classes and identifies the key symptoms and factors contributing to student absenteeism. It begins with an introduction to Pareto diagrams and how they can be used to stratify problems. The document then analyzes data showing an increase in the number of students missing lectures each year. It identifies several common symptoms for absenteeism, and determines that poor teaching skills account for 80% of the frequency. Potential problems from bunking classes are defined, including students falling behind and wastage of resources. The team's key lesson is that absenteeism disrupts the learning environment.
1) The document outlines a daily lesson log for a 6th grade mathematics class covering percentages, rates, and bases over a week.
2) The lesson objectives are to understand and apply order of operations, ratios, proportions, percentages, exponents, and integers to mathematical and real-world problems.
3) Each day covers different activities and examples to practice calculating percentages, rates, and bases using various strategies and resources.
Better mathematics workshop pack spring 2015: primaryOfsted
This document provides information for participants of a mathematics conference, including example questions, approaches to teaching different topics, and extracts of student work. It discusses identifying and addressing misconceptions, developing conceptual understanding, varying the depth and type of questions asked, and using student work and lessons to check for understanding and inform instruction.
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An Investigation of Errors Related to Solving Problems on Percentages
1. The International Journal Of Engineering And Science (IJES)
|| Volume || 6 || Issue || 3 || Pages || PP 05-09 || 2017 ||
ISSN (e): 2319 – 1813 ISSN (p): 2319 – 1805
DOI: 10.9790/1813-0603020509 www.theijes.com Page 5
An Investigation of Errors Related to Solving Problems on
Percentages
Duong Huu Tong
School of Education, Can Tho University, Vietnam
--------------------------------------------------------ABSTRACT-----------------------------------------------------------
In primary schools of Viet Nam, solving problems on percentages is a very important bit of knowledge because
it not only provides a full range of knowledge of percentages but also a lot of practical applications and has a
great effect in the development of thinking for students. However, it is a kind of new and difficult problem, so
students often commit errors to solve problems on percentages. A survey of 149 primary school students was
done. The students had to answer 7 questions about the problems on percentages. Results show that they suffer
some errors such as: misunderstanding kinds of problems, doing wrong calculation, confusing the units of
measurements. At the end of the paper, some suggestions in mathematics education are made to teachers to
support students avoiding errors in solving problems on percentages.
Keywords: Error, reason,solving problems on percentages, mathematics education.
-------------------------------------------------------------------------------------------------------------------------------------
Date of Submission: 02 March 2017 Date of Accepted: 27 March 2017
--------------------------------------------------------------------------------------------------------------------------------------
I. INTRODUCTION
Error topics usually attract great interest in academic theories. For example, the doctrine of behavior considers
an error as a reflection of ignorance or negligence. Meanwhile, according to the constructivist theory, the error is
an important factor in building the cognitive activity of students for some reasons. First, when creating an
imbalance in the subject's thinking system, recognizing errors facilitates good conditions for students to
overcome them and leads to a new incremental balance. Moreover, it is assumed that the error is not a minor
event that occurs in a cognitive process. For this reason, it does not exist outside knowledge, but it is a reflection
of knowledge.A French mathematical educator, Brousseau also emphasizes the importance of researching errors
in teaching mathematics.
Errors are not only ambiguous or random things but also they are considered as the results of knowedge that
has previously been found to be useful and successful, but now it is useless or unsuitable in new situations.
These errors are not normal or unpredictable. They form obstacles. In teacher’s activity as well as in student’s
activity, the errors always contribute to building the meaning of acquired knowledge.
(Brousseau, quoted in Bessot’s book)
A Vietnamese mathematical educator, P.Đ. Thuc also shares the same point of view, and he says that correcting
errors has an important significance in developing students' thinking, reinforcing their knowledge and skills.
Futhermore, he thinks that the errors of students are due to many different reasons.
In addition to Thuc's view, the error was also studied by my colleague, Nguyen Phu Loc. He surveyed 12th grade
students’ errors in calculating the integrals in 2014 and solving problems on coordinate methods in space in
2015. Moreover, he raised some advantages of teachers’ attention to students’ errors such as: recognizing the
errors of their students; adjusting their teaching methods; doing action research to check the effectiveness of
their teaching. Solving problems on percentages is introduced in the 5th grade mathematics textbook of Vietnam.
Besides, it is said to be a kind of exciting problem. Thus, to solve these problems, students must know how to
analyze, synthesize and apply lots of learned knowledge to use that knowledge in a creative way. In fact, not all
students solve the problems correctly, they also have many mistakes. For example, they still apply the wrong rule
to find the percentages of the two numbers. Here, to better understand this, we clarify three basic kinds of
percentage problems and ways to solve them.
Kind 1: Find the percentages of the two numbers
Example: There are 315 schoolgirls in Van Tho Primary School out of all 600 students. Find the percentage of
schoolgirls.
Solution:
The ratio of schoolgirls to all students in the school is 315 : 600 . We have:
315 : 600 0.525
0.525 100 :100 52.5 :100 52.5%
2. An Investigation Of Errors Related To Solving Problems On Percentages Duong Huu Tong
DOI: 10.9790/1813-0603020509 www.theijes.com Page 6
So the percentage of schoolgirls is 52.5% .
A process of solving this problem:
To find the percentage of 315 to 600, we do the following steps:
- Find the quotient when dividing 315 by 600.
- Multiply the found quotient by 100 and add the symbol “%” to the right of the product.
Kind 2: Find the percentage value of a number
Example: A primary school has 800 students, 52.5% of which are schoolgirls. How many schoolgirls are there in
that school?
Solution:
1% of students of the whole school is: 800 :100 8 (students)
The number of schoolgirls or 52.5% of all students is: 8 52.5 420 (students)
The textbook mentions a rule: To find 52.5% of 800, we divide 800 by 100 then multiply the quotient by 52.5, or
multiply 800 by 52.5 then divide the product by 100.
Kind 3: Find a number knowing its percentage
Example: There are 420 girls in a school, who account for 52.5% of all students. How many students are there in
the school?
Solution:
1% of all students are: 420 : 52.5 8 (students)
The total number of students in the school or 100% students of the schoool are: 8 100 800 (students)
Those steps can be merged as: 420 : 52.5 100 800
A solving rule is raised in the textbook: To find a number knowing that 52.5% of it is 420, we divide 420 by
52.5% then multiply the quotient by 100 or multiply 420 by 100 then divide the product by 52.5.
The process of solving the above problems is rather complex. In addition, students must usually manipulate on
decimals. Also, their practical skills needed in analyzing and synthesizing diagrams and tables, and establishing
the relationship between the data in the percentage problems are limited almost. Therefore, it is inevitable for
students to commit errors to solve these kinds of problems.
The research question: Do students have errors in solving the problems on percentages? Which errors
can they commit?
II. METHODOLOGY
2.1. Participants
The experiment was conducted in four classes in Ngo Quyen Primary School in Cantho city, Vietnam. There
were all 149 5th grade students. They are eleven years old.
2.2. Instrument and procedure
Students have to answer 7 objective questions. These test types are true-false and multiple choices.
The student questionnaire
You just circle the correct answer
1. To find the percentage of 13 out of 25, we have to do:
A. 25 :13 B. 13 : 25 C. 25 : 38 D. 13 : 38
2. To find the percentage of 1 out of 6 knowing 1 : 6 0.166666.... The percentage of 1 out of 6 is:
A. 16% B.16.66% C.17% D. All of them are correct.
3. There are 2.8kg of salt in 80kg of sea water. Find the percentage of salt to sea water.
The following solution is true or false?
Solution
The percentage of salt to sea water is:
2.8 : 80 0.035%
Answer: 0.035%
A. True B. False
4. 0.07%
A.
7
1 0
B.
7
1 0 0
C.
7
1000
D.
7
1 0 0 0 0
5. Find 10% of 8dm:
A. 8cm B.0.8 C. Both of A and B are correct D. Both of A and B are wrong
6.
a. Find 30% of 72. Choose the correct calculation
A. 72 30 :100 21.6 B. 72 : 30 100 240 C. 30 : 72 100 41.67
b. Find a number of which 30% is 72. Choose the correct calculation
3. An Investigation Of Errors Related To Solving Problems On Percentages Duong Huu Tong
DOI: 10.9790/1813-0603020509 www.theijes.com Page 7
A. 72 30 :100 21.6 B. 72 : 30 100 240 C. 30 : 72 100 41.67
7. A primary school has 600 students, 52% of which are schoolgirls. How many schoolgirls are there in that
school?
The following solution is true or false?
Solution
1% of students of the whole school is: 600 :100% 6 (students)
The number of schoolgirls is: 6 52% 312 (students)
Answer: 312 students.
A. True B. False
a. The class context of the experimental questions
Students learnt three kinds of problems on percentages. The methods of solving them were specifically
introduced to students by their teachers.
b. The corrcect answers expected for questions in the context of Vietnam
The right answers to the given questions were presented in Table 1.
Table 1: The correct answers expected to 8 questions
Questions 1 2 3 4 5 6a 6b 7
Answers B B B D A A B B
III. RESULTS AND DISCUSSION
Table 2: The percentages of students choosing the answers
Question 1: This question was used to check students’ ability to find the percentage of the two numbers.
Specifically, did they really find the quotient of the two numbers corrcectly?. From the survey results, 87.92% of
students chose the right result (B). However, 18 students were still confused. The reason was that they did not
distinguish between the object to compare and the object selected as a comparison unit.
Question 2: When finding the percentage of two numbers and the quotient was a infinite remainder, 17.45% of
students got the wrong results. They also calculated wrongly due to lack of knowledge. Students forgot that when
they found the percentage, the result had to be a four-figure decimal.
Question 3: To find the percentage of the two numbers, students will go through two steps. The first step is
finding the quotient of the two numbers. The other step is multiplying the found quotient by 100 and adding the
symbol “%” to the right of the product. However, according to the survey, up to 23.49% of students were
confused when calculating this form of problem, because they were subjective or careless while doing the
homework. Some children missed the step of multiplying the quotien by 100, in particular, they only found the
quotient, then added the symbol “%” to the right of the quotient. It led to wrong results.
Question 4: According to Table 2, the correct answer of the fourth question was D, but only 8.05% of students
chose this answer. That proves that the majority of students made the mistake of writing the percentage into
decimal fractions. The children calculated incorrectly because they confused this kind of problem with the
problem “writing a decimal into a decimal fraction”. Meanwhile, some children's calculation skills were limited
to find the exact result.
Question 5: When finding a percentage value of a number with a unit attached (maybe cm, dm, kg, g,...), only
24.16% of students identified the correct result. The remaining children found the wrong result due to forgetting
the accompanying unit behind it. Also, some children knew that there were units attached but in the answers
there were no units like the given question, they chose the answer D “Both of A and B are wrong”. Nevertheless,
the unit was calculated, transferred to another unit, and the result was still true. It revealed that students were
absent-minded while doing their homework.
4. An Investigation Of Errors Related To Solving Problems On Percentages Duong Huu Tong
DOI: 10.9790/1813-0603020509 www.theijes.com Page 8
Questions 6a and 6b: The percentages of correct answers were respectively 81.88% in question 6a and 78.52%
in question 6b. It was clear to say that students also made the mistakes of solving problems “find the percentage
value of a number” and “find a number knowing its percentage”. The main reason was due to students’
confusion between their solutions. Indeed, some children have a habit of mechanically remembering, for
example, one will multiply by 100 and the other will divide by 100. Because they did not understand the nature
of the problems, they applied the rules wrongly. If the students do not master the knowledge, it is easy for them
to have errors in new situations.
Question 7: From the results of the survey, 86.58% of students made mistakes as they did not understand the
nature and meaning of the "%" symbol. In this case, they found the right result, but they misrepresented. By way
of consequences, they was indiscriminate in using the "%" symbol, leading to a mathematical misnomer. One
more thing is that because they are absent-minded during the test, when they found the result “312”, similar to
the result of the answer they was not interested in the presentation. Only a small number of students (14.42% -
B) were careful to do the right choice. A student's work is presented below:
5. An Investigation Of Errors Related To Solving Problems On Percentages Duong Huu Tong
DOI: 10.9790/1813-0603020509 www.theijes.com Page 9
IV. CONCLUSION
The survey results show that many students make the mistakes of solving the problem on percentages.
Additionally, the causes of the errors are also varied. The sstudents may be careless, misunderstand the problems
or do not still discriminate among the kinds of problems on percentages. Therefore, it is important to say that the
teachers should know the errors and find their causes so that they need to take practical measures to help their
students overcome such errors. The necessities in mathematics education that teachers must pay attention to
during instruction to help students learn the percentage well are:
- Combining teaching methods with proficient use of teaching media.
- Paying attention to the basic knowledge when teaching new lessons.
- Practicing step by step clearly, specifically, do not turn off the steps when practicing the sample.
- Carefully analyzing the causes of the errors to correct promptly, then let students do the same exercises.
- Appreciating the method of practice in teaching the problems on percentages in elementary schools.
REFERENCES
[1]. Bessot, A., Comiti, C., Chau, L.T.H., Tien, L.V.,(2009). The fundamental elements of Mathematics Didactic, Ho Chi Minh city:
Publishing house of The national university of Ho Chi Minh.
[2]. Hoan, Đ. Đ (editor). (2007). Mathematics 5 (Toán 5), Hanoi: Publishing house of Education.
[3]. Loc, N. P. & Hoc, T.C.T. (2014).A Survey of 12th Grade Students’ Errors in Solving Calculus Problems. International Journal of
Scientific & Technology Research, Volume 3, Issue 6, June 2014 ISSN 2277-8616.
[4]. Loc, N.P. & Kha, N.T. (2015). Students’ errors in solving problems on coordinate methods in space: Results from an investigation
in Vietnam, European Academic Research, Vol.III, and Issue 2/May.
[5]. Thuc, P.Đ. (2009). Methods of teaching mathematics in primary schools, Hanoi: Publishing house of Education.