An Effective Approach in Solving Math Problems

1 | Page

Numerical Expressions and Word Problems: Identifying an Effective Approach in Solving Grade 6 Mathematical Problems

A Study presented to The Faculty of Junior High School Department Asian College of Technology- Integrated School Cebu City

AZCUNA, DONESA RHAE BERONIO, LUWIL ELUMBARING, JOSH FLORITA, LORNA MAE MAGALLANES, GLYNDEL SUSUSCO, PRINCE ANTHONY

March 2020

2 | Page

ACKNOWLEDGEMENT

In the present world of competition there is a race of existence in which those who are having will come forward to succeed. First of all, the researchers would like to thank the Almighty God who is obviously the one who guided the researchers throughout the process and guided the researchers to the right path.

Next to him are the parents, with their encouragement and guidance. This paper and the research behind it would not have been possible without the teamwork of the members: Azcuna, Beronio, Elumbaring, Florita, Magallanes, and Sususco.

The researchers would also like to thank the friends and the teachers, especially Ms. Loudelyn Venanzuela, Ms. Roxanne Mae Jao, and Ms. Mylyn Beringuela.

They are one of the reasons why this research is made because of sharing their knowledge to the researchers.

And lastly, the researchers would place on record, sense of gratitude to one and all who directly or indirectly have lent their helping hand in this venture.

3 | Page

TABLE OF CONTENTS

Abstract Chapter 1: The Problem and Its Scope Rationale

…..pg. 6

Theoretical Background

….. pg.7

Theoretical Framework

….. pg.8

Statement of the Problem

….. pg.9

Significance of the Study

….. pg.9

Scope and Limitation

….. pg.10

Definition of Terms

….. pg.10

Chapter 2: Review of Related Literature

….. pg.12

Chapter 3: Methodology Research Design

….. pg.20

Research Respondents

….. pg.20

Research Environment

….. pg.20

Research Instrument

….. pg.21

Research Procedure

….. pg.21

Date Gathering Procedure

….. pg.21

Chapter 4: Presentation, Analysis and Interpretation of Data

…..pg. 23

Chapter 5: Findings, Conclusions and Recommendations Findings

….. pg.28

4 | Page

Conclusion

…..pg. 29

Recommendation

…..pg. 30

Appendices

…..pg. 31

Bibliography

…..pg. 42

5 | Page

ABSTRACT

Math anxiety is one of many difficulties students encounter when learning the Math subject. In this anxiety, students tend to avoid activities regarding Mathematics. One of the reasons why students have this kind of anxiety is the approach taken into account in solving Math problems. Grade six students, especially, need an effective approach since they are getting ready to move up to high school. If they can’t cope up with their current approach there might be a possibility they would get low marks in higher Mathematics. That is why the researchers’ purpose is to identify an effective approach in solving grade six mathematical problems through numerical expressions and word problems. It is a quantitative study which uses test questionnaires to let the students answer and to let the researchers identify which approach is effective. The findings of this study shows that both Word Problems and Numerical Expressions are an effective approach, but Numerical Expressions is the approach which got students higher marks.

6 | Page

CHAPTER I THE PROBLEM AND ITS SCOPE

Rationale of the Study Math is related to stress, fear and anxiety. The higher one's math anxiety, the more one increases activity in regions associated with acute threat recognition, and sometimes the perception of pain itself, in anticipation of an upcoming math task (Lyons, Beilock, 2012).

Mathematics is the science which involves the logic of quantity and arrangement (Hom, 2013). It involves calculations and logical reasoning (Gray, Berggren, Folkerts, Fraser et al., 2019). Mathematicians use patterns to formulate new conclusions; they resolve a conclusion's truth and falsehood through mathematical proof.

The teaching methods and lack of understanding are two possible reasons why students don't learn mathematics (Kollosche, 2019). The students might correctly answer the given problems, but when it comes to the real world, they can't be able to apply these methods of solving. That is why, in this study, researchers are comparing which method is much more effective in solving grade six mathematical problems. Methods of two will be tested out, namely giving students activities of mathematical problems with the application of word problems and using numerical expressions only.

7 | Page

The researchers aim to identify an effective approach in solving grade 6 mathematical problems either through numeracy or word problems. Furthermore, they aim to improve the solving skills of the grade 6 students.

Theoretical Background The study is to identify an effective approach in solving grade 6 mathematical problems with the use of the numeracy and word problems approach. Numeracy is a mathematical sentence with one or more operating symbols and numbers only while word problems is any mathematical exercise in which significant background information on the issue is presented as text rather than

mathematical

notation.

These

approaches are shown through a

questionnaire survey that is answered by the grade 6 students.

The researchers’ study is supported by the theory of Realistic Mathematics Education by Barnes (2005). In RME, "realistic" circumstances take a prominent place in the learning process. Such situations serve as a basis for initiating the creation of mathematical concepts, methods, and procedures and as a framework in which students can apply their mathematical knowledge at a later stage, which has then slowly become more systematic and general and less context-specific (Barnes, 2005).

In Arsaythamby and Zubainur (2014) study, it was found that mathematics behaviors are higher for those who were taught using RME than for those who used the traditional method. Lestari and Surya (2017) also stated the findings of

8 | Page

their research show that the Realistic Mathematics Education approach is successful in explaining the mathematical definition of the students.

To relate this to the study, the researchers will be giving situations that relate to the everyday life of the students. By giving out these kinds of situations, students will be able to understand the tests given.

Theoretical Framework

9 | Page

Statement of the Problem 1. How effective are word problems in solving grade 6 mathematical problems?

2. How effective is numeracy in solving grade 6 mathematical problems?

3. What are the effective ways to improve solving skills of grade 6 in mathematical problems? Word Problems or Numerical Expressions?

Significance of the Study The purpose of this study is to help the students enhance and develop their skills in mathematics. It may give benefit to the following: Students. It helps the students understand math better, either letting students explain their understanding and reasoning about a topic, solving problems through real life situations or using visual presentations while teaching. It helps them enjoy learning math and it also expands their learning capacity in math.

Teachers. It helps the teachers in applying the effective strategy to let their students develop their skills in math. Although they have tried these techniques, they will be able to find out the loopholes which are the reason why students can’t understand math in this way.

Parents. It encourages the parents to help the teachers in teaching their kids math and to help their kids understand mathematics. In this way they can also have bonding time with each other.

10 | Page

Scope and Limitation The study will be conducted within the corners of Asian College of Technology Bulacao Campus. The study will be conducted for approximately six months ranging from September 2019 to February 2020. The respondents will be sixth grade students of the said campus. In this study, the scope of lessons that is going to be used is from the second quarter of the school year, September 2019 to October 2019. The second quarter covered percentage.

Definition of Terms Numerical Expressions – It is a mathematical sentence with one or more operating symbols and numbers only.

-

In the study, it is used as one of the effective approach in solving grade six math problems

Word Problems - It is any mathematical exercise in which significant background information on the issue is presented as text rather than mathematical notation.

-

In the study, it is used as one of the effective approach in solving grade six math problems

Effectiveness - The degree to which targets are met and to what extent targeted issues are solved.

-

In the study, it is one of the targets that the researcher aims to reach

11 | Page

Mathematics – The study of numbers, quantities, geometry and shapes sciences.

-

It is used as the subject being studied about and the subject the researchers are aiming to identify an approach

Math Anxiety – The anxiety that cannot be effectively performed in situations involving the use of mathematics -

It is used as one of the reasons why the researchers conducted the study

Academic Performance – It is the degree to which a student has achieved their educational goals in the short or long term.

-

It is used as the basis for the respondents

12 | Page

CHAPTER II REVIEW OF RELATED LITERATURE

Most students think math is difficult. As stated by Fleming (2019), Math seems to be hard because time and energy are required. Most people don't have enough time to "learn" math lessons, and as the instructor goes on, they fall back. Most move on with a shaky foundation to learn more complex concepts.

Often we end up with a weak foundation that at some stage is doomed to collapse.

Mathematics is a key skill for students from kindergarten to school (Gabriel, Atkins, Chokshi, Midence et al., 2019).The subject could also become a health problem called Math anxiety. Prior research has shown that mathematical anxiety is prevalent among students and is often associated with reduced academic performance in mathematical evaluations. Coming with this is the inability to grasp the subject well and students get confused about the methods and all the formulas.

Because of Mathematics, students have already developed an illness called Math anxiety. In people with math anxiety, a negative emotional reaction can be caused by opening a math textbook or even entering a math classroom, but it doesn't end there. One theory is that math anxiety is actually a metaphor for poor math ability, which suggests that math anxious individuals are less qualified or experienced in mathematics than their non-anxious counterparts (Maloney, Beilock, 2012).

13 | Page

Low activities in posterior parietal and dorsolateral prefrontal cortex regions, which is necessary in mathematical reasoning, is one of the effects that let the students trigger math anxiety (Young, Wu et al., 2012).

In a recent study, researchers’ early detection and treatment of mathematical anxieties is critical because these early anxieties can snowball and eventually lead students with the greatest potential to avoid math and career choices (Ramirez, Gunderson et al., 2013).

But, in this study, the researchers are showing the effectiveness of possible techniques or skills that could be used: Problem-solving skills and numeracy skills.

A basic skill which a person should have is a problem-solving skill. This skill involves critical and logical thinking (Widodo, 2017). Problem-solving, in an educational institution, is now one of the learning styles for a student to learn Mathematics. Problem-solving is not like the traditional method of teaching. It gives real-life scenarios for a student to understand how Math is related in real-life situations.

Word problems require students to apply their understanding in a certain topic to a real-life situation. As Ali, Akhter and Khan (2010) stated, the problem-solving method is more effective in letting students understand the different processes in Math. They stated if students were to stick to the traditional method, they would just have the basic knowledge of mathematics.

14 | Page

Word problems let students decide on a strategy to come up with a result.

They make choices for them to reach their goals. They could also use alternatives to come up with unexpected results for their problems (Star, Carononga, Foegen, Furgeson et al., 2015).

A recent study showed that the ability to interpret a mathematical word problem and return a comprehensive answer helps students by providing them with specific steps of an answer (Morton, Qu, 2013).

Current "word problems" include an important early mathematical modeling experience. Mathematical modeling is a powerful type of word problem.

Word problems are also used as inspiring a link between logic and arithmetic (Sangwin, 2011).

Another study showed that its researchers tested the results of a newly collected corpus of algebra word problems and also demonstrated that the device used could correctly answer nearly 70 percent of the data set questions (Kushman, Artzi et al., 2014).

Another, reading comprehension skills in mathematical word problems were able to reach the success of the students' high marks more than numerical expressions (Bjork, Bowyer-Crane, 2013).

Word problems are important to students as it improves the intellectual ability of the pupil, creates critical reasoning and encourages imaginative thought. It is also important because it enables them to be more rational about life and to navigate it better. It also shows students how to use reasoning and

15 | Page

imaginative thought in the execution of the task. This also lets the students take responsibility for them and face the truth of life (Marsh, 2018).

On the other hand, numerical expressions are made up of symbols such as variables, numbers, coefficients and more that make up a mathematical sentence more abstract. There are different kinds of numerical expressions --namely arithmetic operations, algebraic equations, summations, fractional expressions and more (Brown, 2017).

According to Star, Carononga, Foegen, Furgeson et al., (2015), numerical expressions let students think more abstractly. They stated expressions do not make students derive logical reasoning which can limit their learning capacity.

Numerical expressions can also be applied in everyday life. This can be used in household budgeting, especially in recognizing bank statements, paying gas, water and tax bills, operating a vehicle, recognizing drug labels, purchasing appliances and using credit cards (Kissane, 2012).

Word problems involve students’ ability to read and understand the problem, calculation of the problem and complete the calculations (Anisa, 2014).

Whereas numerical expressions, the simplest form is the most abstract for the students (Star, Carononga, Foegen, Furgeson et al., 2015).

Students have higher achievements with the problem-solving strategy (Ali, Akhter, Khan, 2010). It requires a fun learning process to make students actively participate in class and that includes teaching problem based strategies (Supriyono, Setiawan, Trapsilasiwi, 2014). While numerical expressions, as

16 | Page

stated by Widodo (2017), mathematical problems through numerical expressions cannot be solved completely. Algebraic expressions, for example, have too many formulas to use according to the number polynomials (Widodo, 2014).

To develop word problem-solving and sense-making capabilities for second language learners, the research demonstrated the benefits of facilitating the use of dialogue and argumentation strategies as a tool (Sepeng, 2010).

There are also problems with the problem-solving strategy. Some students have difficulty in reading and understanding the problem. They also dislike reading long texts. They don’t understand important keywords in the problem and they also don’t understand what the problem is asking for (Phonapichat, Wongwanich, Sujiva, 2014).

To add to these difficulties, students are lacking in inspiration, and some students are hesitant to address word problems. Students with inadequate word problem solving skills easily pick a simple solution and this solution can be hasty on certain theological issues (Sajadi, Amiripour, et al., 2013).

Numerical expressions also possess some problems. Students have problems in computing and applying formulas. In quadratic formulas, for example, students have a hard time computing operations like addition, subtraction, multiplication and division. They also have a hard time using negative and positive signs (Zakaria, 2010).

Another set of key problems in numerical expressions include the identification of expressions, the identification and interpretation of symbols, the

17 | Page

study of symbol form and the creation of sense representations (Zanibbi, Blostein, 2012).

Although, most educators use problem-solving as a tool for teaching.

Problem-solving makes their students enhance their learning and improve their independent learning skill (Ali, Akhter, Khan, 2010).

Same goes for numerical expressions. Expressions help students make a connection between problems and representations that may be different, but are actually similar mathematically (Star, Carononga, Foegen, Furgeson et al., 2015).

The study is supported by RME or Realistic Mathematics Education. RME is where "realistic" scenarios have a prominent role in the learning process. Such situations serve as a source for initiating the development of mathematical concepts in which students can later apply their mathematical knowledge.

"Realistic" means offering students situations they can imagine to be having problems. At RME, the problems that students face may come from the real world, but also from the future (Van den Heuvel-Panhuizen, Drijvers, 2014).

RME has principles namely activity principle, reality principle, level principle, intertwinement principle, interaction principle and guided reinvention principle.

A study suggested another principle, the producer principle. Producer principle states that learning math requires producing men. The next step for

18 | Page

work in Realistic Mathematics Education is to investigate and refinish these consequences (Peck, 2015).

In recent studies, it was found that mathematics behaviors are higher for those who have been taught using RME than those who use the traditional method (Arsaythamby, Zubainur, 2014). This result was also shown in Saleh et al, 2018 study. In another study, the results show that the Realistic Mathematics Education approach is successful in understanding the mathematical definition of the students (Lestari, Surya, 2017).

Another study used the Think-Pair-Share strategy, strategy in which students work with each other to solve a problem, and the RME theory. The results show that the TPS model using RME methodology can be extended to studying mathematics so that students can learn more effectively and understand the subject, and studying mathematics becomes more relevant (Afthina, Pramudya, 2017).

Mathematics, like some regions in Indonesia, the teacher is the main instructional guide, so only one form of textbook is used. Learning tends to be monotonous and repetitive, and students prefer to be compliant and do as taught by the instructor. Students' abstract reasoning ability is not well educated in studying mathematics. Students are simply taught how to memorize and use the solution to solve the problem. That is why the use of realistic mathematics education (RME) to enhance the standard of mathematics instruction should be considered in those regions (Tanujaya, et al., 2017).

19 | Page

Thus, based on the related literature and studies the researchers have gathered, numerical expressions and problem-solving strategies are effective ways on how to make students develop their skills in Mathematics and will be supported by the Realistic Mathematics Education (RME).

20 | Page

CHAPTER III METHODOLOGY

Research Design The method used for this study is quantitative. The students are given Mathematical questions for them to answer and to let the researchers assess what approach is more effective to them. Quantitative methods are designed to discover how many people think, behave or react in a particular way.

Research Respondents/Participants The study’s respondents are sixth grade students. Sixth grade, in the Philippines, is the last year of elementary school and could also be the preparatory year before students move up to secondary level. The researchers’ chose these respondents to prepare the students in moving up to secondary level. In Math, the researchers are aiming to find an effective approach, so that one these sixth graders move up to secondary they will have an approach in solving their Math problems.

Research Environment/Locale Asian College of Technology (ACT) is a private college in the Philippines, in Cebu City and Talisay City, in the province of Cebu. The environment of the study is the ACT - South Campus, located in Cebu South Road, Bulacao, Talisay City. It was founded by Rodrigo Abellanosa, a Cebu City Congressman. The

21 | Page

school is headed by the president, Dr. Joseph Stephen Descallar. ACT – South Campus is headed by their regular program principal, Nina Teresa C. Alilin.

Research Instrument The researchers used two questionnaires. The first questionnaire includes solving numerical expressions and the other one is solving word problems.

Research Procedure The first step before going to the testing is to make a request letter. Upon approval, the researcher-made questionnaire will be distributed to the respondents to gather data and information. The respondents will answer the given questionnaire then after all the questionnaires are answered, the researchers will start gathering the data.

Data Gathering Procedure The researchers made permit letters to the principal. The letters permit the researchers to excuse the study’s respondents and to also show the second quarter grades of the respondents. The researchers also asked the Grade 6 Mathematics adviser for the list of students who have average grade and above average grade in Math.

The researchers made test questionnaires of both word problems and numeracy covering the ‘Percentage’ lesson. The test was standardized from the Grade 6 Math adviser. Each method contains five items and students also need to fill out the given interview question.

22 | Page

After, the researchers will be tallying their scores and computing averages.

Then, they will be deriving a result of which approach is effective in solving grade 6 mathematical problems

23 | Page

CHAPTER IV PRESENTATION, ANALYSIS AND INTERPRETATION OF DATA TABLE 1 PUPIL NO. 1

1 ✔

2 3 4 5 6 7 8 9

✔

10

✔

WORD PROBLEM ITEM NO. 2 3 4 ✔

✔ ✔

11 12 13

✔

14

✔

15

✔

✔

16

✔

✔

✔

17 ✔

19

✔

20 21 22

✔

23

✔

✔

✔

✔

✔ ✔

18

5 ✔

✔ ✔

24 | Page

24

✔

25 26

✔

27 28

✔

✔

✔

29 30 TOTAL 12 AVERAGE 40%

✔

✔

7 23.33%

10 33.33%

0 0%

3 10%

Descriptor: AVERAGE 40 – 31 30 – 21 20 – 11 10 – 0 1st Question: 40% - Outstanding 2nd Question: 23.22%

- Very Satisfactory

3rd Question: 33.33%

- Outstanding

4th Question: 0

– Needs Improvement

5th Question: 10%

- Needs Improvement

Word Problems Total Score:

RANKING Outstanding Very Satisfactory Satisfactory Needs Improvement

32

The results show that in the Word Problems test, the numbers with the most correct answers are question number one, which has forty percent out of 30

25 | Page

students, and question number three which has 33.33 percent out of thirty students. Question number one asks for the whole price of a car tool and the percent of the down payment is given while question number three asks for the whole allowance before she went to the mall and the used money was given.

Question number two at 23.22 percent out of thirty students ranks as the third question the students answered correctly. The question asks for the percent of seats occupied in an auditorium. Then, question number five at ten percent and question number four at zero percent come fourth and last. This means these are the questions that students least understood. Both of the questions asked for the percent of how much budget used and how many carpenters were present.

TABLE 2 PUPIL NO.

NUMERICAL EXPRESSIONS ITEM NO. 2 3 4 ✔ ✔

1

1 ✔

2 3 4 5

✔

✔

6

✔

✔

7

✔

✔

8 9

✔

✔

✔

✔

10

✔

✔

✔

✔

11

✔

✔

✔

✔

5

26 | Page

12

✔

✔

13

✔

✔

14

✔

✔

15

✔

✔

✔

✔

✔

✔

✔

✔

16

✔

✔

17

✔

18 19

✔

20

✔

✔

✔

21

✔

✔

✔

✔

✔

22 23 24 25 26 27 28 29

✔

✔

✔

✔

30

✔

✔

✔

✔

TOTAL 14 AVERAGE 46.67%

15 50%

10 33.33%

15 50%

✔

✔

✔ 4 13.33%

Descriptor: AVERAGE 50 – 41 40 – 31 30 – 21

RANKING Outstanding Very Satisfactory Satisfactory

27 | Page

20 – 11 10 – 0

Needs Improvement Failed

1st Question: 46.67%

- Outstanding

2nd Question: 50%

- Outstanding

3rd Question: 33.33%

- Very Satisfactory

4th Question: 50%

- Outstanding

5th Question: 13.33%

- Needs Improvement

Numerical Expressions Total Score:

58

On the other hand, in Numerical Expressions, question number two and number four are the questions with the most correct answers with both at fifty percent out of thirty students. Question number two asks for the seventy percent of forty pets while number four asks for the fifty-eight percent of 10,100 people.

Question number one is also ranked as outstanding with 46.6 percent out of thirty students. The question asks for forty-five percent of PHP8, 300. Ranked as Very Satisfactory, question number three comes as the third most correctly answered question which asks for the seventy-five percent of sixty-eight students. Coming last, question number five asks for the ninety-one percent of 9.15 ounces.

28 | Page

As a result, out of thirty respondents, the students understood the Numerical Expressions more than Word Problems. Numerical Expressions got a total of fifty-eight correct answers while Word Problems got a total of thirty-two.

29 | Page

CHAPTER V FINDINGS, CONCLUSIONS AND RECOMMENDATIONS

Findings Word Problems is effective by letting the students solve problems that are much more related to their everyday lives. Example, one of the questions was about going to a mall and spending money. The topic of money is much related to the students since it is part of our everyday life. Thus, questions that students can relate to help them get high remarks.

Numerical Expressions are effective by giving the students direct problems. Students get higher remarks in questions which the given questions ask directly. Example, fifty-eight percent of 10, 100 surveyed people, this question lets students answer it directly as the given is divisible by ten or ends with zeros. The same results go to this example; seventy percent of 40 pets, students got higher remarks in this question because both given are divisible by ten or ends with zeros.

Both word problems and numerical expressions are effective approaches in solving grade six mathematical problems. Word problems let students relate real life events while numerical expressions let students analyze and answer the question directly.

30 | Page

Conclusion Mathematics has already developed an anxiety called Math Anxiety. This results in the study aiming to identify an effective approach in solving grade six mathematical problems through the use of word problems and numerical expressions. The study is supported by RME or Realistic Mathematics Education, a concept in which realistic or real life events are applied to the problems.

Word problems let students apply different strategies to answer a problem, but students could also fail in this approach if they lack the ability to analyze properly a problem while numerical expressions can also be used in everyday situations like household bills but this approach limits the students in their learning capacity.

The results show that students excel in numerical expressions rather than word problems. It was found that it was easy for them to answer such questions because what the problem asked was already given while word problems they still had to analyze what was given and what was asked.

Therefore, according to results and findings, the effective approach in solving grade six mathematical problems is numerical expressions.

31 | Page

Recommendation The results of the study show that students get low remarks in word problems while they get high remarks in numerical expressions. Both are approaches in solving grade six mathematical problems, but in the process, both also have its negative side in the students' learning ability.

The researchers recommend the students to use the numerical expressions as an approach since the results show students excel more in numerical expressions tests and they could analyze the question directly. But students also have to train themselves in reading and comprehension, so that in any word problems item test, they could analyze and generalize the problem easily.

The researchers recommend the parents and teachers to teach students reading and comprehension. During the process, it was found that students have low remarks in word problems because they could not analyze what the problem is asking for. Reading and comprehension is a skill needed to let them be able to understand the problem. So, teachers and parents recommend this skill to the students.

Lastly, the researchers recommend future researchers to also take note of the students’ abilities in solving problems. The students may be lacking the ability to analyze questions or the ability to apply the mathematical process in their tests.

32 | Page

APPENDICES January 13, 2020 NINA TERESA C. ALILIN, MAed Junior High School Principal Asian College of Technology Bulacao, Talisay City, Cebu Ma’am: Good day!

In line with the research subject, we, the Grade 9–Prudence would like to humbly ask permission to allow us to pull out 7 students from Grade 6-Wisdom as they are the research respondents in our research entitled, “Numerical Expressions and Word Problems: Identifying an Effective Approach in Solving Grade 6 Mathematical Problems”. They will be out for 20-minute time estimation, for they will answer the prepared interview questions designed to meet the necessary data for the success and accomplishment of our study.

We will start excusing students on January 14 until the desired or chosen respondents are interviewed. This will be conducted in the Grade 9-Prudence classroom.

Thank you for spending your time reading this. We hope that the undersigned begets a favorable response.

Thank you.

Sincerely yours, GRADE 9-PRUDENCE RESEARCHERS Group #1 Noted by: ROXAN MAE T. JAO, LPT Research Adviser

FLORAMAE S. ARAIN JHS Coordinator Approved by: NINA TERESA ALILIN, MAed School Principal

33 | Page

WORD PROBLEM (SAMPLE TEST) Solve the following then answer the interview questions.

1. Mr. Vicente intended to buy a car tool. He makes a down payment of 30%.

He paid P1,500. How much is the price of the car tool?

2. An auditorium has 500 seats, of which 325 are occupied . Express the attendance at a percent of capacity occupied?

3. Shane spent 50% of her allowance at the mall. If she spent P300 only, how much money did she have when she went to the mall?

4. Mrs. Dy spent P3,400 out of her P7,000 on buying grocery items. What percent of her money was spent on groceries?

5. There are 35 carpenters in the crew. On a certain day, 21 were present.

What percent showed up for work?

34 | Page

NUMERICAL EXPRESSIONS (SAMPLE TEST) Solve the following then answer the interview questions.

1. 45% of P8,300

2. 70% of 40 pets

3. 75% of 68 students

4. 58% of 10,100 surveyed people

5. 91% of 9.15 ounces

35 | Page

BIBLIOGRAPHY Afthina, H., & Pramudya, I. (2017, September). Think pair share using realistic mathematics education approach in geometry learning. In Journal of Physics: Conference Series (Vol. 895, No. 1, p. 012025). IOP Publishing.

Ali, R., Akhter, A., & Khan, A. (2010). Effect of using problem solving methods in teaching mathematics on the achievement of mathematics students. Asian Social Science, 6(2), 67.

Anisa, W. N. (2014). Improvement of Problem Solving Ability and Mathematical Communication Through Learning Realistic Mathematics Education for State Junior High School Students in Garut Regency. Journal of Education and Culture, 1 (1).

Arsaythamby, V., & Zubainur, C. M. (2014). How a realistic mathematics educational approach affect students’ activities in primary schools.

Procedia-Social and Behavioral Sciences, 159, 309-313.

Barnes, H. (2005). The theory of Realistic Mathematics Education as a theoretical framework for teaching low attainers in mathematics.

Pythagoras, 0(61), 42-57.

Bjork, I. M., & Bowyer-Crane, C. (2013). Cognitive skills used to solve mathematical word problems and numerical operations: a study of 6-to 7-year-old children. European journal of psychology of education, 28(4), 1345-1360.

36 | Page

Brown

N.

(2017).

What

is

a

Mathematical

Expression?.

retrieved

from: https://sciencing.com/mathematical-expression-8698419.html Fleming, G. (2019). Why Math Is More Difficult For Some Students. Retrieved from: https://www.thoughtco.com/why-math-seems-more-difficult-for-some-stude nts-1857216 Freudenthal, H. (1987). Mathematics starting and staying in reality. In Proceedings of the USCMP Conference on Mathematics Education on Development in School Mathematics around the World (pp. 279–295). Reston, VA: NCTM. Gabriel, M. H., Atkins, D., Chokshi, A., Midence, S., & Bowdon, M. (2019).

Exploring

Math

Anxiety

and

Math

Self-Efficacy

among

Health

Administration Students. Journal of Health Administration Education, 36(2), 151-168.

Gray, Berggren, Folkerts, Fraser, Knorr (2019). Mathematics. Encyclopedia Britannica.

Retrieved

from:

https://www.britannica.com/science/mathematics Hom

(2013).

LiveScience.

What

is

Mathematics?.

https://www.livescience.com/38936-mathematics.html

Retrieved

from:

37 | Page

Kissane, B. (2012). Numeracy: connecting mathematics. In Reasoning, Communication And Connections In Mathematics: Yearbook 2012, Association of Mathematics Educators (pp. 261-287).

Kollosche, D. (2019). Reasons for Auto-exclusion:Why Students Reject Mathematics. In Inclusive Mathematics Education (pp.449-465). Springer, Cham Kushman, N., Artzi, Y., Zettlemoyer, L., & Barzilay, R. (2014, June). Learning to automatically solve algebra word problems. In Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) (pp. 271-281).

Lestari, L., & Surya, E. (2017). The Effectiveness of Realistic Mathematics Education Approach on Ability of Students’ Mathematical Concept Understanding. International Journal of Sciences: Basic and Applied Research (IJSBAR), 34(1), 91-100.

Lyons, I. M., & Beilock, S. L. (2012). When math hurts: math anxiety predicts pain network activation in anticipation of doing math. PloS one, 7(10), e48076. https://doi.org/10.1371/journal.pone.0048076 Maloney, E. A., & Beilock, S. L. (2012). Math anxiety: Who has it, why it develops, and how to guard against it. Trends in cognitive sciences, 16(8), 404-406.

38 | Page

Marsh, J. (2018). Why Math Word Problems are Important?. Retrieved from: https://medium.com/@john_marsh7/why-math-word-problems-are-importa nt-14c5d0670b6b McCombes

(2019).

Descriptive

Research.

Scribbr.

Retrieved

from:

https://www.scribbr.com/methodology/descriptive-research/ Morton, K., & Qu, Y. (2013). A novel framework for math word problem solving.

International Journal of Information and Education Technology, 3(1), 88.

Peck, F. A. (2015). The intertwinement of activity and artifacts: A cultural perspective on Realistic Mathematics Education.

Phonapichat, P., Wongwanich, S., & Sujiva, S. (2014). An analysis of elementary school

students’

difficulties

in

mathematical

problem

solving. Procedia-Social and Behavioral Sciences, 116, 3169-3174.

Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (2013). Math anxiety, working memory, and math achievement in early elementary school. Journal of Cognition and Development, 14(2), 187-202.

Sajadi, M., Amiripour, P., & Rostamy-Malkhalifeh, M. (2013). The examining mathematical word problems solving ability under efficient representation aspect. Mathematics Education Trends and Research, 2013, 1-11.

Saleh, M., Prahmana, R. C. I., & Isa, M. (2018). Improving the Reasoning Ability of

Elementary

School

Student

through

the

Indonesian Realistic

Mathematics Education. Journal on Mathematics Education, 9(1), 41-54.

39 | Page

Sangwin, C. J. (2011). Modelling the journey from elementary word problems to mathematical research. Notices of the American Mathematical Society, 58(10).

Sepeng, J. P. (2010). Grade 9 second-language learners in township schools: Issues of language and mathematics when solving word problems.

Unpublished

doctoral

dissertation.

Nelson

Mandela

Metropolitan

University, Port Elizabeth, South Africa. Available from http://www. nmmu. ac. za/documents/theses/Johannes, 20.

Star, J. R., Caronongan, P., Foegen, A. M., Furgeson, J., Keating, B., Larson, M. R., ... & Zbiek, R. M. (2015). Teaching strategies for improving algebra knowledge in middle and high school students.

Supriyono, Setiawan, T. B., & Trapsilasiwi, D. (2014). Development of Mathematics Learning Tools for Student Facilitator and Explaining Setting Contextual Teaching and Learning (CTL) Models in Prism and Limas Sub Subjects for Class VIII Even Semester. PANCARAN Journal of Education and Learning, 3 (2), 53-62.

Tanujaya, B., Prahmana, R. C., & Mumu, J. (2017). Mathematics instruction, problems, challenges, and opportunities: A case study in Manokwari regency, Indonesia. World Transactions on Engineering and Technology Education, 15(3), 287-291.

40 | Page

Treffers, A. (1987). Three dimensions: A model of goal and theory description in mathematics

instruction—The

Wiskobas

Project.

Dordrecht,

The

Netherlands: Reidel.

Van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic mathematics education. Encyclopedia of mathematics education, (s 521), 525.

Widodo, S. A. (2014). Numerical Method. Yogyakarta: Graha Science.

Widodo, S. A. (2017). Development of teaching materials algebraic equation to improve problem solving. Infinity Journal, 6(1), 59.

Young, C. B., Wu, S. S., & Menon, V. (2012). The neurodevelopmental basis of math anxiety. Psychological science, 23(5), 492-501.

Zakaria, E. (2010). Analysis of Students' Error in Learning of Quadratic Equations. International Education Studies, 3(3), 105-110.

Zanibbi, R., & Blostein, D. (2012). Recognition and retrieval of mathematical expressions. International Journal on Document Analysis and Recognition (IJDAR), 15(4), 331-357.

41 | Page