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CHAPTER 1 The Problem and its Setting Introduction Mathematics is the one of the most important subject in our life. Without the knowledge mathematics we can say nothing is possible in this world. Now a days mathematics is globally accepted has been as an important component in formal education from ancient period to the present day. Our history shows that ancient scholars developed mathematics practically being obliged day- to- day problem. In the ancient period, mathematics has developed by great shepherds. Mathematical problem is the tool used as not only to help students develop their thinking ability but it also helps them to develop their basic skills of solving the problems especially a problem in daily life. The goal of teaching mathematics to be affective was that the students were able to solve its problems. As a matter of fact, the experience in solving the problems of the subject is very important to develop students’ thinking skills in solving the problem in daily life. Problem- solving is considered as the heart of mathematics learning because the skill is not only for learning the subject but it emphasizes on developing thinking skill method as well. Students can apply their knowledge and problem solving skills to be useful in daily life since the processes of solving the mathematics problem are similar to the general problem solving.

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Mathematics is the body of knowledge in the area of science and technology. The subject mathematics is beautiful and interesting because

its

own

symbols,

language,

terms,

technology

etc.

Mathematics is being main part of human lifestyle. In the world, each society has their own mathematical languages, terms, symbols, counting system in different countries. The National Research Council purported that students learn mathematics well only when they construct their own mathematical understanding and that this understanding requires them to examine, represent,

transform,

solve,

apply,

prove,

and

communicate.

Mathematic is the significant subject in our life. As mathematics has emphasized like language most of students have been failed in mathematics as a difficult subject and majority of students fail in mathematics. Students’ achievement may be influenced by attitude toward problem solving. According to Ma and Kishor (1997) the variable ‘attitude’ is one of the most potent factors that relates to achievement. Borasi (1990) adds that the conceptions, attitudes, and expectations of students regarding mathematics and mathematics teaching have been considered to be very significant factor underlying their school experience and achievement. Patton et al. (1997) propose that learning to solve problems is a primary objective in learning mathematics, as problems are inevitable fact of life. According to Effandi and Normah (2009), a student needs to think and make decisions using appropriate strategies to

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mathematic problems. They add that students’ success in achieving their goals encourage them to develop positive attitude towards mathematics and other problem solving activities. Positive attitudes are

assumed

to

have

significant

relationship

with

students’

achievement. Therefore, this study seeks to identify the level of tolerance and confidence towards problem solving and investigate how these two factors contribute to their mathematic achievement. Theoretical Framework This study was guided by Representational change theory. It is an attempt to incorporate some Gestalt ideas into working theory (Ohlsson1992). This theory suggests that because a problem solver has all the required knowledge at hand, their failure to find a solution is due to the way they are mentally representing the problem. If the problem is not represented in such a way as to accommodate retrieval of the necessary knowledge, the solver will reach a block or impasse that will prevent further progress. It further suggests that insight occurs when the solver’s mental representation changes to allow retrieval of the required knowledge. It is based on the following assumptions: A problem is represented in a certain way in the person’s mind these serves as a probe for information from long-term memory. The retrieval process spreads activation over ‘relevant’ long term memory items. A block occurs if the way a problem is represented does not lead to a helpful memory search. The way the problem is represented changes the memory search is extended,

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making new information available. Representational change can occur due the ‘elaboration’ (addition of new information) ‘constraint relaxation’ (rules are represented) or

‘ re encoding’ (functional

fixedness is removed). Insight occurs when a block is broken and retrieved knowledge result in solution.

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Chapter 2 Review and Related Literature Alvaera, Bayan, & Martinez (2009) of De LaSalle University, Manila conducted study intended to determine whether involvement and autonomy (mothers and fathers), and teaching approach can predict public schools students’ achievement as measured by the general average grades of students. In determining which variable has significant relationship with student achievement, it showed that mother involvement was significantly related with the student academic achievement. Of all the predictors of achievement used by the researchers, it was only mother involvement that had significantly predicted student achievement. This does not mean that teaching approach, father involvement, father autonomy and mother autonomy does not contribute in predicting achievement. This simply implies that their contribution in the achievement of the students is not a significant as compared to the contribution of mother involvement. The current study focuses on academic achievement as measured by the general average grade of the students from the previous grading period. It has been well established how academic achievement is influence by a particular factor. Parent involvement in the child schooling like assisting the child in making their assignment explain much the grade can predict student achievement.

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According to Jackson &Eipstien (2006), over the past 15 years, there has been a simultaneous increase in the attention

given to the

role of parental involvement in education. Federal, state, and local governments have mandated that districts make efforts to involve parents. However, there has been no research as to the roles these curricular materials actually afford for parents with regard to their children homework. The Australian Council of Educational Research (2008) reported that literature review indicates that strong partnerships between school, parents, businesses and local community organizations can make a significant difference to outcomes for young people. Research shows a range of positive outcomes associated with school-community partnership, including increased skills, greater engagement with learning, more positive attitudes, and improved transitions into the workforce, Further education or training (schools first, 2008). Montecalvo (2000) assessed the problem solving skills and attitude in Mathematics in of Grade six pupils in Linamon District, Division of Lanao del Norte during thr school year 1999-2000. Results shows that majority of the pupils had average performance in problem solving skills along fractions, decimals, and percentage. Likewise, they had a fair attitude level towards mathematics and perceived that mathematics is useful for problems in everyday life. Furthermore, significant relationship existed between pupil performance in problem solving skills test and type of school as well as pupils’ average grade in

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Mathematics. Finally, no significant relationship existed between pupil’s performance in problem solving skills test and the following pupil-related factors, namely: family income, size of family, and attitudes towards mathematics. According to Hoover-Dempsey & Sandler (1995), parental support for student achievement as well as parental involvement in school activity has had positive impact in student academic success. A review of Walberg & Paik (2000) on dozens of studies had shown that home environment has a powerful effect on what children and youth

learn

within

and

outside

school.

This

environment

is

considerably more powerful than the parents’ income and education in influencing what children learn in the first six years of life and during the twelve years of primary and secondary education. They stressed that one major reason that parental influence is so strong is that from infancy until the age of 18, children spend approximately 92% of their time outside school under the influence of their parents. Rondez (1997) studied grade six pupils in Iligan City wherein the attempted to associate high achievement in mathematics with the following factors: home environment, quality and quantity of math instruction received by pupils, and pupil attitude towards math. The factors significantly associated with high achievement in math are the following: pupil respondents father educational attainment, number of influencing household member, seminar attended and math awards received with the teachers respondents and pupils’ attitude towards

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math. This indicated that pupil academic achievement not only in mathematics but also with other subject is greatly influenced by other factors not only pupil and parents factors. According to Henderson &Mapp (2000), the evidence

is

consistent, positive, and convincing: families have a major influence on their children’s achievement in school and through life. Studies have linked parental involvement with student benefits of higher grades and test scores, enrolment in more challenging academic programs, increases in the number of classes passed and credits earned, better attendace. Rongjin& Leung (2002) studied the parental influence on Chinese children’s mathematics teaming and found out that parents held very high expectations for their children’s education and highly involved themselves in their children’s mathematics, irrespective of their educational background and social economic status. Cai (2003) investigated the roles parents in the United State of America and parents in the People’s Republic of China play in their children‘s mathematics leaming. It also examined the relationship between

parental

involvement

and

the

student’s

mathematical

problem-solving performance. The results of this study support the argument, from a broader cross-national perspective, that the parental involvement is a statistically significant predictor of their children’s

mathematics

achievement.

Cross-nationally,

Chinese

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parents seemed to play a more positive role than do the US parents (Cai, 2003). Deutcher & Ibe’s (2004) project examined the role that parent involvement has on 7tt1 through 11th graders in a large rural area in Southern California. Various types of parent involvement, were assessed, including volunteering, home involvement, attending parent classes, school political involvement, talking, to staff, talking to teachers, etc. Academic performance was measured by STAR test score and by grades. Overall, the results indicated that those who did the selfreport survey, went to the parent class, or were involved in more home-type involvement (such as checking child’s planner, talking to child at home about school-related topics, or engaging in educational activities outside of school) had children that performed better in various areas of the STAR test or had better grades. Parent involvement has been shown to be an important variable that positively influences children’s education. Cao et al (2006) conducted an investigation that explored the differences and similarities in parents’ influence on students’ mathematics learning as perceived by different of students in China and Australia. The result showed that parents play an important role in influencing students’ mathematics reaming, but parents

from

different cultural backgrounds and in different societies may influence their students’ reaming differently . (Co et al, 2006).

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Olatoye

&

Agbatogun

(2009)

stated

that

term

Parent

involvement includes several different forms of participation in education and with schools and that experts in the field agree about the importance of linkages between families and school. Their study that investigated the achievement of pupils in the public. According to Lightner (1999), researches show an abundance of people have voiced fears in regard to the socioeconomic impacts resulting from the low academic skills of today’s employees. Studies also recognize the workplace trend, of demanding ever increasing levels of mathematics, communication and science skills from the employees. Gallo & Johnson (2008) administered a test of basic math skills to 696 students enrolled in various college economics courses in order to understand the factors influencing student’s ability to apply basic math skills in practical settings. Students with strong elementary math skills performed significantly better in applied contexts and that taking more math classes in college improves a student’s ability to apply mathematics substantially. One of the major conclussion of their paper is that among the controls for mathematical background, mastery of very elementary math skills as measured by performance on their administered exam is of utmost importance. The results of their research pointed out that as substantial number students lack the mastery of very elementary math concepts. Hence, they suggested that professors identify students with weak basic math skills early on

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so that some type of remediation can be done to bring these students up to par (Gallo & Johnson, 2008). Lee-Chua (2006) discussed efforts spearheaded by virus groups to develop a successful problem-solving culture. “We have learns to focus on certain critical variables”. According to the researcher, this variable include: extensive parental support, early exposure, mental toughness, excellent master teachers, and good textbooks. Cañete’s (2002) study determined the teacher and pupil factors affecting problem solving difficulties in mathematics it concluded that pupils had satisfactory performance in problem solving achievement test. A significant relationship existed between pupils problem solving skills in mathematics and some teachers factors, namely, educational qualification, and possession of master units/degree , specialized training, performance rating and strategies in teaching math. No sufficient evidence was seen to show significant relationship between pupils’ skills in mathematics and the pupil factors, mothers’ educational attainment and family annual income. Silva et al (2006) investigated the factors associated with nonperforming Filipino students in mathematics in selected accredited schools in the Philippines (Private and Public Institutions from Metro Manila and Provinces). Results showed that, thought the students have average mental ability; they encountered difficulties attributed to reading deficiencies and learning styles.

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According to Math Fluency (2011), educators and cognitive scientists agree that the ability to recall basic math facts fluently is necessary

for

students

attain

higher-order

math

skills.

The

implication for mathematics is that some of the sub-processes, particularly basic facts, need to be developed to the point that they are done automatically. If this fluent retrieval does not develop then the development of higher order mathematics skills- such as multipledigit addition and subtraction, long division, and fractions – may be severely impaired. Indeed, studies have found that lack of math fact retrieval

can

impede

participation

in

math

class

discussions,

successful mathematics problem -solving, and even the development of everyday life skills. And rapid math- facts retrieval has been shown be a strong predictor of performance on mathematics achievement tests. Little consensus exists in the research literature concerning the relationship between attitude toward mathematics and achievement mathematics. The variable “attitude” is one of the most potent factors that relates to achievement. In general, attitudes, beliefs and emotions are the major descriptors of the affective domain in mathematics education. Rather than attempt to explain all the components of the affective domain, mathematics educators have traditionally taken the relationship between attitudes towards mathematics and achievement in mathematics as their major concern (Ma &Kishor, 1997). Also, Gomez-Chacon (2000) found that one of the variables with most

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influence on mathematics teaching and learning relate to the pupils’ attitude, their perspective on the world of mathematics, and their social identity. Nicolaido & Philippou (2003) explored the relationship between attitudes towards mathematics, self-efficacy beliefs and problem solving and achievement of fifth-grade pupils and found significant relationship between attitudes and achievement. Ignacio et al (2006) analysed the beliefs, attitudes, and emotional reactions that students experience in the process of learning mathematics. The aim was to be able to demonstrate that the existence

of

positive

attributes,

beliefs,

and

attitudes

about

themselves as learners are a source of motivation and expectations of success in dealing with this subject. Basing on the results of his finding, he recommended establishment of projects and programs of prevention and intervention in difficulties of mathematics learning and of emotional education in this area of knowledge. The aim will be stimulate the attractions of the taste for mathematics, and to improve attitudes, beliefs, and the emotional reaction that pupils experience when they are learning it. According to Effandi & Normah (2009), students’ attitudes towards mathematics are closely related to their attitude towards problem- solving in general; Negative attitudes need to be overcome, so that students will not suffer from poor problem- solving skills later in life. Olatunde (2010) opined that the process of learning depends

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not

only

on

family

factors

but

also

on

students’

personal

characteristics that are naturally correlated with family characteristics but have an effect on their own. Therefore, in order to analyse achievement, some students’ personal characteristics must be taken into account. The researcher of Mohd, Mahmood&Mohd (2011) entitled “Factors that influence students in Mathematics Achievement” revealed that there is significant relationship between the level of patience towards problem-solving and mathematics achievement. It also reflects that there is significant relationship between attitudes toward problem solving and mathematics achievement. On the other hand, the finding shows that there is no significant relationship between the level of confidence and willingness towards problem solving and mathematics achievement. This research also reflects that there is significant relationship between attitude (patience, confidence and

willingness)

toward

problem

solving

and

mathematics

achievement. According to Manoah (2011), attitude towards mathematics has been considered an important factor in influencing participation and success in mathematics. In their study “Influence of attitude on performance of studentsin mathematics curriculum”, it is worth noting that the independent variable (Attitude) for girls and boys had significant association with dependent variable (Mathematics Test).

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Buan

(1997)

tested

other

variables

possibly

related

to

mathematics achievement and attitude. It was aimed to compare the effect of cooperative and individualistic instructions and student achievement in mathematics and their attitudes toward the subject. It was found that there is a significant difference the pre-test to post-test scores of the cooperative group in the achievement test and attitude scale. In the individualistic group there is significant different in the pre- test and post- test achievement scores only but there is no significant change in attitudes scores. Angay’s (1998) research work on pupils difficulties in basic operations involving fraction concluded that the pupils performance poorly in the four fundamental operations of fraction. Moreover, the finding showed that there is significant difference

between

the

pupil

achievement

and

theirparents

educational attainment. According

to

Lucero

(1999),

parental

involvement

was

significantly correlated with both pupil mathematics achievement and attitudes. Mathematics achievement was significantly correlated with both father’s education and mathematics attitudes while mathematics attitude was significantly correlated with parent monthly income. Bigornia(2000) mathematical

determined

proficiency

level

the of

factors

grade

VI

affecting pupils.

the

Teacher

competence, pupils’ background and communication skills were found to have highly significant relationship with pupil mathematics achievement.

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A study conducted in Lanao Del Norte by Caliao (2000) aimed to determine the factors associated with the pupils ability to solve problems

in

mathematics

by

associating

pupils’

mathematics

achievement with the following factors: home environment, quality of mathematics instructions received by the pupils, attitudes towards mathematics mental ability, and readingcomprehension ability. The factors identified to be significantly associated with the pupils mathematics achievement were the following: fathers education neighbours, friends and relatives who took care of the child, buying things of educational value, teachers profile such as number of math seminars attended, number of years in teaching math, number of awards received, lesson plan preparation, teachers activity like conducting reviews classes, coaching during math competitions, encouraging

and

supporting

pupils

to

participate

in

math

competitions and the number of skills taught, mothers hours spent at home and t work, mental ability, and reading comprehension. Here are seven steps for an effective problem- solving process; Identify the issues ; Understand everyone’s interests List the possible solutions (options); Evaluate the options ; Select an option or options; document the agreement(s); agree on contingencies, monitoring, and evaluation.

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CHAPTER 3 Methodology This chapter deals with the methods and procedure use in conducting the study. This chapter comprises the following contents respondents of the study, data gathering, and locale of the study.

Locale of the study This study will be conducted in the factors affecting student performance in solving problem in mathematics who those student were able solve its problems.

Respondents The respondents of this study are the factors affecting student performance in solving problem in mathematics in the Alberto Olarte Sr. National High School.

Data gathering In data gathering relevant for the students the most preferred source of information about on factors affecting student performance in solving problem in mathematics and the research distributed

the

close ended questioners to the respondents for them to answer

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accurately.

Instructions

were

also

applied

in

answering

the

questioners. Book, magazines, internet and the other resources were used to help in this study.

Delimitation of the Study The

study

focused

on

the

factors

affecting

student’s

performance in solving problem in mathematics. Only grade seven students are allowed in this study. This study was conducted at Alberto Olarte Sr. National High School, in the school year 2018-2019. Some of the grade seven student’s are not capable in Mathematics. They are lack of understanding and comprehension. There are many times to confused in the performance in terms of problem solving skills test. Considering that this problem are encountered difficulties, they experienced escalating as they attempt to master required of problem.

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Chapter 4 Presentation, Analysis and Interpretation of Data

This chapter presents the presentation, analysis and interpretation of data

Do You Like Problem Solving? yes

no

don’t know

7% 13%

80%

It can be gleaned in the presentation that when the participants were ask if they like problem solving, the Yes answer got a highest percentage which is 80% out of 100%. This means that most of the respondents in grade 7 likes math problem solving.

The remaining

13% does not like problem solving. While the 7% they don’t know about math problem solving. According to Lee-Chua (2006) discussed

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efforts spearheaded by virus groups to develop a successful problemsolving culture.

DO YOU LIKE MATH yes

no

don’t know

3% 0%

97%

As can be observed to the graph presentation, 97% of the respondents like math and 3% of them does not like math. According to Monoah (2011), attitude towards mathematics has been considered an important

factor

mathematics

in

influencing

participation

and

success

in

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Do you think you are good at math? yes

no

don’t know 40%

40%

20%

As we can observed in the graph, Yes and Don’t Know got the same percentage which is 40% and No got 20% in the survey which mean that there is student who are good in mathematic and some of these are not sure. According to Hoover-Dempsey & Sandler (1995), parental support for student achievement as well as parental involvement in school activity has had positive impact in student academic success.

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Do you find maths easy? yes

no

don’t know

13%

57%

30%

As can be seen in the graph that most of the respondents found math easy which got 57% out of 100%.

Followed by 30% which means the

respondents don’t find math easy. While the remain 13% the respondents don’t know if math find easy. According to Math Fluency (2011), educators and cognitive scientists agree that the ability to recall basic math facts fluently is necessary for students attain higher-order math skills.

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