MATHEMATICS STUDENTS’ PERCEPTION OF THEIR
INTRODUCTION
Mathematics Students’ Perceptions of their Classroom Environment
Mathematics Classroom cannot be far from its components like surroundings, objects, effects or situations, and these effective elements create the environment of mathematics classroom. Basically, here are two types of environments, “external and internal” (Bhattrai, 2004, p.51) affecting the mathematics classroom and this study is concerned about the internal mathematics classroom environment. Internal mathematics classroom environment relates to those elements, which are particularly faced inside the classroom. Maybe the learning process of students is influenced under the mathematics classroom environment as “learning environment” of classroom affects the teaching and learning of mathematics (Yilmaz & Cavas, 2006, cited as in Ntow, 2009, p.1).
Process of learning mathematics is either self-developed in students or it can be created through learning environments inside the mathematics classroom. Sammons and Michelle (2011) agreed on class room learning environment which included real life math task, data analysis, math word walls, instruments of measurement, mathematical communication, class created math charts, graphic organizer, calendars, evidence of problem solving, circulation of fresh air inside the classroom and classroom infrastructure to play a vital role in the learning process.
When I was in grade 7 at a community school, I used to sleep in mathematics class. We were 70 students in a dimly light classroom that had only one window. It seemed that it was due to the classroom environment, that I felt sleepy in the class. I did not pay attention to the teacher in the math class due to laziness. As a result, I always failed in mathematics. My parents changed my school due to my poor performance in all subjects. They believed that the so-called better school would be better for students and help achieve good marks in every subject. I really found that the learning pattern was different in the new school whilst the classroom infrastructure, classroom decoration was similar as of the previous school. It seems that there is no significant difference between the attributes of these two school classrooms except the classroom-learning environment. I was in grade 9 when I was shifted to another school where I enjoyed my math class. My new mathematics teacher dealt with mathematical problems in a different way. My mathematics teacher taught me in both grade nine and grade ten. We had to present the solution of class work, even if it was incorrect. My mathematics teacher guided me during the presentation in front of the class. I got similar chances every 4/5 classes. It was not only for me, but for others also. Really, I got both theoretical and practical concepts about mathematics whilst in the secondary school.
Those who can make a good “tuning” (Presmeg, 2014, p. 11) in practice and understanding on mathematics will have opportunities and options for shaping their future (National Council of Teachers of Mathematics, 2000). It seems that mathematics can be important for easy and better life. If so, isn’t it important to work hard to improve the performance of math teachers in teaching and learning mathematics in the Nepalese context?
Assertion of Ailing
In this era of science and technology, the teaching and learning process in mathematics is changing day by day. Instructional pedagogy is being used in mathematics education inside the classroom, and students are engaged in it. Although, the fail rate of students in mathematic is still a problem for all stakeholders, mainly for mathematics education researchers. This is a problem for the whole world. In the context of our country Nepal, students' fail rate is going up in mathematics subject in the School Leaving Certificate (SLC) exam year by year. From the past analysis, 22.46% in 2009, 24.72% in 2010, 35.97% in 2011, 47.29% in 2012, 52.90% in 2013, 65% in 2014, and 70% in 2015 have failed in mathematics subjects only.
The given statistical data shows that the fail rate of students in mathematics subject in the SLC exam is very high, which is increasing year by year. So is happening with other developed countries. Camoy and Rothstein (2013) state that in the USA there is very poor performance in mathematics and they had unacceptable results for grade eight students. This problem is not only a matter of concern for us, but for others also. To find out the reason, many researchers have done several studies as to understand the achievement as well as performance of students in mathematics. Likewise, Koirala (2012) wrote that lack of long term learning pedagogy inside the classroom also increases the fail rate in mathematics. It is a big issue, but we are not much clear about the particular reason why students are failing in mathematics.
Maybe the classroom environment can minimize the problems. Danso (2009) states that the classroom environment is an important factor for better performance in mathematics for higher level students; it seems that classroom environment may support better performance of students in mathematics subjects, but there arises a question--what are the students’ perceptions of mathematics in our context? Is it only for senior students? Or, it might be useful for only secondary level students? Thus, I intend to measure
the perception of grade nine students towards Mathematics classroom environment and this might be an important factor for creating interest in learning mathematics in Nepalese context for further study. It is clear that the classroom-learning environment is important for mathematics learning but what type of learning environment is necessary to be established inside the classroom? What kind of learning environment is in the students’ interest? How students think about their classroom environment? This study attempts to answer these questions.
Research Questions
Following research questions have been framed or the study:
1. What are students’ perceptions of their mathematics classroom environment?
2. Does mathematics classroom environment differ on the basis of the students’ age, their gender and religion?
3. Does mathematics classroom environment differ with the students’ selection of optional mathematics?
Research Hypothesis
By making the assumptions we start hypothesis testing. Generally, in research hypothesis, we test the hypothesized value and actual value from the sample data, which are collected from the population size.
Sthapit (2003) states, hypothesis is used to examine “whether the prior knowledge is supported by the sample information or not” (p. 225). Researchers compare and analyse by using some inferential statistics concepts for hypothesis testing. For this, the researcher follows the types of hypothesis, null hypothesis and alternative hypothesis tested. Levin and Rubin (1998) state, “we cannot accept or reject a hypothesis about a population parameter simply by intuition, instead, we need to learn how to decide objectively, on the basis of sample information, whether to accept or reject a hunch” (p.402). Those hypotheses, for the present study are given below:
1. Hypothesis 1: There is difference between students’ gender towards the environment of their mathematics classroom.
2. Hypothesis 2: There is difference between students having various age groups towards the environment of their mathematics classroom.
3. Hypothesis 3: there is difference between the involvement in mathematics group and religion towards the environment of their mathematics classroom.
4. Hypothesis 4: there is difference between the religions towards the environment of their mathematics classroom.
Mathematics Classroom Environment
Things around in mathematics classroom are a part of the overall mathematics classroom environment. The physical infrastructure of mathematics classroom, as well as the psychosocial aspect of the mathematics classroom both contribute to enhance the learning and teaching environment in mathematics.
However, there is relationship between learning environment and classroom environment. Learning environment inside the mathematics classroom includes students’ perceptions of the classroom goal structure and teachers’ instructional discourse (Turner et al., 2002). It is clear from past research, mathematics classroom environment can boost up the students’ confidence so that they can achieve better results in mathematics, and thus the perception of students should be addressed in their mathematics classroom environment. So, different elements or factors of classroom structure can be taken as an indicator of mathematics classroom environment, which is important for this study.
Indicators of Mathematics Classroom Environment
Simply, the indicator can be defined as the measuring scale. The measuring scale about progress, direction, condition or perception is also known as indicators. Indicators are used to measure the effects of classroom, perception of students and teachers (Friedrich, Flunger, Nagengast, Jonkmann, & Trautwein, 2015). The brief indicators talk about the 7 scales of the What is Happening in the Classroom? (WIHIC) questionnaire, which is a valid measure of classroom environment (Dorman, 2003). Defining the measuring, the perception of students about classroom environment, Taylor (2004) wrote as, although the WIHIC instrument has seven scales, the Mathematics Classroom Environment Instrument (MCEI) comprises only five scales namely;
1) Student cohesiveness 2) Teacher support 3) Involvement,
4) Cooperation and
5) Equity.
In this research, these five indicators are used to measure the perceptions of students about their mathematics classroom environment. This research is focused on measuring the perceptions of students about mathematics classroom environment. In the context of Nepal, students can be classified into two genders:
male and female. The third gender is not considered due to their negligent number. The “role of gender”
indicator is used for measuring motivational learning environment (Yang, Cho, & Watson, 2015) and that there is a relation between gender and mathematics classroom environment.
Collaborative Approach in Mathematics Teaching
To promote foundation of study in a particular topic collaborative approach might be effective.
Group discussion brings a lot of ideas among the learners. Creating ideas and sharing of knowledge might be fruitful for understanding the concept. Whatever is discussed in a group or such activities, reinforces the idea to solve the problem. Collaborative learning is a group work where students can share their ideas through “group activities” (O'Donnell, Hmelo-Silver, & Erkens, 2013). So, group activities are one of the major activities for collaborative learning. Forming of group activities is not only sufficient to make a successful learner but collection of ideas among students, and sharing is most important in collaborative approach in teaching. “Collaborative learning can only succeed when students share their doubts, comments and questions with other students who share the same or common education goal” (Olguin, Delgardo, &
Ricarte, 2000, cited as in Innerney & Roberts, 2005, p. 322).
RESEARCH METHODOLOGY
This study is based on quantitative analysis involving the survey method aimed to measure the perceptions of students of the mathematics classroom environment. Survey is a popular technique in education field (Creswell, 2011), which is focused, to determine individual opinions about the aim of this study by taking closed ended questionnaires to “identify important beliefs and attitudes of individuals”
(Creswell, 2011).
Lalitpur sub – Metropolitan city was taken as a population study city in which total 695 students were taken for survey from grade nine of 16 community schools. To avoid biasness in sampling, random sampling, “method of drawing a portion or sample of a population or universe that each number of the population or universe has an equal chance of being selected” (kerlinger, 1998, p: 118), is used. The National Education Association Bulletin (1960) states, the sampling for small sample can be determined by using the sampling technique (p. 99). The sampling formula is presented below and used to calculate for student sampling.
1
1 1
1.96 695 0.50 0.50
0.05 694 0.25 247.5 248 Where,
X2 = Z2 (tabulated value of Z from normal distribution)
P = the population proportion (assumed to be 0.50 since this would provide the maximum sample size).
d = degree of accuracy expressed as a portion 0.05.
With the help of this sample number of students the researcher selected sample number of schools by using card selection method. For this, the average number of students from sixteen schools is calculated;
that is
44 43.43 16 695
n observatio of
number
school 16 from students of numbers
; students of no Average
The researcher needs 248 students. That’s why 248 is divided by 44 average students and got 5.63 5.63 6. Now, the researcher needed 6 schools for sample and took all students from these sample schools.
The number of students in all the schools was in a homogeneous form. So, there is no bias for selection in this card method. Under the title of random sampling, the researcher used card method under the simple random sampling. With this card method, the researcher wrote the name of all 16 schools in sixteen- play cards and well shuffled, drew six cards, one by one without replacement system. Out of these selected six schools the total number of students taken for sample study are represented below in Table 1.
Table 1. Sample Participants
Name of School No of Boys No of Girls Total participants
A 16 18 34
B - 33 33
C 37 35 72
D 32 25 57
E 32 22 54
F 13 16 29
Total 130 149 279
Out of the 279 respondents, 23 (7 boys and 16 girls) respondents’ responses remained invalid.
Other 256 were used for analysis. Out of the total candidates 47.68% were girls (149), 44.08 % were boys (123), and 8.24% were invalid responses.
Tools for the Study
Five indicators or dependent variables (student’s cohesiveness, teacher support, involvement, cooperation and equity) and four independent variables (gender, age group, mathematics group, and religions) were analysed using Likert scale with the help of 40 closed ended questions, which were taken and managed from the similar type of research “Senior Secondary School Students‟ Perception of Their Core Mathematics Classroom Environment and Attitude towards Core Mathematics” (Ntow, 2011).
All the statements of survey or questionnaire are positive towards mathematics classroom environment. A value of 5 is allocated for very often, 4 is for often, 3 is for sometimes, 2 for seldom and 1 for almost never on the Likert scale.
Validity and Reliability
In the beginning phase of pilot survey, the researcher selected 20 students of grade 9 from a private school for reliability test. The researcher translated the questionnaire into Nepali language, and did a pilot survey. The reliability was negative at the beginning but the researcher changed some terminologies and tried to make it contextual to the environment. The reliability test gave negative Cronbach’s alpha α of - 0.049 from first pilot survey. After analysing the result some key words were changed and another survey was done using 20 students (grade 9) from another school and got the value of Cranach’s alpha as + 0.919.
Ethical Consideration
The survey approach practices and ethical considerations occur at multiple points in the research process (Creswell, 2011). The researcher must focus on the sampling, respect participants and take an informed consent. Privacy, dignity and safety was followed during the survey. In case of privacy, the researcher collected the surname only and not the first name. There is no category of the students as so called talented students and weak students, which respects the dignity of the students. The collected information is also kept safe by the researcher.
Data Collection and Data Analysis Procedures
Primary data collection process will be used for the study. Data are originally collected through closed ended questionnaires. The Statistical package for Social Sciences (SPSS) software will be used to describe
the data in some manner. Descriptive statistic helps to answer such question as, “How widely dispersed is this data?”, ‘are there a lot of different values?’ ‘What value is in the centre?’ Some visual representation also can be used under the descriptive statistics like, histogram, bar diagram, pie chart, and square and circle diagram but, the researcher mainly used mean and standard deviation.
When we need to collect data from very large population, then inferential statistics comes into play.
Probability distribution, hypothesis testing, correlation testing and regression analysis can be used under the inferential statistics, but the researcher used only hypothesis testing concept. Hypothesis testing was taken through the comparable mean between two groups and more than two groups, t-test was used for testing mean between two groups, and one-way ANOVA was used for more than two variables for testing of mean.
Sample Characteristics
Mainly the indirect variables, age group and gender of students were taken for the study by using five subscales or indicators in this chapter. Out of all 279 respondents from the six sample schools, only 256 respondents (91.76%) filled all information in a valid manner, and 23 respondents (8.24%) were rejected for data analysis due to incomplete questionnaires. Out of correct respondents, 51.95% were female and 48.05%
were male. The detailed participants are listed in the given table below on the basis of the variables. The percentage of gender, age group of students, religion and mathematics groups are presented.
Table 5. Sample Characteristics
Gender N %
Male
Female 123
133 48.04
51.96
Age N %
14 15 16 17 18 & above
15 57 89 60 35
5.85 22.26 34.76 23.43 13.70
Religion N %
Hindu Buddhist Christian & Others
186 54 16
72.65 21.09 6.26
Math Group N %
Optional Mathematics (Y)
Optional Mathematics (N) 77
179 30.08
69.92 The maximum participants are female from gender variable, which are 51.96%. The highest participants from age group category are 34.76% (sixteen years old). From the religion variable, 72.65% are from Hindu religion, which are the highest participants from religion. The number of students not taking optional mathematics is high, which is 69.92% from the total students.
Students’ Perceptions of MCE
Students’ perceptions of Mathematics Classroom Environment deals with the first research question,
“What are the grade nine students’ perceptions of their mathematics classroom environment?” All respondents belonged to the community schools from Lalitpur sub – Metropolitan city. All of them responded to all forty questions. The average mean value of all indicators is 3.0, which is obtained from the ratio of the sum of types of scale and numbers of types of scale. 3.0. Mean and standard deviation of all five indicators are presented in the given table below;
Table 6. Grade IX Students’ Perceptions of Mathematics Classroom Environment Student
Cohesiveness Teacher
support Involvement Cooperation Equity Number of
Respondents
(N) 256 256 256 256 256
M 3.67 3.76 3.37 3.59 3.77
SD 0.640 0.540 0.785 0.645 0.657
The highest average value is 3.77 from the perception of equity. There is no bias in mathematics classroom while teaching mathematics to all students. We can represent the indictors in a descending order, Equity > Teacher Support> Student Cohesiveness> Cooperation>Involvement and there is more homogeneity in teacher support which is, SD = 0.540 the minimum SD value among all indicators.
Students’ Perceptions of MCE by Gender of Students
In this section, the researcher used both types of statistics; descriptive and inferential statistics.
Descriptive statistics used are mean and standard deviation and inferential statistics is used in the form of t – test on gender of students. If the significance level is more than 0.05 (p> 0.05) then the null hypothesis is accepted else, alternative hypothesis is accepted.
The below given Table 7 talks about the descriptive and inferential statistics. For comparison, male and female genders were taken for the study and the study was based on the “H0: there is no difference between the perceptions of male and female students towards mathematics classroom environment”. With the help of the given data, which is represented below, the researcher tests this hypothesis.
Table 7. Comparison of Male and Female Students’ Perceptions of MCE
Indicator Gender N Mean SD t - value P
Sig (2 – tailed) Student Cohesiveness Female 133 3.77 0.60 Male 123 3.56 0.67 -0.218 0.006* Teacher Support Female 133 3.84 0.51 Male 123 3.67 0.56 -2.660 0.008*
Involvement Female 133 3.43 0.77 Male 123 3.30 0.80 -1.316 0.190
Co – operation Female 133 3.66 0.65 Male 123 3.52 0.63 -1.658 0.099
Equity Female 133 3.85 0.57 Male 123 3.70 0.74 -1.831 0.068
t – value significant at *p< 0.05, SD = Standard Deviation
From the above table, it can be seen that the total no of male respondents was 123 and 133 are female who responded equally on all indicators. By the help of this table, the researcher tests the null hypothesis about the perceptions of Mathematics Classroom Environment based on the gender of students.
The average value of a male is 3.56, which is less than the average value of female i.e. 3.77. There is more
positive relation
of girl students’ perceptions of the students’ cohesiveness. Inferential statistic states that there is very low value of significance (t – value = -0.218) for p< 0.05. Thus, the null hypothesis is rejected. This means that there is difference between male and female students’ perceptions of students’ cohesiveness. The null hypothesis also stands rejected in case of Teacher Support as significant difference in means is reported. That means, there is difference between male and female students perceptions towards teacher support.