# A Quantitative Analysis Gender And Mathematical Achievement Education Essay

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In quantitative research, the study begins with the formulation of the hypothesis. This hypothesis is tested based on a framework using collected data. Quantitative research provides guidance through these numbers or data. From these data, conclusion can then be drawn through deductive reasoning.

The quantitative method's strength depends upon its reliability or repeatability. Furthermore, the results of quantitative research are based on mathematical models, accepted theories and rules. The strong statistical foundation of quantitative research systematizes and formalizes the proceedings of a study. The rules that are applied to analyse and test the data are widely accepted, thus, differences in interpretations are minimal compared to that of qualitative research.

There are two ways to approach quantitative research using the research design. The experimental design and non experimental design are both very broad categories. Essentially, the difference between the two is how the independent variable is treated. In the experimental design, the independent variable is manipulated. A set-up is created where in there are controlled and experimental variables.

In a non-experimental design, the relationship or association between variables are explored based on given parameters and data. The independent variables are not manipulated and are therefore, not randomized. Here, the research is much easier to conduct compared to an experimental one. However, it should be clear that the relationship being tested here do not imply causality. Another term to describe this kind of design is correlation design since, basically, the reason for the relationship is left unclear.

The evidences from a non-experimental design are not as powerful as that of experimental designs. If an experiment is designed and executed properly, not only can it determine relationships, it can also determine causality. However, a flawlessly executed experimentation is very difficult to achieve. It requires a lot of ingenuity, resources, experiences and time.

As mentioned earlier, quantitative research design is a very broad category. The non-experimental design is subdivided into survey studies and relationship/difference studies. The survey designs are further classified as description, exploratory and comparative. Difference or relationship studies are categorised as correlational and developmental. Developmental designs have subgroups of cross-sectional, longitudinal and prospective, and retrospective / ex post facto (Davies 2007; LoBiondo-Wood 2006; Brown 1998).

In the interest of this assignment, concentration will be based on statistical methods - descriptive and inferential statistics. The former allows the researcher to describe and summarize data whilst the latter allows a researcher to make predictions and generalise findings based on the data.

## Aim

The main aim of this study is to explore whether gender makes a difference to mathematics achievement in primary school. The study has the purpose of filling the gaps and to contribute to the existing debate on gender and mathematics attainment.

## Background of the study

This assignment data draw from a longitudinal survey of pupils in eight English primary schools to explore the effects of gender on mathematics attainment. To ensure proper representative sample and equal chance of selection, pupils were selected by simple random sampling in rural areas, urban areas and different socioeconomic background. The researchers chose these pupils from enrolment register to study the mathematics test scores in October and June

## Objectives

To whether mathematics attainment is higher in males than females at year 4 October tests.

To explore if mathematics attainment is higher in males than females across years.

To fill gaps in this area and add to the debate on the relationship between gender and maths achievement at primary school.

## Hypothesis

Since this study involves gender difference and mathematical attainment, nominal measurement will be used to clarify variables into categories which will make them mutually exclusive. This kind of measurement will allow the least amount of mathematical manipulation where the frequency of each event can be counted and the total of each category is represented in percentage. In this case the nominal variable is considered to be dichotomous - gender (male / female). A research hypothesis is used to guide this study. The independent variable (predictor) is gender (male and female) and dependent variable (criterion) is maths attainment as total mean score.

Null hypothesis (H0): Gender has no effect on mathematics attainment.

Research hypothesis (H1): Gender has effect on mathematics attainment.

## Legal-ethical issues

It is expected that the rights of the pupils (subjects) have been well protected. It is also assumed that the researchers explained the purpose of the study to parents and teachers and informed consent was obtained from the parents / teachers before the pupils undertook these tests. Also to ensure confidentiality of the results, researchers might have given the participants with pseudonyms and their names were not made public (Davies 2007; Sarantakos 2005).

## Sample / Measures / procedure

This study is based on the national test in mathematics for pupils year 2 (about 7 years) with different levels though not all pupils achieve or take the test as required. A stratified random sample of 389 participants was obtained from the eight participating schools where there were 206 males and 183 females. A 95% confidence interval was accepted throughout computation.

## Outline of the research question / area

This study aims to determine whether there is a relationship between sex and results in mathematics examinations. It will seek to answer the question "Is sex related to attainment?" In order to address the research question, statistical analysis using descriptive and inferential statistics shall be performed.

The descriptive statistics will reduce the bulk of the data by summarizing the features as a whole. Measures of central tendency such as mean, median and mode, and measures of variability such as range and standard deviation are commonly used to describe datasets. Charts (pie chart) and graphs (histogram) will also be produced to visually represent the distribution of the data. A histogram in statistic is a graphical display of tabulated frequencies which are shown as bars. It is a form of data binning and shows what proportion of cases fall into each of several categories. However, these chart and graph merely describe or show us the data. They do not test any hypothesis though they are very useful when it comes to exploratory data analysis.

In nominal data, mode is the descriptive statistic that is most commonly used despite the fact that it is not stable and can vary extensively from sample to sample. However, descriptive statistics can only describe the data. It does not give any inferential insight regarding the relationships of the variables.

The null hypothesis is gender has no effect on mathematics attainments. In order to test this hypothesis, inferential tests can be performed. The Pearson's Chi Square test for independence is very popular and widely used. However, that is applicable only if the two variables being tested are both dichotomous and categorical. In the case of this study, only the variable sex is categorical. The test scores for the mathematics examination is continuous. In order to determine if there is any relationship between the math scores and sex, the Pearson's Correlation coefficient is computed. In this test of association, the null hypothesis being tested is the independence of the variables (sex versus mathematics score).

The t-test is also a useful test if there is any significant difference between the mean scores of two groups. In order to employ this test, some assumptions about the variance should be made first.

The Levene's test is a statistical tool that tests the equality of variances. Therefore, if the variances turn out to be equal or unequal, then the proper assumption can be made for the t-tests (Brown 1998; Diamond 2001; LoBiondo-Wood 2006)..

## Methodological approach / Data of the analysis

Since this study involves gender difference and mathematical attainment, nominal measurement will be used to clarify variables into categories which will make them mutually exclusive. This kind of measurement will allow the least amount of mathematical manipulation where the frequency of each event can be counted and the total of each category is represented in percentage. In this case the nominal variable is considered to be dichotomous - gender (male / female). Statistical software SPSS for Windows, version 17.0 was used to analyse the data. By using descriptive statistics such as percentages and frequencies, all the research variables were computed.

## Results

Chart 1. A pie chart that shows the demographics of the respondents.

Table 1. Basic Frequencies

Minimum

Maximum

Mean

Std. Deviation

Y4_O_M_age

5.35

11.93

8.7945

1.3

Y4_J_M_age

5.778

12.138

9.50704

1.3

Y5_O_M_age

6.49

13.06

9.4287

1.3

Y5_J_M_age

6.76

13.51

10.2508

1.5

Y6_O_M_age

7.532

14.392

1.09232E1

1.6

Y6_J_M_age

7.630

14.294

1.17147E1

1.5

SEX

N

Mean

Std. Deviation

Std. Error Mean

Y4_O_M_age

Male

193

8.9

1.3

0.1

Female

174

8.7

1.

0.1

Y4_J_M_age

Male

196

9.7

3

0.1

Female

177

9.3

1.4

0.1

Y5_O_M_age

Male

190

9.6

1.3

0.1

Female

167

9.2

1.2

0.1

Y5_J_M_age

Male

185

10.4

1.5

0.1

Female

166

10.1

1.4

0.1

Y6_O_M_age

Male

170

1.1

1.5

0.1

Female

158

1.1

1.6

0.1

Y6_J_M_age

Male

169

1.9

1.5

0.1

Female

153

1.2

1.4

0.1

HISTOGRAMS

## Distribution of test scores of Y4 October mathematics age

Figure 1. Shows the distribution of test scores of Y4 October mathematics age

## The distribution of test scores of Y4 June mathematics age

Figure 2. Presents the distribution of test scores of Y4 June mathematics age

## The Distribution of test scores of Y5 October mathematics age

Figure 3. Shows the distribution of test scores of Y5 October mathematics age

## The Distribution of test scores of Y5 June mathematics age

Figure 4. Shows the distribution of test scores of Y5 June mathematics age

## The distribution of test scores of Y6 October mathematics age

Figure 5. Shows the distribution of test scores of Y6 October mathematics age

## The distribution of test scores of Y6 June mathematics age

Figure 6. Shows the distribution of test scores of Y6 June mathematics age

## Correlations

Table 3. Pearson's Correlation

SEX

Y4_O_M_age

Pearson Correlation

-.088

Sig. (2-tailed)

.094

N

367

Y4_J_M_age

Pearson Correlation

-.119*

Sig. (2-tailed)

.021

N

373

Y5_O_M_age

Pearson Correlation

-.139**

Sig. (2-tailed)

.009

N

357

Y5_J_M_age

Pearson Correlation

-.106*

Sig. (2-tailed)

.046

N

351

Y6_O_M_age

Pearson Correlation

-.104

Sig. (2-tailed)

.059

N

328

Y6_J_M_age

Pearson Correlation

-.065

Sig. (2-tailed)

.247

N

322

Table 4

## Independent Samples Test

Levene's Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

Sig. (2-tailed)

Mean Difference

Std. Error Difference

95% Confidence Interval of the Difference

Lower

Upper

Y4_O_M_age

Equal variances assumed

1.6

.21

1.68

365

.09

.23

.13

-.04

.50

Equal variances not assumed

1.69

364.54

.09

.23

.13

-.04

.49

Y4_J_M_age

Equal variances assumed

.71

.40

2.31

371

.02

.31

.14

.05

.58

Equal variances not assumed

2.30

359.29

.02

.31

.13

.05

.59

Y5_O_M_age

Equal variances assumed

2.75

.09

2.6

355

.01

.35

.13

.09

.62

Equal variances not assumed

2.66

354.83

.01

.35

.13

.09

.62

Y5_J_M_age

Equal variances assumed

.56

.46

2.0

349

.05

.31

.16

.01

.62

Equal variances not assumed

2.0

347.12

.05

.31

.16

.01

.63

Y6_O_M_age

Equal variances assumed

.04

.85

1.89

326

.06

.32

.17

-.01

.67

Equal variances not assumed

1.89

323.36

.06

.33

.17

-.01

.67

Y6_J_M_age

Equal variances assumed

.41

.52

1.16

320

.25

.19

.16

-.13

.51

Equal variances not assumed

1.16

319.29

.25

.19

.16

-.13

.51

## Discussion

There are total of 389 respondents in this study. Based on Chart 1, 47.04 % of the respondents are females and 52.96% are males.

Six mathematics examination scores were investigated in this study, year 4 October and June math age, year 5 October and June math age, year 6 October and June math age.

Based on Table 1, the mean score of students for the year 4 October math age is 8.79, and with a minimum score of 5.35 and a maximum of 11.93. The mean score of students for the year 4 June math age is 9.51, and with a minimum score of 5.78 and a maximum of 12.14. The mean score of students for the year 5 October math age is 9.43, and with a minimum score of 6.49 and a maximum of 13.06. The mean score of students for the year 5 June math age is 10.25, and with a minimum score of 6.76 and a maximum of 13.51. The mean score of students for the year 6 October math age is 1.1, and with a minimum score of 7.53 and a maximum of 14.39. The mean score of students for the year 6 June math age is 1.2, and with a minimum score of 7.63 and a maximum of 14.29.

The mean scores for the year 6 October and June math age are very small. This figure seems wrong at first. But the reason why the means are very small is due to the fact that a lot of respondents do not have available scores for these examinations. SPSS uses the total number of respondents as the divisor for the computation of the means. However, if you look at the minimum and maximum scores, the computed means would not fall between the two values. But, if the mean scores per exam were computed without taking into consideration the missing values, it would be valid. The measures for variation however, are all valid since missing values do not affect the computation for the range. The range is only the difference between the maximum score and the minimum score.

So, in order to obtain the mean scores without taking into consideration the missing values using SPSS, the histograms for each of the 6 math examination were obtained. The summary statistics that are used in the computation of the histograms are valid. Since the values of the mean scores and standard deviations are used in generating the histograms, the missing values are not taken into consideration for the computations.

In order to determine the presence of any relationship or association between sex and the math scores, the Pearson's correlation coefficient is computed. Based on Table 3, scores for Y4_J_M_age, Y5_O_M_age and Y5_J_M_age are correlated with sex at a 0.05 level of significance.

The Levene's tests show that for each of the math scores, the variance of the males is equal to the variance of the females. Thus, for the t-tests, equality of variances shall be assumed.

Based on table 4, for Y4_J_M_age, there is a significant difference between the mean scores of the males and females at the 0.05 level of significance. The same results hold for Y5_O_M_age and Y5_J_M_age.

The results of the Pearson's test for correlation and the t-tests are consistent.

## Conclusion / recommendation

A generalization about the overall association of sex with mathematics attainment cannot be obviously generalized. From the six sets of math scores that were tested in this study, only three of those sets of scores appear to have an association with sex. The three sets of scores that were found to be associated with sex are the scores from year 4 June math age, year 5 October math age and year 5 June math age.

Undeniably, this study has suggested that further in-depth, longitudinal studies that gender makes a difference to mathematical attainment will be a way forward. It can also be recommended that care should be taken before one can use the outcome of the study as statistically the null hypothesis is accepted but in reality that may not be case. This conclusion has only been based on the statistical results computed and analysed. Furthermore, it should be remembered that the strength and quality of any study / research evidence are enhanced by repeated trials which have consistent findings. This will thereby increase the credibility of the findings and applicability to any practice. But this cannot be said to be the case, for instance, some rows were deleted due to the fact that some students had not sat any test the month and in doing so might have affected the entire results.