## Introduction

Criterion-Referenced Competency Test (CRCT) is a test that is administered at all public schools at the end of the year in the state of Georgia before a student proceeds to the next grade. These tests are conducted for mathematics, English/language arts (ELA), sciences, and social studies. CRCTs were enacted in the year 2000 to strengthen the performance of students in elementary and middle schools. This is because the students in the United States were performing poorly in their exams especially in mathematics as compared to students in Canada, Australia, Britain, and many other countries in the world with only 7% of students between the fourth and eighth grade attaining advanced level scores (Robinette, 2006 ). To improve the performance of students in the United States, President George Bush allocated $260 million to be used in the CRCT with the aim of making them be more competitive in the globe (Robinette, 2006).

The methods which have been used to prepare students for this test include flexible grouping, adjusted questions, pre-assessments, and differentiated instruction. These methods employ rigorous training which strengthens the performance of the students by familiarizing the students with the CRCT questions and the mode of approaching and solving them. As a result therefore students are expected to have positive progress in their school scores and attain an even higher score in the CRCT.

## Problem Statement

Several methods have been used to improve the performance of students in the preparation of CRCT. Flexible grouping is among the best methods which have been implemented in the program. This method has been working well especially in strengthening students’ performance in mathematics (Perie et al, 2005). This research will therefore focus on the effects of flexible grouping on mathematics scores in one year in K-4 students with a comparison to their end-year CRCT performance.

## Purpose Statement

The main aim of this study is to identify the factors which lead to poor performance of students between kindergarten and fourth grade in mathematics and to come up with appropriate solutions to the problem and also to evaluate the effectiveness of CRCT in the schools of the United States. This will help to improve the academic base of students in the United States which will help them in their future studies.

## Literature Review

Students need an early development of their mathematical skills which will assist them to be successful in their higher education levels and career development in the future (National Research Council, 2001). The government of the United States has come up with a lot of programs to improve the performance of children in their early education. One of the projects which they came up with was Criterion-Referenced Competency Tests (CRCT) which students have to undertake at the end of the year before proceeding to the next grade. The students who pass this test normally proceed to the next grade while those who failed remain at the present grade for further tuition until they are competent enough to pass the CRCT which will be offered the preceding year. According to Perie et al (2005) more than 30% of students below the fourth grade in the year 2004 scored below the national average of 36% in mathematics.

To prepare them for the CRCT teachers in various schools have used a method known as a flexible grouping to strengthen the performance of students especially in mathematics (Perie et al, 2005). In this method, students are divided into small study groups where they learn the content, processes, and skills with a mixture of different students. Students are grouped according to the goals and needs which their teachers want to achieve. The success of this method can be determined by the outcome of periodical student assessments on the scores they get within the year and its correlation to the scores which they will attain in the CRCT.

On several occasions, there has been a huge difference in the class performance and the CRCT scores which students get, particularly in mathematics and social studies (Reed, 2008). This may be due to the rigorous standards of CRCT which the students are not familiar with or due to the fact that the students are not adequately trained by their teachers. However, the Georgia Department of Education has stated that the students are undergoing vigorous training every day thus they cannot account for the poor scores in mathematics and social studies (Ho et al, 2005). With regard to this, people have started to question the efficiency of CRCT in improving the performance of their children because the outcome of the program has so far not been satisfactory.

According to Gelpi (2009) researches which have been conducted about the use of flexible groups show that they tend to improve the performance of students in their studies. On many occasions, the math scores of students for assignments and pre-assessment tests have been improving as a result of students working in groups (Singer and Wallet, 2003). This progress has also been reflected in the CRCT scores of the students which have been increasing over the years in schools that have applied for the program. However, there have been cases of fluctuation of results, especially in K-4 students. This has been the normal case in many schools with an exception of only a few schools.

### Research Questions

The questions which should be answered by this study are as follows:

- Is CRCT an appropriate program to improve the performance of children especially in mathematics?
- What is the relationship between flexible group math scores in each grade K-4 for a specific year and end year scores on CRCT?
- Does flexible grouping strengthen the performance of weak students without compromising the performance of the strong students?
- Does CRCT consider students with special needs in its application for example children with disabilities?

### Research Hypothesis

A research hypothesis is a core statement of the study which is used to define the main aim of the experiment (Shuttleworth, 2008). The research hypothesis will formulate by using the process of inductive reasoning where normal observations are used to formulate the hypothesis. In most cases, a research question is used to formulate the hypothesis of the study. For this study we can formulate the following question; do students respond to CRCT? This statement is somehow broad thus to narrow it to our research topic we can formulate the following statement; flexible groupings have a positive impact on the performance of students on their CRCTs. This is our study’s hypothesis.

In the research, we have two forms of hypothesis: the null hypothesis and the alternate hypothesis. A null hypothesis is a statement that agrees with the independent variable of the study while an alternate hypothesis is a statement which disagrees with the independent variable of the study. The following statements will be the null and alternate hypotheses of this study (Quick MBA, 2010).

The following statements will be the null and alternate hypotheses of this study.

**Null hypothesis(HO):**flexible groupings have a positive impact in the perfomance of students on their CRCTs**Altrnate hypothesis(H1):**flexible groupings do not have a positive impact in the perfomance of students on their CRCTs

The validity of the hypothesis will be determined after inferential statistics has been done. If the results will be in a certain range of the confidence level then the null hypothesis will be true. However, if the results will be below the accepted range of confidence level then the null hypothesis will be seen as being a false statement and the alternate hypothesis will now be the true statement (Marshall, 2008).

## Methodology

Students will be divided into different groups which will be used as the flexible groupings of this study. A quasi-experimental method will be used to determine the effectiveness of CRCT in students between kindergarten and fourth grade. Their performance and progress will be recoreded all through the year. The data which will be collected will include results of assignments and pre-assesment tests. These results will then be compared with the CRCT scores which the students would have gotten at the end of the year after which conclusions will be drawn.

The study will only consider a sample of K-4 students of selected schools only. The schools that will be eligible for the study will be those with fluctuating CRCT score for the last five years. We will therefore have to collect qualitative (secondary) and quantitative (primary) data to get solid results for the study. Before one decides to spend a lot of time and money in collecting primary data, it is advised that secondary data should first be reviewed.

### Quanlitative data (Secondary data)

Secondary data can be obtained by reviewing works which have been done on the topic of study and forms the literature review. This data is important because it helps in attaining a better understanding of the topic of research and can be obtained from peer reviewed journals, magazines, books, articles and other relevant sources. Previous works which have been done in this topic will be reveiwed and their findings and recommendations will be considered. Secondary data can also come in handy in formulating the most appropriate methods of designing the questionaires which will be used to gather primary information of the research. As result, the questionaires which will be designed will contain questions that will lead to the collection of relevant data for the study. However, there are some instances where secondary data is really not helpful. Secondary data can be irrelevant if they do not have a direct relationship with the topic of study. This gives room for decrease in the accuracy and reliability of data that has been collected.

### Quantitative data (Primary data)

Primary data is used to suppliment the data which was collected during literature review. Primary data is the data which has been collected directly from the field. This data can be obtained by conducting interviews, administering questionaires and by analyzing the trends of internal exams and CRCT. Primary data will help us to obtain first hand information which will help to explore the research objectives and gain statistical data that is necessary for data analysis. The questionnaires will be structured in such a way so as to minimize the occurrence of errors and which may make the data collected from the field to become unreliable. Careful measures will be taken to avoid this. Prior to the conduction of the interviews the validity of the questionnaires will have been tested and approved for use.

## Data analysis

Raw data from the field is of no use since it does not make sense. It is mainly composed of numbers and needs to be coded and analyzed in order to make sense. Analysis of data involves three major steps:

- Data preparation which involves the organization of the data which has been collected for easy analysis.
- Descriptive statistics which entails the description and interpretation of the data which has been collected. This can be done by the use of charts and bar graphs to explain the trends which have been observed.
- Inferential statistics that is done to test whether the data which has been collected is consistent with the hypothesis of the study.

For accurate analysis of the statistical data a computer programme called SPSS 16.0 will be used for descriptive data analysis. The data will be explored using descriptive statistics and histogram plots will be used to determine the shape of the distribution for each sample variable. The name given to each variable for the purpose of the data analysis will be given in a table. Data analysis will be carried out using parametric tests where the data will follow a normal distribution and where the sample number will equal to or greater statistical power. Where the data will not follow a normal distribution or where the data will be split into groups of less than the sample size (n), non-parametric test will be used. For example a Pearson correlation test will be carried out on the data to explore any linear relationships between the variables.

## Presentation of findings and conclusions

Formulating the conclusion and recommendations of the study will be the next step. From here the final dissertation can be compiled which will have an additional section of discussing the results. It is here where the arguments for and against the research are raised in response to the data that was collected and analyzed. If need be the final dissertation can be published in peer reviewed journals and further studies on the topic can be conducted.

## References

Gelpi, G. (2009). CRCT Math Scores Vary Widely. *The Augusta Chronicles. *

Ho, D., Imai, K., King, G., and Stuart, E. (2005). *MatchIt: Nonparametric Preprocessing **for Parametric Causal Inference. *

Marshall, P. (2008). Null Hypothesis. *Experimental resources.*

National Research Council. (2001). *Adding it up: Helping Children Learn Mathematics. *Washington, DC: National Academy Press.

Perie, M., Grigg, W. S., and Dion, G. S. (2005). *The Nation’s Report Card-Mathematics **2005. *Washington, DC: National Center for Education Statistics.

Quick MBA. (2010). *Marketing research*.

Reed, K. (2008). 400 Barrow eighth graders fail math CRCT. *Barrowjournal.com. *Web.

Robinette, M. (2006). *The Results of a Computer-Based Extended Learning Time on **the Math Achievement and Perceptions of Low-Performing Students*. Valdosta State University: Georgia.

Singer, J. D., and Willett, J. B. (2003). *Applied Longitudinal Data Analysis: Modeling **Change and Event Occurrence. *New York: Oxford University Press.

Shuttleworth, M. (2008) Research hypothesis. *Experiment Resources*. Web.