Third Grade Students Mathematics and Reading Achievement

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The purpose of this chapter is to explain the methods used to complete the quantitative research study. This study will examine which organizational structure, traditional (self-contained, one teacher for all academic subjects) or departmentalized (math and reading taught by a different teacher), has the greatest effect on general third-grade students' reading and math achievement as measured by the FCAT (Florida Comprehensive Assessment Test).

From the above problem area, the following research questions and hypotheses were developed and will be addressed:

Research Question 1: Do general education third-grade students have a higher mean scale score on the FCAT mathematics in a traditional (self-contained, one teacher for all academic subjects) classroom than third-grade students in a departmentalized (math taught by different teacher) classroom setting?

Null Hypothesis 1-H01: There will be no significant difference in the mathematics achievement of traditional (self-contained, one teacher for all academic subjects) third-grade general education mathematics students as compared to departmentalized (math taught by different teacher) third-grade general education mathematics students as shown by the mean scale score on the FCAT mathematics scores.

Research Question 2: Do general education third-grade students have a higher mean scale score on the FCAT reading in a traditional (self-contained, one teacher for all academic subjects) classroom than third-grade students in a departmentalized (reading taught by different teacher) classroom setting?

Null Hypothesis 2-H02: There will be no significant difference in the reading achievement of traditional (self-contained, one teacher for all academic subjects) third-grade general education reading students as compared to departmentalized (reading taught by different teacher) third-grade general education reading students as shown by the mean scale score on the FCAT reading scores.

Research Question 3: Do general education third-grade students have a higher percentage of students scoring at or above the minimum state expectations on the FCAT mathematics in a traditional (self-contained, one teacher for all academic subjects) classroom or in a departmentalized (math taught by a different teacher) classroom setting?

Null Hypothesis 3-H03: There will be no significant difference in mathematics achievement of traditional, self-contained (one-teacher for all academic subjects) third - grade general education students as compared to departmentalized (math taught by another teacher) third - grade general education students as shown by the percentage passing results of the FCAT mathematics scores.

Research Question 4: Do general education third-grade students have a higher percentage of students scoring at or above the minimum state expectations on the FCAT reading in a traditional (self-contained, one teacher for all academic subjects) classroom or in a departmentalized (reading taught by a different teacher) classroom setting?

Null Hypothesis 4-H04: There will be no significant difference in reading achievement of traditional, self-contained (one-teacher for all academic subjects) third - grade general education students as compared to departmentalized (reading taught by another teacher) third - grade general education students as shown by the percentage passing results of the FCAT reading scores.

The methodology section, chapter three, includes the following components: (a) design of study; (b) data gathering methods; (c) instruments; (d) procedures.

Design of the Study

A causal-comparative research design will be used to test the null hypotheses in this ex-post facto research study. The participants will be predetermined by the participating school and students will not be randomly assigned by the researcher. The researcher will examine the archival data of two different classroom organizational instruction techniques-traditional (self-contained, one teacher) and departmentalized formats (reading & math taught by a different teacher). This procedure will be accomplished by analyzing the mathematical and reading FCAT achievement data of the third-grade students to investigate the cause-and-effect relationships of the two different types of instructional organizations (independent variables), as measured by the FCAT (dependent variable).

Research participants. Southeast Florida is a diverse multicultural/multi-ethnic population. The study will consist of about 34, 730 third-grade students from 263 elementary schools in this region.

Data Gathering Methods

Permission to use the information will be provided by each school district in the study. Data will be separated by means and percentages and categorized either as traditional (self-contained, one teacher) or departmentalized formats (reading & math taught by a different teacher). FCAT math and reading means and percentages (2008-2009) will be used as a pre-test to make sure that each of counties are comparable. An Analysis of Variance (ANOVA) will be used to analyze the means of all groups within this pre-test observance.

Instruments

The instrument that will be used to measure student achievement is the FCAT. The FCAT will be used to measure the reading and math achievement of the third - grade students participating in the study and will address Research Questions 1, 2, 3, and 4. As an established measurement for student achievement, the validity and reliability issues are necessary. The Florida Comprehensive Assessment Test (FCAT) was designed to assess student achievement of the Sunshine State Standards (SSS).

In An Assessment and Accountability Brief by the Florida Department of

Education (FDOE) (2007), reliability and validity are two constructs that are generally used to indicate the quality of a standardized test. Reliability can be represented in several ways, but the concept essentially means that the test is a consistent measurement of an examinee's knowledge. Reliability measures help users general­ize student performances from one time to another. Four kinds of reliability coefficients are used in relation to the FCAT:

(a) internal consistency

(b) test-retest reliability

(c) inter-rater reliability

(d) reliability of classifications

For any of the four types of reliability, the coefficient is expressed as a number from zero to one (0.0-1.00). A value of zero indicates a lack of reliability that results in inconsistent scores from one test administration to the next. On the other hand, a value of one indicates perfect consistency. The most common measure of reliability is the internal consistency reliability coefficient. The reliability coefficient (Cronbach's alpha) is computed for the 2006 FCAT math to equate to .89 for third grade mathematics and 2006 FCAT reading to equate to .90 for third grade reading. This confirms that FCAT is a highly reliable test for assessing the educational achievement of Florida students.

Validity refers to the extent to which the test claims to measure what it is suppose to measure. FCAT is intended to measure a student's achievement of the skills and con­tent described in the SSS. Validity depends on various pieces of evidence that indicate the presence or absence of validity. The types of validity evidence are often categorized into these three unified groups:

(a) content-related validity evidence

(b) criterion-related validity evidence

(c) construct-related validity evidence

The FCAT is designed to assess SSS that were developed with involve­ment of instructional specialists.

"To ensure high content validity of FCAT, the Department of Education (2007) has implemented the following steps for all of the items included on FCAT:

Educators and citizens judged the standards and skills acceptable.

Item specifications were written.

Test items were written according to the guidelines provided by the item specifications.

The items were pilot tested using randomly selected groups of students at appropriate grade levels.

All items were reviewed for cultural, ethnic, language and gender bias and for issues of general concern to Florida citizens.

Instructional specialists and practicing teachers reviewed the items.

The items were field tested to determine their psychometric properties.

The tests were carefully constructed with items that met specific psychometric standards.

The constructed tests were equated to the base test to match both content coverage and test statistics" (FDOE., 2007, p. 40).

Because FCAT assesses the content of the NGSSS and is developed using credible and trustworthy methods, the content validity of the test is substantiated. The evidence of reliability and validity supports the claim that FCAT is technically sound and meets or exceeds the professional standards for standardized achievement tests.

Achievement Levels describe the success a student has achieved on the SSS tested on the FCAT Reading and Mathematics. FCAT scores are reported as Achievement Levels, as shown in table 1, are based on scale scores which range from 1 (lowest) to 5 (highest). Scale scores are reported for all FCAT NGSSS subjects and range from 100 (lowest) to 500 (highest), as shown in tables 1 and 2. A student scoring at or above Achievement Level 3 is considered to be performing at or above grade level.

Table 1:

Achievement Level

Level 5

This student has success with the most challenging content of the Sunshine State Standards. A student scoring in Level 5 answers most of the test questions correctly, including the most challenging questions.

Level 4

This student has success with the challenging content of the Sunshine State Standards. A student scoring in Level 4 answers most of the test questions correctly, but may have only some success with questions that reflect the most challenging content.

Level 3

This student has partial success with the challenging content of the Sunshine State Standards, but performance is inconsistent. A student scoring in Level 3 answers many of the test questions correctly but is generally less successful with questions that are the most challenging.

Level 2

This student has limited success with the challenging content of the Sunshine State Standards.

Level 1

This student has little success with the challenging content of the Sunshine State Standards.

FCAT 3rd Grade Reading Scale Scores. Table 2

Level 1

Level 2

Level 3

Level 4

Level 5

100 - 258

259 - 283

284 - 331

332 - 393

394 - 500

FCAT 3rd Grade Math Scale Scores. Table 3

Level 1

Level 2

Level 3

Level 4

Level 5

100 - 252

253 - 293

294 - 345

346 - 397

398 - 500

Procedures

Sampling procedures. The participants will be predetermined by the participating schools so students cannot be randomly assigned by the researcher. The groups will be assigned to different conditions - one being a traditional setting and the other being a departmentalized setting. According to Ary et al. (2006) "the most important characteristic of a sample is its representativeness, not its size" (p.176). Each group will be assessed on the NGSSS and will be measured by the FCAT at the end of the year.

Data Analysis Procedures. This causal-comparative study will compare two different types of instructional organizations (independent variables), as measured by the FCAT (dependent variable). The hypothesis for the study will be there is no significant difference in math and reading achievement of traditional, self-contained (one-teacher for all academic subjects) third - grade general education students as compared to departmentalized (math and reading taught by another teacher) third - grade general education students as shown by the mean scores and percentage passing results of the FCAT math and reading scores. A two-sample t test will be used to determine significant differences between mean scale scores of the traditional (self-contained, one-teacher) classroom of students and the departmentalized (math and reading taught by another teacher) students. A chi square will be used to determine significant differences between percentage of students scoring at or above the minimum state expectations of the traditional (self-contained, one-teacher) classroom of students and the departmentalized (math and reading taught by another teacher) students.

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