# Teaching Math Concepts to Improve Test Scores Term Paper

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Elementary Measurement: Area, Perimeter, Volume

In an era of increased demands for teacher and student accountability, identifying better ways of delivering educational services represents a timely and worthwhile endeavor. There are some significant constraints involved in teaching young learners about mathematics concepts, though, that must be taken into account in devising such approaches. Nevertheless, the mandate is clear and state-level high-stakes testing regimens across the country currently require that all students achieve minimum performance standards on reading and mathematics tests in order to be promoted to the next grade. In this environment, identifying what works best and what does not is an important first step, and these issues are discussed further below.

Problem Statement and Needs Analysis

Background of the problem

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for only $8.97. Today, primary school teachers are faced with a three-fold challenge when it comes to providing their pupils with quality educational services. The first challenge is the increasingly multicultural and diverse nature of the student body itself. This first challenge is also combined with the second challenge concerning the mandates of various high-stakes testing regimens, inclusion and accountability requirements established by the No Child Left Behind Act (NCLB) of 2001 and the Individuals with Disabilities Education Act (IDEA) that make success in mathematics and reading for all students absolutely essential. For instance, in their book, American Standards: Quality Education in a Complex World, the Texas Case, Horn and Kincheloe (2001) report that in Texas, "District/school approval is being linked to student performance rather than compliance to regulations; accountability is focused more on schools as the unit of improvement, continuous improvement strategies involving school-level decisions around specific performance targets are being adopted, new approaches to classroom inspection are being developed; more categories or levels are being developed; school-level test scores are being publicly reported; and more consequences are being attached to performance levels" (p. 124).

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The third challenge is the fact that there are even some significant gender differences that must be taken into account among these young learners. For example, "By the second grade, students already have identified mathematics and science as "male" domains. By third grade, females rate their own competence in mathematics lower than that of their male classmates, even when they received the same or better grades" (Plymate & Ashley, 2003, p. 162). Finally, because resources are by definition scarce, it is important for educators and administrators alike to identify what works best, and because schools are not factories and young learners are not products, there is absolutely no room for false starts and very little room for experimentation available.

Definition of the problem

In their recent study, "The Effects of Task Demands and Additive Interspersal Ratios on Fifth-Grade Students' Mathematics Accuracy," Hawkins, Skinner and Oliver (2005) report that a number of careers require a keen grasp of mathematics, including engineering, architecture, and financial planning. Mathematics and geometry involve several important measurement concepts such as length and width, perimeter, area, volume, and angles (Baroody & Coslick, 1998). These authors note that, "In the traditional skills approach, instruction focuses on memorizing measurement procedures and formulas. Unfortunately, premature use of instruments or formulas leaves children without the understanding necessary for solving measurement problems. Moreover, a focus on memorizing facts (e.g., metric equivalents such as 1 meter = 39.37 inches), procedures (e.g., metric conversion methods), and formulas (e.g., area formulas) turns off many students" (p. 15-4). Because there is so much riding on successful academic outcomes for mathematics instruction in Texas public schools today, providing young learners with the level of instruction that they need to become more proficient in measurement concepts represents a timely and worthwhile initiative.

Needs analysis

The Texas Education Agency reports that Texas students received the highest passing rate on the state's 5th grade mathematics test to date with 85% of students mastering the English-language version of the exam and 39% achieving the prestigious "Commended Performance" level (Passing rates on 5th grade math, 2007). In order to receive the "Commended Performance" rating on the 5th grade Texas Assessment of Knowledge and Skills (TAKS) math test, Texas public school students must answer at least 40 of the 44 questions correctly (Pass rates on 5th grade math, 2007).

There have been some indications that English-speaking Texas students are becoming more proficient at passing these testing regimens; however, whether this is an indication of teachers "teaching to the test" or reflects actual gains in knowledge and mathematics expertise remains unclear. In this regard, the Texas Education Agency (2007) reports that, "The passing rate has risen from 79% in 2005, when the passing standards were first fully phased in, to 81% in 2006 to 85% in 2007. This year, 299,337 students took the English-language math test, and 254,233 passed it. An additional 5,834 students took the math test in Spanish, and 2,895, or 50%, passed it. This was also the highest passing rate ever achieved on the Spanish-language math test" (Passing rates on 5th grade math, 2007, p. 2).

By sharp contrast, though, while the passing rate for Spanish-speaking students also increased from 44% in 2005 to 47% in 2006, the percentage of Spanish-speaking students that earned a "Commended Performance" designation was 11% in Spring 2007, representing a decrease from 12% in 2006 (Passing rates on 5th grade math, 2007). Students were also required to answer one less question correctly (39 or more questions correctly on the Spanish-version test) to earn the commended label (Passing rates on 5th grade math, 2007).

According to the Texas Education Agency Accountability Manual (2007), "For grades 3 and 5 reading and grade 5 mathematics performance, a cumulative percent passing is calculated by combining the first and second administrations of the TAKS. The results include performance on the Spanish versions of these tests" (p. 3). Today, all fifth-grade students in Texas public schools must successfully pass the TAKS reading and math tests, together with their classes, in order to be promoted to sixth grade under Texas law, although they are provided with additional opportunities to take the tests each year (Passing rates on 5th grade math, 2007). In addition, Texas state law currently requires these students to receive intensive instruction immediately to help improve their skills. Many of these students have already received extra instruction, such as small-group tutoring (Passing rates on 5th grade math, 2007).

In those cases where students fail to pass one of the high-stakes tests after three attempts, the student is retained in fifth grade; however, a student's parents have the authority to appeal the retention and a committee of the child's parents, teachers and principal must be created in response (Passing rates on 5th grade math, 2007). These committees, termed "Grade Placement Committees" are responsible for reviewing students' class work and any other relevant information. According to the Texas Education Agency, "If all committee members agree that the student can be successful if promoted and given extra instructional assistance, then the child may be promoted to the next grade. In 2006, 93% of the 5th grade students tested in English ultimately passed the math test after three attempts, as did 74% of those tested in Spanish" (Passing rates on 5th grade math, 2007, p. 3).

Rationale for the need for instruction

Many careers in which fifth-grade students may be interested require a good grasp of mathematic fundamentals. Moreover, the requirements of high-stakes testing regimens have made mathematics a high priority for educators today. According to Chanter and Welsh (2000), "The goals set forth in National Council of Teachers of Mathematics' Principles and Standards for School Mathematics (2000) recommend that students learn to value mathematics, become confident in their abilities, become mathematical problem solvers, and learn to reason and communicate mathematically" (p. 236). Furthermore, the existing NCTM standards recommend that fifth graders become acquainted with a number of geometry concepts at this point in their academic careers.

In this regard, NCTM Standard 13 for grades 5-8 recommends that "the mathematics curriculum should include extensive concrete experiences using measurement so that students can:

In an era of increased demands for teacher and student accountability, identifying better ways of delivering educational services represents a timely and worthwhile endeavor. There are some significant constraints involved in teaching young learners about mathematics concepts, though, that must be taken into account in devising such approaches. Nevertheless, the mandate is clear and state-level high-stakes testing regimens across the country currently require that all students achieve minimum performance standards on reading and mathematics tests in order to be promoted to the next grade. In this environment, identifying what works best and what does not is an important first step, and these issues are discussed further below.

Problem Statement and Needs Analysis

Background of the problem

Get full access

for only $8.97. Today, primary school teachers are faced with a three-fold challenge when it comes to providing their pupils with quality educational services. The first challenge is the increasingly multicultural and diverse nature of the student body itself. This first challenge is also combined with the second challenge concerning the mandates of various high-stakes testing regimens, inclusion and accountability requirements established by the No Child Left Behind Act (NCLB) of 2001 and the Individuals with Disabilities Education Act (IDEA) that make success in mathematics and reading for all students absolutely essential. For instance, in their book, American Standards: Quality Education in a Complex World, the Texas Case, Horn and Kincheloe (2001) report that in Texas, "District/school approval is being linked to student performance rather than compliance to regulations; accountability is focused more on schools as the unit of improvement, continuous improvement strategies involving school-level decisions around specific performance targets are being adopted, new approaches to classroom inspection are being developed; more categories or levels are being developed; school-level test scores are being publicly reported; and more consequences are being attached to performance levels" (p. 124).

## Term Paper on *Teaching Math Concepts to Improve Test Scores* Assignment

The third challenge is the fact that there are even some significant gender differences that must be taken into account among these young learners. For example, "By the second grade, students already have identified mathematics and science as "male" domains. By third grade, females rate their own competence in mathematics lower than that of their male classmates, even when they received the same or better grades" (Plymate & Ashley, 2003, p. 162). Finally, because resources are by definition scarce, it is important for educators and administrators alike to identify what works best, and because schools are not factories and young learners are not products, there is absolutely no room for false starts and very little room for experimentation available.Definition of the problem

In their recent study, "The Effects of Task Demands and Additive Interspersal Ratios on Fifth-Grade Students' Mathematics Accuracy," Hawkins, Skinner and Oliver (2005) report that a number of careers require a keen grasp of mathematics, including engineering, architecture, and financial planning. Mathematics and geometry involve several important measurement concepts such as length and width, perimeter, area, volume, and angles (Baroody & Coslick, 1998). These authors note that, "In the traditional skills approach, instruction focuses on memorizing measurement procedures and formulas. Unfortunately, premature use of instruments or formulas leaves children without the understanding necessary for solving measurement problems. Moreover, a focus on memorizing facts (e.g., metric equivalents such as 1 meter = 39.37 inches), procedures (e.g., metric conversion methods), and formulas (e.g., area formulas) turns off many students" (p. 15-4). Because there is so much riding on successful academic outcomes for mathematics instruction in Texas public schools today, providing young learners with the level of instruction that they need to become more proficient in measurement concepts represents a timely and worthwhile initiative.

Needs analysis

The Texas Education Agency reports that Texas students received the highest passing rate on the state's 5th grade mathematics test to date with 85% of students mastering the English-language version of the exam and 39% achieving the prestigious "Commended Performance" level (Passing rates on 5th grade math, 2007). In order to receive the "Commended Performance" rating on the 5th grade Texas Assessment of Knowledge and Skills (TAKS) math test, Texas public school students must answer at least 40 of the 44 questions correctly (Pass rates on 5th grade math, 2007).

There have been some indications that English-speaking Texas students are becoming more proficient at passing these testing regimens; however, whether this is an indication of teachers "teaching to the test" or reflects actual gains in knowledge and mathematics expertise remains unclear. In this regard, the Texas Education Agency (2007) reports that, "The passing rate has risen from 79% in 2005, when the passing standards were first fully phased in, to 81% in 2006 to 85% in 2007. This year, 299,337 students took the English-language math test, and 254,233 passed it. An additional 5,834 students took the math test in Spanish, and 2,895, or 50%, passed it. This was also the highest passing rate ever achieved on the Spanish-language math test" (Passing rates on 5th grade math, 2007, p. 2).

By sharp contrast, though, while the passing rate for Spanish-speaking students also increased from 44% in 2005 to 47% in 2006, the percentage of Spanish-speaking students that earned a "Commended Performance" designation was 11% in Spring 2007, representing a decrease from 12% in 2006 (Passing rates on 5th grade math, 2007). Students were also required to answer one less question correctly (39 or more questions correctly on the Spanish-version test) to earn the commended label (Passing rates on 5th grade math, 2007).

According to the Texas Education Agency Accountability Manual (2007), "For grades 3 and 5 reading and grade 5 mathematics performance, a cumulative percent passing is calculated by combining the first and second administrations of the TAKS. The results include performance on the Spanish versions of these tests" (p. 3). Today, all fifth-grade students in Texas public schools must successfully pass the TAKS reading and math tests, together with their classes, in order to be promoted to sixth grade under Texas law, although they are provided with additional opportunities to take the tests each year (Passing rates on 5th grade math, 2007). In addition, Texas state law currently requires these students to receive intensive instruction immediately to help improve their skills. Many of these students have already received extra instruction, such as small-group tutoring (Passing rates on 5th grade math, 2007).

In those cases where students fail to pass one of the high-stakes tests after three attempts, the student is retained in fifth grade; however, a student's parents have the authority to appeal the retention and a committee of the child's parents, teachers and principal must be created in response (Passing rates on 5th grade math, 2007). These committees, termed "Grade Placement Committees" are responsible for reviewing students' class work and any other relevant information. According to the Texas Education Agency, "If all committee members agree that the student can be successful if promoted and given extra instructional assistance, then the child may be promoted to the next grade. In 2006, 93% of the 5th grade students tested in English ultimately passed the math test after three attempts, as did 74% of those tested in Spanish" (Passing rates on 5th grade math, 2007, p. 3).

Rationale for the need for instruction

Many careers in which fifth-grade students may be interested require a good grasp of mathematic fundamentals. Moreover, the requirements of high-stakes testing regimens have made mathematics a high priority for educators today. According to Chanter and Welsh (2000), "The goals set forth in National Council of Teachers of Mathematics' Principles and Standards for School Mathematics (2000) recommend that students learn to value mathematics, become confident in their abilities, become mathematical problem solvers, and learn to reason and communicate mathematically" (p. 236). Furthermore, the existing NCTM standards recommend that fifth graders become acquainted with a number of geometry concepts at this point in their academic careers.

In this regard, NCTM Standard 13 for grades 5-8 recommends that "the mathematics curriculum should include extensive concrete experiences using measurement so that students can:

- Extend their understanding of the process of measurement;
- Estimate, make, and use measurements to describe and compare phenomena;
- Select appropriate units and tools to measure to the degree of accuracy required in a particular situation;
- Understand the structure use of systems of measurements;
- Extend their understanding of the concepts of perimeter, area, volume, angle measurement, capacity, and weight and mass;
- Develop the concepts of rates and other derived and indirect measurements; and,
- Develop formulas and procedures for determining measures to solve problems" (p. 116 quoted in Baroody & Coslick, 1998 at p. 15-4).

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