# Mathematics Education Research Proposal

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PERCEPTIONS of EDUCATORS in a Massachusetts URBAN SCHOOL DISTRICT of CHANGES in REFORM-RELATED PRACTICES in MATHEMATICS INSTRUCTION SINCE the IMPLEMENTATION of STATEWIDE TESTING

This study, which examined the effects of mathematics reform on teacher practices in Massachusetts, had two central purposes: (a) to identify reform-related practices in mathematics instruction that have increased, decreased, or not changed since the implementation of high-stakes testing according to educators' perceptions and (b) to determine educators' perceptions of the effects of reform-related practices on student achievement since the implementation of high-stakes testing. High-stakes testing is a dramatic change in education practice and has changed the face of mathematics instruction, yet there is only limited research on its effects. This study investigated the perceptions of educators, both generally and by demographic, regarding the effects of mathematics reform on students since the implementation of outcomes-based testing.

ACKNOWLEDGMENTS

I would like to acknowledge my wife and family for their support during this time. I would like to thank my committee members for their time effort and support. I want to recognize all my teachers and friends whose support through the years has made this journey possible.

TABLE of CONTENTS

ABSTRACT

ii iii

TABLE of CONTENTS

iv iv

LIST of FIGURES

vi

CHAPTER Page

1. INTRODUCTION

1

Statement of the Problem

3

Get full access

for only $8.97. Purpose of the Study

4

Research Question

4

Significance of the Study

5

Methods and Procedures

7

Definitions of Terms

9

CHAPTER 2: LITERATURE REVIEW

11

Introduction

11

Components of Massachusetts Education Reform Act (MERA)

14

Perspectives of Educators Regarding Standardized Education Reforms## Research Proposal on

19

Standards and Assessments

20

Changes in Curriculum and Modes of Instruction

20

Effects of Accountability Systems on Individual Teachers

24

Effects of Accountability Systems on School Capacity

29

Effects of Accountability Systems on Student Learning

30

Alignment of Curriculum and Instruction

32

Connecting NCTM to Reform in Mathematics Instruction 33

Conclusion

33

Theoretical and Conceptual Frameworks

36

CHAPTER 3: METHODOLOGY

40

Research Design

40

Sample Description

40

Survey Permission and Procedures for Human Subject Protection

42

Survey Distribution

43

Survey Returns

44

Instruments, Measures, and Validity

44

Data Analysis

46

Specific Data Analysis Plan for Each Research Question

48

Limitations

50

CHAPTER 4: RESULTS

52

Research Question 1

55

Research Question 2

58

Research Question 3

64

Research Question 4

65

Research Question 5

73

Research Question 6

75

Research Question 7

77

CHAPTER 5: SUMMARY and DISCUSSION

79

Summary

79

Discussion

83

Implications of the Outcome of the Data

86

Implications of for Future Research

87

Conclusion

89

REFERENCES

91

APPENDIX a: SURVEY INSTRUMENT

APPENDIX B: IRB PERMISSION

APPENDIX C: Sample Letter to School SuperintendentS

Table 1. Survey Return Rates for Individual Schools and for Total Group

44

Table 2. Frequency Counts for Selected Variables

53

Table 3. Descriptive Statistics for Ratings of District Implemented Practice

56

Table 4. Descriptive Statistics for Ratings of Classroom Practice

57

Table 5. Pearson Correlations for Factor Scores with Selected Variables

59

Table 6. Comparison of Factor Scores Based on the Role of the Educator. One-Way ANOVA with Scheffe Posthoc Tests

60

Table 7. Prediction of the District Increase Factor Score Based on Demographic

Factors

61

Table 8. Prediction of the Classroom Increase Factor Score Based on Demographic Factors

62

Table 9. Descriptive Statistics for the Effectiveness Ratings of District Implemented Practice

68

Table 10. Descriptive Statistics for Effectiveness Ratings of Classroom Practice

69

Table 11. Prediction of the District Effectiveness Factor Score Based on Demographic Factors

71

Table 12. Prediction of the Classroom Effectiveness Factor Score Based on Demographic Factors

72

Table 13. Comparison of Effectiveness Ratings Based on Different Groups of Students Within-Subjects ANOVA with Bonferroni Posthoc Tests

73

Table 14. Pearson Correlations for Student Group Difference Scores with Selected Demographic Variables

76

LIST of FIGURES

Figure 1: Flow Chart of Planned Examination of Reform Efforts

37

Figure 2. Chrispeel's (1992) Diagram Showing the Interrelatedness of Systems

38

Figure 3. Effectiveness Ratings for the Different Student Groups

74

Figure 4. Percent change in scores for SAT, ACT, and MCAS by nation and city

77

Figure 5. Percent change in scores for SAT, ACT, and MCAS by state and city

78

CHAPTER 1:

Introduction

The state of public education in the United States over the past 75 years has been the focus of reformers, textbook writers, school boards, parents, teachers, and industry. Different groups, depending on their context, have different ideas of what might be most effective in improving the performance of American public school students: making teachers more effective, changing the way information is presented, and school changes in organization and culture that ranged from the open school to those that required uniforms. Certainly some of these worked in some places and for some students and communities, but none of these measures were widely applied, and the lagging academic achievement of American students received wide press in media throughout the country.

Many experts stated that this problem was especially serious in the areas of mathematics and science education (Hagel, 2006, p. 10) with a significant difference between demographic groups, including minorities as well as those in lower income brackets. These groups typically attend schools in districts with less financial support and hence have fewer special resources or the kinds of enrichment activities these students need (Bracey, 2006, p. 151).

In 2003, the "No Child Left Behind" (NCLB) Act became law, the keystone of which was that there would be annual school testing so that schools could be compared with other schools in other districts or states. Although it was left up to the states to determine how to pay for and carry out its mandates, the act was supposed to reduce inconsistency of educational quality across states, increase academic achievement, and ensure transparency and accountability of schools and their administrations (NCLB).

In Massachusetts, the education revolution initiated by the Massachusetts Education Reform Act (MERA) of 1993 had already led to changes in the way mathematics was taught and assessed. The major focus of the commission that created the new standards under MERA was to ensure that the standards in Massachusetts were equivalent to those nationwide as well as to international standards. To do this, a great deal of effort went into development of curriculum, strengthening of teaching practices, introduction to ways to improve scores on standardized tests, and increased accountability measures in public schools (Arvidson, 1997).

However, the frameworks that were created to raise the standards of mathematics education did not invite large-scale consensus; as a result, they were revised many times. Since these changes did not receive final approval of the Massachusetts Department of Elementary and Secondary Education (MDESE) until the summer of 2000, 7 years after the reforms were introduced, mathematics frameworks had been used in the schools of Massachusetts for 7 years without any research to determine their efficacy.

Only one study, conducted by the MDESE in 2004, has been commissioned since MERA was introduced in 1993. The study concluded that education reform was improving student achievement but an achievement gap existed based on socio-economic factors and students with disabilities. The value of the study is questioned, however, because MDESE had not implemented multiple methods of assessing student proficiency as prescribed in MERA at that time. In fact, MDESE relied on only a single method -- high-stakes testing -- under the Massachusetts Comprehensive Assessment System (MCAS), a measure that many educators have questioned the value of (Tench, 2002).

Other questions related to the MDESE implementation of MERA include the following:

1. Do standardized achievement tests provide an accurate view of actual mathematics achievement?

2. Are they an accurate and reliable tool for assessment of a school's education program?

3. Should school reform measures depend exclusively on standardized tests for measuring accountability?

4. Do they accurately align high school mathematics instruction with the achievement of individual students?

Because of these unanswered questions, there was a need for research that studied and evaluated the effectiveness of reforms in mathematics instruction and accountability. The study that follows is a response to that need. It first identifies trends in reform-related practices that have increased, decreased, or not changed and then evaluate their efficacy exclusively from the point-of-view of mathematics educators. It then develops recommendations for educators regarding which instructional practices have proved to be more effective than others and which have the potential to help districts and teachers align their instruction to those practices.

Statement of the Problem

The effectiveness of the effort to reform mathematics education has not been determined. In Massachusetts, only one study has been commissioned since the passage of the Education Act of 1993 (MDESE, 2004). Although the act called for multiple methods of assessing student proficiency, the MDESE has relied on just one method -- a series of high-stakes tests called the Massachusetts Comprehensive Assessment System or MCAS. Yet experts at all levels disagree on whether high-stakes testing accurately measures student achievement (Hull, 2007).

Purpose of the Study

This study examined the effects of mathematics reform on teacher practices in a town called Waynesville here, a real, large urban community… [END OF PREVIEW] . . . READ MORE

This study, which examined the effects of mathematics reform on teacher practices in Massachusetts, had two central purposes: (a) to identify reform-related practices in mathematics instruction that have increased, decreased, or not changed since the implementation of high-stakes testing according to educators' perceptions and (b) to determine educators' perceptions of the effects of reform-related practices on student achievement since the implementation of high-stakes testing. High-stakes testing is a dramatic change in education practice and has changed the face of mathematics instruction, yet there is only limited research on its effects. This study investigated the perceptions of educators, both generally and by demographic, regarding the effects of mathematics reform on students since the implementation of outcomes-based testing.

ACKNOWLEDGMENTS

I would like to acknowledge my wife and family for their support during this time. I would like to thank my committee members for their time effort and support. I want to recognize all my teachers and friends whose support through the years has made this journey possible.

TABLE of CONTENTS

ABSTRACT

ii iii

TABLE of CONTENTS

iv iv

LIST of FIGURES

vi

CHAPTER Page

1. INTRODUCTION

1

Statement of the Problem

3

Get full access

for only $8.97. Purpose of the Study

4

Research Question

4

Significance of the Study

5

Methods and Procedures

7

Definitions of Terms

9

CHAPTER 2: LITERATURE REVIEW

11

Introduction

11

Components of Massachusetts Education Reform Act (MERA)

14

Perspectives of Educators Regarding Standardized Education Reforms

## Research Proposal on *Mathematics Education* Assignment

19Standards and Assessments

20

Changes in Curriculum and Modes of Instruction

20

Effects of Accountability Systems on Individual Teachers

24

Effects of Accountability Systems on School Capacity

29

Effects of Accountability Systems on Student Learning

30

Alignment of Curriculum and Instruction

32

Connecting NCTM to Reform in Mathematics Instruction 33

Conclusion

33

Theoretical and Conceptual Frameworks

36

CHAPTER 3: METHODOLOGY

40

Research Design

40

Sample Description

40

Survey Permission and Procedures for Human Subject Protection

42

Survey Distribution

43

Survey Returns

44

Instruments, Measures, and Validity

44

Data Analysis

46

Specific Data Analysis Plan for Each Research Question

48

Limitations

50

CHAPTER 4: RESULTS

52

Research Question 1

55

Research Question 2

58

Research Question 3

64

Research Question 4

65

Research Question 5

73

Research Question 6

75

Research Question 7

77

CHAPTER 5: SUMMARY and DISCUSSION

79

Summary

79

Discussion

83

Implications of the Outcome of the Data

86

Implications of for Future Research

87

Conclusion

89

REFERENCES

91

APPENDIX a: SURVEY INSTRUMENT

APPENDIX B: IRB PERMISSION

APPENDIX C: Sample Letter to School SuperintendentS

Table 1. Survey Return Rates for Individual Schools and for Total Group

44

Table 2. Frequency Counts for Selected Variables

53

Table 3. Descriptive Statistics for Ratings of District Implemented Practice

56

Table 4. Descriptive Statistics for Ratings of Classroom Practice

57

Table 5. Pearson Correlations for Factor Scores with Selected Variables

59

Table 6. Comparison of Factor Scores Based on the Role of the Educator. One-Way ANOVA with Scheffe Posthoc Tests

60

Table 7. Prediction of the District Increase Factor Score Based on Demographic

Factors

61

Table 8. Prediction of the Classroom Increase Factor Score Based on Demographic Factors

62

Table 9. Descriptive Statistics for the Effectiveness Ratings of District Implemented Practice

68

Table 10. Descriptive Statistics for Effectiveness Ratings of Classroom Practice

69

Table 11. Prediction of the District Effectiveness Factor Score Based on Demographic Factors

71

Table 12. Prediction of the Classroom Effectiveness Factor Score Based on Demographic Factors

72

Table 13. Comparison of Effectiveness Ratings Based on Different Groups of Students Within-Subjects ANOVA with Bonferroni Posthoc Tests

73

Table 14. Pearson Correlations for Student Group Difference Scores with Selected Demographic Variables

76

LIST of FIGURES

Figure 1: Flow Chart of Planned Examination of Reform Efforts

37

Figure 2. Chrispeel's (1992) Diagram Showing the Interrelatedness of Systems

38

Figure 3. Effectiveness Ratings for the Different Student Groups

74

Figure 4. Percent change in scores for SAT, ACT, and MCAS by nation and city

77

Figure 5. Percent change in scores for SAT, ACT, and MCAS by state and city

78

CHAPTER 1:

Introduction

The state of public education in the United States over the past 75 years has been the focus of reformers, textbook writers, school boards, parents, teachers, and industry. Different groups, depending on their context, have different ideas of what might be most effective in improving the performance of American public school students: making teachers more effective, changing the way information is presented, and school changes in organization and culture that ranged from the open school to those that required uniforms. Certainly some of these worked in some places and for some students and communities, but none of these measures were widely applied, and the lagging academic achievement of American students received wide press in media throughout the country.

Many experts stated that this problem was especially serious in the areas of mathematics and science education (Hagel, 2006, p. 10) with a significant difference between demographic groups, including minorities as well as those in lower income brackets. These groups typically attend schools in districts with less financial support and hence have fewer special resources or the kinds of enrichment activities these students need (Bracey, 2006, p. 151).

In 2003, the "No Child Left Behind" (NCLB) Act became law, the keystone of which was that there would be annual school testing so that schools could be compared with other schools in other districts or states. Although it was left up to the states to determine how to pay for and carry out its mandates, the act was supposed to reduce inconsistency of educational quality across states, increase academic achievement, and ensure transparency and accountability of schools and their administrations (NCLB).

In Massachusetts, the education revolution initiated by the Massachusetts Education Reform Act (MERA) of 1993 had already led to changes in the way mathematics was taught and assessed. The major focus of the commission that created the new standards under MERA was to ensure that the standards in Massachusetts were equivalent to those nationwide as well as to international standards. To do this, a great deal of effort went into development of curriculum, strengthening of teaching practices, introduction to ways to improve scores on standardized tests, and increased accountability measures in public schools (Arvidson, 1997).

However, the frameworks that were created to raise the standards of mathematics education did not invite large-scale consensus; as a result, they were revised many times. Since these changes did not receive final approval of the Massachusetts Department of Elementary and Secondary Education (MDESE) until the summer of 2000, 7 years after the reforms were introduced, mathematics frameworks had been used in the schools of Massachusetts for 7 years without any research to determine their efficacy.

Only one study, conducted by the MDESE in 2004, has been commissioned since MERA was introduced in 1993. The study concluded that education reform was improving student achievement but an achievement gap existed based on socio-economic factors and students with disabilities. The value of the study is questioned, however, because MDESE had not implemented multiple methods of assessing student proficiency as prescribed in MERA at that time. In fact, MDESE relied on only a single method -- high-stakes testing -- under the Massachusetts Comprehensive Assessment System (MCAS), a measure that many educators have questioned the value of (Tench, 2002).

Other questions related to the MDESE implementation of MERA include the following:

1. Do standardized achievement tests provide an accurate view of actual mathematics achievement?

2. Are they an accurate and reliable tool for assessment of a school's education program?

3. Should school reform measures depend exclusively on standardized tests for measuring accountability?

4. Do they accurately align high school mathematics instruction with the achievement of individual students?

Because of these unanswered questions, there was a need for research that studied and evaluated the effectiveness of reforms in mathematics instruction and accountability. The study that follows is a response to that need. It first identifies trends in reform-related practices that have increased, decreased, or not changed and then evaluate their efficacy exclusively from the point-of-view of mathematics educators. It then develops recommendations for educators regarding which instructional practices have proved to be more effective than others and which have the potential to help districts and teachers align their instruction to those practices.

Statement of the Problem

The effectiveness of the effort to reform mathematics education has not been determined. In Massachusetts, only one study has been commissioned since the passage of the Education Act of 1993 (MDESE, 2004). Although the act called for multiple methods of assessing student proficiency, the MDESE has relied on just one method -- a series of high-stakes tests called the Massachusetts Comprehensive Assessment System or MCAS. Yet experts at all levels disagree on whether high-stakes testing accurately measures student achievement (Hull, 2007).

Purpose of the Study

This study examined the effects of mathematics reform on teacher practices in a town called Waynesville here, a real, large urban community… [END OF PREVIEW] . . . READ MORE

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