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Opportunity to Learn (OTL) and the Alignment of Upper Division Mathematics Learning Outcomes, Textbooks, and the National Assessment in Belize

ProQuest Dissertations and Theses, 2011
Dissertation
Author: Gabriel Cal
Abstract:
In this study I investigate the degree of alignment among the learning outcomes, textbooks, and the national assessment in Belize. To establish the degree of alignment, Webb's Four Cognitive Levels of Depth of Knowledge was used to analyze the levels of cognitive demand for each curriculum. The degree of alignment of the learning outcomes with the test items and textbooks was used to determine the extent to which the textbooks provide students with the opportunity to study the learning outcomes assessed by the national assessment. The opportunity to learn (OTL) measures addressed were the curricular content coverage and types of instructional segments in the context of the four upper division mathematics textbooks ( Let's Pass Mathematics , Caribbean Primary Mathematics , Active Mathematics - A Student's Workbook , and PSE Mathematics - Practice Problems and Test ) currently used in Belize. Findings from the study indicate that the relationship among the three types of curriculum varied in the degree of alignment. A strong relationship was noted between the test items of the national assessment and the instructional segments of the textbooks. With respect to the instructional segments from the textbooks and the learning outcomes, only the Standard 5 textbook had strong alignment while the Standard 6 textbooks exhibited lower cognitive levels than the learning outcomes. A similar case was observed between the cognitive levels of the learning outcomes and the test items. The learning outcomes were at a higher level than the test items, resulting in limited alignment. It is to be noted that the cognitive demand level of the learning outcome set high expectations which fell short of a strong alignment as a result of the high proportions of low cognitive demand levels of the other curricula in the study. In light of these findings, I recommend that special attention be given to the textbooks, an important component in the curricular link, that play a significant role in providing support for students to study the learning outcomes and in turn the opportunity to do well in the national assessment.

Table of Contents

List of Tables

................................ ................................ ................................ ....................

i v

List of Figures

................................ ................................ ................................ ....................

vi

Abstract

................................ ................................ ................................ ............................

viii

Chapter 1: Introduction

................................ ................................ ................................ ........ 1

Statement of the Problem

................................ ................................ ........................ 5

Purpose of the Study

................................ ................................ ................................ 7

Research Questions

................................ ................................ ................................ .. 8

Significance of the Study

................................ ................................ ......................... 9

Definition s

of Terms

................................ ................................ .............................. 11

Chapter 2: L iter ature R eview

................................ ................................ ............................. 15

Theoretical Considerations

................................ ................................ .................... 15

Interrelationship in Curricula

................................ ................................ ................ 16

Types of Curriculum

................................ ................................ .................. 17

Opportunity to Learn ................................ ................................ ............................ 19

Indicators of Opportunity to Learn

................................ ........................... 21

Role of Textbooks

................................ ................................ ................................ .. 2 3

Textbooks as the Written Curriculum

................................ ........................ 25

Functions of Textbooks ................................ ................................ .............. 27

Curricul a

Alignment

................................ ................................ .............................. 29

Alignment of Stand ards, Written Curriculum , and Assessment

............................ 30

Alignment Models

................................ ................................ ..................... 3 2

Summary of Curriculum Alignment

Models

................................ ......................... 34

Analyses of Textbooks

................................ ................................ ........................... 35

Analyses of Curriculum Standards Documents

................................ ........ 39

Role of Learning Outcomes

................................ ................................ .................. 4 2

Summary

of Analyses of Textbooks and Learning Outcomes

.............................. 4 4

Textbook

Mathematical Tasks

................................ ................................ ............... 44

Cognitive Demands of Mathematical Tasks

................................ ............. 4 8

Summary of the Literature Review

................................ ................................ ........ 49

Chapter 3: Research Design and M ethodology

................................ ................................ . 50

Education al

System

in Belize

................................ ................................ ............... 51

Research Ques tions

................................ ................................ ................................ 5 2

ii

Sample ................................ ................................ ................................ .................... 5 2

Learning Outcomes

................................ ................................ .................... 5 3

National P rimary Selection Examination ................................ ................... 5 5

Upper Division Textbooks

................................ ................................ ......... 5 8

Why Choose Upper Division

................................ ................................ ..... 62

Foundation for Alignment and Opportunity to Learn

................................ ............ 62

Depth of Knowledge: Learning Outcomes

................................ ................ 6 6

Content Coverage of

the Test Items

................................ ........................... 6 8

Depth of Knowledge: Test Items

................................ ............................... 6 9

Coding of Test Items Cognitive Levels

................................ ..................... 70

Alignment of Learni ng Outcomes and the Test Items

............................... 7 1

Analysis of Textbook‘s Instructional Segments

................................ ........ 7 2

Reliability of Coding ................................ ................................ .............................. 7 5

Reliability Procedures

................................ ................................ ................ 7 6

S ummary of Research Design and Methodology

................................ .................. 7 9

Chapter 4: Results

................................ ................................ ................................ ............. 80

Cognitive Levels of Learning Outcomes

................................ ............................... 82

Cognitive Levels of Test Items

................................ ................................ .............. 83

Coverage of Learning Outcomes by Test Items

................................ .................... 8 4

Alignment of Cognitive Demand of Learning Outcomes and Test Items

............. 85

Alignment of Learning Outcomes and 2009 Test Items

............................ 85

Alignment of Learning Outcomes and 2010 Test Items

............................ 88

Summary of Coverage and Alignment of Learning Outcomes and Test Items

................................ ................................ ................................ ....................... 9 0

Learning Outcomes and the Instructio nal Segments of the Textbooks

................. 91

Caribbean Primary Mathematics

Textbook (Standard 5)

......................... 9 1

Let’s Pass Mathematics

(Standard 6)

................................ ........................ 93

Active Mathematics –

A St udent’s Workbook

(Standard 6)

....................... 94

PSE Mathematics –

Practice Problems and Test with Solutions

............... 9 6

Summary of the Learning Outcomes

and Upper Division Textbooks

................... 98

Alignment of Instructional S egments and Learning Outcomes

........................... 100

Summary of Learning Outcomes

and Instructional Segments Alignm ent

.......... 10 8

Instructional Segm ents and Test Item Alignment

................................ ................ 10 9

Summary of the Test Items and Instructional S egments from Textbooks

........... 11 9

Nature of Alignment Between T ypes of Curriculum

................................ ........... 1 20

Summary of the Results

................................ ................................ ....................... 1 2 1

Chapter 5: Summary, Discussion and Recommendations

................................ ............... 1 2 2

Summary of the Study

................................ ................................ ......................... 1 2 2

Results of the Study

................................ ................................ ................. 12 3

Learning Outcomes Alignment with Test Item s

.......................... 12 3

Opportunity to Study the Learning Outcomes

............................. 125

iii

Alignment of Cognitive Demand of Instructional Segments with the Learning Outcomes

................................ ........................ 12 7

Alignment of Instructional Segments with Test Items

................ 12 8

Nature of Alignment Am ong the Three Types of Curriculum

................................ ................................ ................... 130

Discussion

................................ ................................ ................................ ............ 1 30

Significance of the Study

................................ ................................ ..................... 13 7

Limitations of the Study ................................ ................................ ....................... 140

Recomm endations for Future Research

................................ ............................... 14 1

Conclusion

................................ ................................ ................................ ........... 14 2

List of References

................................ ................................ ................................ ............ 14 3

Appendix A:

P ilo t Study

................................ ................................ ................................ 16 1

Appendix B :

Co ding Instrument for Learning Outcomes

Depth of Knowledge

........... 19 1

Appendix C :

Coding Instrument for Content Coverage for the P rimary S election Ex amination

Mathematics Test ................................ ................................ 19 2

Appendix D :

Coding Instrument for Cognitive Demand Level

of Test Items

.............. 19 3

Appendix

E :

Coding Instrument for the Types of Instructional Seg ments

................... 19 4

Appendix

F :

Coding Instrument for Level of Cognitive Demand of Instructional

Se gments

................................ ................................ ................................ . 19 5

Appendix

G :

Coding Instrument for the Alignment of the Learning Outcomes and Te xtbooks

................................ ................................ .......................... 19 6

Appendix H :

Training Manual ................................ ................................ ....................... 19 7

About the Author

................................ ................................ ................................ ...

End Page

iv

List of Tables

Table 1:

Upper Division Learning Outcomes

................................ ................................ 54

Table 2:

Description of Primar y Selection Examination Tests

................................ ...... 57

Table 3 :

T extbooks by Standard Level

................................ ................................ ......... 58

Table 4 :

Chapter Titles for the Caribbean Primary Mathematics

Textbook

................. 59

Table 5 :

Topi cs Covered by Standard 6 Textbooks

................................ ....................... 6 1

Table 6 :

Webb‘s Four Cognitive Levels of Depth of Knowledge

................................ . 65

Tabl e 7:

Mathematical Descriptors

of Webb ‘ s Four Levels

................................ .......... 67

Table 8:

Table of Specification for the

Primary Selection Examination

....................... 70

Table 9 :

Coding of Test Items Cognitive Lev els

................................ ........................... 7 1

Table 10 :

Proportion of Instructional Segments for each Textbook

................................ 73

Table 11 :

Inter - Coder Reliability Estimates for Learning Outcomes, Test Items, and

Instructional Segments

................................ ................................ ............. 7 8

Table 12 :

Instructional Segments by Content Domain and Segment Ty pe in the Caribbean Primary Mathematics

Textbook

................................ .................... 9 1

Table 13 :

Instructional Segments by Content Domain and Segment Type in the

Let’s Pass Math ematics

Textbook

................................ ................................ ... 9 3

Table 14 :

Instructional Segments by Content Domain and Segment Type in the

Active Mathemat ics

Textbook ................................ ................................ .......... 95

Table

1 5 :

Instructional Segments by Content Domain and Segment Type in the

Primary Selection Examination

Textbook

................................ ....................... 96

Table 1 6 :

Proportion of Instructional Segments Alignment with the Learning Outcomes for the Caribbean Primary Mathematic s

Textbook

..................... 102

v

Table 1 7 :

Proportion of Instructional Segments Alignment with the Learning Outcomes for the Let’s Pass Mathematics

Textbook

................................ .... 103

Table 1 8 : Proportion of Instructional Segments Alignment with the Learning Outcomes for the Active Mathemati cs

Textbook

................................ ........... 105

Table 1 9 : Proportion of Instructional Segments Alignment with the Learning Outcomes for the Primary Selection Examination

Textbook

........................ 106

Table 20 :

Proportion of Instructional Segments Alignment with the Learning Outcomes for the Standard 6 Textbooks

................................ ........................ 107

Table 21 :

Number of Test Items at Different Level of Alignment with Textbooks by Grade Level

................................ ................................ ............................... 119

vi

List of Figures

Figure 1:

Mean Performance of Belize Primary Selection Examination

......................... 4

Figure 2:

Relationship among Learning Outc omes, Text books , and Assessments

......... 2 9

Figure 3:

Framework of

Alignment and Opportunity to Learn

................................ ....... 63

Figure 4:

Sample

Coding of the Learning Outcome

................................ ...................... 68

Figure 5:

Sample Coding of the Test Item Coverage

................................ ..................... 69

Figure 6:

Sample Coding of an Active Math ematics

Instructional Segment

.................. 74

Figure 7:

Sample Coding of the Caribbean Primary Mathematics

Ins tructional Segment ................................ ................................ ................................ ........... 75

Figure 8 :

Cognitive Levels of the Learning Outcomes

................................ ................... 82

Figure 9 :

Cognitive Level of Test Items ................................ ................................ .......... 83

Figure 1 0 :

Coverage of Learn ing Outcomes by

Test Items

................................ .............. 84

Figure

1 1 :

Learning Outcomes and 2009 Test Items Cognitive Demand Level

.............. 87

Figure 1 2 :

Learning Outcomes and 2010 Test Items Cognitive Demand Level

............... 89

Figure 13:

Proportion of Instructional Segments in ea ch tex tbook by Co ntent Domain

................................ ................................ ................................ ............. 99

Figure 14:

Proportion of Instructional Segments by Grade Level

................................ .. 100

Figure 15:

Cognitive Level of Test Items and Instructional Segments for Number Operations and Concepts

................................ ................................ ............... 111

Figure 16:

Cognitive Level of Test Items and Instructional Se gments for Rate/Ratio/Proportion

................................ ................................ .................... 112

vii

Figure 17:

Cognitive Level of Test Items and Instructional Segments for Geometry ................................ ................................ ................................ ........ 11 3

Figure 18:

Cognitive Level of Test Items and Instru ctional Segments Measurement

................................ ................................ ................................ .. 11 4

Figure 19:

Cognitive Level of Test Items and I nstructiona l Segments for B usiness Math

................................ ................................ ................................ ............... 115

Figure 20:

Cognitive Level of Test Items and Instru ctional Segments for Algebra

....... 116

Figure 21:

Cognitive Level of Test Items and Instructional Segments for Graphs

and Statistics

................................ ................................ ................................ . 117

Figure 22:

Cognitive Lev el of Test Items and Ins tru ctional Segments for Sets

.............. 118

Figure 23:

Cognitive Level of Test Items and Instructio nal Segments for Probability

................................ ................................ ................................ ...... 118

viii

Abstract

In this study I investigate the degree of alignment among the learning outcomes, textbooks, and the national assessment

in Belize.

To establish the degree of alignment, Webb‘s Four Cognitive Levels of Depth of Knowledge

was used to analyze the levels

of cognitive demand for each curriculum. The degree of alignment of the learning outcomes with th e test items and textbooks was used to determine the extent to which the textbooks provide students with the opportunity to study the learning outcomes assessed by the national assessment. The opportunity to learn (OTL) measures addressed were the curricu lar content coverage and types of instructional segments in the context of the four upper division mathematics textbooks ( Let’s Pass Mathematics, Caribbean Primary Mathematics, Active Mathematics –

A Student’s Workbook, and PSE Mathematics –

Practice Probl ems and Test) currently used in Belize.

Findings from the study indicate that the relationship among the three types of curriculum varied in the degree of alignment. A strong relationship was noted between the test items of the national assessment and th e instructional segments of the textbooks. With respect to the instructional segments from the textbooks and the learning outcomes, only the Standard 5 textbook had strong alignment while the Standard 6 textbooks exhibited lower cognitive levels than the learning outcomes. A similar case was observed between the cognitive levels of the learning outcomes and the test items. The learning outcomes were at a higher level than the test items , result ing

in limited alignment.

It is to

ix

be noted that the cognit ive demand level of the learning outcome set high expectations

which fell short of a strong alignment as a result of the high proportions of low cognitive

demand levels of the other curricula in the study .

In light of these findings, I recommend that spec ial attention be given to the textbooks, an important component in the curricular link, that play a significant role in providing support for students to study the learning outcomes and in turn the opportunity to do well in the national assessment.

1

Chap ter 1

Introduction

Over the past century, m athematics curricula in the United States have undergone several shifts in content and procedures with less emphasis on computation.

Early in the twentieth century, instruction focused on drill and practice, em phasizing rote memorization and procedural understanding (Kloosterman & Walcott, 2007). Around the 1960‘s, curricula began to focus on meaningful mathematics which led students to investigate the underlying structure of the discipline. In the late 1970s t he back - to - basics movement moved curricula back toward procedures and skills. With the publication of the Curriculum and Evaluation Standards for School Mathematics

by the N ational C ouncil of T eachers of M athematics (NCTM,

1989), a major shift toward prob lem solving and conceptual understanding was initiated. The latter became known as the reform movement or Standards

Era.

Advocates of reform envisioned that standards outlining what students should know and be able to do would also spur other reforms th at mobilize resources for student learning, such as high quality curriculum frameworks, materials, and assessments tied to the standards (O‘Day & Smith, 1993). In response, states across the U . S .

have weighed in with their own versions of standards - based reform, including new curricula, testing systems, accountability schemes, and promotion or graduation requirements. The latter approaches taken by most states have resulted in a variety of curriculum materials. More

2

specifically, some of these curricular materials may have be en

designed for specific purposes: skill remediation, test preparation, competitions, problem solving practice, software enhancement, and hands - on activities (Usiskin, 2010).

The shift in content in the mathematics curriculum is not

unique to the U . S. In Belize, the Ministry of Education (MOE) adopted the four pillars proposed in the report of the International Commission on Education for the Twenty First Century appointed by the United Nations Educational, Scientific and Cultural O rganization (UNESCO) as Belize‘s foundation of education: learning to live together, learning to know, learning to do, and learning to be. Consequently, the National Comprehensive Curriculum (NCC) and the Primary Selection Examination (PSE) were introduced

into the educational system in Belize under the auspices of the Ministry of Education in 1999. Although the NCC continues to be phased in, the PSE is the instrument designed under the NCC to assess each student‘s general development in the content areas tested. Concomitantly, the PSE serves as the entrance exam for admission to secondary school, specifically high school.

O ne common educational issue shared by most countries, including Belize, is accountability for results. Underperformance of students in

the many content areas of mathematics has contributed to escalating demands for accountability in most schools. However, t he focus on accountability is leading to concerns about the fairness of holding students responsible for reaching high academic stand ards when they have not been provided with the opportunity to learn what the standards expect. On that note, it seems appropriate to pose the question: What factors are contributing to the poor performance

3

of students in mathematics in Belize? Marzano (2 003) contends that the number one factor impacting student achievement is a ―guaranteed and viable curriculum.‖

Anderson (2005) states that one key component of an accountability

system is that the system must be built upon aligned components : o bjective s, assessments, and resources . In addition, Anderson further suggests that t he foundation of results - based accountability systems

is clear expectations for student learning, both what

students are to learn and how that learning is to be demonstrated.

Thus,

content standards and assessments are the components on

which instructional materials

such as textbooks

must be aligned. When

content standards, assessments, and instructional materials

[textbooks]

are aligned, students have the maximum opportunity to

lea rn the state standards (Anderson, 2005).

As standards, accountability, and equity interact and redefine values embedded in education systems , the measurement of student Opportunity - to - Learn (OTL) and the fundamental role standards play in students‘ lear ning are

increasing in significance . Standards homogenize expectations for schooling across social and physical geographies. These standards act as the pillars of accountability that hold schools responsible for student achievement to promote equity in ed ucation (Murphy & Datnow, 2003).

Coupled with the standards is the need to focus

on assessment, especially when assessment is used to support

learning in addition to being used as a measure of

learning; it is fundamental to the whole teaching/learning pr ocess. Th e

act of assessing can provide students with an opportunity to learn, and specifically, learn important mathematics (Steen, 1999; van den Heuvel - Panhuizen & Fosnot, 2001). However, Steen (1999)

4

suggests that the impact of high stakes assessment i s a continuing source of deep anxiety over issues of fairness and appropriate use . Even when a ssessments consist of items that are psychometrically un biased , they

can have an unbalanced impact because of the context in which they are given (e.g., to studen ts of uneven preparation) or the way they are used (e.g., to award admissions to higher education or scholarships).

Data on students‘ performance on the national assessment in Belize raise concerns similar to those in other countries.

On average,

in May of every year, 6,500 school - leaving students, age s

12 to 14

years , take

the National Mathematics Examination which is a major component of the Primary Selection Examination (PSE) .

Scores o n

the PSE are used by high schools countrywide as an entry requireme nt. T he national mean for mathematics has remained more or less constant over the last six years as shown in F igure 1 ,

with spikes in 2004 and 2008.

The results highlighted in F igure 1 indicate that mathematics continues to be an area of significant chall enge for students

and the educational system in Belize.

Figure 1 . Mean Per cent Correct

on the Belize Primary Selection Examination 2004 - 2009

Note . Belize Ministry of Education 2009 Press Release of PSE Results

54.9

42.8

45.8

45.6

53.7

46.2

0 10 20 30 40 50 60 2004 2005 2006 2007 2008 2009 P e r c e n t

Year

5

N otwithstanding the apparent increase in mathematics performance in 2008, the o verall performance on the PSE from 2004 to 2009 indicates that students are below the satisfactory level (60 - 69) and remain at the inadequate level (Grade E ,

0 - 49 ) .

Considering the various social, economic, cogniti ve ,

and psychological factors that impact the learning of mathematics, it is difficult to determine which factor or combination of factors contribute to students‘ poor performance . Nevertheless, examining the textbooks for students‘ potential opportunity to study the content assessed by

the national assessment can be a valuable measure. Examining the textbooks can also be a useful guide to both explain the alignment

between the learning outcomes [intended curriculum] and the written curriculum [ textbooks]

and their alignment with the national assessment in Belize. Hiebert and Grouws (2007) contend that opportunity to learn is ―more nuanced and complex than simply exposure to subject matter‖ and argue that there is a need for a more detailed, richer, and c oherent knowledge base of the potential opportunity to learn to inform policy and practice. In agreement with Hiebert and Grouws , an analysis of upper division textbooks to examine the extent textbooks support students‘ opportunity to study the standards tested on the national assessment would be beneficial to the stakeholders in the education system at large as a first step toward alignment. Subsequent research might determine the extent to which appropriate textbook content is actually enacted in the cl assroom.

Statement of the Problem

The situations in which schools make decisions about which curriculum materials

(e.g., textbooks) are best to promote students‘ learning tend to vary significantly from

6

place to place (Hudson, Lahann, & Lee, 2010). Howe ver, literature suggests that teachers are turning to state standards as their primary guide for identifying what mathematics should be taught and learned by students (Tarr et al., 2006). Such a shift seems to reflect the use of student performance on sta ndardized tests as an indicator of school effectiveness, which seems to be the norm in today‘s education systems (Fitz - Gibbon & Kochan, 2000).

When high - stakes assessments

are used to measure student learning , evidence must be provided that the students have had adequate opportunity to learn the material o n which they are being tested. T extbooks are a strong determinant of what students have the opportunity to learn (OTL).

However, concerns have been expressed about the quality of textbooks and about the ir persuasive influence since textbook content is a significant influence on students‘ opportunity to learn and their subsequent achievement (Robitaille & Travers, 1992). In essence, textbooks are essential in providing students access to knowledge, suppor ting their achievement, and meeting a specific state‘s content standards. For students, not having access to appropriate textbooks

or textbooks aligned to standards and assessment

may have critical consequences in a standards - based educational system (Oake s & Saunders, 2004).

Th erefore,

the prominent role textbooks play in students‘ learning calls for th e analysis of important factors : content coverage within the books of important mathematics, the nature of mathematical tasks, and alignment with state sta ndards and assessment. Thus, the mathematical content of a textbook is an

important aspect to evaluate for its coherence, focus on important mathematics, and extent of coverage across

7

grades (NCTM, 2000). However, a

search of the literature found very li mited content analysis studies of middle school mathematics textbooks series and their alignment with mathematical standards, cognitive demand frameworks, and national assessments. Furthermore, a search of the limited literature related to curriculum in B elize revealed that there have been no studies on upper division

mathematics textbooks and students‘ opportunity to learn in Belize.

As a developing country ,

Belize has undertaken steps towards the develo pment of its educational system and information on the alignment of curriculum is fundamental in the developmental process of the national curricula .

P urpose of the Study

The purpose of this study is to examine the extent to which upper division

mathematics textbooks provide opportunities for students to

study

the learning outcomes assessed in the national assessment (PSE) in Belize. Another objective is to examine the nature of alignment among the learning outcomes, textbooks, and te s t items. I achieved these goals by examining all f our

textbooks presen tly used in the

upper division

in Belize on the

following

criteria: the Belize National Comprehensive Mathematics Curricula

and the Belize Primary Selection Examination (PSE (200 9 - 2010)).

The Belize National Comprehensive Mathematics Curriculum ( BNCMC )

p hilosophy is translated in learning outcomes which are outlined in the mathematics curriculum guides for specific grade levels. In the upper division , there are 15 learning outcomes (LOs) that students are expected to study

as they transition from standar d 5 to 6 (grades 7 and 8) and which are assessed in the national assessment .

8

Of interest in this study is the extent to which students are provided with the opportunity to study

the learning outcomes tested in the national assessment. As a first step t o achieve such a goal, the alignment of the learning outcomes with the test items and textbooks is necessary to understand the

extent to which the textbooks provide students with the opportunit ies to study the learn ing outcomes assessed by the national exa minations. The opportunity to learn measures that this study address ed are the curricular content (topics) coverage and the types of instructional segments in the context of the

four upper division

mathematics textb ooks currently used in Belize. In additi on to the alignment and opportunity to learn measures, the cognitive level of learning outcomes , instructional segments,

and the national test items used as a high stake s

test in Belize

were analyzed.

Because there are important consequences attached to t est performance that can dramatically impact students‘ futures, fairness demands that all students be provided with appropriate opportunities to achieve the desired standards. Policies may provide students the motivation to achieve, but unless the educatio nal system does its job in providing educational opportunities, students will be unable to perform at expected levels.

Research Questions

The study investigate d

the extent to which currently used middle school mathematics textbooks in Belize provide stu dents with an opportunity to learn the mathematics on which students are assessed. Specifically, the study address es

the following research questions:

1.

To what extent are the learning outcomes of the Upper Division Mathematics Curriculum aligned with the n ational assessment test items?

9

2.

To what extent do the

upper division textbooks in Belize provide students with the opportunities to study the

learning outcomes of the Upper Division Mathematics Curriculum?

3.

To what extent are the cognitive demands of

the instructional segments in the upper division textbooks in Belize aligned with the learning outcome s?

4.

To what extent are the

instructional segments in the upper division textbooks in Belize aligned with the content of the test items of the national examinat ion?

5.

What is the nature of alignment of upper division

learning outcomes, written curriculum [textbooks], and test items from the national examination in Belize?

Significance of the Study

The Belize educational system has a National Comprehensive Curricu lum (NCC) in mathematics. One limitation of the NCC standards is that they only describe general expectations for mathematics content domains for the three Divisions of primary school. Division I -

Infant I, II and Standard I (pre - kindergarten to grade 2) , Division II -

Standards II, III, and IV ( grades 3 - 6) , and Division III -

Standards V and VI ( grades 7 - 8) . For instance, the upper division , Division III

(grades 7

-

8) ,

encompasses nine content domains. By the end of the eighth grade, all students are ex pected to have strong background knowledge of mathematics in nine content areas: Number Concepts, Number Operations, Rate/Ratio/Proportion, Algebra, Graphs and Statistics, Sets, Measureme nt, Business Math, and Geometry. Content of the nine domains is

asse ssed through a criterion referenced test consisting of 50 multiple - choice items. Based on test score results, the student may or may not be eligible for entry into secondary schools.

10

Accordingly, students with the highest test score s

get accepted in to

th e ―high performing secondary schools‖ and students with the lowest scores only have the option of being accepted in the ―low performing schools‖ or vocational training schools.

To date there is little formal data in Belize regarding the effectiveness of the National Comprehensive Curriculum materials. That is, no study has yet examined how the Learning Outcomes ( LOs )

documents align with the upper division textbooks and test items. Determining the extent of alignment between the LOs and the mathematics t extbooks and the te s t items is important in developing and improving mathematics textbooks that serve the needs for students in meeting the countr y‘s

mandated learning outcomes. Independent reviews of textbooks are not readily available. There are

no dat a with which to document the appropriateness of textbooks in conveying the aims and goals of the curriculum or the evidences of progress in the overall component s of curriculum in Belize. Thus, this study is significant because it examined (1) the extent to which the learning outcomes align with the test items, (2) the extent to which the textbook provides students opportunities to study

Full document contains 220 pages
Abstract: In this study I investigate the degree of alignment among the learning outcomes, textbooks, and the national assessment in Belize. To establish the degree of alignment, Webb's Four Cognitive Levels of Depth of Knowledge was used to analyze the levels of cognitive demand for each curriculum. The degree of alignment of the learning outcomes with the test items and textbooks was used to determine the extent to which the textbooks provide students with the opportunity to study the learning outcomes assessed by the national assessment. The opportunity to learn (OTL) measures addressed were the curricular content coverage and types of instructional segments in the context of the four upper division mathematics textbooks ( Let's Pass Mathematics , Caribbean Primary Mathematics , Active Mathematics - A Student's Workbook , and PSE Mathematics - Practice Problems and Test ) currently used in Belize. Findings from the study indicate that the relationship among the three types of curriculum varied in the degree of alignment. A strong relationship was noted between the test items of the national assessment and the instructional segments of the textbooks. With respect to the instructional segments from the textbooks and the learning outcomes, only the Standard 5 textbook had strong alignment while the Standard 6 textbooks exhibited lower cognitive levels than the learning outcomes. A similar case was observed between the cognitive levels of the learning outcomes and the test items. The learning outcomes were at a higher level than the test items, resulting in limited alignment. It is to be noted that the cognitive demand level of the learning outcome set high expectations which fell short of a strong alignment as a result of the high proportions of low cognitive demand levels of the other curricula in the study. In light of these findings, I recommend that special attention be given to the textbooks, an important component in the curricular link, that play a significant role in providing support for students to study the learning outcomes and in turn the opportunity to do well in the national assessment.