Measuring Teachers’ Use of Standards-based Instructional MaterialsKaren D. KingThis material is based upon work supported by the National Science Foundation under Grant No. DRL-0732184. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation

OverviewOur framing of the problem -

measuring textbook useResearch questionData collectionResultsInterpretation Implications for practice and

future researchOther areas of research

Instructional Materials vs. Curriculum• Instructional materials are not curriculum• Curriculum is a plan or pathway envisioned from

students' current understanding to target understandings as outlined in Standards

• Instructional materials are tools and resources comprised of a series of instructional tasks and exposition teachers can use to teach the curriculum

• Often, without curriculum guidance, the textbook/instructional materials become the curriculum, substituting instructional materials designers' goals and plans for that of the district or teacher

Why does this distinction matter?A major concern in

implementation is alignment with often conflicting policies◦State Standards◦District Curriculum◦District/School Textbook/Instructional

Materials Adoption◦State Assessments

Our Perspective on Measuring Implementation• Considers the alignment of textbook

to curriculum (Mitchell, King & Gearhardt, in revision)

• Considers alignment of curriculum to state standards (Mitchell, et al., in revision; Porter, 2002)

• Considers alignment of textbook, curriculum, and state standards to state achievement tests (King, et al., in revision)

An Example

0.00 0.20 0.40 0.60 0.80

Memorize/Recall

Perform Procedures

Demonstrate Understanding

Conjecture, Generalize, Prove

Solve non-routine problems/ Make Connections

Fig 3. Grade 8 Cognitive Demand

NJ Stnds 2009 Gr. 8 CMP2 All Units Gr.8

Research Question• What is the relationship between middle grades mathematics teachers' use and adaptation of Standards-based instructional materials and students' achievement?

Research Setting• Newark, NJ in 2008-2009 school year• Had adopted Connected Mathematics

Project (CMP) in 2002, started using CMP 2 in 2008-2009

• Had an NSF-funded Local Systemic Change project that provided substantial professional development on CMP and middle grades mathematics education through 2008

Data Collection • Part of a larger mixed methods study• Surveyed 159 middle grades mathematics

teachers and the student achievement data from 2528 of their students in their first mathematics class of the week

• In Spring 2009, teachers completed the Surveys of Enacted Curriculum Instructional Content and Instructional Practices surveys and project-developed CMP

• Students took the NJ ASK during Spring 2009

Surveys of Enacted CurriculumDemographic information on the teacher,

teacher qualifications, and professional development experiences

Information on the teachers’ instructional practices

Information on the content and cognitive demand of the instruction

To ensure accurate responses, we conducted a professional development session on assessing the cognitive demand of tasks for students prior to teachers completing the survey

SEC Instructional Content SurveyTime on Topic For 188 content areas ranging from

number to advanced algebra, the SEC-IC asks what proportion of time is spent teaching the topic

Emphasis For each content area that the teacher indicates he or she teaches, the SEC-IC asks what proportion of time spent teaching the topic was spent at 5 levels of cognitive demand◦ Memorize facts, perform procedures, demonstrate

understanding, conjecture/generalize/prove, solve non-routine problems/make connections

Prior to survey administration, teachers participated in professional development to ensure that the meanings for each was established and common

CMP Implementation SurveyBackground information on

teachers’ experiences with CMPGeneral questions about the

teachers’ use of other materials and context of teaching

For each lesson organized by units, we asked teachers to describe their use of each lesson in the textbook with the following instruction:

To answer the following questions, use the following definitions of textbook use

Use without modification – Follows the outline of the lesson as described in the teachers’ materials. No changes are made to the task and the structure of the lesson follows the Launch, Explore, Summarize routine described in the CMP materials. The goals and objectives of the lesson remain the same.

Use with adaptation – Follows the outline of the lesson as described in the teachers’ materials with changes made to the task, but not the structure of the lesson. The goals and objectives of the lesson remain the same. The structure of the lesson follows the Launch, Explore, Summarize routine described in the CMP materials, but the task is modified in one of several ways

Use as a one of many resources – Takes tasks from the materials but uses them to create own lesson with own lesson structure.

Replace – Does not use the materials but takes tasks or lessons from other materials to teach the goals and objectives of the lesson.

Does not use – Does not use any materials to teach the goals and objectives of the lesson.

Alignment of NJ ASK to New Jersey Mathematics Standards and Instructional Materials

NJASK2009

State Mathematics Standards

Connected Mathematics 2 Instructional Materials

Grade 6 .29 .21*  

Grade 7 .30 .26  

Grade 8 .30 .25  

Alignment considers both the content and cognitive demand alignment (see Porter, et al., 2008)

Data Analysis• Includes 143 teachers and their 2107

students• Removes teachers we did not have

information on: • their position type (general or special

education), • teachers whose classrooms were comprised of

very mobile students• students for whom we did not have 2008 math

scores • About 1/3 of teachers in the sample were

special education teachers

Measure construction• To measure use of the materials, we

created the curriculum coverage index (CCI) and to measure adaptation, we created the lesson modification index (LMI). • CCI is a simple proportion of the CMP lessons

that were not taught during the year• LMI represents the extent to which the teacher

has modified the lesson, expressed on a three-point scale where the low score represents all lessons as used without adaptation and the high score represents all lessons used as one of many resources.

Measure ConstructionThe SEC creates cognitive demand

measures that sum to 1 based on emphasis of each of the types of cognitive demand Memorize facts, perform procedures, demonstrate

understanding, conjecture/generalize/prove, solve non-routine problems/make connections

Using factor analysis on these SEC measures, we created a new cognitive demand measure which is characterized by stressing "procedures" and  avoiding "non-routine problems"

Results: Incomplete table ofHLM Fixed Effects Estimates for a Model of 2009 NJ ASK Mathematics Scale Score with Robust Errors

Fixed Effect Model

Intercept 203.54 (2.41)

Level 1

2008 Math Score 0.72** (0.03)

Special Education -14.52** (2.39)

LEP -0.73 (3.27)

Black -3.76 (2.43)

Latino -0.96 (2.02)

Level 2

LMI 4.191* (2.06)

CCI -0.26**( 0.07)

Cognitive Demand Factor 2.82* (1.28)

Summary of Results Teachers’ increased use of the CMP instructional

materials as compared to average is significantly related to higher student achievement.

However, in relationship to traditional measures of fidelity, where the focus is on use without adaptation, our findings suggest that greater than average adaptation on the part of the teacher is related to increased achievement of students.

A focus on procedures and decreased emphasis on non-routine problems is significantly related to higher student achievement.

Instructional Practice scales were not statistically significant.

Teachers’ alignment was not statistically significant association with student achievement.

Also, while 2008 achievement and special education classifications of students remained significant factors in predicting 2009 student achievement, race/ethnicity and LEP status did not.

O’Donnell’s 5 Criteria for Measuring FOI

Adherence—whether the components of the intervention are being delivered as designed;

Duration—the number, length, or frequency of sessions implemented;

Quality of delivery— the manner in which the implementer delivers the program using the techniques, processes, or methods prescribed;

Participant responsiveness—the extent to which participants are engaged by and involved in the activities and content of the program; and

Program differentiation—whether critical features that distinguish the program from the comparison condition are present or absent during implementation. (O’Donnell, 2008, p. 34)

Difference in measures of FOI

Our Study O’Donnell’s Criteria Curriculum Coverage (CCI)

Alignment (includes time and cognitive demand emphasis

adaptation to local contexts of the materials (LMI)

Decreased cognitive demand

Extent of use or adherence

Duration

Quality of Delivery

LimitationsWe do not account for teachers’

mathematical knowledge for teaching in our model. ◦ The SEC asks questions about certifications and

degrees, but, there was little variability in teacher qualifications of this type Only 6 teachers (3.8%) had secondary mathematics

certification Only 11 teachers (7.1%) had a major in mathematics or

mathematics education at either the undergraduate or Masters level.

The lack of fine-grained data collection for teachers’ years of experience, especially in the early years when student learning gains are most pronounced (Clotfelter et al., 2007). ◦ However, given our results for years teaching with

the CMP instructional materials, we may have produced the same general results for teaching experience with a better measure.

Limitations Continued

Proficient

Advanced Proficient

Partially Proficient

Returning to the Example

0.00 0.20 0.40 0.60 0.80

Memorize/Recall

Perform Procedures

Demonstrate Understanding

Conjecture, Generalize, Prove

Solve non-routine problems/ Make Connections

Fig 3. Grade 8 Cognitive Demand

NJ Stnds 2009 Gr. 8 CMP2 All Units Gr.8

0.00 0.20 0.40 0.60 0.80

Memorize/Recall

Perform Procedures

Demonstrate Understanding

Conjecture, Generalize, Prove

Solve non-routine problems/ Make Connections

Fig. 2 Grade 7 Cognitive Demand

NJ Stnds 2009 Gr. 7 CMP2 All Units Gr.7

NJ ASK Item Types by Grade Grade 6 Grade 7 Grade 8

Item Count by

Type

MC 42 42 42

SCR 8 (non-calculator) 10 10

ECR 5 5 5

# of sections 5 5 5

Total raw score

points possible

(excluding field test items)

50 52 52

Approximate total testing time 120 min. 124 min. 133 min.

MC - multiple choice, 1 raw score point

SCR - short constructed response, 1 raw score point

ECR – extended constructed response, 3 raw score points

Implications for Research in an Era of CCSSM To the extent there was lack of alignment between the NJ

ASK, the standards, and the instructional materials, it was to decrease cognitive demand as opposed to content coverage.

How well the outcome measure aligns with the standards, curriculum and the instructional materials is a critical factor in the results of such studies.

How well the PARCC and SBAC assessments will align with the CCSSM, particularly the Standards for Mathematical Practice will have implications for cross-state research on instructional materials use

In an era of openness and the Internet, we need to better understand what teachers use outside the adopted instructional materials, and how this use supports or detracts from a cohesive and coherent curriculum

Suggestions for Policy and Practice

As districts adopt new instructional materials and regimes, implementation strategies and monitoring should focus on both fidelity to structure and process.

As textbook authors design and modify texts, they should consider guidance to districts and teachers that support implementation by providing sufficient description of both the structure and the process of implementation that allow them to make appropriate adaptations.