Teachers' Attitudes toward Teaching Carnegie Curriculum · Koendinger and Corbett (2000), “students completing the three-course Cognitive Tutor sequence (Algebra 1, Geometry and

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Teachers' Attitudes toward Teaching Carnegie Curriculum

in Algebra 2 Class at Valley View District

Anna Teper

Master of Science in Mathematics Project

University of Texas Rio Grande Valley

ABSTRACT

Non-cognitive factors of mathematics teachers such as attitudes toward the subject and

particular teaching strategies are known to play a role in students’ learning of mathematics. In

particular, attitudes of teachers toward an object of education (particular subjects or teaching strategies)

affect their actions in the classroom, and therefore, their students’ learning. In this study, we explore the

attitudes of high school mathematics teachers toward teaching Algebra 2 under Carnegie Curriculum. To

collect data, a 30-question survey was developed. Data were collected from teachers at two high schools

in the suburb of Chicago. The questions and responses were classified by the taxonomical construct that

classifies attitude into three components: affective, behavioral and cognitive. Findings of the study

suggest positive feelings regarding the approach to utilize the curriculum and the potential benefits of the

inquiry-based instructional design. Some of the negative feelings and behaviors found in the study were

geared towards using the curriculum as a resource for struggling students.

1. INTRODUCTION

The Algebra 2 Carnegie program was introduced to many high schools in recent years. Prior to

the introduction, the Valley View School District in Illinois had been using Prentice Hall Mathematics

Algebra 2 Curriculum. One of the major differences between Carnegie Learning and a traditional Algebra

2 curriculum is the instructional design. In Carnegie, lessons are structured to provide students with an

opener, pre-written methods used by other students, error analysis, sorting activities and worked examples

which are designed to “promote analysis and higher order thinking skills beyond “yes” or “no” responses”

(Carnegie Learning, 2014-2016). Traditional mathematics curriculum might not always allow opportunity

to inquire and develop deeper understanding of math connections (The K-12 Mathematics Curriculum

Center, 2005). Furthermore, Roseman (2001) argues that “today's textbooks cover too many topics

without developing any of them well; central concepts are not covered in enough depth to give students a

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chance to truly understand them.” Recently, researchers have shown that the Carnegie Learning

curriculum was shown to be more effective to student learning than traditional Algebra 2 curriculum

(Koendinger, (2000). However, while studying the attitudes toward and the views of the teachers of a

specific curriculum can provide insight on the “influence of their thinking” (Pedro da Ponte, 2012), no

major attention has been paid to the attitudes held by teachers who teach Algebra 2 under Carnegie

Learning curriculum.

The author of this paper has 6 years of experience teaching Algebra 2, three in the district, during

which she has interacted with other teachers teaching the same subject under the Carnegie Learning

curriculum during professional development sessions and peer collaboration in the district. Via the

interaction, many in-service teachers have expressed negative feelings towards several aspects of the

Carnegie Curriculum in Algebra 2 classes. Additionally, students and parents have commented on the

difficulty of the Carnegie workbook and some of them asked for a recommendation of a different Algebra

2 textbook they could be using as a resource at home. Therefore, the goal of the research was to measure

teachers’ feelings, beliefs and actions toward specific components of the Carnegie Learning Algebra 2

curriculum. In order to develop understanding of the non-cognitive factors for teachers teaching Carnegie

Learning Algebra 2, the research study in this paper aims at exploring teachers’ attitudes towards teaching

Carnegie Learning program in Algebra 2.

2. BACKGROUND INFORMATION

2.1. CARNEGIE LEARNING CURRICULUM

Carnegie Curriculum was co-funded by Dr. Steve Ritter as a part of his postdoctoral research in

cognitive psychology at Carnegie Mellon University in 1998. Dr. Ritter has published and presented

numerous research studies on “the design, architecture and evaluation of Intelligent Tutoring Systems” of

Carnegie Learning curriculum (Carnegie Learning, 2014-2016). The curriculum portion adopted by the

school district consists of a student and teacher edition of consumable text, assignments, skills practice

and online resources available for viewing and printing. The part of the Carnegie Curriculum Algebra 2

that was not implemented in the district is Cognitive Tutor Software, an individualized software that

features differentiated instruction, motivational aspects and dynamic visual enhancements. According to

Koendinger and Corbett (2000), “students completing the three-course Cognitive Tutor sequence

(Algebra 1, Geometry and Algebra II) have been shown to perform better in the TIMSS (Trends in

International Mathematics and Science Study) assessment (by 30%) and real-world problem solving

assessment (by 227%).” The data were consistent among diverse students.




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According to Carnegie Learning Research and Results (2014-2016), “based on more than 20

years of cognitive science research, the company continually re-invents math education to bring the most

effective instructional practices to the classroom”. Furthermore, Carnegie Learning states that they

conduct and take part in independent research to improve strategies that empower students and results in

“improved math scores in a diverse spectrum of school districts across the nation”. Although, grades

earned throughout one’s education do not define the student, they are good indicators of many attributes

and skills one has accomplished: perseverance, fortitude, hard, consistent work, collaboration, and self-

reflection (Hattie, 1996). It is perceived through the academic research (Carnegie Research & Results)

that the Carnegie Learning program was designed by similar principles and when implemented

effectively, it benefits the learning of all students. The results of the 5-Essentials Survey (Figure 1) show

that, students in the district reported above average rigorous math instruction implementation in the

school year 2015/2016.

Figure 1. Five-Essentials Survey - Ambitious Instruction Domain (2015/2016)

(Source: The University of Chicago Urban Education Institute)




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Valley View District board-approved and implemented Carnegie Curriculum for Algebra I

classes in August of 2013. In 2015, the district formed a curriculum team consisting of five teachers from

each high school (general and special education teachers), core math administrators from each building

and the district K6-12 math coordinator with the purpose of selecting new curriculum for Algebra 2. The

curriculum team reviewed several curricula, Agile Mind among others, compared chapters, activities, and

the rigor of instructional design and voted for Carnegie. New curriculum was implemented in all junior

classes in 2015/2016 school year. Carnegie curriculum consists of online resources for students and

teachers (notes, assessments, assignments, skills practice and pacing guides) and a workbook for each

student. In the sophomore year, students study geometry through the Agile Mind curriculum that has an

interactive software component that students use regularly in class. According to the core math

administrator at Romeoville High School (RHS), Carnegie curriculum was considered for adoption for

Geometry classes.

Each chapter of Carnegie Curriculum covers a specific topic in a discovery approach, with the

implementation of Common Core Standards and Eight Mathematical Practices. Students are encouraged

to study a real-life problem, engage in team work to brainstorm answers to posed questions, model the

situation using different representations and arrive at a meaningful conclusion after peer-reviewing the

methodology. The RHS and Bolingbrook High School (BHS) offer Algebra 2 at three levels: honors,

regular and block period. The curriculum for honors classes has a faster pace and covers more material

from the Carnegie book. The curriculum for the regular and block classes consists of the same content.

However, the block class has 90 minutes compared to 55 minutes per period to accommodate the learning

needs of students, who had struggled in math classes in the past. Common summative unit and end-of-

semester assessments are created collaboratively and continuously modified by teams of teachers from

both schools.

2.2. COMPONENTS OF ATTITUDES

In the science of teaching, the teacher’s behavior and teacher’s attitude toward a specific subject

has a significant impact on students’ learning and their own attitude towards the subject. Researching

teaching practice and factors that influence teacher’s work facilitates the development of “the

practitioners ability to identify problems, gather information about them, consider the different sides of

the issues, test solutions, analyze data, and interpret results” (De Ponte, 2012). Therefore, teacher’s

attitude towards mathematics has been of special interest to researchers (Dossey, 1992). Measuring

attitude of teachers towards an objective of education has a purpose of predicting a potential influence on

students by actions stemming from the attitude. The objective of the research questions revolves around a




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new curriculum introduced to junior math classes in Valley View District in the school year of

2015/2016.

Based on various attitude models (Jain, 2014), attitude constitutes positive or negative mental and

neural willingness towards a person, place, object or event. The attitude has three major components:

affective component (neural- feeling/emotion), behavioral component (readiness - response/action), and

cognitive component (mental - belief/evaluation). Attitude is a dynamic factor in individual inclinations to

feel, regard and act toward the Carnegie Curriculum. Table 1 shows the classification of all survey items

into the three pedagogical components. The attitude in the psychological frame cannot be observed, but

rather evaluated through appropriate measuring tools (Fazio & Williams, 1986, as cited in Jain).

This research paper used generally accepted pedagogical components of the term “attitude” (as

cited in Martins, 2012) in the survey:

(a) Affective: feelings about teaching Carnegie Curriculum;

(b) Cognitive: the person’s self-perception/belief as regards to teaching Carnegie Curriculum;

(c) Behavioral: the person’s inclination to act towards teaching Carnegie Curriculum.

The categorization of pedagogical components of attitude was the basis for constructing the research

project, as well as, developing the instrument.

Table 1. Survey Items categorized by their pedagogical components of attitude.

Pedagogical Component of Survey Items

Affective Cognitive Behavioral

1, 3, 10, 11, 14,

23, 25, 26, 27

4, 5, 6, 7, 8, 15,

24, 28 29, 30

2, 9, 12, 13, 16, 17,

18, 19, 20, 21, 22

3. METHODS

3.1 TARGET POPULATION

To collect relevant data, the author surveyed 13 high school teachers from the two high school

buildings in the district, who have taught both Algebra 2 curricula: Romeoville High School and




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Bolingbrook High School. Romeoville High School (RHS) is one of the two high schools in the Valley

View School District in Romeoville, Illinois, which serves a population of 17,020 students in the suburb

of Chicago. The population of students consists of 1,900 students, approximately 450 juniors.

Bolingbrook High School (BHS) serves 3,600 students at the grade band 9-12, and 810 juniors.

According to the Illinois Board of Education, among 5,500 students who attend both high

schools, 57.2% are from low-income households, and 2% are homeless. The ethnic diversity of student

body in each school is shown in Table 2.

Table 2. Students Diversity at Romeoville High School (RHS) and Bolingbrook High School (BHS)

(Source: Illinois Report Card)

Ethnicity RHS BHS State Average

Hispanic 40 % 38 % 25 %

White 39 % 21 % 50 %

Black 14 % 29 % 18 %

Asian 4 % 8 % 4 %

The freshman on track to graduating, as well as graduation rate of seniors, is 85%. In the past,

Romeoville High School (RHS) had been trailing behind other high schools in the Will County in math

test scores and standardized assessments. In 2015, according to PARCC Assessment results (Partnership

for Readiness for College and Career) RHS surpassed in math scores the other high school in the district,

Bolingbrook High School for the first time since its opening (Figure 2). Additionally, the 2014/2015

school year the ACT composite score exceeded 20.1 points for the first time for the entire junior cohort.

The positive trend is also documented by a significant increase in students taking AP classes, students

taking AP exams and the average AP scores of 3 or higher achieved by Romeoville High School students

in the 2015/2016 school year.




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Figure 2. PARCC Mathematics Scores 2015-2016 (Source: Illinois Report Card)

3.2 PARTICIPANTS

The survey was administered to 13 teachers who teach Algebra 2 to junior classes in two high

schools in the district. The survey was created via Google Forms and was sent out to the participants via

work e-mail. The survey link was active for a period of one week in the month of October of 2016. The

teachers were asked to answer 35 open-ended questions. Out of 13 participants, eight were female and

eight were male. The ages of the teachers range from 25 to 50. 61% of the teachers have been working as

mathematics teachers for more than 10 years. 38% of the teacher participants worked between 6-10 years

and 1% less than two years at the Valley View School District (Figure 3). Five teachers, all females, were

from BHS, and eight teachers were from RHS.




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Figure 3. Years of Teaching Experience at Valley View School District

The highest level of education among the teachers was: 4 teachers have masters plus post

graduate credit, 5 teachers have a master degree and 4 teachers have a bachelor degree plus post

undergraduate credit. The last question on the biometric part of the survey was about approximate number

of professional development hours completed in 2015/2016 school year, the first year of the Carnegie

Algebra 2 Curriculum implementation in the district. Three of the teachers had 10 hours or less, four

teachers 20 hours, three teachers 30, and the last three teachers more than 45 hours of professional

development in the previous school year (Figure 4). Significant number of professional development

hours was in collaboration with teachers in other grade levels in the district. This practice is an effective

method of “examining connections between middle grades and high school mathematics” (CBMS, 2012).

Figure 4. Number of Professional Development Hours among Participants in 2015/2016

23%

23%39%

15%

Years of Teaching Experience

>10

6-10

2-5

<2




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3.3 INSTRUMENT

The survey comprised of 30 questions regarding the attitude towards Carnegie Curriculum and 5

biometric questions (Appendix 1). The survey model was based on the Teacher Efficacy and Attitude

toward STEM Survey developed by The William & Ida Friday Institute for Educational Innovation. The

model survey is a measuring tool to gather data regarding teachers’ perception and attitude towards

STEM subject curriculum and delivery in 21st century classrooms. The survey additionally measures

leadership attitudes among the teachers and STEM career awareness. The survey was modified to

measure the attitudes towards Carnegie Learning program for Algebra 2 students. Out of 30 items, 19

items were positively-worded and 11 were negatively-worded. All items were free responses with a 3-

point scale for positive responses and negative 3-point scale for responses that disagree with the same

survey item. The purpose of this scale was to measure the overall like or dislike the Carnegie Curriculum

through the arithmetic mean and standard deviation. The positive scale was reversed to negative values

for negatively-worded questions. For example, question 23 stated “I do not like the sequence of activities

in each Carnegie Curriculum lesson”. Answers that contradicted that statement were scored with a scale

of positive 1 through 3 points. Answers that agreed with the statement were scored with negative values

between 1 and 3, negative 3 being the strongest agreement. The aggregated scores were used to find the

arithmetic average and the standard deviation for each item. For the detailed item analysis in the results

section, only selected items with the lowest or highest mean will be discussed in details, as they portray a

better picture of teachers attitudes toward teaching Algebra 2 using Carnegie curriculum (Estrada, as cited

in Martin, 2002).

4. SURVEY RESULTS

The 13 participants answered 30 questions of the survey in the month of October 2016, producing

an arithmetic mean score of 0.6 on the scale from 0 to 3. For the negatively worded items, the scale was

reversed to negative values. Standard deviation for all questions was 2.2 points, showing that 68% of the

participants responded within positive 2.2 points or negative 2.2 points from the arithmetic mean for all

items of 0.6 (Figure 6). The tendency displays that there was a wide range of responses for most survey

items. In particular, only four questions, 3, 8, 13, 19, scored a standard deviation lower than 2.0 points

(Figure 6). Those four items measured the perception of the teachers of the extent of the use of several of

the 8 mathematical practices in the Carnegie Curriculum. As illustrated in Figure 5, the values of positive

and negative responses varied with each question. Some questions, which produced an arithmetic mean




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close to zero, had comparably equal number of negative and positive responses. Overall, the prevailing

attitude among the participants towards Carnegie Curriculum was positive.

Based on the reported responses, 54% of the teachers had 20 hours of professional development

or less in the school year of 2015/2016, while the 46% of the participants had between 21 and 30 hours. It

is unclear from the data, if there was a lack of time provided for preparation, training or the quality of the

supporting materials. Ponte (1994) states that “working at the level of knowledge (of mathematics,

instruction, curriculum, students’ learning, technology, educational issues, etc.) does not equip teachers to

change their practices, for example, adopting new curriculum orientations, selecting new kinds of tasks,

creating new classroom environments, and promoting dialogic communication.” However, Carnegie

Learning representatives conducted 2-day training for Algebra 2 teachers at the district prior to the

curriculum implementation. Teachers were also given an opportunity to participate in peer observation

and follow-up collaborative meeting led by a Carnegie coordinator, with a purpose of improving their

implementation of the curriculum.

Figure 5. Survey Responses Negative to Positive Comparison




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Figure 6. Statistical Analysis for Each Item

4.1 AFFECTIVE COMPONENT

The affective component of attitude of this research aimed to capture the emotional response

towards Carnegie Curriculum. The nine items of the survey were designed to measure the likes and

dislikes of the teachers regarding the new curriculum that was introduced in junior classes in the school

year of 2015/2016, “because emotion works simultaneously with the cognitive process about an attitude

object.” (Agarwal & Malhotra, as cited in Jain). The questions were worded with phrases: “ I like”, “I

feel”, “I do not like” and combined with elements asking about effectiveness the curriculum, the

perception of students utilizing the book, the layout of each lesson and the sequence of activities in the

book. Figure 7 represents a visual comparison of positive and negative responses to nine questions in the

survey that measured the affective element of attitude.




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Items 1, 11, 14 and 26 scored an average of close to a zero value of positive/negative responses.

Standard deviation for all four items ranged from 2.3 to 2.6, showing a wide range of responses. Some of

the responses to Item 1: “I like teaching Algebra 2 with the use of Carnegie Curriculum” are: “Agree, it’s

a text that allows opportunities for communication and student thinking”, “I like the way Carnegie

develops some of the concepts within each lesson. However, I feel it is very easy for the lesson to lose

focus on what is actually being taught.”, and “For some sections, Carnegie needs to provide more skills-

based problems to allow students to practice”.

Figure 7. Affective Component of Attitude Questions

Items 10, 23 and 25 show a positive attitude from the respondents with standard deviation ranging

from 2.2 to 2.6 points. Item 3: “I feel comfortable explaining to students mathematical strategies used in

Carnegie Algebra 2 book” had the most positive responses for the affective component part of the survey

(Figure 7). Overwhelming number of participants expressed feeling comfortable when explaining

mathematical strategies used in the Carnegie Curriculum, producing a mean of 1.9 and 1.8-point standard

deviation. The only overwhelmingly negative arithmetic mean was scored for item 27. The item stated: “I

feel some of the examples in Carnegie Curriculum are too confusing for students”. As a result, 77% of the

participants answered that they agree that some of the examples might be too confusing for the students.

The arithmetic mean for all affective component items in the survey was a positive 0.3 with 2.3 of

standard deviation. The conclusion is that overall, most high school math teachers at Valley View School

District feel positively about the Carnegie Curriculum in Algebra 2 classes.




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4.2 COGNITIVE COMPONENT

Cognitive component of attitude refers to beliefs and thoughts about Carnegie Curriculum.

Teachers were asked 10 questions (Items: 4, 5, 6, 7, 8, 15, 24, 28, 29, 30) about their self-perception in

regards to the effectiveness of the curriculum. Teachers’ beliefs are measured, because they could

influence teachers’ actions in classroom, which in turn affects the students (Ponte, 2012). Figure 8

represents a visual comparison of positive and negative responses to ten questions in the survey that

measured the cognitive element of attitude. Three questions (Items 5, 28 and 30) yielded responses with

an arithmetic mean of 0.03 points and the standard deviation 2.66. Four questions in the cognitive

classification averaged a positive mean. Three of them (items: 7, 15, and 24) have an overwhelming

majority of responses in the positive spectrum. Some of the responses are: “If a student is not successful

in any mathematics course there typically isn't one reason, blaming the text would be foolish.”,

“[Carnegie] Focuses on the calculator and graphical representation more“ and “Yes. Some of the word

problems mention STEM related context.”(Appendix 2).

Figure 8. Cognitive Component of Attitude Questions

Four questions, items 4, 6, 8 and 29, produced more negative responses among the participants

(Figure 8). Item 4: “When a student has difficulty understanding a mathematics concept in Carnegie book,

I believe I can help the student effectively, using the book.” resulted in a negative mean of 0.5 points and

2.2-point standard deviation. Item 6 responses to the following statement: “Carnegie workbook is

generally well designed for students’ learning in mathematics” had an average of negative 0.6 points and

2.5-point standard deviation. Item 8 stated: “Students enjoy learning Algebra 2 with Carnegie




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Curriculum.” Teachers’ responses averaged a negative 0.8 points and 1.7-point standard deviation -

second lowest value in the survey data. However, 69% of the responses included messages that most

students do not enjoy learning Algebra 2, regardless of the curriculum. Finally item 29 - “Algebra 2

Carnegie Curriculum makes my lesson planning easier” scored a mean of negative 0.3 points and 2.8 of

standard deviation. The average score for all cognitive components of the survey was negative 0.016 with

2.4-point standard deviation. The arithmetic mean of the cognitive component was close to a zero with

68% of the survey participant responding with a level of strength of opinion between positive and

negative 2.4 points away from 0.016. Therefore, in general teachers at Valley View School District have

neutral beliefs about the Carnegie Curriculum in Algebra 2 classes.

4.3 BEHAVIORAL COMPONENT

Behavior component of attitude results in favorable or unfavorable action towards Carnegie

Curriculum. Defleur & Westie (as cited in Jain) states that a series of responses toward a given object of

attitude will have some predictability. The goal of 11 survey items (2, 9, 12, 13, 16, 17, 18, 19, 20, 23, 22)

was to determine a pattern of behavior towards using the Carnegie book for instruction in Algebra 2

classes. Figure 9 represents a visual comparison of positive and negative responses to 11 questions in the

survey that measured the behavioral element of attitude. All items, with the exception of two questions,

averaged positively or overwhelmingly positively (Figure 12). Question 13 - “I tend to help students solve

problems through investigations (e.g. scientific, design or theoretical investigations more under Carnegie

Curriculum than traditional curriculum.” had all positive responses with an average score of 2.7 and the

lowest standard deviation of 0.6 for all 30 items in the survey. Items 16 and 19 pertained to a perceived

increase in students’ reasonable explanations and engagement in content-driven dialogue. The questions

averaged 1.8 and 1.7 points and 2.1, 1.8 standard deviation respectively.

The only negative average in the behavioral component portion of the survey was item 12: “When

my students ask for additional practice worksheets I give them another assignment from Carnegie

resources.” Some of the responses were: “No, not enough material”, “Rarely. Sometimes the skills

practice is good, but usually I create my own practice”, and “Sometimes, but sometimes we create or

search out other supplements.” The total average score for all behavioral components of the survey was a

positive 1.2 points with 2.0 of standard deviation. In a summary, teachers act positively towards utilizing

the Carnegie Curriculum resources in Algebra 2 classes.




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Figure 9. Behavioral Component of Attitude Questions

4.4 ALL ITEMS ANALYSIS

When the itemized responses are compared, data supports sentiments shared among the teachers

during collaborative meetings. Carnegie curriculum is perceived to increase student inquiry, peer

collaboration, content driven discussion and real-world application among students, but especially those,

who have been exposed to inquiry-based curriculum in previous mathematics classes (honors for example

(positive averages for item 16 through 21). Carnegie Curriculum appears to promote “guided discovery

activities that encourage the construction of meaning for the mathematics being taught” (Sparks, 2015).

Students, who struggle with basic skills, might not have opportunities to develop those skills with the

curriculum. Additionally, there are examples in Carnegie lessons observed to be too difficult for some

students, and teachers have expressed feeling “intimidated” with the some strategies used as well.

Moreover, teachers need to supplement the lessons from other sources to provide additional support

(negative averages for items 4 and 12). As for recommending the Carnegie curriculum to other school

districts, teachers were divided in their responses resulting in 0.2-point average.

List of survey items classified from most positive averages to most negative averages:

1) Item 13. I tend to help students solve problems through investigations (e.g. scientific,

design or theoretical investigations more under Carnegie Curriculum than traditional

curriculum.




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2) Item 2. Given a choice, I would invite a colleague to peer observe how I implement

Carnegie learning in my classroom.

3) Item 3. I feel comfortable explaining to students mathematical strategies used in Carnegie

Algebra 2 book.

4) Item 16. Students learning Algebra 2 under Carnegie curriculum as opposed to the

traditional curriculum can create more reasonable explanations of results of an experiment

or investigation.


traditional curriculum can more successfully complete activities with a real-world context.


traditional curriculum more often engage in content-driven dialogue.

7) Item 9. I have expressed positive comments about the Carnegie Workbook to my students

and other teachers.


traditional curriculum more often critique the reasoning of others.

9) Item 23. I do not like the sequence of activities in each Carnegie Curriculum lesson.

10) Item 24. Algebra 2 Carnegie curriculum uses real-life scenarios related to STEM.


traditional curriculum can make a better choice of the most appropriate methods to express

results (e.g. drawings, models, charts, graphs, technical language, etc.).

12) Item 7. If students’ learning is less than expected in Algebra 2, it is most likely due to

ineffective Carnegie resources students have access to.


traditional curriculum can more effectively reason abstractly and quantitatively.

14) Item 1. I like teaching Algebra 2 with the use of Carnegie Curriculum.

15) Item 10. If given a choice, I would prefer to teach Algebra 2 without the use of Carnegie

Resources.

16) Item 15. Carnegie curriculum provides better opportunity to use tools to gather data (e.g.

calculators, computers, computer programs, scales, rulers, compasses, etc.) than traditional

curriculum.

17) Item 25. I like using Carnegie Algebra 2 for homework assignments.

18) Item 14. I feel adopting Carnegie Curriculum was not the best choice for our students

19) Item 30. I would recommend Algebra 2 Carnegie Curriculum to another high school

district.




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traditional curriculum are more exposed to STEM careers context

21) Item 11. I am frustrated with how the layout of the Algebra 2 Carnegie book is designed.

22) Item 26. I feel intimidated with some of the examples used in Carnegie book.

23) Item 5. When a student does better than usual in Carnegie book activities, it is often

because I provided the student with other resources to study/use.

24) Item 28. I believe Carnegie Assessment Resources are well designed for formative

assessment.

25) Item 29. Algebra 2 Carnegie Curriculum makes my lesson planning easier.

26) Item 4. When a student has difficulty understanding a mathematics concept in Carnegie

book, I believe I can help the student effectively, using the book.

27) Item 12. When my students ask for additional practice worksheets I give them another

assignment from Carnegie resources.

28) Item 6. Carnegie workbook is generally well designed for student learning in mathematics.

29) Item 8. Students enjoy learning Algebra 2 with Carnegie Curriculum

30) Item 27. I feel some of the examples in Carnegie curriculum are too confusing for students.

5. CONCLUSIONS

Carnegie Research & Results reports that “ on average Carnegie Learning Blended Curriculum

(software and worktexts) moved students at the 50th percentile to the 58th—nearly double the gains of a

typical year’s worth of learning” based on 2007-2009 study in 147 schools in seven states. Although

Valley View School District did not adopt the software component (Cognitive Tutor) of the Carnegie

Curriculum, the increase in the standardized test scores, as shown in Figure 2, might indicate the

introduction of the Carnegie worktext in all freshmen Algebra I classes has been a right choice.

Additionally, survey item 18 - “Students learning Algebra 2 under Carnegie curriculum as opposed to the

traditional curriculum can more successfully complete activities with a real-world context”

overwhelmingly scored positive responses with an average of 1.8 points.

An overwhelmingly positive responses for the item 13: “I tend to help students solve problems

through investigations (e.g. scientific, design or theoretical investigations more under Carnegie

Curriculum than traditional curriculum.” indicate that the Valley View high school teachers strive to

create “inquiry classrooms are places where students explore problems, make and test conjectures,

explain and justify their ideas, and attempt to make sense of and evaluate the ideas of others” (McGraw,

2002). Additionally, item 13 is one of the four questions with the lowest standard deviation (below 2.0




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points). The other items were 3, 8, and 19, out of which only item 8 (Students enjoy learning Algebra 2

with Carnegie Curriculum.) scored a negative arithmetic mean. Positive responses to items 19, 20 and 21

suggest that students spend time in groups exploring and discussing exploratory problems, contributing

their ideas, and building upon the ideas of other students and the teacher. Ideally, teachers should aim at

facilitating students learning of mathematics beyond mere memorization of facts and formulas.

Cooney states that “the clever teacher is the one who envisions a different world and searches for

ways to realize that world within the usual classroom constraints”, and many responses teachers provided

when they stated they use supplements and outside resources to enrich instruction indicate the tendency to

expand the math instruction beyond given curriculum. For example, item 5: “When a student does better

than usual in Carnegie book activities, it is often because I provided the student with other resources to

study/use” resulted in negative average, suggests that teachers’ perception of success attributions to

ability was not based on the curriculum but “on children's task persistence as well as math performance.”

(Tõeväli, 2015). Moving forward, teachers at both schools should continue supplementing the Carnegie

curriculum to differentiate instruction and support learning needs of all their students.

In a summary, the reasons for studying the views and attitudes of teachers are grounded in the

assumption that these have a significant influence on pedagogical thinking (Pedro da Ponte, 2012). The

affective component questions averaged positive 0.3 points, the cognitive component questions averaged

negative 0.016 and the last set of questions, behavior component, scored an average of a positive 1.2

point. The averages suggests respectively that the Valley View high school teacher, have positive feelings

towards teaching Carnegie Curriculum and they are inclined to act positively toward using Carnegie

Curriculum in Algebra 2 classes. Moreover, the teachers had wide range of opinions regarding the

perception, use and actions towards the Carnegie Curriculum, as the close to a zero average with 2.4-point

standard deviation demonstrates.

ACKNOWLEDGMENTS

The research would not be possible without the guidance and support of Dr. Hyung Won Kim at

The University of Texas Rio Grande Valley. The teachers from Romeoville High School and from

Bolingbrook High School contributed their time and responses to provide data for the research. Mrs.

Jessica Ehmann, Core Math Administrator at Romeoville High School provided data about Carnegie

Curriculum selection and initial implementation process.




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REFERENCES

Carnegie Learning Research and Results (2014-2016)

[Online: https://www.carnegielearning.com/research-results/]

Christy, D., Sparks, R. (2015). Abstract Algebra to Secondary School Algebra: Building Bridges, Journal

of Mathematics Education at Teachers College. [Online: http://journals.tc-

library.org/index.php/matheducation/article/view/1138/703]

Conference Board of the Mathematical Sciences (CBMS). (2012). The Mathematical Education of

Teachers II. Issues in Mathematics Education 17. [Online:http://cbmsweb.org/MET2/met2.pdf.]

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APPENDIX 1 TEACHERS’ SURVEY

1. I like teaching Algebra 2 with the use of Carnegie Curriculum.

2. Given a choice, I would invite a colleague to peer observe how I implement Carnegie learning in

my classroom.

3. I feel comfortable explaining to students mathematical strategies used in Carnegie Algebra 2 book.

4. When a student has difficulty understanding a mathematics concept in Carnegie book, I believe I

can help the student effectively, using the book.

5. When a student does better than usual in Carnegie book activities, it is often because I provided the

student with other resources to study/use.

6. Carnegie workbook is generally well designed for students’ learning in mathematics.

7. If students’ learning is less than expected in Algebra 2, it is most likely due to ineffective Carnegie

resources students have access to.

8. Students enjoy learning Algebra 2 with Carnegie Curriculum.

9. I have expressed positive comments about the Carnegie Workbook to my students and other

teachers.

10. If given a choice, I would prefer to teach Algebra 2 without the use of Carnegie Resources.

11. I am frustrated with how the layout of the Algebra 2 Carnegie book is designed.

12. When my students ask for additional practice worksheets I give them another assignment from

Carnegie resources.

13. I tend to help students solve problems through investigations (e.g. scientific, design or theoretical

investigations more under Carnegie Curriculum than traditional curriculum.

14. I feel adopting Carnegie Curriculum was not the best choice for our students.

15. Carnegie curriculum provides better opportunity to use tools to gather data (e.g. calculators,

computers, computer programs, scales, rulers, compasses, etc.) than traditional curriculum.

16. Students learning Algebra 2 under Carnegie curriculum as opposed to the traditional curriculum can

create more reasonable explanations of results of an experiment or investigation.


make a better choice of the most appropriate methods to express results (e.g. drawings, models,

charts, graphs, technical language, etc.)


more successfully complete activities with a real-world context.

19. Students learning Algebra 2 under Carnegie curriculum as opposed to the traditional curriculum

more often engage in content-driven dialogue.




23


more effectively reason abstractly and quantitatively.

21. Students learning Algebra 2 under Carnegie curriculum as opposed to the traditional curriculum

more often critique the reasoning of others.

22. Students learning Algebra 2 under Carnegie curriculum as opposed to the traditional curriculum are

more exposed to STEM careers context.

23. I do not like the sequence of activities in each Carnegie Curriculum lesson.

24. Algebra 2 Carnegie curriculum uses real-life scenarios related to STEM.

25. I like using Carnegie Algebra 2 for homework assignments.

26. I feel intimidated with some of the examples used in Carnegie book.

27. I feel some of the examples in Carnegie curriculum are too confusing for students.

28. I believe Carnegie Assessment Resources are well designed for formative assessment.

29. Algebra 2 Carnegie Curriculum makes my lesson planning easier.

30. I would recommend Algebra 2 Carnegie Curriculum to another high school district.

Biometric Questions

31. How old are you?

32. What is your gender?

33. How long have you worked full time as a teacher?

34. How long have you been teaching at RHS?

35. What is your highest level of formal education you completed?

36. Approximately how many hours of professional development have you completed in 2015/2016

school year?




24

APPENDIX 2. TABLE OF CONTENT ANALYSIS EXAMPLES FOR THE ITEMS OF

POSITIVE AND NEGATIVE ATTITUDES.

Positive Attitude Scale 1 to 3

3 being the strongest opinion

Negative Attitude Scale -1 to -3

-3 being the strongest opinion

1. I like teaching Algebra 2 with the use of Carnegie Curriculum.

● Yes, I do (3) ● Agree, it’s a text that allows

opportunities for communication and student thinking. (3)

● Agree (3) ● Usually (2) ● yes (3) ● I like teaching it much better the second

year; however I do not always do it the "Carnegie" way (2)

● I do at times.(1)

● I do like the approach of the Carnegie curriculum. I do not feel it is a complete curriculum for our students (2)

● I like the way Carnegie develops some of the concepts within each lesson. However I feel it is very easy for the lesson to lose focus on what is actually being taught.(2)

● I like parts of the curriculum but not

everything. I feel like we are still supplementing at of our own stuff. (2)

● For some sections, Carnegie needs to provide more skills-based problems to allow students to practice. (2)

● i love teaching it, but it is not quite algebra II (1)

● no (3)

2. Given a choice, I would invite a colleague to peer observe how I implement Carnegie learning in my classroom.

● Yes (3) ● Yes (3) ● Sure (2) ● On the days i do it...sure (2) ● Yes, I would and I have in the past (3) ● Yes (3) ● Yes (3)

● Not really. I am not a pro, but sure, come and see me. (2)

● I do not believe I do the curriculum justice at this time. (3)




25

● Of course I would! (3) ● Agree (3) ● Yes. I feel like I do a well enough job

implementing the Carnegie curriculum and would be fine having another teacher observe. (3)

3. I feel comfortable explaining to students mathematical strategies used in Carnegie Algebra 2 book.

● Yes (3) ● Yes (3) ● In general I do. There were cases when

the method was new to me (2) ● Yes (3) ● Yes, I think we must be sharing and

explaining them to our students (2) ● I do in fact (3) ● Strongly agree (3) ● Most of the time (1) ● Yes (3) ● Yes (3) ● Yes (3)

● Some yes, some no. The context of some of the problems doesn’t seem to be built with teenage students in mind. What teenager cares about plantar boxes?? I feel it’s our responsibility to create buy-in, because the book is no help. (2)

● Sometimes (2)

4. When a student has difficulty understanding a mathematics concept in Carnegie book, I believe I can help the student effectively, using the book.

● I do. I have done it in the past. (3) ● Strongly Agree (3) ● I always try and use the book first but

sometimes I have gone outside the book. (2)

● I feel that I can use the book as well as other resources that support the book’s ideas. (1)

● Not using the book...I usually have to pull outside resources (2)

● Sometimes (1) ● Not using the book, but yes (2) ● No (3) ● I can help, but not using the book (2) ● Sometimes (1) ● Sometimes. Many of my students

struggles occur within the skills of completing a task. The text does a good job of inter-weaving concepts together however more skills practice is required within the lesson. (1)




26

● No. Most need help tackling the skill. (3)

● I usually do not use the book to clarify. Carnegie has a lot of sections that conceptualize the concepts without skills practice. For a student that is struggling I break it down to more simple concepts; which is not in Carnegie (3)

5. When a student does better than usual in Carnegie book activities, it is often because I provided the student with other resources to study/use.

● Not really (3) ● Sometimes (1) ● Disagree (3) ● Not necessarily, I feel that each student

has the opportunity to use the book effectively, but since each student learns in different manners there are many ways to show successful understanding (3)

● No it is because they come with better prior knowledge..usually an honors drop out (3)

● Yes (3) ● Some problems are better than others in

Carnegie. It's apples to oranges depending on the chapter. (2)

● Yes. I provide a lot of additional notes and resources for my students (1)

● Usually, yes (2) ● Yes (3) ● yes (3) ● Confusing question (neutral) (0)

6. Carnegie workbook is generally well designed for students’ learning in mathematics.

● It is skill based yes (3) ● Yes, I believe it is designed to develop

ideas. It however, does not allow students the opportunity to practice those ideas.(1)

● I agree. (3) ● Agree (3) ● For students that are more advanced in

math and are driven to succeed, even when struggling (2)

● No (3) ● No (3) ● No (3) ● No, it is well designed for students who

know mathematics and want to deepen their knowledge, but it is challenging for many students (2)

● That depends. I think most students do not like learning math with carnegie book.(2)

● For our students--not always (2)




27

● It will be better suited to students who are raised in common core settings.(2)

● I do believe there is a lot we cut out of the book. And students have a hard time taking notes that go along with the book (3)

7. If students’ learning is less than expected in Algebra 2, it is most likely due to ineffective Carnegie resources students have access to.

● Not necessarily true. I believe the text is a resource. The effectiveness of the lesson is up to how the teacher uses the resource.(2)

● False. Lots of factors: student life outside of school, maturity level, teacher effectiveness, classroom management, but sometimes the lack of resources can be a problem.(2)

● I disagree (3) ● If a student is not successful in any

mathematics course there typically isn't one reason, blaming the text would be foolish. (2)

● Disagree (3) ● No. It is usually due to difficulty in

concepts (3) ● No it is due to their lack effort and work

completion (3) ● No (3)

● That depends. Some students would be more successful with a traditional textbook in math. (1)

● true for our students (3) ● Yes (3) ● Yes (3) ● I am not sure what is expected of them,

but it would take a lot of independent study for students to understand the Carnegie curriculum (2)

8. Students enjoy learning Algebra 2 with Carnegie Curriculum.

● Sometimes (1) ● Sometimes (1) ● I have not heard any complaints about

the Carnegie curriculum specifically. It’s more about Algebra 2 in general.(2)

● Sometimes (1)

● I do not think so (2) ● No (3) ● Students don't enjoy learning Algebra 2

in general, Carnegie curriculum doesn't change that (2)

● Most do not without supplements.(2) ● No. My students have a difficult time




28

completing a set of questions in the text within their groups without student to teacher communication.

● Not really (3) ● I do not know for sure (Neutral) (0) ● Every student is different, some enjoy

the text and others would prefer a more traditional option.(1)

● Neutral (0)

9. I have expressed positive comments about the Carnegie Workbook to my students and other teachers. .

● Yes, I have (3) ● Yes--but we need to supplement (1) ● Yes. I think the text does a good job

developing critical thinking skills. I just don't know if our students are ready for level of critical thinking that Carnegie expects. (2)

● I have. I don't want to be a negative part of the department.(1)

● I have no other common core based curriculum to compare it to but I have said positive things about it to other people. (2)

● Absolutely! (3) ● Agree (3) ● I have indicated it allows them to work

through concepts in their groups or individually (3)

● occasionally (2) ● At times (2)

● No (3) ● No (3) ● I do not talk about the workbook with

my students parents or teachers (0)




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10. If given a choice, I would prefer to teach Algebra 2 without the use of Carnegie Resources.

● I like some of them....I do not like being tied down to one resource (2)

● No (3) ● I don't think I would prefer that. (2) ● Disagree (3) ● Not unless there was a proven option as

an alternative.(2) ● Disagree (3) ● The addition of more skills-based

practice would improve the use of Carnegie (1)

● There are some lessons that I choose to steer away from the text. I believe the Carnegie textbook is a good resource however it is not our only resource.(2)

● No opinion (Neutral)

● Yes (3) ● Yes (3) ● Yes (3) ● Yes. It's very dry. The visuals are so

boring. (3)

11. I am frustrated with how the layout of the Algebra 2 Carnegie book is designed.

● NO. I believe that there are some lessons that may but inefficiently designed or incorporate concepts that are unrelated but as a whole the layout is not bad.(3)

● I don't think I would 100% love how any book is designed and laid out. I think it is fine and easy to make changes in the order of concepts for example. (2)

● There are times where the main idea in a section isn't clear. However, the text flows well and the main idea throughout is mostly easy to identify. (2)

● Disagree (3) ● It makes more sense after teaching it

one year through and now going through the second time; I now see why things are done the way they are done. I also see the connection between Algebra I and Algebra II (3)

● I would like more practice materials. one or two follow up problems is not enough for all of our students (1)

● It's an incredibly boring design. (3) ● Yes, the layout of some activities is not

coherent.(2) ● Yes (3) ● Yes (3) ● Sometimes (2) ● For some sections/chapters (2)




30

● No. we just pick and choose what to teach.(3)

12. When my students ask for additional practice worksheets I give them another assignment from Carnegie resources.

● Sometimes (1) ● Sometimes (1) ● Yes (3) ● Sometimes, sometimes we create or

search out other supplements.(1) ● sometimes. other times I make my own

worksheets.(1) ● Sometimes I will provide the Carnegie

skills practice, the Carnegie assignment, or sometimes another resource that is either designed by myself or another teacher.(1)

● Agree (3)

● No (3) ● No (3) ● No (3) ● I do not.(3) ● No, not enough material (3) ● Rarely. Sometimes the skills practice is

good, but usually I create my own practice (2)

13. I tend to help students solve problems through investigations (e.g. scientific, design or theoretical investigations more under Carnegie Curriculum than traditional curriculum.

● Yes I do (3) ● True (3) ● Sometimes (1) ● Absolutely.(3) ● Agree (3) ● True. (3) ● Agree (3) ● The opportunity is provided by carnegie

and I try to utilize it (2) ● Yes (3) ● Yes (3) ● Yes (3) ● Carnegie does a good job setting these

up (2)




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● True (3)

14. I feel adopting Carnegie Curriculum was not the best choice for our students.

● I do not know if picking a different resource would make a difference (1)

● I disagree (3) ● disagree (3) ● Not true. (3) ● Disagree (3) ● Not necessarily. There is just a lot of

stuff that isn't necessary for our students.(2)

● Yes (3) ● Yes (3) ● Sometimes (1) ● Sometimes (1) ● I feel like initially it was, but I hope

something out there is better. (2) ● Without supplements---I do not feel this

was the best choice (2)

15. Carnegie curriculum provides better opportunity to use tools to gather data (e.g. calculators, computers, computer programs, scales, rulers, compasses, etc.) than traditional curriculum.

● Agree (3) ● I agree.(3) ● Agree (3) ● Yes (3) ● Yes (3) ● Yes (3) ● Focuses on the calculator and graphical

representation more (2) ● Sometimes (1)

● No (3) ● No (3) ● I disagree. Not too many assignments

require additional tools (other than calculators). (2)

● From an Algebra 2 perspective, I do not feel it is a better opportunity (3)

● NO (3)

16. Students learning Algebra 2 under Carnegie curriculum as opposed to the traditional curriculum can create more reasonable explanations of results of an experiment or investigation.

● They are asked to explain more which is a good thing; getting students talking is something most of us need to work on (3)

● Yes (3) ● Yes (3)

● No (3) ● Not sure (1) ● Not usually (2)




32

● I agree (3) ● yes (3) ● Yes. I believe that carnegie does a lot

more function analysis than our previous curriculum. Students are more likely to answer questions based on the graph than on the algebraic result. (3)

● Yes.(3) ● Agree (3) ● I agree.(3) ● Agree (3)

17. Students learning Algebra 2 under Carnegie curriculum as opposed to the traditional curriculum can make a better choice of the most appropriate methods to express results (e.g. drawings, models, charts, graphs, technical language, etc.)

● Agree (3) ● I agree.(3) ● Agree (3) ● They are exposed to the options, but

can't necessarily choose from different options (2)

● I agree (3) ● Sometimes (1) ● Yes (3)

● False (3) ● Probably not. We do not really diversify

methods within a concept. As a team I feel like we always decide on one method to approach a problem. (2)

● I do not know (neutral) ● Not sure Carnegie does this (neutral) ● No (3) ● Not sure (neutral)

18. Students learning Algebra 2 under Carnegie curriculum as opposed to the traditional curriculum can more successfully complete activities with a real-world context.

● Yes (3) ● Yes (3) ● Yes (3) ● True (3) ● Probably (1) ● Yes. All of their tasks are within a

context. This helps the student try to relate the material to the real world. Sometimes the application is not very relevant to the students lives. (2)

● Yes. (3)

● No (3) ● No. They focus on the skill portion of it

but miss out on the application (3)




33

● Agree (3) ● I agree.(3) ● Agree (3) ● Definitely yes (3)

19. Students learning Algebra 2 under Carnegie curriculum as opposed to the traditional curriculum more often engage in content-driven dialogue..

● Yes. I believe the curriculum encourages more student to student interaction.(3)

● Yes. Though, it's rarely enjoyable for the students.(3)

● Agree (3) ● I agree.(3) ● Agree (3) ● I think yes. Some of the questions

require students to use appropriate content language and to justify their answer.(2)

● Sometimes (1) ● Sometimes (1) ● Yes (3) ● Yes (3)

● No (3) ● Depends on the teacher (neutral) ● Not because of Carnegie...because of

teacher (neutral)

20. Students learning Algebra 2 under Carnegie curriculum as opposed to the traditional curriculum can more effectively reason abstractly and quantitatively.

● Yes (3) ● Yes (3) ● Sometimes (1) ● Not sure, we definitely do more of it in

class (1) ● Yes. (3) ● Agree (3) ● I agree. (3) ● Agree (3)

● No (3) ● No (3) ● No (3) ● No (3) ● Not sure (neutral)




34

21. Students learning Algebra 2 under Carnegie curriculum as opposed to the traditional curriculum more often critique the reasoning of others.

● I agree. Critiquing other responses are embedded in many questions.(3)

● Yes. There are numerous problems in the text that require the identification of a mistake and the justification of why it is a mistake.(3)

● Agree (3) ● I agree.(3) ● Agree (3) ● Sometimes (1) ● Sometimes (1) ● Sometimes...again depends on the

teacher (1) ● Yes (3)

● No. That is a skill that can be developed with any curriculum (3)

● Depends on the teacher (1) ● Don’t know (neutral) ● I think we are not at that level yet (2)

22. Students learning Algebra 2 under Carnegie curriculum as opposed to the traditional curriculum are more exposed to STEM careers context.

● Sometimes (1) ● Yes (3) ● Agree (3) ● Sometimes (1) ● Agree (3) ● There is some exposure, I don't know

how it would compare to a traditional curriculum (2)

● No (3) ● No (3) ● I do not think so. STEM careers are not

a focus in Carnegie book. (3) ● NO (3) ● Don’t know(neutral) ● Not sure if this is true or not.(neutral) ● Not sure (neutral)

23. I do not like the sequence of activities in each Carnegie Curriculum lesson.

● Seems fine to me. The lesson's build towards discovery which is nice. Though, I believe the pacing is too slow at times. (2)

● For the most part I think the sequence is fine. if not it has not been difficult to

● Agree, some of the activities are out of sequence.(3)

● Sometimes (1) ● Sometimes (1) ● Yes (3)




35

change the order in my lessons (2) ● I do not agree with the above

statement.(3) ● Disagree (3) ● In some sections/chapters it is ok (2) ● False (3) ● I am ok with it (2) ● No (3) ● I do like them (3)

24. Algebra 2 Carnegie curriculum uses real-life scenarios related to STEM.

● Sometimes (1) ● Sometimes (1) ● Yes (3) ● Yes. Some of the word problems

mention STEM related context.(2) ● sometimes (1) ● agree (3) ● Yes.(3) ● Agree (3) ● In some sections (2) ● Yes, but most are boring. I don't see

how the book draws students to STEM career paths.(1)

● Do not know (neutral) ● Have not seen one yet (3) ● NO (3)

25. I like using Carnegie Algebra 2 for homework assignments.

● Yes, I do. (3) ● With supplements-yes (2) ● Their skills practice is great, I just wish

there was more.(3) ● I find the skills practice worksheets

useful for this.(3) ● Agree (3) ● I use them to make my own (2) ● Do not mind it (1) ● Yes (3)

● NO. I usually create my own homework assignment that are shorter. (3)

● Disagree. I usually make my own homework assignments. Sometimes I take parts from the Carnegie assignments or skills practice but I usually make them myself.(2)

● Not always. I usually create my own, some of which is pulled from carnegie (2)

● No (3) ● No (3)




36

26. I feel intimidated with some of the examples used in Carnegie book.

● They never scare me, just confuse sometimes (1)

● No (3) ● NO (3) ● Disagree. I am able to follow the

teacher’s guide if I am confused or stuck or I just as a colleague.(3)

● Not true.(3) ● Disagree (3)

● Yes (3) ● Yes (3) ● Yes (3) ● The first year yes… this year no ● Sometimes (2) ● Some of the example are too involved

for what the actual concept is. (1) ● Absolutely. "How do I make this

relatable to students??" (3)

27. I feel some of the examples in Carnegie curriculum are too confusing for students.

● Yes. but that is where I feel the teachers need to be there for further explanation. I think it is challenging which is good. That way the higher level students in our classes get that challenge and then we are there to make adjustments for those who cannot grasp some of the more challenging topics/problems.(2)

● This can be true, but through small group discussion clarity can be achieved.(2)

● Disagree (3)

● Yes (3) ● Yes (3) ● Yes...great for honors students (2) ● Yes (3) ● They are confusing even for me (3) ● I agree (3) ● yes (3) ● Yes. This is mostly because of their

lacking foundational algebra skills (1) ● Absolutely. (3) ● Yes (3)

28. I believe Carnegie Assessment Resources are well designed for formative assessment.

● In general, I agree. (2) ● Yes (3) ● Skills practice does.(3) ● The CFU's can be a good resource for

this.(3) ● Agree (3) ● Yes (3)

● No (3) ● No only because we cut certain sections

or parts of sections.(2) ● No, too involved (3) ● No (3) ● No (3) ● Not really.....(3) ● Never used them (3)




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29. Algebra 2 Carnegie Curriculum makes my lesson planning easier.

● Yes (3) ● Any curriculum makes planning

easier.(1) ● yes. I definitely use it to drive my

planning. I always start with the Carnegie curriculum and resources and then make my own materials where needed.(3)

● Yes. (3) ● Agree (3) ● Definitely yes! (3)

● No (3) ● No (3) ● No (3) ● No (3) ● no (3) ● NO because we are constantly changing

what we want to include or not include in the curriculum. (3)

● I spend a lot of time cutting and supplementing (2)

30. I would recommend Algebra 2 Carnegie Curriculum to another high school district.

● yes (3) ● Yes (3) ● yes. (3) ● Yes. (3) ● Agree (3) ● Maybe (1) ● Maybe (modified) (1)

● I am not sure. I heard Agile Mind Algebra 2 is a better curriculum in comparison. (1)

● Not necessarily (2) ● No (3) ● No (3) ● No (3) ● No (3)




Documents

Teachers' Attitudes toward Teaching Carnegie Curriculum · Koendinger and Corbett (2000), “students completing the three-course Cognitive Tutor sequence (Algebra 1, Geometry and