A. Project Rationale - PEI-LING...

Course: TED 5300 Instructor: Dr. Pei-Ling Hsu

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Template 04

Project Report (Minimum: 3000 words)

Name: Korin Ortiz

Student ID: 80226471

A. Project Rationale

1. Project title

Rational Functions Vocabulary Acquisition Through the use of an Eight-Flap Foldable

2. Problems and the importance of the project

The idea of the implementation of this project came from a constant struggle of the

researcher to teach characteristics of rational functions effectively. Rational functions

require students to be proficient with vocabulary definitions, graphing skills and graph

interpretations. The researcher has tried different approaches to teach rational functions in

his pre-calculus class, due to the fact that students have always struggled in this particular

unit as a consequence of the many concepts that it includes and the many skills that

students must possess to perform proficiently.

This project was a Quasi-experimental study that included a pre-test-post-test intact

group design. The study addressed the implementation of the eight-flap foldable as an

aide in vocabulary acquisition in a Pre-Calculus class in high school. The lesson where

the foldable was implemented had the name “characteristics of rational functions from a

graph, table, and algebraic perspective”.

In math classrooms at all levels of instruction, teachers address mathematical instruction

mainly through the manipulation of symbols, variables and operations. It is extremely

rare for mathematics teachers to implement reading or writing strategies that would help

with student conceptual understanding. The importance of vocabulary in a mathematics

classroom resides in the fact that if students know the multiple representations of a

mathematical definition, then they will be more likely to understand the underlying

concepts of such definition. Activities that address vocabulary learning enable students to

understand complex mathematical concepts and procedures (Baxter, Woodward, &

Olson, 2005; Hoffert, 2009). Kostos and Shin (2010) stated that communication is crucial

in a mathematics classroom because it opens a channel of dialogue among teachers and

students while at the same time it helps students internalize the concepts being learned (p.

223). The use of writing strategies also helps support English Language Learners

(ELL’s), since it addresses key academic vocabulary and in the particular case of

foldables, it allows non-native English speakers to make sense of vocabulary with the use

of multiple representations (Lee & Herner-Patnode, 2007). Addressing vocabulary using

multiple representations is a main component of the Sheltered Instruction (SI) teaching

pedagogy (Short, 2013). The main idea of sheltered instruction is to support ELL’s

through the use of strategies in reading, writing, speaking, and listening areas of language

acquisition. However, it is important to mention that even though SI was designed to help

ELL’s, in a mathematics classroom all students benefit from this approach. Students


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benefit from foldables because these activities engage auditory, visual and kinesthetic

learners (Barrow, 2014; Casteel, & Narkawicz, 2007; Narkawicz & Casteel, 2012).

Teaching with foldables is very similar to the “capsule vocabulary” described by, Hanus,

Sulentic, Rebouche, and Smaldino (1991). In capsule vocabulary, students use multiple

representations and approaches to learn vocabulary such as writing, defining, and

discussing terms (p. 38). Foldables provide the same learning opportunities as capsule

vocabulary but the main difference is that foldable activities are highly interactive and

maintain students engaged throughout the learning activity. These interactive activities

are crucial for student engagement and relevant learning (Casteel, & Narkawicz, 2007;

Pierce & Fontaine, 2009). In this particular study, students learned the characteristics of

rational functions and were able to identify these components with the use of an eight-

flap foldable. The characteristics that students learned are: Domain, Range, Vertical

Asymptote, Horizontal Asymptote, Increasing Behavior, Decreasing Behavior, X-

Intercepts, and Y-Intercept.

3. Project objectives:

This project was designed to prove that the implementation of an eight-flap foldable,

helped with students’ retention of key vocabulary and increased student performance in

mathematical tasks such as identifying the key characteristics of rational functions. This

study also tried to prove that the combination of instruction and the eight-flap foldable

are effective tools for student understanding and conceptualization of key vocabulary.

The key research question that this study tried to answer was:

Does the use of an eight-flap foldable help with students’ conceptual understanding of the

key characteristics of Rational Functions?

4. TEKS Alignment

§111.35. Precalculus (One-Half to One Credit).

(c) Knowledge and skills.

(1) The student defines functions, describes characteristics of functions, and

translates among verbal, numerical, graphical, and symbolic representations of

functions, including polynomial, rational, power (including radical), exponential,

logarithmic, trigonometric, and piecewise-defined functions. The student is

expected to:

(B) determine the domain and range of functions using graphs, tables, and

symbols;

(D) recognize and use connections among significant values of a function (zeros,

maximum values, minimum values, etc.), points on the graph of a function, and

the symbolic representation of a function; and


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(E) investigate the concepts of continuity, end behavior, asymptotes, and limits

and connect these characteristics to functions represented graphically and

numerically.

B. Project Design

1. Collaborator(s):

This study on the effect of the eight-flap foldable on vocabulary retention was

implemented in a Pre-calculus class at Cesar Chavez Academy in El Paso, Texas. The

collaborator for this project was an instructional aide (Ms. Hand). Ms. Hand helped the

researcher write detailed classroom observations about student attitudes and classroom

interactions during the implementation of the study; she was instructed to make the

observations as detailed as possible in order to attempt to offer some validity to the

qualitative data generated. Ms. Hand also administered a survey (Appendix A) that took

students’ opinions about the usefulness of the eight-flap foldable in their mathematics

class.

2. Age of the participants:

The age of the participants in this study was between 16 and 17 years old.

3. Number of participants:

The study group consisted of nine high school seniors, six women and 2 male, the teacher

had been working with four of these students for eight weeks, while the other three

students had only been in this particular class for less than 3 weeks.

All of the participants in the study were considered at risk students due to behavior,

offenses punishable by law, and low socioeconomic status.

4. Participant recruitment plan:

The participants of this study were chosen from the only pre-calculus class in an

alternative school setting. This group of students was chosen due to the atypical

population number at this particular school during this time of the year. Usually, as

December approaches the population of this alternative school increases dramatically.

However, at this point in time, the biggest mathematical classroom consisted of 9

students in a Pre-Calculus class. Therefore, this group of students was selected merely

because of the number of students taking the same class, in order to implement the study

with students with a similar academic setting that are taking the same class.

5. Timeline of activities (including date and time):

All of the activities were implemented during the first period of class in this particular

high school, first period ran from 9:10 A.M. to 10:10 A.M. For a general overview of the

activities see Figure 1.

9/20/14

Students used simulation software to determine the basic shapes of the parent

rational functions and changes to their domain and range graphically (Facilitated

by Mr.Ortiz).


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Observation of students’ attitudes and behaviors(Ms. Hand completed behavioral

observations)

9/21/14

Introduction to the characteristics of rational functions. Specifically, Domain,

Range, Increasing Behavior, Decreasing Behavior, x-Intercepts, y-Intercept,

Vertical Asymptotes, and Horizontal Asymptotes (Traditional lecturing conducted

by the researcher)

Pre-Test (Appendix B) administered by the researcher

Observation of students’ attitudes and behaviors (Appendix C) completed by the

researcher and Ms. Hand

9/22/14

Students elaborated the eight-flap foldable (Appendix D) using previous in-class

definitions, the foldable had to include color, own definition, vocabulary word,

and pictorial representation (Instructions to students given by the researcher)

Students identified characteristics of rational functions using their foldable

Observation of students’ attitudes and behaviors (Appendix C) completed by the

researcher and Ms. Hand

9/23/14

Post-Test (Appendix B). Students were given a problem in which they had to

correctly identify the characteristics of a given rational function verbally and

algebraically (Administered by the researcher)

9/24/14

Survey (Appendix A) about students’ perception of eight-flap foldable

administered by Ms. Hand

Figure 1. Implementation stages, data collection and analysis of results


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6. Materials and resources required:

Calculator Emulator Software and Interactive board to show projected image of target

functions, pre-cut foldable templates for definitions, TI-Nspire color calculators, Colored

Pencils, teacher generated problems, Written Assessment, Rubric to Evaluate Foldable,

Template for classroom observations.

7. Plan to obtain these materials and resources:

The materials and resources were already obtained through various sources.

8. Safety consideration:

Due to the disciplinary nature of the campus where the project was implemented, scissors

with round edges were provided to the students.

9. Scientific topics involved:

Key Characteristics of Rational Functions such as:

Domain. Is the set of all real numbers variable x can take such that the expression

defining a function is real

Range. Is the set of all values that the function takes when x takes values in the

domain

Increasing intervals. A function is increasing when the y-value increases as the x-

value increases

Decreasing intervals. The y-value decreases as the x-value increases

Y intercepts. The point where the graph crosses the y-axis

X intercepts. The points where the graph crosses the x-axis. Algebraically, the x

intercepts correspond to zeros in the numerator of the rational function

Vertical Asymptotes. Vertical asymptotes are vertical lines which correspond to

the zeroes of the denominator of a rational function

Horizontal asymptotes. The horizontal asymptote tells me, roughly, where the

graph will go when x is really, really big. Algebraically, horizontal asymptotes

can be determined using the following rules:

a) If the highest degree of a polynomial in the numerator is GREATER than

the highest degree of a polynomial in the denominator, then there is no

horizontal asymptote.

b) If the highest degree of a polynomial in the numerator is EQUAL to the

highest degree of a polynomial in the denominator, then there is a

horizontal asymptote.

c) If the highest degree of a polynomial in the numerator is LESS than the

highest degree of a polynomial in the denominator, then the horizontal

asymptote is y = 0

C. Evaluation Plan

1. Formative assessments:


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Classroom observations (Template for classroom observations can be found in Appendix

C) were used to develop student profiles and give a better representation of classroom

communication, as suggested by Baxter et al (2005). These observations tried to

determine students’ disposition to complete the assigned work, and will serve as a

complement to the quantitative data collection. In other words, the classroom

observations were implemented to find out if students’ possible failure in the activity was

tied to behaviors that are not usually discovered by quantitative data collection.

The foldable activity was also used to assess students’ learning progression; since it

helped the teacher analyze student responses before the instructional activity was

concluded (The rubric to assess the foldable can be found in Appendix E).

2. Summative assessments:

A basic test (see post-test in Appendix B) designed by the researcher was administered at

the end of the lesson; the idea was for students to show understanding of vocabulary

words in connection with mathematical understanding of the characteristics of rational

functions.

A survey (included in Appendix A) created by the researcher was also be administered to

students on the last day of instruction as a way to find out students’ personal opinions

about the implementation and benefits of using foldables in mathematics.

D. Project Evaluation Result

1. Evaluation Result

This study focused on the implementation of the eight-flap foldable in an effort to find

out if this foldable technique increases vocabulary learning and students’ performance on

mathematical problems, specifically in identifying the key characteristics of rational

functions. During the implementation of this study four sources of data were considered

in order for each source to complement possible gaps in findings of the data gathering

instruments. A pre-test and post-test were administered to the students to measure

academic improvement. A survey was completed by the students to measure their

perception on the effectiveness of the implementation of the foldable activity. The

foldable activity was evaluated with a rubric to assure that students followed instructions.

The last data source utilized in this study was in the form of classroom observations to

measure students’ attitudes and behavior during the implementation. The data sources

above mentioned will be addressed with greater detail in the following paragraphs.

Pre-Test and Post-Test Analysis (Pre-Test & Post-Test can be found in Appendix B)

In this study, students were required to complete a pre and post assessment that consisted

of problem 1 which is considered a “traditional problem”, and problems 2 and 3 which

are considered to be high cognitive level problems. Students needed to graph the

functions and analyze them in order to present the key features of the rational functions

given. Problem 1 was a transformation of a rational function of the form 𝑦 =1

𝑥 and was

very similar to the function that the students used to create their foldable. The objective

of problem 1 was to find out student performance and retention of information and

vocabulary with the use of the eight-flap foldable. Windsor, Verona and Arrick showed a

significant increase on their performance in problem 1 within the range of 45 to 65

percent. Kahlo showed a lower score by 25 percent from the pre-test to the post-test,


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while Andres and Alex showed an almost negligible increase and decrease in their scores

respectively. The lowest performing student in the class, Sophie had an increase of 15

percent points even though her performance was still less than optimal (Results of

individual students can be seen in Table 1).

Problems 2 and 3 in the pre and post-test tried to find out if students could apply

generalizations from the information that they learned with the implementation of the

eight-flap foldable. However, results in the overall score of the tests were less than

optimal and any increase in score between the pre and post assessment was due to the

impact of the score given by problem 1. In other words, students could not apply

generalizations to other rational functions that were not based on the parent function

𝑦 =1

𝑥 . Students generally struggled to apply newly learned concepts and vocabulary to

new situations, but this issue would need to be studied in a different project. The main

idea of problems 2 and 3 was to find out the extent of the impact of the eight-flap

foldable in students’ cognitive performance. Each problem in the Pre-Test and Post-Test

consisted of 10 key characteristics of rational functions that the students needed to

represent algebraically and verbally. Each algebraic and verbal answer has a weight of 1

point in the test for a total of 60 points possible. The grade in the Pre-Test and Post-Test

was calculated using a simple percentage grade calculated with the formula:

𝑆𝑐𝑜𝑟𝑒 = 𝐶𝑜𝑟𝑟𝑒𝑐𝑡 𝑄𝑢𝑒𝑠𝑡𝑖𝑜𝑛𝑠

𝑇𝑜𝑡𝑎𝑙 𝑇𝑒𝑠𝑡 𝑄𝑢𝑒𝑠𝑡𝑖𝑜𝑛𝑠𝑋 100

Table 1. Individual Pre-Test and Post-Test grades and grade for problem 1 with percent

increase or decrease (difference in grades)

An extra component added to the pre-test and post-test was a section where students

needed to verbalize the definition of each single characteristics of the rational function

that was identified by the students. In mathematics, there is a strong relationship between

student mathematical performance and their command of vocabulary and definitions in a

particular lesson. Before the implementation of the foldable activity, students had a basic

knowledge of the characteristics of rational functions. The idea of the foldable was to get

students to understand the specific definitions of such characteristics and then measure

the impact that the foldable had on students’ learning of specific mathematical definitions

(Table 2 shows students’ vocabulary scores and the percentage of definitions that

students answered correctly). In each of the three problems on the Post-Test, students had


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to identify 10 characteristics of rational functions algebraically and verbally, thus having

a total of 30 verbal answers that should show an understanding of vocabulary. Each

correct answer had a weigh of 1 point and the percentage of correct responses was

calculated using the following formula:

𝐶𝑜𝑟𝑟𝑒𝑐𝑡 𝑅𝑒𝑠𝑝𝑜𝑛𝑠𝑒𝑠 % =𝐶𝑜𝑟𝑟𝑒𝑐𝑡 𝑉𝑜𝑐𝑎𝑏𝑢𝑙𝑎𝑟𝑦 𝑄𝑢𝑒𝑠𝑡𝑖𝑜𝑛𝑠

𝑇𝑜𝑡𝑎𝑙 𝑃𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑆𝑐𝑜𝑟𝑒 (30)𝑋 100

The main idea was to show if the vocabulary scores in the post-test had a direct impact on

students’ academic performance. However, the data obtained is inconclusive, in the

particular case of Sophie, she had a vocabulary score of 100% but her post-test scores

were really low.

Table 2. Vocabulary and definition scores on the post-test

Survey

A survey (The survey template can be found in Appendix A) was implemented in this

project in an effort to find out students’ perceptions in terms of the eight-flap foldable

activity. The survey consisted of four basic questions in which students would show their

opinion about the usefulness of the eight-flap foldable in their mathematics class. The

score for each one of the survey’s questions was assigned a value from one to four, with

one being no use at all and four being really useful. A total score in the survey of 0-4

points represented that students did not find the activity useful at all, a score of 5-8

showed that students thought that the foldable was slightly useful. Students with a total

score of 9-12 perceived the foldable to be moderately useful, and students with a score of

13-16 found the activity to be extremely useful (Individual student scores can be found in

Table 3).

Table 3. Survey results on students’ perceptions


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Most students thought that the foldable helped them understand the mathematical

concepts and vocabulary covered in the lesson. However, Sophie scored the foldable with

a maximum of 16 points but she did not finish the assignment and her gain in the Post-

Test was neither significant nor satisfactory. Raymond assigned the rubric the lowest

score of the class with a total of 9 points from a total of 16 possible points. It is important

to mention that Raymond was the top performer in this class in terms of the Post-Test, his

low score on the survey reflected the fact that he had previous knowledge on the topic

and he understood the vocabulary clearly before the foldable activity took place.

Rubric (The rubric to score the foldable activity can be found in Appendix E)

Some authors claim that the use of foldables in mathematics classrooms enhances

students’ understanding of mathematical terminology and mathematical concepts. The

eight-flap foldable was chosen to be implemented in the rational functions lesson due to

the need to address multiple mathematical concepts such as the characteristics of rational

functions previously mentioned in this paper. The main idea was to assure that all

students had an opportunity to produce a consistent eight-flap foldable aligned with the

instructions given by the teacher. A letter grade from A-F grade was assigned to the

foldable and the score of each student was obtained with the implementation of a rubric,

with A being the highest and F being the lowest score (Rubric details and scoring rules

can be found in Appendix E). The foldable was evaluated in the following areas:

Completeness. Students were instructed to display the vocabulary definition,

pictorial representation, and an explanation on how to find the key characteristics

of rational functions from a given graph.

Legibility. Measured the clarity of the presentation of pictures and handwriting,

students should be able to use the foldable in class, so legibility is extremely

important.

Accuracy. Measure of how accurately are pictures and definitions displayed in the

foldable.

Requirements. Attention to detail and color assignment to the different

definitions.

Grammar. Correctness of students’ academic language use.

It is important to mention that most students obtained an A as a grade for the foldable

activity. The foldables elaborated by the students were of acceptable quality even though

some students were reluctant to use colors in the activity. Sophie was present in the

activity but failed to complete the assignment before the class period was over, her

definitions and pictures were incomplete, and this is the reason why she obtained a D for

the assignment (A summary of individual student’s rubric scores is displayed in Table 4).


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Table 4. Foldable scores based on rubric

The results obtained with the rubric are a reflection of the classroom observations

discussed in the next section of this paper and provide with the necessary validity for this

strategy needed to move forward with the study.

Classroom Observations (The template used for classroom observations can be found in

Appendix C)

Two sets of observations were implemented in this classroom in order to complement

information and findings. Ms. Hand and the researcher followed the same basic format to

record student attitudes and behavior during the lesson. The results of the observations

show that the overall environment in the class was productive, students were on task and

they were making relevant questions and asking for clarification from the teacher during

the traditional teaching section of the activities. When students started elaborating their

foldable they were on task and fully engaged on the activity and all but one student

completed the foldable. The researcher knows his students well and offered the following

explanation on individual students drawn from classroom observations during the lesson

and from previous talks with the students:

Sophie

Sophie has gaps on her learning due to the fact that she ran away from home and did not

attend school for more than a year, she has been attending school on an off due to family

issues. She requires a lot of time to process mathematical information and constantly falls

behind on classroom assignments.

Windsor

Windsor generally refuses help from the teacher and rarely asks for clarification. Further

analysis of Windsor’s work in this study by the researcher revealed that she created

misconceptions and stood by these misconceptions as the ultimate truth. Windsor

misconceptions hindered her performance on problem 2 and 3 of the post test, but her

performance on problem 1 showed a gain of 45 percent points.

Andres

Andres struggled with the concept of Range and he was generally giving random answers

before the foldable implementation and it is important to mention that his score gains in

pre and post tests were negligible. Andres also decided not to answer the vocabulary

section of the Post-Test completely and this affected his Post-Test score.

The rest of the students had typical behaviors during the learning process; most of them

asked relevant questions and required clarification. However, the individual behaviors

mentioned above had a great impact on the overall performance for the particular


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students above mentioned. It is also important to mention that after the implementation of

the foldable activity, the use of academic language in the classroom increased. Students

were using the terminology and definitions fairly comfortably. However, students’ use of

specific language did not reflect in cognitive gains in all cases.

2. Project activity pictures

Figure 1. Vocabulary in the eight-flap foldable (Exterior view)


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Figure 2. Verbal and pictorial notes on how to find characteristic of rational

functions (Interior view of foldable)

Figure 3. Complete foldable (Interior view)


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Figure 4. Raymond’s foldable with more information than required in assignment

Figure 5. TI-Nspire Graphing Calculator


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Figure 6. Explaining the lesson with the interactive board and calculator emulator

Software.

Figure 7. The parent rational function (Inverse linear function)


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Figure 8. Student graphing problem 1 and finding key characteristics of the function

Figure 9. Sophie’s survey and definition score did not have a positive impact on

mathematical performance


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Figure 10. Raymond’s perfect post-test score, he underscored the survey because he did

not have a cognitive need for it.

E. Discussion The implementation of the eight-flap foldable activity seemed to have positive effect on

vocabulary retention in terms of the definition of the key characteristics of rational

functions according to scores of definitions on the post-test and classroom observations.

Classroom observations seemed to support that students’ use of vocabulary specific to the

lesson increased, and post- test scores suggested that on average students answered

correctly to 67% of definitions. However, the retention of definitions did not seem to

have a positive effect on mathematical cognitive performance of students. Three specific

cases were those of Andres, Sophie, and Kahlo. Andres did not answer most of the

definition questions in the post test and he was the student with the smallest gain in the

class. On the other hand, Sophie answered all the definition questions correctly but was

unable to increase her cognitive gain significantly. Finally, Kahlo performed well on the

pre-test but decreased her cognitive score in the post-test by 25 percent.

Even though the results of this study did not provide a definite proof of the effectiveness

of the eight-flap foldable in students’ mathematical performance in a unit about rational

functions, students were engaged in the activity. The foldable activity kept students

focused and engaged in note taking, and it provided an alternative to traditional lecturing

(Casteel, & Narkawicz, 2007). There seemed to be a correlation with the scores of certain

students and their academic vocabulary command, and this might be a consequence of

students’ increased participation in the lesson. It is also important to mention that the

foldable activity provided an inclusion activity for students that are visual and kinesthetic

learners, in contrast with a regular lecture that addresses only auditory learners (Casteel,

& Narkawicz, 2007; Narkawicz, & Casteel, 2012). Even though the results of this study

were not completely satisfactory, it is extremely important to implement of alternative

approaches to teaching vocabulary (Barrow, 2014; Pierce, & Fontaine, 2009). The main

idea is to get away from the textbook definitions and instead present vocabulary to the

students in relevant ways that require pupils to get engaged in the construction of their

own knowledge (Pflaum, 1973). If teachers do not try diverse ways of approaching


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academic vocabulary instruction, then students run the risk of not making progress and

thus not enjoying their mathematical studies (Freeman, & Crawford, 2008). In this

particular study, Windsor, Verona and Arrick seemed to benefit from the foldable activity

and this shows in the scores obtained in the post-test and definition scores. However,

Windsor and Arrick considered that the effect of the eight-flap foldable in their learning

was moderate, while Verona considered that the foldable activity had a great impact on

her learning (see results in Tables 1, 2 & 3).

Recommendations

The main limitation of this study was the reduced number of participants in the

implementation process. This reduced number of participants was due to the instructional

setting where the study was implemented. The researcher teaches in an alternative

campus and by state mandate classes cannot be of more than 15 students, the amount of

students in any given classroom is determined by disciplinary placement of bigger

campuses. Therefore, a first recommendation is to implement a similar study in a

different setting with a greater number of participants in order to be able to better

determine tendencies in the data analysis phase. A second recommendation is to establish

an experimental and a control group, exposing the experimental group to the treatment

(foldable activity) and measuring the outcome at the end of the lesson to see the

tendencies in both groups. A third recommendation would be the implementation of

similar studies in other mathematical subjects such as Geometry and Algebra in order to

present diverse perspectives on the effectiveness of foldables on vocabulary acquisition

and cognitive development. It is equally important to mention that there is not enough

peer review literature that supports the benefits of the implementation of foldables

(Casteel, & Narkawicz 2007; Narkawicz, & Casteel, 2012). Current studies that address

the implementation of foldables are also not grade or content specific and this

complicates the investigation on the topic, so a last recommendation of the author of this

study is to implement further content specific action research projects that can help

determine the usefulness of foldables across the curriculum.


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F. References

Barrow, M. A. (2014). Even math requires learning academic language. Phi Delta

Kappan, 95(6), 35-38.

Baxter, J. A., Woodward, J., & Olson, D. (2005). Writing in mathematics: An alternative

form of communication for academically low-achieving students. Learning

Disabilities Research & Practice. 20(2), 119-135

Casteel, D. B., Narkawicz, M.G. (2007). Effectiveness of foldables versus

lecture/worksheet in teaching social studies in third grade classrooms. Forum in

Public Policy, 2007(3), 1-10. Retrieved from:

www.forumonpublicpolicy.com/archivesum07/casteel.pdf

Freeman, B.,& Crawford. L. (2008). Creating a middle school mathematics curriculum

for English-Language Learners. Remedial & Special Education, 29(1), 9-19.

Hanus, K. S., Sulentic, M.M., Rebouche, R., & Smaldino, S. (1991). Six whole class

vocabulary strategies for the content areas. Middle School Journal, 22(3), 36-39.

Hoffert, S. B. (2009). Mathematics: The universal language?. The Mathematics Teacher,

103(2), 130-139.

Kostos, K., & Shin, E. (2010). Using math journals to enhance second graders'

communication of mathematical thinking. Early Childhood Education Journal,

38(3), 223-231

Lee, H. J., & Herner-Patnode, L.M. (2007). Teaching mathematics vocabulary to diverse

groups. Intervention in School and Clinic, 43(2), 121-126.

Narkawicz, M., & Casteel, D. B. (2012). Improving accelerated college courses: how

foldable graphic organizers can help learners retain information. Delta Journal of

Education, 2(2), 113-120. Retrieved from:

http://staging.deltastate.edu/PDFFiles/DJE/Narkawicz%20and%20Casteel%20Fin

al%20For%20Publication.pdf

Pflaum, S. W. (1973). Expansion of meaning vocabulary: Strategies for classroom

instruction. Elementary English, 50(1), 89-93.

Pierce, M.E., & Fontaine, L. M. (2009). Designing vocabulary instruction in

mathematics. The Reading Teacher, 63(3), 239-243.

Short, D. (2013). Training and sustaining effective teachers of sheltered instruction.

Theory into Practice, 52, 118-127.

http://www.forumonpublicpolicy.com/archivesum07/casteel.pdf

http://staging.deltastate.edu/PDFFiles/DJE/Narkawicz%20and%20Casteel%20Final%20For%20Publication.pdf

http://staging.deltastate.edu/PDFFiles/DJE/Narkawicz%20and%20Casteel%20Final%20For%20Publication.pdf


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G. Appendixes

Appendix A. Survey STUDENT PERCEPTION SURVEY Directions: Please mark the number that best reflects your answer to the

question. These questions are about your perception of the benefits of using foldables in

the classroom. Using the scale below, please mark the number that best reflects your opinion.

1 = Strongly Disagree 2 = Disagree 3 = Agree 4 = Strongly Agree

How did the use of foldables help you in these areas?

a. Understanding vocabulary that otherwise would have been

difficult.

1

2

3

4

b. Seeing a picture of the definition helps me understand it.

1

2

3

4

c. Foldables would help me review for a test.

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d. Seeing a picture helps me write a definition using my own words

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Created by K. Ortiz


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Appendix B. Pre-Test and Post-Test

Pre-Test

Characteristics of Rational Functions Name: ______________________________________ For the following rational functions find the following characteristics and explain their meaning (use at least one “complete” sentence for your descriptions).

1. 𝑓(𝑥) =1

𝑥−2+ 2 2. 𝑓(𝑥) =

𝑥2+3𝑥+2

3−𝑥 3. 𝑓(𝑥) =

𝑥−1

𝑥2

Domain:________ Description:___________________________________________________________________________ Range: ________ Description:___________________________________________________________________________ Vertical Asymptote:________ Description:__________________________________________________________________________ Horizontal Asymptote:_________ Description:__________________________________________________________________________ Increasing:____________ Description:__________________________________________________________________________ Decreasing:___________ Description:__________________________________________________________________________ X-Intercepts:___________ Description:__________________________________________________________________________ Y-Intercepts:____________ Description:_________________________________________________________________________ Maximum:________________ Description:_________________________________________________________________________ Minimum:________________ Description:_________________________________________________________________________


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Post-Test

Characteristics of Rational Functions Name: ______________________________________ For the following rational functions find the following characteristics and explain their meaning (use at least one “complete” sentence for your descriptions).

1. 𝑓(𝑥) =1

𝑥+3− 3 2. 𝑓(𝑥) =

𝑥2+5𝑥+6

3−𝑥 3. 𝑓(𝑥) =

𝑥−3

𝑥2

Domain:________ Description:___________________________________________________________________________ Range: ________ Description:___________________________________________________________________________ Vertical Asymptote:________ Description:__________________________________________________________________________ Horizontal Asymptote:_________ Description:__________________________________________________________________________ Increasing:____________ Description:__________________________________________________________________________ Decreasing:___________ Description:__________________________________________________________________________ X-Intercepts:___________ Description:__________________________________________________________________________ Y-Intercepts:____________ Description:_________________________________________________________________________ Maximum:________________ Description:_________________________________________________________________________ Minimum:________________ Description:_________________________________________________________________________

Created by K. Ortiz


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Apendix C. Classroom Observations Describe the following behaviors observed during instruction (Be as descriptive as possible):

1. Students on-task or off-task

2. How did the teacher approach students that did not understand the

lesson

3. Were alternative approaches to teaching present?

4. Did students interact and helped each other during the lesson?

5. Were there any particular points in the lesson where students

struggled more?

6. What is the usual in-class behavior of students?

Describe specific behaviors of each student: 1. Sophie

2. Windsor

3. Verona

4. Kahlo

5. Alex

6. Andres

7. Arrick

8. Raymond

Created by K.Ortiz


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Appendix D. Foldable Template

Retrieved from:

http://www.teacherspayteachers.com/Product/Interactive-Notebook-8-Flap-Book-

Editable-Templates-in-Word-Free-Foldables-847419

http://www.teacherspayteachers.com/Product/Interactive-Notebook-8-Flap-Book-Editable-Templates-in-Word-Free-Foldables-847419

http://www.teacherspayteachers.com/Product/Interactive-Notebook-8-Flap-Book-Editable-Templates-in-Word-Free-Foldables-847419


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Appendix E. Rubric to Assess Foldables

Retrieved from:

http://www.rcampus.com/rubricshowc.cfm?code=R65856&sp=yes&

http://www.rcampus.com/rubricshowc.cfm?code=R65856&sp=yes&

A. Project Rationale - PEI-LING...

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