The Effects of Direct Teaching of Vocabulary in Geometry.
A Capstone Project Submitted in Partial Fulfillment
of the Requirements for the Degree
of Master of Arts in Teaching: Mathematics
Heather Kostelecky
Department of Mathematics and Computer Science
College of Arts and Sciences
Graduate School
Minot State University
Minot, North Dakota
July 5, 2011
ii
This capstone project was submitted by
Heather Kostelecky
Graduate Committee:
Dr. Kodwo Annon, Chairperson
Mr. Larry Goodman
Dr. Ryan Winburn
Dean of Graduate School
Dr. Linda Cresap
Date of defense: July 5, 2011
iii
Abstract
The purpose of this action research project was to study the effects of direct
teaching on vocabulary comprehension and confidence regarding vocabulary in
the geometry classroom. The teacher administered a , as well as a survey at the
beginning and culmination of the study to analyze the effects of the study.
Activities such as games and flash cards were implemented throughout the course
of the study. Both the pre- and post-test and the survey displayed students
improved in their vocabulary comprehension, as well as in their confidence in the
geometry material.
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Acknowledgements
I would like to thank my family for allowing me to pursue my Masters of
Art in Teaching-Math degree, for allowing me to spend time away from you the
last two summers, and for allowing me to spend time working on my paper
instead of spending time with you. Joel, you were so understanding and
encouraging while I was working on my paper; thank you for being a wonderful
husband. Mallory and Madison, I am so blessed to have you as my daughters. I
love you so much and thank you for being patient while mommy was working.
I would also like to thank my fellow teachers, including those who were
going through the graduate study process along with me. Kristine, thank you for
helping me talk through ideas. Ron and Dawn, thank you for your editing skills;
my paper and project is better because of your help. Jenny, by now I think we
have read about each other’s projects enough we could recite passages and page
numbers from each other’s papers!
Lastly, I would like to thank my teachers from Minot State University,
especially Mr. Goodman, who served as my advisor.
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Table of Contents
Page
Abstract .................................................................................................................. iii
Acknowledgements ................................................................................................ iv
List of Tables ........................................................................................................ viii
List of Figures ........................................................................................................ ix
Chapter One: Introduction ....................................................................................... 1
Motivation for the Project ........................................................................... 2
Background on the Problem ........................................................................ 2
Statement of the Problem ............................................................................ 3
Statement of Purpose................................................................................... 3
Research Questions/Hypotheses ................................................................. 4
Summary ..................................................................................................... 4
Chapter Two: Review of Literature ........................................................................ 6
Vocabulary and Comprehension ................................................................. 7
Direct Instruction of Vocabulary............................................................... 10
Strategies ................................................................................................... 13
Summary ................................................................................................... 15
Chapter Three: Research Design and Method....................................................... 16
Setting ....................................................................................................... 16
Intervention/Innovation ............................................................................. 18
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Design ....................................................................................................... 18
Description of Methods ............................................................................. 19
Expected Results ....................................................................................... 21
Timeline for the Study............................................................................... 21
Summary ................................................................................................... 22
Chapter Four: Data Analysis and Interpretation of Results .................................. 23
Data Analysis ............................................................................................ 23
Interpretation of Results ............................................................................ 28
Summary ................................................................................................... 34
Chapter Five: Conclusions, Action Plan, Reflections, and Recommendations .... 35
Conclusions ............................................................................................... 35
Action Plan ................................................................................................ 36
Reflections and Recommendations for Other Teachers ............................ 38
Summary ................................................................................................... 39
References ............................................................................................................. 40
Appendices ............................................................................................................ 42
Appendix A: Principal Consent Form ....................................................... 43
Appendix B: Parent Consent Form ........................................................... 44
Appendix C: Student Consent Form ......................................................... 46
Appendix D: Vocabulary Survey .............................................................. 48
Appendix E: Pre and Post Test.................................................................. 49
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Appendix F: IRB Approval Letter ............................................................ 51
viii
List of Tables
Table
Page
1.
Vocabulary Pre and Post Test Results ...................................................... 24
2.
Vocabulary Survey Results ....................................................................... 25
ix
List of Figures
Figure
Page
1.
Frequency of methods used to study vocabulary ...................................... 26
2.
Frequency of methods chosen as effective ................................................ 27
3.
Frequency of situations in which knowing math vocabulary helped ........ 28
Chapter One
Introduction
Working in a middle school offers an advantage when collaborating with
teachers from different disciplines. The English teacher on my 9th grade team
decided to introduce words to her students that were not traditionally “English”
vocabulary words. She asked each person on our team if there were vocabulary
words we would like students to practice. As a math teacher, it was tempting to
exclude myself from the conversation, but then I remembered grading yet another
test where my students displayed ignorance of a term we had been using since the
beginning of the course. Why aren’t students remembering these words when we
use them over and over again in class?
As I reflected on this issue, I realized that I was laying the blame on
students when the fault was my own. Every good teacher reflects on his or her
teaching, and thinks of possible solutions for what is not working. The emphasis
of my action research project was vocabulary because teachers and students
typically do not see the importance of vocabulary in mathematics. Instead of
maintaining the status quo and not reforming my pedagogy, or teaching methods,
I sought to increase mathematical knowledge by directly teaching vocabulary as it
pertained to content being covered.
2
Motivation for the Project
Frustration with geometry students forgetting vital vocabulary words from
one chapter to the next motivated me to research engaging methods to increase
vocabulary comprehension and retention. Teachers discuss the words in class, but
the students are not internalizing or applying them. Therefore, I felt vocabulary
drives geometry comprehension, and I realized the specific need to address it. My
school started to put an emphasis on vocabulary in all content areas recently. The
faculty attended several staff meetings on how to implement engaging vocabulary
strategies. I began looking at the geometry curriculum and realized the strategies
we were learning as a staff could easily be implemented into the classroom to help
my students learn the vocabulary of the course.
Background on the Problem
Students tend to think studying vocabulary is meant for other courses,
such as science and English. They focus their study habits on how to do a math
problem, but the questions in geometry are not always cookie-cutter problems.
They need to be able to synthesize all their background knowledge to produce an
answer. During lecture, students would copy vocabulary words into their notes,
but they did not study them after class was over. This resulted in students hearing
the word a few times, but not enough to commit them to long term memory. I
reinforced their belief when I did not stress vocabulary comprehension in class.
3
Time is valuable, and it is hard to take time to teach vocabulary when
there is so much information students need to learn. In order to justify taking time
to work on vocabulary, an improvement was needed in student understanding. It
was worth studying the effects of directly teaching vocabulary in the classroom,
and whether the increased instruction in this area improved vocabulary
comprehension.
Statement of the Problem
A common misconception of mathematics is that it involves only
numbers. Students’ study habits reflected this attitude because they tended to
focus on the mechanics of a math problem and forgot about the vocabulary
driving the course. Math teachers contributed to this issue by failing to explain the
importance of vocabulary and not practicing vocabulary comprehension in class. I
was guilty in the sense that we did not practice vocabulary as much as solving
math problems in class. My action research project was directed toward learning
vocabulary in an engaging, comprehensive way. When more focus was put on
vocabulary, students modeled the behavior and started studying the words on their
own. Students started to notice they had less difficulty with their assignments
because they understood the vocabulary behind the math.
Statement of Purpose
The purpose of my action research project was to understand how direct
instruction of vocabulary affected the geometry classroom. I planned to
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implement engaging vocabulary activities to help students understand the
essential vocabulary in geometry; this in turn helped them execute the traditional
math questions of the course. My notes tracked how engaged the students were in
the activities and informally assessed whether they remembered the words after
the activities or not. I planned to journal regarding whether the students felt
knowing the vocabulary helped them with other aspects of the material, like
homework assignments and assessments. A pre-test and post-test helped the
students see how much they learned and helped them track their own growth in
the class.
Research Questions/Hypotheses
There are two questions I addressed in my research project: How did
implementing activities to practice vocabulary in the classroom affect vocabulary
comprehension in geometry? How did vocabulary instruction affect student
confidence concerning geometry concepts?
Summary
A responsible educator reflects on their teaching to identify their strengths
and weaknesses. When a weakness is identified, a person must research methods
to improve their current practices. One weakness identified in my teaching was
helping students understand the vocabulary they needed in order to be successful
in mathematics, specifically geometry. In order to address this weakness, I
implemented activities stressing vocabulary. By stressing vocabulary, students
5
were taught the terms needed for understanding the mathematical concepts they
were learning. Before changing my teaching practices, it was important that what
I implemented in my classroom was supported by research.
Chapter Two
Review of Literature
The purpose of my action research project was to understand how direct
instruction of vocabulary affected the geometry classroom. The research available
for content vocabulary focused on reading in content areas, but not specifically
how it affected content understanding. There were more studies available that
discussed the importance of teaching vocabulary to younger children, but more
needs to be done to demonstrate how essential it is to continue vocabulary
instruction into older grades. The strategies available for direct teaching of
vocabulary are numerous and can be engaging and worthwhile for students.
It is important to have a repertoire of words to pull from; it is also
important to improve on existing vocabulary. Content specific vocabulary consists
of words not necessarily used outside the educational setting. In order for students
to fully grasp what must be learned in a class, they must understand the meaning
behind the words used in the class. The method used to teach students content
vocabulary affects how willing they are to learn the words and how well they
retain the words afterwards (Beck, McKeown, & Kucan, 2008). In a study
conducted by Beck, et al. for their book Creating Robust Vocabulary, the authors
found “type of instruction did make a difference, with the advantage going to
instruction that both encouraged active processing of words and featured a high
number of encounters” (p. 4). Bromley (2007) wrote:
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The goal of vocabulary instruction should be to build students’
independent word learning strategies that can empower them for lifelong
learning. This requires teachers who are passionate about words and
language, who immerse their students in language, and who provide direct
instruction that is thoughtful, intentional, and varied (p. 536).
Vocabulary and Comprehension
Bromley (2007) stated, “Vocabulary is a principle contributor to
comprehension, fluency, and achievement” (p. 528). When students do not
comprehend the words they are exposed to while learning new concepts, they
must learn the new words as well as the new material. Students can fully
concentrate on learning new material when they already have a working
knowledge of the vocabulary words they need (Beck et al., 2008). According to
Beck et al., “More efficient retrieval in turn promotes comprehension, whereas
effortful retrieval jeopardizes it” (p. 262). The ability a student has to comprehend
math in general is dependent upon comprehension of the vocabulary words they
encounter (Pierce & Fontaine, 2009). A student, who struggles with the
vocabulary in a class, will most likely fall behind because they cannot keep pace
with the class (Palumbo & Loicacono, 2009). According to Bromley (2007),
“Students with large vocabularies understand text better and score higher on
achievement tests than students with small vocabularies” (p. 528). Pierce and
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Fontaine (2009) discussed the correlation between vocabulary instruction in
mathematics and other subject areas:
Reading research has provided the field of education with invaluable
insight to effective methods of teaching vocabulary, an endeavor of
critical importance to our students’ reading comprehension. However, the
importance of vocabulary knowledge extends well beyond the domain of
the language arts. In particular, proficiency in mathematics has
increasingly hinged upon a child’s ability to understand and use two kinds
of math vocabulary words: math-specific words and ambiguous, multiplemeaning words with math denotations (p. 242).
Mathematical vocabulary can be broken into four subgroups: technical,
subtechnical, general, and symbolic (Monroe & Panchyshyn, 1995). Technical
vocabulary is specific to mathematics and presents challenges to teachers because
students do not see these words outside of the mathematics classroom or text.
Monroe and Panchyshyn considered “learning a technical vocabulary is
comparable to learning a foreign language” (p. 80). A subtechnical vocabulary
consists of terms that have multiple meanings, sometimes math and non-math
definitions as well as multiple math definitions. According to Monroe and
Panchyshyn, “Because of this nature, subtechnical terms may be even harder to
learn and remember than technical terms” (p. 80). General vocabulary is another
subgroup consisting of words that students are familiar with and use often.
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Symbolic vocabulary is troublesome to students and difficult for teachers to teach
because this category includes abbreviations and symbols (Monroe &
Panchyshyn, 1995). There are several abbreviations students must learn, as well
as new symbols, in the mathematics classroom.
Students need to understand the words the teacher is using in lectures and
discussions in order to process the information they are learning to the best of
their ability. When encountering an unfamiliar word in a literature passage, a
person can conjecture the basic definition of the word through contextual clues.
Reading in content classes, such as mathematics, does not afford students the
same situation. The vocabulary in content classes is often very specific to a class
or subject matter, and the students must be able to decode the vocabulary since
the material builds on itself (Spencer & Guillaume, 2006). Instruction in math
specific terms is needed to help students due to the technical nature of the words
(Bromley, 2007). In order for students to be able to understand the text’s
information, they must have a basic understanding of the subject and vocabulary
(Palumbo & Loicacono, 2009). It is necessary for the teacher to directly teach the
words to the students for them to learn the vocabulary in a math classroom
(Bromley, 2007). Because the material in content classes such as math keep
building on previous knowledge, it is important for the teacher to focus on
strategies to help students internalize the vocabulary (Spencer & Guillaume,
2006).
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Vocabulary is essential to language skills, which have become more
important through the years. The National Council of Teachers of Mathematics
(NCTM), has included Communication as one of the process standards in
Principles and Standards for School Mathematics (Pierce & Fontaine, 2009).
Students must be able to explain their methods of solving problems both by
written and oral means. In order to coherently organize their thoughts, students
need to possess content knowledge as well as vocabulary knowledge.
The importance of vocabulary is shown in greater detail when confronted
with students from a lower socioeconomic status. Hirsch (2003) explained this
issue as starting in the early grades, but becoming more pronounced during and
after fourth grade (p. 10). “In vocabulary acquisition, a small early advantage
grows into a much bigger one unless we intervene very intelligently to help the
disadvantaged student learn words at an accelerated rate” (p.16). Direct teaching
of vocabulary can potentially close the gap between students who initially have a
lower expanse of vocabulary (Hirsch, 2003).
Direct Instruction of Vocabulary
Although it makes sense students will learn vocabulary if they are
instructed in the words they are to learn, it is common for teachers to spend little
time on the instruction of the words (Beck et al., 2008). A common approach to
teaching vocabulary is to either give students definitions to memorize or use the
textbook’s explanation of vocabulary terms. This type of instruction tends to
11
promote superficial memorization (Spencer & Guillaume, 2006). Monroe and
Panchyshyn (1995) stated, “Teachers can draw upon their existing repertoire of
strategies to help students construct vocabulary meanings in a variety of subject
areas” (p. 83). Spencer and Guillame (2006) indicated, “Research in word
learning indicates that in order to enhance vocabulary, students need multiple
exposures to words in different contexts and opportunities to build background
knowledge in the domains in which the vocabulary is likely to occur” (p. 207).
Beck et al. (2008) conducted two studies regarding how direct instruction
affected children’s understanding of vocabulary. The children involved in the
study were in kindergarten and first-grade. The first study examined the effect of
direct instruction compared to no instruction. The groups of students were
comparable in size with the group receiving direct instruction containing 52
children compared to the group receiving no instruction at 46. The researchers
stated in the study, “The findings indicate that there was significantly more
vocabulary learning in the instructed group compared to the group that received
no instruction” (p. 258). The second study dealt with the effect of time spent on
direct instruction of vocabulary. One group of children received twice as much
time as the other group specifically working on vocabulary. The researchers’
summation of the second study is as follows, “The results of Study 2 indicate that
more instruction was beneficial, with gains about twice as large for words given
more instruction, in both kindergarten and first grade” (p. 262).
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Robert J. Marzano (2004) listed eight characteristics of direct teaching
with regard to vocabulary. The first characteristic referred to the reliance on
definitions: because students can memorize definitions without comprehending
them, definitions alone may be an ineffective method of vocabulary instruction.
The second characteristic discussed by Marzano, instruction of vocabulary,
should be presented using both language and images. Mental images, graphic
organizers, and pictures are examples of non-linguistic methods. The third
characteristic was to provide several experiences with the vocabulary words
because frequency seems to correlate with deepening understanding.
The fourth and fifth characteristic addressed the parts and types of words.
Morphological analysis was the fourth characteristic of direct instruction
mentioned by Marzano (2004). This process involves analyzing word parts, such
as prefixes, suffixes, and root words. Students can use this method to break a
complex word into smaller bits of information they understand. Common affixes
(prefixes and suffixes) and root words can be found in tables, which aid content
teachers in choosing the most applicable words for their classes. The fifth
characteristic of direct vocabulary instruction mentioned in the book was related
to the type of word. Nouns and verbs have different functions in the English
language, and students may need help in deciphering the function of the word as
well as the definition.
13
Using the vocabulary words in class was the sixth characteristic Marzano
(2004) discussed. Teachers should use the words during instruction as well as
discussion, and promote the use of the vocabulary terms through activities. These
activities could be facilitated by the teacher grouping students for the sole purpose
of discussing the words.
Games are the seventh characteristic of direct instruction. Students enjoy
playing games in class and the competition is an unpredictable challenge
encouraging memory of the vocabulary words. Eric Jensen (1997) stated body
movement during learning, such as experienced during games, helps students
remember what they have learned. The last characteristic of direct instruction
Marzano (2004) discussed is to choose terms specifically for their use in
education. Content classes, such as mathematics, have selective vocabulary terms.
Students must learn the content specific terms to be successful in the class, and
the teacher is responsible for focusing instruction and learning on those words.
Strategies
Numerous strategies for direct teaching of vocabulary have been found to
be effective. Pierce and Fontaine (2009) noted using “student-friendly” language
and engaging activities are two strategies that help students increase vocabulary.
They recommend “offering student-friendly definitions of math terms,
encouraging deep processing of word meanings, providing extended opportunities
to encounter words, and enriching the verbal environment of the mathematics
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classroom” (p. 241). Karen Bromley (2007) listed several examples of effective
approaches to teaching vocabulary: word walls, stressing bold or highlighted
terms, and pre-teaching content specific vocabulary. Several suggestions for
effective teaching of vocabulary were given by Beck, et al. (2008). One
suggestion was to always teach vocabulary words in context because the word
will be applicable to the lesson and students are more apt to remember the word in
context. Using “friendly explanations” was another suggestion given by the
authors of Creating Robust Vocabulary. By using less formal language, students
are able to understand and remember the definition of a word.
Beck, et al. (2008) indicated the use of activities forcing the learner to use
a term in some way helped them remember the word better than memorizing lists
of basic definitions. This process helps connect prior knowledge with the new
term, which makes the new word’s definition more accessible. When students
hear, see, and use the new vocabulary words frequently, they are increasing the
likelihood of remembering the words; because of this view, the authors suggested
using new vocabulary words often and over several days.
A fun and interactive way to learn vocabulary is to play games in the
classroom, which was Marzano’s (2004) seventh characteristic of direct
instruction. Ideas for playing games were mentioned by Eric Jensen (1997). One
idea was a ball toss with small groups as a way to encourage student collaboration
in a fun way while thinking quickly. In ball toss, students lightly toss a soft object
15
to each other. The only student allowed to speak is the person holding the object,
and they must answer some type of question. Jensen also recommended using the
space around the classroom to post vocabulary words; so students are exposed to
the words even when there is no instruction taking place. The visuals should be
colorful, interesting, and can be created by the students.
Additional suggestions for teaching vocabulary were presented by Monroe
and Panchyshyn (1995). Manipulatives are a way for students to connect the
abstract to the concrete. Pre-teaching important vocabulary from the textbook is
another suggestion, including teaching the symbols and abbreviations students
will encounter. They also stress the importance of the teacher using the
vocabulary as much as possible when they speak.
Summary
The literature available regarding vocabulary shows teachers can help
students learn vocabulary by direct instruction using techniques that engaged
students in the learning process. Although studies mentioned earlier focused on
younger children, it is easy to imagine the effects would be similar with older
students. This action research project implemented direct instruction of
vocabulary to examine the effects in the geometry classroom.
Chapter Three
Research Design and Method
The purpose of my action research project was to understand how direct
instruction of vocabulary affects the geometry classroom. In the past, I had not
put an emphasis on vocabulary in my classroom. At the same time, I would
become frustrated when students did not remember significant vocabulary words
which affected their understanding of geometry concepts. I conducted this action
research project to uncover the effects of explicitly teaching vocabulary in the
geometry classroom.
Relevant information to the action research project such as setting, design,
and intervention are contained in this chapter. The setting discusses the location
and demographics of the school. The intervention is the change that was
implemented in the classroom for the project. The design of the action research
project, as well as the specific methods, and timeline are discussed. The expected
results of the researcher are also included.
Setting
I have taught algebra and geometry for six years to ninth grade students.
My school is located in an upper Midwestern town in the United States and is a
middle school consisting of seventh, eighth, and ninth grade students. The school
demographics changed with regard to socio-economic status in recent years. It
went from a primarily middle-class family school, to qualification as a Title I
17
school for the 2011-2012 school year. I taught 104 students throughout the year
out of a total of 834 students registered in the school. The class studied for this
research project was a morning geometry class that contained 28 students: ten
male, 18 female, no students of a minority race, and no students classified as
needing special education services.
The school day was organized into a block schedule, which was broken
into four 90-minute class periods. Traditionally, ninth grade students who were in
geometry were considered to be in advanced math. Block schedule created a
unique situation where students could be placed in geometry during the second
semester if they were in algebra during eighth grade, or they were able to take
algebra during the first semester of the school year and geometry during the
second semester. This created a diverse ninth grade geometry class that consisted
of advanced students who started math after a seven month break along with
students who were not originally considered advanced, but recently finished
Algebra I. Because of this circumstance, the class contained students who had
gaps in their mathematical knowledge from time spent away from mathematics.
These students tended to “catch on” quickly, but some re-teaching of algebra
concepts were needed. The students who continued from algebra into geometry
during their ninth grade year had fewer gaps in their memories, but traditionally
were not as strong in mathematics as those that took algebra during their eighth
grade year.
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Intervention/Innovation
In previous years, I addressed vocabulary as it pertained to a chapter in the
geometry curriculum. My students would take notes, including copying
definitions of important vocabulary terms. I discussed the wording in the book,
and we would break it down into less formal wording, so students had more of a
working knowledge of the vocabulary. After a section was taught, we would not
review the vocabulary words or refer to them again.
The intervention changed the way vocabulary was addressed in my class
by putting much more focus on vocabulary than in the past. I discussed the
definitions of vocabulary terms with the class, and I extended vocabulary into
more areas of my teaching. The students participated in engaging activities to help
them review the vocabulary terms. They also took pre- and post-tests which
demonstrated their growth in understanding of important vocabulary terms.
Simply making vocabulary a regular part of geometry instruction, instead of a
superficial covering, was a major change in the way I taught geometry.
Design
The design for this research project was a mixed-methods approach. I
chose a mixed-methods approach because I wanted to compare pre-tests and posttests to see how direct teaching of vocabulary improved understanding of
geometry problems. I also wanted to use more qualitative sources of research
through open-ended questions and a teacher journal. I wanted to use the
19
qualitative research methods to see if students felt the focus on vocabulary was
beneficial.
Description of Methods
I started the action research project process by obtaining permission from
my building principal (See Appendix A). After approval from administration, I
sent a permission slip home to the parents of students who were involved in the
study (See Appendix B), and the students signed their own consent form (See
Appendix C). The project started early in geometry, so the students were given
approximately two weeks to hand in the signed consent forms. If they were not
handed in after one week, I contacted parents for the forms. If the parents refused
to allow their children to participate, their children were excluded from all data
collection.
After all consent forms were collected and approved, the students filled
out a survey containing questions regarding their confidence with geometry
concepts and how they felt about the importance of vocabulary in the math
classroom (See Appendix D). They were given a pre-test (no notes) for the
content included in the research project (See Appendix E). The pre-test included
vocabulary as well as geometry concepts. The students repeated the same pre-test
as their post-test (no notes) after direct instruction of vocabulary. During this span
of time, a teacher journal was used to record any observations pertinent to the
project. At the conclusion of the action research project, the students filled out the
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original survey given at the beginning of the study to see if there were changes
due to the implementation of the project.
The data collected excluded any identifying information, as approved by
Minot State University’s Institutional Review Board (See Appendix F). Data was
collected through a survey, pre- and post-tests, and a teacher journal. The survey
was anonymous to encourage free-thinking and honest answers. The pre- and
post-tests needed an identifier so that growth of each student could be tracked;
however, the student was assigned a number instead of using their name. The
teacher journal did not use any identifying information.
The timeline for collection of data depended on the instrument used. The
survey was given in the beginning of the project, as well as the end to see if the
students demonstrated any change before and after the project with regard to
vocabulary. The pre- and post-tests were administered before and after the project
because continuous monitoring of student growth was important to identify any
changes because of the interventions being implemented. A teacher journal was
also utilized to note any important observations throughout the project.
The data collection tools for this action research project were surveys, preand post-tests, and a teacher journal. Each data collection tool was used to help
answer the two research questions. “How will implementing activities to practice
vocabulary in the classroom affect comprehension in geometry?” was the first
research question which was measured through pre- and post-tests and the teacher
21
journal. The pre- and post-tests were used to find a relationship between direct
instruction of vocabulary and knowledge of geometry material. The teacher
journal was used to record observations regarding how vocabulary knowledge
affected knowledge of geometry material. “How does vocabulary instruction
affect student confidence concerning geometry concepts?” was the second
research question which was measured through the survey and the teacher journal.
The survey was used to identify the level of confidence with geometry concepts
before and after the action research project. The teacher journal was used to
record observations regarding student attitudes toward geometry concepts after
direct instruction of vocabulary.
Expected Results
I expected direct teaching of vocabulary and practicing vocabulary during
class would improve the students’ understanding of geometry vocabulary as well
as their confidence in using the vocabulary words. Finding time to fit in the
activities for teaching vocabulary was difficult, but the time spent working on
vocabulary was worth it because the students had a much better understanding of
what they needed to learn because of the work they had done on vocabulary.
Timeline for the Study
The timeline for the intervention and data collection process took place
over approximately five weeks, which was during the first semester of geometry.
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Summary
Vocabulary is an essential part of mathematics, but students were often
taught how to do mathematics without instruction of the vital vocabulary words.
Surveys, pre- and post-tests, and a teacher journal helped uncover the effects of
direct instruction of vocabulary in the mathematics classroom. The area of
geometry studied was heavily dependent on vocabulary. Engaging activities were
used to teach and review the vocabulary as well as keep the students interested.
The data collected from surveys, pre- and post-tests, and journals helped answer
the two research questions in this study.
Chapter Four
Data Analysis and Interpretation of Results
The purpose of my action research project was to understand how direct
instruction of vocabulary affects the geometry classroom. In order to answer the
questions of whether direct instruction increased vocabulary comprehension, I
used three data collection methods. The first method was a pre- and post-test, the
second method was a survey regarding vocabulary, and the third method was a
teacher journal.
Data Analysis
The first data collection method administered was an identical pre- and posttest in order to gauge the difference in vocabulary understanding from the
beginning to the end of the intervention. The test had a list of 33 vocabulary
words students were expected to know by the end of the unit of study. They were
required to choose one of four categories on the test for each vocabulary word.
The first three categories required the students to write a description
demonstrating they knew the word well, they knew something about the word, or
they had seen or heard of the word. The fourth category required a check mark if
they did not know anything about the word in question.
In order to analyze the data for the pre- and post-test, the amount of words that
were selected in each category were tallied. Students were given three points for
each word in the Know It Well category, two points for the Know Something
24
About It category, one point for the Have Seen or Heard of It category, and no
points for the Do Not Know category. Students could score a maximum of 99
points on the test. Table 1 summarizes the class average data for pre- and posttests.
Table 1
Vocabulary Pre and Post Test Results
Tests
(n=22)
Ma
Mdn
SD
Mode
1st
Quartile
2nd
Quartile
Pre
50.0
51.5
9.5
55
46.3
55
Post
93.0
95
6.1
99
91
97
a
Maximum 99 points possible.
The students filled out a survey regarding vocabulary which was given at
the beginning and end of the intervention as an additional data collection
technique. For questions one through three, students were asked to circle a
number, one through five, correlating to how often the question applied to them.
For questions four and five, they were asked to circle a number, one through four,
which asked about understanding definitions from a textbook and whether they
felt vocabulary was important in math. There were also three open ended
questions on the survey. The results from the first five questions are summarized
in Table 2. According to the data, the percentage of students who have studied
25
vocabulary in math increased after the intervention, as did the percentage of
students who study vocabulary on their own.
Table 2
Vocabulary Survey Results
Question 1: I have studied vocabulary in math class.
Never
Rarely
Sometimes
Frequently
Everyday
Pre:
4%
16%
44%
24%
12%
Post:
0%
4%
16%
48%
28%
Question 2: I review vocabulary on my own.
Never
Rarely
Sometimes
Frequently
Everyday
Pre:
4%
44%
40%
12%
0%
Post:
0%
20%
64%
16%
0%
Question 3: It helps when the teacher explains definitions to me.
Never
Rarely
Sometimes
Frequently
Everyday
Pre:
0%
0%
8%
44%
48%
Post:
0%
0%
8%
44%
48%
Question 4: I understand the definition of words in the textbook.
Never
Somewhat
Often
Always
Pre:
0%
24%
72%
4%
Post:
0%
24%
68%
8%
Question 5: I think vocabulary is important in math.
Never
Somewhat
Often
Always
Pre:
0%
28%
36%
36%
Post:
0%
4%
32%
64%
26
The last three questions on the survey were open ended questions where
students were able to answer freely and more than one type of response was
possible. Question six on the survey asked what types of methods for studying
vocabulary students had used in previous math classes. The frequency of the
different types of methods that appeared in answers was measured in order to
analyze the difference between the pre-survey and the post-survey. In order to
organize the data, the methods were coded into eight categories. Figure 1
summarizes the data collected from question 6 on the survey. According to the
data, the frequency of methods such as Games and Study Tools increased, while
methods like Teacher Explanations and Visual Displays decreased. The category
coded Nothing was not present on the post-test results.
Figure 1. Frequency of methods used to study vocabulary.
27
Question 7 on the survey asked the students to describe the methods they
thought were the most effective for leaning vocabulary. The student answers were
coded and eight categories were found. Figure 2 summarizes the data collected
from question 7.
Figure 2. Frequency of methods chosen as effective
Question 8 on the survey asked students to describe a situation where
knowing math vocabulary would help. The responses were grouped into six
categories according to similarities and the results are summarized in Figure 3.
28
Figure 3. Frequency of situations in which knowing math vocabulary helped.
Interpretation of Results
The first question posed for this research project was, “How will
implementing activities to practice vocabulary in the classroom affect vocabulary
comprehension in geometry?” The data from the vocabulary pre- and post-test
demonstrated the interventions taken place during the unit improved student
comprehension of the vocabulary words involved in the intervention. This was an
expected result because of the work done in class focusing on vocabulary. The
scores increased from pre-test to post-test, which showed more students were able
to answer in higher point categories on the post-test indicating growth in
comprehension. The pre-test mean was 50.0 with a standard deviation of 9.5,
where the post-test mean was 93.0 with a standard deviation of 6.1. The increase
in mean score showed the class overall showed increased vocabulary
29
comprehension, and the smaller standard deviation for the post-test also displayed
less variance between student tests.
Similar to the increased scores on the pre- and post-tests, the explanations
on the post-test were in greater detail and more accurate, which also displayed an
increase in vocabulary comprehension. Students wrote very general explanations
on the pre-test, and several of the explanations were incorrect. The post-test
answers to the same terms were frequently written in great detail and included
diagrams when applicable. One student explained an isosceles triangle on the pretest as “The two sides are longer than the other.” On the post-test, the same
student explained an isosceles triangle as “Two sides are congruent,” and she
included a sketch of an isosceles triangle with two sides marked congruent.
Another example which showed the growth in comprehension from the pre-test to
the post-test was a student’s explanation of hypotenuse. The pre-test explanation
was “Length from vertex to middle of a polygon.” The post-test explanation was
“Longest line of a right triangle, opposite the right angle.” The post-test
explanation showed he understood a hypotenuse as a part of a right triangle
instead of any polygon, and it is the longest segment of the triangle. The student
was also able to state the location of the hypotenuse as opposite the right angle.
This depth of explanation compared to the pre-test will enable the student to work
with geometry concepts like the Pythagorean Theorem and trigonometry ratios.
30
The first five questions of the survey helped in understanding the increase
in vocabulary comprehension. The first question asked if the students had studied
vocabulary in math class, and an increase would be expected because of the
emphasis on vocabulary instruction during class. Every lesson was designed to
work on vocabulary to some extent, so it was not surprising to see the percentage
of the Everyday category rose from 12% to 28%. The Frequently category also
saw an increase in percentage from 24% to 48%. Between these two categories
alone, 76% of the class marked they had studied vocabulary in math class on at
least a frequent basis. No students marked the category Never on the post-test,
and only one student marked Rarely.
The fifth question asked if the students thought vocabulary was important
in math and showed an increase in the positive areas of Often and Always. The
Often and Always categories increased in percentage from 72% to 96%, which
showed the majority of students thought vocabulary was an important part of
math. This result might have explained why the results increased for the second
question. The second question asked if the students reviewed vocabulary on their
own. The increase would be expected, because as students started to see the
importance of knowing vocabulary, they became more willing to study
vocabulary on their own time. Several journal observations were made regarding
this concept. Students were given time in class to create flashcards, and they
frequently took time to look over them and quiz each other. After the requirement
31
was fulfilled, several students still added to the notecards continually and would
use them as their main study tool.
From pre-survey to post-survey, the third and fourth question on the
survey showed little to no change. The third question asked students if teacher
explanations helped them understand vocabulary. The percentages were high in
the Frequently and Everyday categories, but there was no change in the data
between post-test and pre-test. The intervention most likely did not change the
fact that students felt teacher explanations are helpful. The fourth question saw a
4% increase in students who felt they always understood the definition of words
in the textbook.
The data from the pre- and post-test and the data from the pre and postsurvey show implementation of activities and direct instruction of vocabulary
increased comprehension of vocabulary.
The second question posed for the research project was, “How does
vocabulary instruction affect student confidence concerning geometry concepts?”
This question was best answered by the last question on the survey, “Explain a
situation where knowing vocabulary in math helped you.” Four out of the six
types of answers showed an increase in frequency regarding situations where
vocabulary helped the students. One category with a decrease in frequency was
Everything, which could be explained by a student answering more specifically
on the post-survey. The other category with a decrease in frequency was Not
32
Used, because this description did not appear on any post-surveys. A person could
assume the reason for the absence of this type of answer on the post-survey was
because there were no students who felt vocabulary was not useful in math.
Interestingly, the written answers students provided for this question were often
emphasized by the use of capital letters, exclamation marks, and repeated writing
of a word. Several students wrote proofs in capital letters for their answer, while
one student wrote proofs, proofs, and more proofs to get his or her point across.
The vocabulary post-test also exposed an increase in confidence regarding
geometry concepts. The answers students wrote in the Know it Well category on
the pre-test were often followed by question marks indicating they were unsure of
their answer. On the post-test, the students were able to answer with a complete
and correct explanation. For the term transformation, one student wrote
“Becoming bigger or smaller?” on the pre-test. On the post-test, the same student
wrote, “Something you do to change an object’s position, but still keep it
congruent.” The absence of the question mark showed the student’s confidence in
the post-test explanation, while the more accurate explanation indicated a clearer
understanding of the term. Several students wrote only in the Know it Well
category, which shows the confidence they have in their ability to explain all the
terms.
Students used ActivExpressions, which are learner response devices,
sporadically throughout the intervention. Journal entries from the days when
33
students used ActivExpressions indicated an increase in confidence of the
vocabulary terms learned that day. Students were asked in the beginning and the
end of the lesson to choose their confidence level using a likert scale. One journal
entry stated all students selected unsure or highly unsure at the beginning of the
lesson. All but three students indicated they were fairly confident or above after
the activities that day.
Although the research questions were answered through the data,
circumstances occurred worth mentioning. During implementation of the
intervention, there were three students who went on an extended vacation of eight
school days. I was unable to use their data because they came back to school after
I had finished the intervention, and I was unable to give them the post-test and
post-survey. I had to take out the data from their pre-test and pre-survey as well.
Similarly, I removed three students’ pre- and post-tests because I realized they
had not filled out the back of the pre-test. The results of the study may or may not
have differed with the inclusion of their information.
Another situation I noticed as I was coding the answers from the survey
was student understanding of the open-ended questions on the survey. The phrase
“previous math teachers” in question six resulted in different types of answers
because some students did not use the current class in consideration on the posttest while others did. The frequency of certain types of answers may have
34
increased for the post-test results if students understood they could include the
current class on the post-test.
Another issue that may have affected survey questions was not giving the
pre-survey at the beginning of the class instead of at the beginning of the unit.
Students were already realizing the importance of vocabulary before the research
project started, as seen in some of the answers to their pre-survey when they
mentioned geometry tests as a situation when vocabulary helped them in math. I
had already been speaking to them about the importance of learning vocabulary in
order to be successful in geometry, which may have resulted in higher scores on
certain questions in the survey.
Summary
The analysis of the data from this research project has clearly
demonstrated the importance of teaching vocabulary in the geometry classroom.
The differences between the pre- and post-tests, and the student responses on the
survey show that comprehension and confidence were both increased as a result
of the intervention. The journal entries showed the students depended more on
their vocabulary knowledge to solve problems and became more comfortable with
the vocabulary words. The logical step in the research process is to develop a plan
of action for continuing and extending this research, which will be discussed in
Chapter 5.
Chapter Five
Conclusions, Action Plan, Reflections, and Recommendations
The purpose of my action research project was to understand how
direct instruction of vocabulary affected the geometry classroom. Two research
questions were the focus of the study. The first question asked how implementing
activities to practice vocabulary in the classroom would affect vocabulary
comprehension in geometry. The second question asked how vocabulary
instruction affected student confidence concerning geometry concepts. Data was
collected and analyzed through the use of pre- and post-tests, surveys, and a
teacher journal. Several conclusions could be made after analyzing the data.
Overall, the results of the research study showed direct instruction of vocabulary
to have a positive effect on student comprehension and confidence.
Conclusions
Student accuracy on the post-test, as well as completion of the post-test,
verified the importance of directly teaching vocabulary in geometry. The majority
of the students were able to complete the post-test with almost all of the
vocabulary terms explained in the Know It Well category. Their explanations
were thorough and included diagrams to further explain their description. On the
pre-test, several of the explanations written in the Know It Well category were
incomplete or completely inaccurate, which demonstrated growth over the course
36
of the intervention. Because the intervention dealt only with vocabulary, it is
reasonable to conclude the intervention was the reason for this growth.
There is evidence of improvement in student confidence when looking at
the pre- and post-test as well. The pre-test answers students gave were short and
several students used question marks next to their answers to show their
uncertainty. The post-test answers were lengthy and complete. Some students
asked for additional paper for more room to write their answers, which showed
their understanding of the terms as well as their confidence in being able to
explain them.
The student survey was another tool used to evaluate the two research
questions. The survey showed students became more independent in their study of
vocabulary and felt that vocabulary was important to geometry, which indicated
an increase in confidence with the geometry material. Increase in comprehension
followed from their willingness to study vocabulary out of class as well as in
class.
Action Plan
As a result of this action research study, I will continue to teach
vocabulary as an integral part of geometry throughout this year and every year. I
have felt that vocabulary was an important part of learning geometry, and the
results of this study confirm that explicitly teaching vocabulary had a positive
37
effect on the students. I feel that some components of the study will remain the
same; however, I will take some changes into consideration.
One change that could improve the study would be to separate the pre- and
post-test into different chapters in the geometry book. This intervention took place
over two chapters which impacted the length of the exam. The students took an
entire 90 minute block class to take the vocabulary post-test. I think smaller, but
more frequent tests would be more effective.
Another modification I would make would be to put theorems and
postulates on the pre- and post-tests. I did not place these on the tests for this
intervention, but I taught them in a manner similar to how I taught the vocabulary.
As the intervention was taking place, I found that I regretted not including the
postulates and theorems in the study. In the future, I would include the important
theorems and postulates on the pre- and post-tests to measure student
comprehension of these concepts as well.
My next step in the action research process would be to study the effect
writing has on learning the central concepts of geometry, focusing on the
understanding of vocabulary, postulates, and theorems. I feel strongly that if
students can explain in writing what they have learned, they will remember what
they have learned better and have a clearer understanding of the topics.
38
Reflections and Recommendations for Other Teachers
I truly believed in my action research project, and I enjoyed the process.
There was never a time when I felt that my time was wasted by implementing the
interventions. I believe the students will leave my class with a good understanding
of geometry vocabulary and an appreciation for vocabulary in any math class to
come. I also believe they will leave with strategies that will help them study
vocabulary in the future and become stronger math students.
Although the research questions proposed for this study focused on
vocabulary comprehension and student confidence, I saw additional benefits to
the project that are worth discussing. The first benefit was immediately apparent
when students were working on homework assignments. They learned to refer to
their vocabulary for clarification when working on a geometry problem in their
assignment. I encouraged students to do this and modeled this action by
answering their own questions using vocabulary whenever possible.
The second and third benefits were more noticeable as we moved on from
the study itself. During the study, I required students to make vocabulary note
cards for themselves. I encouraged them to study them and quiz each other, giving
time intermittently during the course of the study for them to do so. Several
students continued this practice after they were no longer required to make
notecards, which showed they felt there was value in making the notecards. It was
39
very encouraging as a teacher to see students continuing a practice you started,
without any grade or obligation attached to it.
The third benefit, remembering the vocabulary longer than one chapter in
geometry, has been apparent since the conclusion of the study. In the past, my
geometry students would remember a vocabulary term for as long as they felt they
needed to know it, which usually meant until the next chapter test. I have been
free to teach new vocabulary without constantly needing to remind them of words
they have already learned because they still remember the words they learned
during the study. If they do not remember a word they know they have learned,
they independently look in their notes, notecard, or the book to refresh their
memories.
Summary
Vocabulary and math should complement each other in a geometry class,
and I see the positive results from this action research study as evidence to keep
teaching them together. I feel encouraged by this study to integrate more
strategies into my classroom to improve vocabulary comprehension.
40
References
Beck, I. L., McKeown, M. G., & Kucan, L. (2008). Creating robust vocabulary,
frequently asked questions & extended examples. New York, NY: The
Guilford Press.
Bromley, K. (2007). Nine things every teacher should know about words and
vocabulary instruction. International Reading Association, 50, 528-537.
doi: 10.1598/JAAL.50.7.2
Hirsch, Jr., E. D. (2003). Reading comprehension requires knowledge of words
and the world. American Educator, 27, 10-29. doi: 10.1.1.141.6106
Jensen, E. (1997). Brain compatible strategies. San Diego, CA: The Brain Store.
Marzano, R. J. (2004). Building background knowledge for academic
achievement. Alexandria, VA: Association for Supervision and
Curriculum Development.
Monroe, E. E., & Panchyshyn, R. (1995). Necessary vocabulary for developing
mathematical concepts. Childhood Education, v72, 80-83.
Palumbo, A., & Loicacono, V. (2009). Understanding the causes of intermediate
and middle school comprehension problems. International Journal of
Special Education, 24(1), 75-81. Retrieved from
http://www.internationaljournalofspecialeducation.com/
41
Pierce, M. E., & Fontaine, L. M. (2009). Designing vocabulary instruction in
mathematics. The Reading Teacher, 63(3), 239-243. doi:
10.1598/RT.63.3.7
Spencer, B. H., & Guillaume, A. M. (2006). Integrating curriculum through the
learning cycle: Content-based reading and vocabulary instruction. The
Reading Teacher, 60(3), 206-219. doi: 10.1598/RT.60.3.1
Appendices
43
Appendix A
Principal Consent Form
I. Research Background (to be completed by researcher)
Title of the Study: The effects of direct instruction of vocabulary in geometry.
Name of Researcher: Heather Kostelecky
Phone: (701) 323-4600
Street address: 4707 Feldspar Dr.
State: North Dakota Zip: 58503
City: Bismarck
E-mail: heather_kostelecky@bismarckschools.org
II. Description of Research Proposal
Researcher is to provide the principal with a copy of the executive summary and the time
requirement form.
III. Agreement (to be completed by principal)
I, ___________________________, principal of _______________________school, understand
• the study and what it requires of the staff, students, and/or parents in my school,
• that the privacy and confidentiality of any staff or student will be protected,
• that I have the right to allow or reject this research study to take place at my school,
• that I have the right to terminate the research study at any time,
• that I have the right to review all consent forms and research documents at any time during
the study and up to three years after the completion of the study.
I grant permission to the researcher to conduct the above named research in my school as
described in the proposal.
I DO NOT grant permission to the researcher to conduct the above named research in my
school as described in the proposal.
I understand that data should be released only by the departments that own them. My staff
and I shall not release data to the researcher without approval from the IRB.
________________________________
Signature of Principal
44
Appendix B
Parent Consent Form
The Effects of Direct Teaching of Vocabulary in Geometry
Invitation to participate: Your child is invited to participate in a study
researching the effects of direct instruction of vocabulary in geometry. This study
is being conducted by Heather Kostelecky, mathematics instructor at Simle
Middle School, and a graduate student at Minot State University.
Basis for Subject Selection: Your child has been selected because he/she is in
Mrs. Kostelecky’s geometry class at Simle Middle School. Your child’s class was
chosen because it is the only geometry class being taught by Mrs. Kostelecky
during the semester of the research study. If everyone agrees to participate there
will be 26 students who meet the criteria for the study.
Overall Purpose of Study: The purpose of this research study is to examine the
effects of direct instruction of vocabulary on the geometry curriculum. In previous
years, vocabulary has been taught in the geometry class along with the
mathematics. The study will examine how emphasizing the importance of
vocabulary, and making it more of an integral part of the geometry curriculum,
affects student knowledge.
Explanation of Procedures: If you decide to allow your child to participate, your
child will be asked to do the following:
a. Take a survey regarding their views on vocabulary before and after the
study.
b. Take a pre-test before and a post-test after the study.
c. Be available for teacher observation.
The identity of all participants will remain confidential. All research will be done
in the classroom. The implementations will occur during the third quarter of the
2010-2011 school year.
Potential Benefits: Students will have a better vocabulary background for
geometry, which will help them understand new concepts. They will also be
exposed to activities that could help them review vocabulary terms in the future.
45
Alternatives to Participation: If you decide to not all your child to participate,
he/she will still take the same pre- and post-tests to demonstrate growth, but the
data will not be recorded. Your child will also be excused from the survey before
and after the study.
Assurance of Confidentiality: The identity of all participants and their data will
remain confidential and stored in a locked file cabinet or on a password-protected
computer. Any data collected will not be linked to the participants or the school
district in any way. Following the study and completion of my master’s degree,
all data will be destroyed.
Withdrawal from the Study: Your child’s participation is voluntary. Your
decision whether or not to allow your child to participate will not affect his/her
grade. If you decide to allow your child’s participation in the study, you are free
to withdraw your consent and discontinue participation at any time.
Feel free to ask questions now or at any time during the study. If you have
questions, you can contact Heather Kostelecky at 323-4600 or
heather_kostelecky@bismarckschools.org. If you have questions about the right
of research subjects, contact the Chairperson of the MSU Institutional Review
Board (IRB), Brent Askvig at 701-858-3052 or Brent.Askvig@minotstateu.edu.
Guardian Consent:
You are voluntarily making a decision whether or not to allow your child or
legal ward to participate. You signature indicates that, having read and
understood the information provided above, you have decided to permit your
child or legal ward to participate. You will be given a copy of this consent
form to keep.
_______________________________
Participant (please print student name)
_______________________________
______________________________
Signature of Parent or Guardian
Relationship to subject
_______________________________
________________
Researcher’s Signature
Date
Date
46
Appendix C
Student Assent Form
The Effects of Direct Teaching of Vocabulary in Geometry
Invitation to participate: You are invited to participate in a study researching
the effects of direct instruction of vocabulary in geometry. This study is being
conducted by Heather Kostelecky, mathematics instructor at Simle Middle
School, and a graduate student at Minot State University.
Basis for Subject Selection: You have been selected because you are in Mrs.
Kostelecky’s geometry class at Simle Middle School. Your class was chosen
because it is the only geometry class being taught by Mrs. Kostelecky during the
semester of the research study. If everyone agrees to participate there will be 26
students who meet the criteria for the study.
Overall Purpose of Study: The purpose of this research study is to examine the
effects of direct instruction of vocabulary on the geometry curriculum. In previous
years, vocabulary has been taught in the geometry class along with the
mathematics. The study will examine how emphasizing the importance of
vocabulary, and making it more of an integral part of the geometry curriculum,
affects student knowledge.
Explanation of Procedures: If you decide to participate, you will be asked to do
the following:
a. Take a survey regarding your views on vocabulary before and after the
study.
b. Take a pre-test before and a post-test after the study.
c. Be available for teacher observation.
Your identity will remain confidential. All research will be done in the classroom.
The implementations will occur during the third quarter of the 2010-2011 school
year.
Potential Benefits: You will have a better vocabulary background for geometry,
which will help understand new concepts. You will also be exposed to activities
that could help review vocabulary terms in the future.
47
Alternatives to Participation: If you decide not to participate, you will still take
the same pre- and post-tests to demonstrate growth, but the data will not be
recorded. You will also be excused from the survey before and after the study.
Assurance of Confidentiality: Your identity and data will remain confidential
and stored in a locked file cabinet or on a password-protected computer. Any data
collected will not be linked to you or the school district in any way. Following the
study and completion of my master’s degree, all data will be destroyed.
Withdrawal from the Study: Your participation is voluntary. Your decision to
participate will not affect your grade. If you decide to participate in the study, you
are free to withdraw your consent and discontinue participation at any time.
Feel free to ask questions now or at any time during the study. If you have
questions, you can contact Heather Kostelecky at 323-4600 or
heather_kostelecky@bismarckschools.org. If you have questions about the right
of research subjects, contact the Chairperson of the MSU Institutional Review
Board (IRB), Brent Askvig at 701-858-3052 or Brent.Askvig@minotstateu.edu.
You are voluntarily making a decision to participate. You signature indicates
that, having read and understood the information provided above, you have
decided to participate. You will be given a copy of this consent form to keep.
_______________________________
Participant (please print name)
_______________________________
________________
Signature of Participant
Date
_______________________________
________________
Researcher’s Signature
Date
48
Appendix D
Vocabulary Survey
Please circle the best number representing your answer for questions 1 through 3.
1 = Never, 2 = Rarely, 3 = Sometimes, 4 = Frequently, 5 = Everyday
1. I have studied vocabulary in math class.
1 2 3 4 5
2. I review vocabulary on my own.
1 2 3 4 5
3. It helps when the teacher explains the definition to me.
1 2 3 4 5
Please circle the best number representing your answer for questions 3 and 5.
1 = Never, 2 = Somewhat, 3 = Often, 4 = Always
4. I understand the definition of words in the textbook.
1 2 3 4
5. I think vocabulary is important in math.
1 2 3 4
Answer the following questions as completely as possible.
6. Describe methods or activities previous math teachers have used to teach
vocabulary.
7. Describe the most effective methods you have used to learn vocabulary in any
class.
8. Explain a situation where knowing vocabulary in math helped you.
49
Appendix E
Pre and Post Test
Name: ______________________
Read each vocabulary word(s). After each word fill in the ONE box that best
shows your knowledge of the word(s). If you know the word(s), think you know
something about it, or have seen or heard of it, make sure to explain it.
Word
Know It Well
Know
Have Seen or
Do
Explain It Or
Something
Heard of it
Not
Use It In a
About It
Explain what
Know
Sentence
Explain It Or
you know
Relate It To
Something
Parallel lines
Skew lines
Parallel planes
Transversal
Corresponding
angles
Alternate
interior angles
Alternate
exterior angles
Consecutive
interior angles
Paragraph proof
Slope
Slope-intercept
form
Standard form
Distance from a
point to a line
Scalene triangle
50
Isosceles
triangle
Equilateral
triangle
Acute triangle
Right triangle
Obtuse triangle
Equiangular
triangle
Interior angles
Exterior angles
Corollary
Congruent
figures
Corresponding
parts
Hypotenuse
Legs of
isosceles ∆
Vertex angle
Base angle
Transformation
Translation
Reflection
Rotation
51
Appendix F
IRB Approval Letter