MATH 5393
MATHEMATICS EDUCATION
LITERATURE & RESEARCH
METHODOLOGY
MATH 5393:
LITERATURE REVIEW AND
RESEARCH METHODOLOGY
Reading, analyzing, and synthesizing mathematics
education research literature for the purpose of informing
teaching practice. Includes a study of qualitative research
with a focus on the components of a research study
(research question(s), literature review, conceptual
framework, methods, analysis, findings) and the
relationships among them.
This course is part of the MS in Mathematics, Curriculum
Content Option. During this course you will prepare and
defend your proposal for a thesis or graduate project.
A proposal is a document that outlines what your thesis or
project will entail, and serves as a contract between you and
your committee. A clearly written proposal will guide you in
completing your thesis or project and delineate exactly what
must be done to successfully complete it.
After completion of this course, you will enroll in MATH 5995
(thesis) or MATH 5997 (project). During that course you will
do your thesis research or write your curriculum project and
defend it.
At this point in your degree plan, you should have taken the six
core courses (5321, 5325, 5326, 5327, and 5329). This course,
MATH 5393, and MATH 5995/7 are a pair of courses designed
to help you demonstrate what you have learned during your
master’s degree program. Your project or thesis will allow you
to make connections across mathematical topics and between
several fields of discipline.
Because you are more than halfway to graduation, you also
need to make sure you have an approved degree plan on file
with your advisor. A degree check will let you know if you have
any substitutions or other paperwork that is needed before
graduation. Please make an appointment with Ida Olivarez, the
MS Math advisor, to go over your degree plan (or to set-up a
degree plan). Ida can be reached at (361) 825-5797.
What is the difference between a
thesis and a project?
A thesis is a traditional research study. You will choose a
research problem, write hypotheses or research
questions, choose a method to gather data, analyze the
data, interpret the results, draw conclusions and determine
the implications of the study.
A project is a curriculum-based product such as lesson
plans, activities with technology, review materials, or
interactive media for use in the 6-12 mathematics
classroom. The materials should be unique, creative, or
from a new perspective. They should address a concern or
problem in mathematics education.
The Committee
Your committee will consist of a committee chair and two
committee members. The chair and at least one other
member must be from the Department of Mathematics and
Statistics. A third member may be from another college if
appropriate for your topic.
The chair is selected prior to enrollment in MATH 5393, the
committee members are selected before the proposal
defense at the end of the course. Your chair will work with
you on the development of your proposal; the committee will
approve and sign your proposal at your defense.
Mathematics education faculty: Dr. George Tintera, Dr.
Elaine Young, Dr. Sarah Ives, Dr. Joe Champion.
What is a proposal defense?
Your defense is an open meeting where you will present
your proposal to your committee and other interested
parties (faculty, graduate students, family members, etc).
You will create and give a PowerPoint presentation to
present and explain your proposed thesis or project,
followed by questions from the audience.
At the end of your presentation, you and any visitors will
be asked to step out while the committee deliberates.
When you come back in, the committee will either sign
your approved proposal or discuss any needed changes
or corrections.
Creating the Proposal
The proposal follows a specific format, and will use the APA
formatting style (5th edition). Please refer to the Graduate
Guidelines for particulars.
The following sections of the proposal should each begin on a
new page:
Cover page (signature page)
Abstract
Introduction
Related Work and Justification
Planned Actions
End Results Intended
Bibliography
Cover Page
The cover page includes your project title, name, and
places for the committee to sign and date. A sample cover
sheet may be found in the Graduate Guidelines. Follow the
format exactly. (NOTE: the 1.5 inch left margin allows for
binding.)
Choose “thesis” or “project” on the second line.
Only include the last two signature lines if you are writing a
thesis proposal.
Style: APA
Issue or Topic of Concern
The research topic is a broad subject matter within a
discipline. For instance, distance learning is a topic in
mathematics education.
The research problem is a specific concern or issue within
that topic. For example, we may be concerned about the
lack of student social interaction during distance education
classes.
Choose a research topic that appeals to you.
Now narrow the topic to a specific issue or concern for
your research problem. Next you will choose your research
questions or hypotheses.
Possible Topics and Issues
Technology
Equity
Writing across the
curriculum
Standardized testing
Classroom discipline
Multiculturalism
Special populations
Diversity
Problem solving
Mathematical
attitudes/beliefs
Afterschool mathematics
Cognitive conflict
Concept maps
Graduation rates
Reading and
mathematics
International education
Bilingual education
Mathematical anxiety
Student autonomy
Preservice teachers
Gender studies
Distance learning
Accessible
mathematics
Learning in museums
Family Math Nights
Learning styles
Creating a Title
Time to brainstorm! Sit down with a piece of paper, and answer
the question, “My study/project is about…” Then divide another
piece of paper into three columns and do the following activity,
one per column.
1. Choose the main concept or issue for your study and list
words or phrases that describe it (tutoring, algebra,
assessment, technology, etc).
2. List words or phrases that describe your population or
sample space (seventh graders, ELL learners, AP students,
struggling learners, GT students, etc).
3. List words or phrases that describe the research site or
situation (high school, after school program, UIL
competition, museum, etc).
Creating a Title, cont’d
Now mix and match words/phrases from the three
columns to form possible titles. Good titles are brief and
concise, using few articles of speech or propositions.
The title should reflect your style and entice the reader. A
subtitle (with a colon) may be used to position the
research.
Example of a poor title: “The Role of Good versus Bad
Use of Calculators in the Sixth Grade Classroom as it
Effects Math and Reading Scores”
A better title is: “Calculators in Sixth Grade: Effects on
Mathematics and Reading”
Abstract
An abstract is a clear and concise (at most one page)
overview of the planned thesis or project.
Although the abstract is the first part of the proposal, it is
best to wait until the very end to write it. An abstract can
be easily created by combining topic sentences from each
section of the proposal.
One way to think about the abstract is imagine a future
graduate students deciding whether to read your thesis or
project. Given them just enough information in the abstract
to make that decision.
Writing Your Proposal
There are several perspectives to consider when writing
your proposal:
Voice -- use the active voice; you are doing the acting, not
being acted upon.
Strong verbs -- use strong verbs that show action.
Tense -- use past tense to review the literature and future
tense for all other parts of the proposal; the research has
been done and your plan will be done.
Trim fat – watch out for wordiness. Use good grammar and
spelling. Check APA for specific punctuation and formatting.
Introduction
The introduction serves as just that, an introduction to the
issue or concern and your suggested intervention or activity.
The introduction should begin with a hook – something to get
the writer interested in what you are concerned or excited
about. Use a superb quote, an intriguing situation, or exciting
data to help engage the reader.
Toward the end of the introduction, include a purpose
statement. The purpose statement is one or two sentences
that tell the reader exactly what you plan to do.
At the end of the introduction, include your research
questions or hypotheses (thesis), or guiding principles
(project).
Purpose Statement
Qualitative example: The purpose/intent/objective of this __________
(methodology) is to ____________ (strong verb) the ______________ (central
phenomenon being studied) for _____________ (participants) at
_____________ (research site).
Quantitative example: The purpose of this __________ (methodology) is to test
the theory of ______________that compares/relates the ______________
(dependent variable) controlling for ____________ (control variables) for
_____________ ( participants) at ___________ (research site).
Mixed methods example: The purpose of this mixed methods study is to ….
The qualitative/quantitative piece will explore ____________ (central
phenomenon) by collecting ___________ (data type) from ___________
(participants) at ___________ (research site). The second phase will be a
qualitative/quantitative exploration of ___________ (central phenomenon) by
collecting ___________ (data type) from _____________ (participants) at
___________ (research site).
Framework
Each project should include a theoretical or philosophical framework that
will “frame” the study and guide the creation of the project. “A
framework provides a structure for conceptualizing and designing
research studies. In particular, a research framework helps determine:
• the nature of the questions asked;
• the manner in which questions are formulated;
• the way the concepts, constructs, and processes
of the research are defined; and
• the principles of discovery and justification
allowed for creating new "knowledge" about the topic
under study” (Lester, 2005, 458).
Lester, F. K. (2005). On the theoretical, conceptual, and philosophical
foundations for research in mathematics education. ZDM, 37(6), 457-67.
Framework, cont’d
There are many theoretical perspectives which can be used as
a framework, some of which are listed below:
• Embodiment of mathematics
• Steffe’s schemes for understanding fractions
• Van Hiele geometric model
• Vygotsky – social constructivism
• Habits of mind
• Culturally relevant mathematics
• Brousseau’s theory of didactical
situations
Research Rundowns
Hypotheses, Objectives &
Research Questions
Hypotheses are declarative
statements in a quantitative
research thesis which make a
conjecture about the outcome of
a relationship. They are typically
based on past research.
Research objectives determine
the direction of the thesis
research. They specify goals to
be achieved. They are
frequently used in surveys.
Research questions are
interrogative statements that
are specific inquiries the
thesis seeks to answer.
Quantitative research
questions relate variables,
while qualitative research
questions include a central
phenomenon to be explored.
Writing Hypotheses
• State the independent, dependent, control or intervening
variables in order
• Define the groups and explicitly state whether they are
compared or related
• Identify the participants and the research site of the study
• Make a predication about changes or no change and the
statistical procedures to be used for testing
• Write null or alternative hypotheses
Creswell, J. W. (2002). Educational Research: Planning, Conducting, and Evaluating
Quantitative and Qualitative Research. Columbus, OH: Merrill Prentice Hall.
Writing Research Questions
• Pose a question or questions
• Begin with how, what or why
• Specify the independent, dependent, mediating or
control variables (as appropriate
• Use the words “describe”, “compare”, or “relate” to
indicate the action or connection among the
variables
• Indicate the participant and research site for the
study
Creswell, J. W. (2002). Educational Research: Planning, Conducting, and
Evaluating Quantitative and Qualitative Research. Columbus, OH: Merrill Prentice
Hall.
Writing Guiding Principles
Guiding principles are theoretical or philosophical statements
that guide the development of the project and support the
outcome of the product. They are written as declarative
statements.
Example:
1. Fraction concepts are difficult for middle school students.
2. Middle school students have misconceptions and
resulting common errors with fraction operations.
3. Concrete manipulatives aid in learning fraction concepts.
Related Works
This section includes your theoretical framework and a review
of the research literature. Your framework is the philosophical
or theoretical foundation that frames your research or project.
Look for seminal or recent theories that can guide you in your
research and writing.
The literature review should include scholarly research that
relates to your concept or issue. You will need to identify key
words or phrases for your topic and research it through the
library or electronic databases.
Be sure to record a full bibliographic reference for all literature
you use. APA format (5th edition) should become your best
friend!
Related Works, cont’d
The campus library has access to books, journals, and
electronic databases that can be accessed from home. Call
the library to set up your remote access.
You can also access scholar.google.com or scirus.com for
scholarly articles.
Wikipedia is a good place to start for general understanding
such as a theoretical framework, but it is not considered a
valid resource. When you find a topic in wikipedia, scroll down
to the bottom to the references there – they may give you
some good research.
Related Works, cont’d
Things to think about when doing a literature review:
• Limit the scope of your inquiry by searching for
descriptive phrases or words that will narrow the results
to what you need. For example, search “high school” +
“geometry” + “technology”. You can also exclude
common words from your search, for example, “high
school” + “geometry” –proof. The negative sign removes
those results with that word.
• Identify gaps in the research, or possible extensions of
previous research.
• Relate your study to a larger body of knowledge.
Where does your study fit into the research in the field?
Justification
At the end of the Related Works section, add a paragraph to
justify why the proposed work should be considered as a
significant component leading to the receipt of a master’s
degree in mathematics.
Indicate the significance of the issue or concern and how the
thesis will add to the body of research in a new and
significant way, or how the project will address the need(s)
by providing a new and significant product.
Who will benefit from your research or project? How will they
benefit?
Planned Actions
THESIS: this section will include information about the
participants, research site, methodology, measures, and
statistical analyses. Each of these topics will be a
subsection of Planned Actions. Carefully choose your
methodology as appropriate to your hypotheses or research
questions. The measures and statistical analyses will be
drawn from the methodology chosen. The methodology
should also be addressed in the Related Words section of
the proposal.
PROJECT: this section will include detailed steps required
to finish the work. Describe the first and ensuing steps that
will be needed.
Timeline
At the end of the Planned Actions section, include a table
with your proposed timeline. The timeline is a list of
estimated deadlines that helps you focus your efforts toward
defending your proposal and finishing your research or
project on time.
Your proposal defense should happen on or before the last
day of classes that semester. Plan on submitting your final
proposal draft to your committee two weeks before your
defense date.
The timeline covers the entire course of the thesis or project,
from proposal writing to defending the final thesis or project.
Your thesis/project defense should happen on or before the
last day of classes for that semester.
Project Timeline Example
ACTIVITY
DATE
Write proposal
January – March 2010
First draft of proposal to committee chair
15 March 2010
Final draft of proposal to committee
15 April 2010
Defend project proposal
First week of May 2010
Extended literature review
May 2010
Write curriculum materials
May-- June 2010
First draft of project to committee chair
1 Jul 2010
Final draft of project to committee
15 Jul 2010
Defend project
First week of August 2010
End Results Intended
THESIS: this section will reiterate (in general) which
research questions will be answered and how the results
will be used to make suggestions, consider implications, or
illuminate the path of future research.
PROJECT: this section is a clear statement of what will be
produced. Make specific statements about how many, what
kind (for example, which lesson plan type?), and what
format (hard copy, online, CD, etc) the project will take.
Also include your plans for dissemination, which parties
may find the product useful, as well as how it is intended to
be used.
Bibliography
The thesis or project proposal will contain a bibliography of
the articles, books, and other research studies or
foundational documents that you consulted in preparation of
the proposal. You should aim for a minimum of five solid
references for your proposal. A deeper review of the literature
can be done later.
In the final manuscript, you will include a list of References –
only those works which are referenced in the manuscript.
Use APA format (5th edition) for your in-text references and
in the bibliography. You must give credit to the source of any
information, data, or image that you use in your study. This is
usually done at the beginning of the paragraph (if you use
their name) or the end of the sentence or paragraph (if you
rephrase their work).
Common Resources
• Principles and Standards for School Mathematics
(NCTM, 2000)
• Curriculum and Evaluation Standards (NCTM, 1989)
• Texas Essential Knowledge and Skills (TEA, 2009)
• Texas district/school TAKS data (AEIS)
• College and Career Readiness Standards (TEA, 2009)
• National Center for Education Statistics (ed.gov)
• Trends in International Math & Science Study (NCES)
• National Math Advisory Panel (USDE, 2008)