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MATH 5393:


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

TechnologyEquityWriting across the curriculumStandardized testingClassroom disciplineMulticulturalismSpecial populationsDiversityProblem solvingMathematical attitudes/beliefsAfterschool mathematicsCognitive conflict

Concept maps

Graduation ratesReading and mathematicsInternational educationBilingual educationMathematical anxiety Student autonomyPreservice teachersGender studiesDistance learningAccessible mathematics Learning in museumsFamily 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.

Choose the main concept or issue for your study and list words or phrases that describe it (tutoring, algebra, assessment, technology, etc).

List words or phrases that describe your population or sample space (seventh graders, ELL learners, AP students, struggling learners, GT students, etc).

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”



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.



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).



  • 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 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.

Research objectives determine the direction of the thesis research. They specify goals to be achieved. They are frequently used in surveys.


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.


Fraction concepts are difficult for middle school students.

Middle school students have misconceptions and resulting common errors with fraction operations.

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 or 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?


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.



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.


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.



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 (
  • Trends in International Math & Science Study (NCES)
  • National Math Advisory Panel (USDE, 2008)