Guidelines for the Ph.D. Qualifying Process in Mathematics Education

Prior to beginning a doctoral dissertation and at or near the time of completion of all coursework, all Ph.D. students in the School of Education must pass a qualifying examination in their major and minor areas of study. For students in the mathematics education doctoral program, this examination takes the form of a qualifying portfolio and an oral examination (a). The qualifying portfolio is intended to assess the student’s understanding of major concepts and issues in mathematics education as well the breadth and depth of her or his preparation in the field. Taken together, the portfolio and the oral are meant to demonstrate that the student is ready to undertake independent research; that is, that the student is qualified to conduct a doctoral dissertation.

SIZE AND FORMAT

In order to insure that the same standards are expected of all students, each portfolio will be about the same size and will have the same general format. Specifically, each portfolio will meet the following requirements:

1. The entire portfolio must fit in a single one-inch notebook.
2. The first page must be a title page.
3. Page 2 must be a table of contents page indicating the main sections of the portfolio and including the page number on which each section begins. (b)
4. Each section of the portfolio must begin with a page describing the purpose of the entries included in that section, together with a brief reflection about that section. (c)
5. Section dividers must be included to insure easy identification of the beginning and end of each section.

(a) For minors inside the School of Education, the student's minor representative will decide what sort of qualifying process (test, portfolio, papers, etc.) suffices. For minors outside the School, the minor representative has the option of requiring some sort of qualifying process or waiving it.

(b) A template for the Table of Contents is given at the end of this document.

(c) A section may contain more than one entry. An entry within a section is a piece of evidence used to document the student's competence in an area.

DUE DATE

A student will negotiate the due date for completion of the qualifying portfolio with members of her or his program advisory committee and in consultation with her or his advisor.

PORTFOLIO ASSESSMENT & ORAL EXAMINATION

All members of the faculty of the Mathematics Education Program will have the opportunity to read and provide comments on a student's portfolio. Mathematics education faculty members of the student's program advisory committee are expected to assess the portfolio. Minor area representatives can read and assess the portfolio if they choose to do so. All faculty members who assess it will use the same rubric for the portfolio. The quality of a portfolio will be based on the following sorts of criteria: (1) breadth of familiarity with the literature in the areas included in the portfolio, (2) depth of understanding of the literature in the areas included in the portfolio, (3) ability to express oneself clearly, coherently, and in a convincing manner, and (4) insightfulness of reflections.

After all faculty evaluations have been completed, an oral examination will always be held. The student's advisory committee will determine the specific nature of the oral examination, but it will always include discussion of concerns and questions about particular entries in the portfolio, as well as opportunities for the student to demonstrate an ability to "think on her or his feet."

FINAL EVALUATION

Upon completion of the oral examination, the student's program advisory committee will determine whether the quality of the student's portfolio and her or his performance on the oral examination warrant passing the student on the qualifying process. A pass will indicate that once the student has completed all necessary coursework, he or she will be admitted to candidacy (D). If the decision is that the student has not passed the qualifying process, the committee will select from among the following options: (1) ask the student to redo all or some potions of the qualifying portfolio, (2) ask the student to retake the oral examination on a future date after completing certain tasks, (3) a combination of options 1 and 2, and (4) inform the student that he or she is dismissed from the doctoral program.

(D) Admission to candidacy designates that the student is eligible to begin work on a doctoral dissertation.

AREAS OF COMPETENCY

The portfolio must document competency in each of the following areas:

Substantial work with inquiry in education (e.g., via a paper based on the early research experience, documentation of involvement with research during an internship, a research paper from a course).
Work related to at least three different N716 seminars taken by the student, with the sort of evidence to be decided via negotiation with the faculty member who taught that seminar (e.g., via a paper written for an N716 seminar, an original paper written since taking a seminar but related to the topic of the seminar, a sit-down test on questions relating to a seminar topic).
Substantial work done in the area of teacher education-either K - 8 or K - 12, depending on the student's program emphasis (e.g., via selected instructional material used in teaching an undergraduate methods course, material developed for use in a professional development workshop, a paper related to theoretical or philosophical issues in teacher education).

PORTFOLIO CONTENTS

The portfolio should include the following required entries as evidence of the competencies discussed above:

Personal information. A current curriculum vitae and any letters of reference that speak to the student's growth and development in some area.
Section reflections. A reflection on each section of the portfolio. (Note. The section containing the "synthesis reflection" need not contain a section reflection.)
Section descriptions. Descriptions of the purpose of the entries included in each section.
Synthesis reflection. A "synthesis reflection" tying together all of the student's work to date and connecting that work to the student's professional goals. [Refer to "Synthesis Reflection" below.]
Original writing. At least one new, original piece of writing.
Student's choice. At least one entry entitled "student's choice." Possibilities include, but are not restricted to: a published or publishable paper, a literature review related to a dissertation, a significant piece of curriculum development work, or a particularly creative web design.
SYNTHESIS REFLECTION

The portfolio must include a written reflection tying together all of the student's work to date and connecting it to professional goals. This reflection should situate the student's work and orientation within the professional literature. It should present a coherent account of the student's vision of herself or himself as a member of the professional mathematics education community, and should also orient reviewers to the samples of work in the portfolio. The reflection should call attention to salient features of the samples of work and also call attention to other relevant accomplishments of the student. The reflection should include a discussion of how each sample in the portfolio is indicative of the student's professional growth and development, especially with respect to competence in designing and conducting empirical research or other forms of scholarly inquiry in the field, or in developing curricular or pedagogical innovations built on sound principles. The reflection should conclude with a discussion of the student's professional plans and intended contributions to the field of mathematics education.

EVIDENCE x COMPETENCIES MATRIX

As indicated above, the portfolio will include entries of several kinds, with each entry serving as evidence of competency in some area. The following matrix, which is intended as a guide to the student in preparing the portfolio, lists various types of entries and competencies to be demonstrated. During preparation of the portfolio, a student can use this matrix to match evidence (entries) and competencies and to identify competencies for which evidence is still needed. For example, a student might notice that he or she does not have any evidence to support competencies in teacher education, even though he or she has included an entry for each type of evidence. This would necessitate the identification of an additional piece of evidence, perhaps an original paper. This matrix should be placed at the end of the portfolio, with checkmarks indicating the match between evidence and competencies. [Note. It is not necessary that every cell of the matrix be filled.]

Table 1
Evidence x Competencies Matrix

Competencies

Evidence Inquiry Work N716 Seminar I N716 Seminar II N716 Seminar III Teacher Education
Personal Information

Section Reflections

Synthesis Reflection

Original Writing

Student's Choice

PORTFOLIO PREPARATION

Because the portfolio is intended in part as evidence that the student is prepared to undertake independent inquiry, the faculty of the Mathematics Education Program and minor area representatives on the student's committee should not assist the student in any way in preparing any materials that will be included in the portfolio(e). No faculty member, including the student's advisor, will read or react to drafts of papers or other materials being considered for the portfolio. The only exception to this policy is that the student's advisor may help the student conceptualize the portfolio. Students may consult with other students or non-mathematics education faculty as they prepare materials for their portfolios.

(e) Of course, some materials will have been produced previously under the direction of or with assistance from faculty members.

SAMPLE TABLE OF CONTENTS

A sample Table of Contents is shown on the next page as an aid in preparing the portfolio. This sample also illustrates the importance of organizing the contents of the portfolio in a way that will make it easy for the reader to determine the competencies a particular entry is evidence of.

Sample Table of Contents: 1 original pieces of writing, 3 student's choice papers, 1 set of teacher education materials

QUALIFYING PORTFOLIO OF WINIFRED S. MCARTHUR

Table of Contents
 
1. Personal Information 3
Curriculum vitae
Letters of reference
Professor J. P. Lewis
Ms. R. T. Sanchez

2. Synthesis Reflection 11

3. Inquiry 17
Purpose
Original paper
Section reflection

4. N716 Seminar I (Critical Theory) 30
Purpose
Revision of seminar paper
Section reflection

5. N716 Seminar II (Philosophy of Mathematics Education) 46
Purpose
Revision of seminar paper
Section reflection

6. N716 Seminar III (History of Mathematics Education) 67
Purpose
Unrevised seminar paper
Section reflection

7. Teacher Education 89
Purpose
Materials developed for Educate Indiana workshops
Section reflection