Degree Requirements

Requirements for completing the Ph.D. in Education with a concentration in Mathematics Education include requirements that are common to all areas of concentration and those that are specific to Mathematics Education (see below).

Requirements Common to All Concentrations

Required Courses 

The following courses are required. Specific requirements of the area of concentration in Educational Policy are described later.

Proseminars (6 credits)

• 16:300:501 Proseminar in Educational Theories and Practice
• 16:300:503 Proseminar in Educational Research

*These courses are typically taken in the first year.

• 16:300:509 Qualitative Research Methods in Education I
• 16:300:511 Quantitative Research Methods in Education I, and Either
• 16:300:515 Quantitative Research Methods in Education II
• 16:300:519 Quantitative Research Methods in Education III, Or
• 16:300:513 Qualitative Research Methods in Education II
• 16:300:517 Qualitative Research Methods in Education III

• 16:300:600 Prethesis Research
• 16:300:601 Prethesis Research

Cognate Courses (6 Credits)

Students take 6 credits outside of Education (i.e., outside of courses offered in School 15 and in 16:300). The courses should be in an area related to the students’ primary area of concentration and should be selected in consultation with the student’s advisor.

Specialization (18 credits)

Six graduate courses in the area of concentration must be taken.

The Qualifying Examination Committee is composed of four members of the Ph.D. faculty in Education who work in the specific area of the concentration. Each area of concentration in the Ph.D. in Education program has different requirements for the qualifying examination.

Students complete an original piece of research as their dissertation project (24 credits of 300:701, 702). The research is expected to contribute to the knowledge base in the student’s particular area of interest. Students cannot enroll in Research in Education until they have been admitted as a candidate for the Ph.D. program after passing their qualifying examinations.

Specific Requirements of the Concentration in Mathematics Education

Qualifying Examinations

Last revised February 28, 2003

Prior Qualification

It is understood that this examination is given subsequent to the student’s having substantially completed the required course sequence, passed a preliminary examination addressing knowledge in the field of mathematics, and worked on the development, analysis, preliminary investigation, and application of research methodology to a question in his or her area of interest. Normally this includes a research presentation at Rutgers satisfactory to the examining committee, or alternatively the presentation of a research report at a national or international conference.

Each part of the examination (Part I and Part II) consists of a written examination and an oral examination. Thus we have Part I (written), Part I (oral), Part II (written), and Part II (oral).

The student prepares each written examination over a fixed period (normally one to three months), in response to specific instructions from the examining committee. Each oral examination (normally 2 hours) will be scheduled by the examining committee after the student has successfully completed each written examination.

Each part of the examination is prepared and evaluated separately, with satisfactory performance required prior to the next part.

The written examinations address the following content:

• (1) Coherent description, development, and discussion of a selected mathematical topic or topics extending from the elementary school level through the college undergraduate level [for example, the topics of linear, polynomial, exponential, and logarithmic growth, from both the continuous and discrete perspectives (up to and including differential equations and difference equations)]; and
• (2) Discussion of the applications of the mathematics to appropriate related domains [for example, in the case of growth models, science and economics].

• (3) Critical discussion and comparison of where and how the mathematical topic(s) are introduced at various school levels in standard and in innovative mathematics curricula;
• (4) Discussion of existing research literature that explicitly addresses the learning and teaching of the designated mathematical topic(s), and/or addresses learning and instruction in other areas of mathematics that might have implications for the designated topic(s);
• (5) Discussion and analysis of whether and how one or two themes or theoretical approaches in the mathematics education literature can be applied to instruction in the designated mathematical topic(s) [for example, cognitive analysis and schema theory, information processing models, constructivist theory, symbol-systems and systems of representation, theories of problem solving]; and
• (6) Identification of significant research questions that need to be addressed regarding what, how, and when students should learn about various aspects of the designated mathematical topic(s).

The oral examinations may refer to but are not limited to material in the written examinations. They will also address the following areas: exposition and understanding of mathematical content; curriculum structure and the sequencing of mathematical ideas; theories of learning and mathematical development; growth of mathematical understanding through context-based individual or group experiences; psychology of mathematical problem solving; the design of qualitative or quantitative research studies appropriate to a mathematical domain.

The student is expected to be familiar with published research studies or analyses in these areas, and to be able to substantiate his or her statements with references to the literature.

Policy Regarding Retaking Parts of the Qualifying Examination:

Under normal circumstances, students will be permitted no more than one opportunity to retake each part of the Qualifying Examination.

Information about specific requirements of the concentration in Mathematics Education will be available shortly.