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Advanced Programs for Teachers**

**Mathematics**

The required courses in the Department of Mathematics and Computer Science for a Master of Arts in Teaching: Mathematics, are as follows:

The mission of the MAT: Mathematics program is to advance knowledge in mathematics, mathematics education, and related technology, foster critical and creative thinking, and enhance the vitality of the community of mathematics teachers and learners.

MAT Program Goals

The goals of the MAT: Mathematics program are as follows:

1. To strengthen the content knowledge and pedagogical knowledge and practices of mathematics teachers.

2. To foster a support network among mathematics teachers.

3. To foster reflection on classroom practices with regard to best practices/student outcomes.

4. To develop mathematics teachers as researchers and knowledgeable consumers of research.

5. To develop leaders in mathematics education.

6. To prepare people for doctoral study in mathematics education.

7. To strengthen the knowledge of technology and its application in the teaching of mathematics.

8. To enable teachers to relate mathematics to the real world through problem solving situations.

9. To foster communication of mathematics between teachers, students, community members, and others.

10. To foster an appreciation for mathematics and its history.

MAT Learning Outcomes

Graduates of the MAT: Mathematics program will be able to do the following:

1. Solve problems that require application of their knowledge of algebra, geometry, probability and statistics, mathematical systems, history, and calculus.

2. Call upon a network of mathematics teachers for assistance and encouragement in teaching mathematics.

3. Mentor fellow mathematics teachers and other teachers.

4. Adjust teaching methods based on observations of their own students and their knowledge of research based best practices.

5. Be local, state, or national leaders in mathematics education.

6. Pursue further graduate study.

7. Use technology in the teaching of mathematics.

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9.5.1 Advanced program courses are designed to result in advanced knowledge, skills, and dispositions. The program reflects consideration of the standards for advanced study of the National Board for Professional Teaching Standards (NBPTS), professional specialty associations, and the National Council for the Accreditation for Teacher Education (NCATE).**

Math 501 Introduction to Research in Mathematics/Mathematics Education is designed to help candidates understand and learn how to conduct research. Candidates are introduced to types of research, research methods, review of literature, research methodology, ethics, APA writing style, and the structure of a research paper. Candidates read, critique, perform, and write research. Candidates are assessed for their understanding of research, ability to critique research, and their ability to develop and write a research paper using the following: participation in classroom discussions, activities, and assignments, critiques of research articles, completion and presentation of a written research proposal/project, and critiques of peer proposals/projects.

Math 505 The Fundamental Topics of Advanced Mathematics includes topics from foundational mathematics such as logic and proof, mathematical induction, set theory, relations and functions. It provides a solid foundation for mathematical reasoning by requiring direct proofs, indirect proofs, proofs by contradiction, proofs by cases, and mathematical induction proofs. Candidates also investigate some of the famous (historical) mathematical proofs. The candidates are assessed through class questions and discussion, homework, and examinations.

Math 507 History of Mathematics introduces candidates to the mathematics developed during different historical periods. Candidates see mathematics from the perspective of different historical cultures and can therefore view mathematics through a different lens. Candidates are also introduced to various methods used to approach common mathematics problems. Candidates are assessed through homework, examinations, in-class questions, and writing assignments.

Math 511 Trends in Mathematics Education provides candidates with opportunities to explore current curricular, technical, and teaching methods issues that impact their teaching of mathematics. Candidates also are provided with an overview of the evolution of mathematics teaching in the United States during the 20th century. Candidates are assessed through writing of papers, examinations, in-class discussion, and candidate presentations.

Math 523 Probability and Statistics is designed to do the following: (a) develop candidates’ understanding, knowledge, skills, and values of the methodologies in statistics and probability; (b) develop candidates’ understanding of how probability and statistics are relevant in real-life situations, decision-making processes, research, and the mathematics classroom; (c) teach candidates how to calculate, use, and interpret statistics correctly so that they may use this knowledge when collecting and analyzing data; (d) increase their understanding of various statistical concepts in order to make them knowledgeable readers of research that contains statistical concepts and terms; and (e) enable candidates to use statistical software and related technology to describe and analyze data. Candidates are assessed through homework, exams, a project, and classroom discussion and participation.

Math 540 Geometry is designed to advance the candidates’ understanding of abstract logic, paragraph proofs in Euclidean geometry, isometries, coordinate geometry and circles. Candidates are introduced to historical and alternative methods in each area. The integration of algebra and geometry is emphasized. Candidates are assessed through homework, examinations, small group and/or individual class presentations, and small group and/or individual projects.

Math 565 Calculus for Teachers is designed to advance candidates’ conceptual understanding of calculus and introduce them to various methods for developing those concepts. Emphasis is given to the geometric interpretation of derivative and integrals and to the application of calculus in the real world. Graphs, number tables, and symbolic representations are used to broaden the understanding of fundamental concepts. Candidates are assessed through homework, examinations, in-class questions, and problem solving activities.

Math 580 Advanced Algebra for High School Teachers is designed to advance the candidates’ understanding of graphing functions, transformations, polynomial and rational functions, sequences and series, PMI proofs, and an axiomatic approach to the Naturals using Peano’s postulates. Candidates are introduced to historical and alternative methods in each area. Candidates are assessed through homework, examinations, small group and/or individual class presentations, and small group and/or individual projects.

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9.5.2 The program requires candidates develop the ability to apply research and research methods relevant to the advanced field of study. The program uses a variety of performance assessments of candidates’ understanding and ability to apply that knowledge.**

Math 501 Introduction to Research in Mathematics/Mathematics Education is designed to help candidates understand and learn how to conduct research as preparation for their theses or formal writing projects. Candidates apply their research knowledge by critiquing published research articles and their classmates’ research project. They also write an abbreviated first three chapters of a thesis (introductory chapter, literature review, and methodology chapter), which they present to the class. Candidates are assessed through participation in classroom discussions, activities, and assignments, critiques of research articles, completion and presentation of a written research proposal/project, and critiques of peer proposals/projects.

Math 523 Probability and Statistics introduces candidates to introductory probability and statistics concepts that are used in research, including descriptive and inferential statistics. Candidates apply this knowledge on exams and during a project in which they collect and analyze data. The project culminates in a final written report and oral presentation. Students are assessed using exams, assignments, and the above described project and presentation.

Math 598/599 Candidates in the Formal Writing Project or Thesis undertake research projects in which they either do an action research project or do basic research. Candidates are continually assessed during their writing and a final assessment is made during the defense of the papers or thesis.

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9.5.3 The program requires study of the role of schools in society and the development of positive relationships with families and the larger community. The program uses varied performance assessments of candidates’ understanding and abilities to apply that knowledge.**

Math 511 In Trends in Mathematics Education candidates discuss the role of mathematics in society as well as the need to develop a more mathematically literate population. Candidates develop methods for gaining parental support to encourage their children to take more mathematics. The candidates also explore ways to get their schools to help families support student learning of mathematics, especially with regard to homework. Candidates are assessed through their writing of papers, in-class discussion, and exams.

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9.5.4 The program requires study of advanced teaching strategies and models of teaching relevant to the advanced field of study. The program uses a variety of performance assessments of candidates’ understanding and ability to apply that knowledge.**

Math 507 In History of Mathematics, candidates are introduced to many historical methods for approaching mathematical problems. This provides the candidates with a repertoire of strategies for helping their students to understand mathematical concepts. Candidates are assessed through homework, examinations, in-class questions, and writing assignments.

Math 511 Candidates in Trends in Mathematics Education are introduced to new technologies, shifts in emphasis on various mathematical topics, and new teaching strategies. They have the opportunity to try some of the new technology and discuss how to incorporate it into their teaching. They also discuss what is appropriate vs. inappropriate use of technology by students and teachers in learning or teaching mathematics. Teaching to the most recent standards published by the National Council of Teachers of Mathematics requires some changes in methods for most teachers. These standards and how to meet them are addressed in classroom discussion, papers, exams, and student presentations.

Math 540 In Geometry, multiple strategies for teaching high school students each of the topics covered are investigated. Differentiation by grade level is also addressed for each topic. Small group projects and presentations are used to create and test materials candidates could use with their high school students. Candidates are assessed through homework, examinations, small group and/or individual class presentations, and small group and/or individual projects.

Math 565 The emphasis in Calculus for Teachers is on the use of multiple representations to develop fundamental concepts. These representations include graphs, geometric drawings, data tables, and symbolic representations. This provides candidates with various strategies to help their students learn calculus. Candidates are assessed through homework, examinations, in-class questions, and problem solving activities.

Math 580 Advanced Algebra for High School Teachers addresses grade level appropriate strategies for teaching graphing of functions, transformations, polynomial and rational functions, sequences and series. PMI proofs and an axiomatic approach to the Naturals using Peano’s postulates are generally for more advanced high school mathematics. Candidates are made aware of the transition students must make from high school to entry-level university mathematics. Candidates are assessed through homework, examinations, small group and/or individual class presentations, and small group and/or individual projects.

Math 598/599 Candidates writing the Formal Paper Project, which requires two papers, are required to address how their topics could be used in the classroom or how they impact the teaching of mathematics. Candidates writing Theses are required to demonstrate the relevance of their research to the teaching and learning of mathematics. Candidates for both options are assessed during the oral defense.

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9.5.5 The program requires the use of current, appropriate instructional technologies. The program uses varied performance assessments of candidates’ understanding and abilities to apply that knowledge.**

Math 501 In Introduction to Research in Mathematics/Mathematics Education, candidates are taken to the library for an instructional session regarding how to search for and find resources so that they can conduct their research project and complete the research required of their theses or formal writing projects. During the course, candidates are also instructed on methods for accurately and effectively collecting, recording, storing, and analyzing qualitative and quantitative data. APA writing style and word processing are also discussed to help prepare candidates for their theses or formal writing projects. Candidates are assessed through participation in classroom discussions, activities, and assignments, critiques of research articles, completion and presentation of a written research proposal/project, and critiques of peer proposals/projects.

Math 523 In Probability and Statistics, candidates use statistical software and TI-83 calculators to simulate probability and statistical concepts and to store and analyze data. They use this technology when they complete their projects, and they can use it to analyze the data their theses. Candidates are assessed through homework, exams, a project, and classroom discussion and participation.

Math 565 In Calculus for Teachers, candidates are given the opportunity to use the graphing calculator to develop fundamental concepts. They are able to represent derivatives and integrals both numerically and graphically. In addition, they are provided with programs that compute integrals using Riemann sums, the Trapezoid Rule, and Simpson’s Rule. Candidates are assessed through homework, examinations, in-class questions, and problem solving activities.

Math 540 In Geometry, candidates are introduced to the use of the graphing calculator as a teaching aid. Many problems are solved by traditional techniques, followed by calculator techniques. Candidates are also introduced to Geometer’s Sketchpad as a computer resource for geometrical investigations and constructions. Candidates are assessed through homework, examinations, small group and/or individual class presentations, and small group and/or individual projects.

Math 580 Advanced Algebra for High School Teachers is a graphing calculator based course. Historical techniques are supplemented by calculator-assisted techniques. Geometer’s Sketchpad is utilized for its function capabilities. Candidates are assessed through homework, examinations, small group and/or individual class presentations, and small group and/or individual projects.

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9.5.6 The program requires a field experience related to the area of advanced study. At least a portion of the practicum experience is designed to demonstrate potential impact on P-12 student learning. The program uses varied assessments of practicum performance.**

The MAT: Mathematics program does not completely address this standard. Faculty are in the process of developing a way to do this.

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9.5.7.A.1 The program’s advanced content area specialization study is designed to reflect the standards of the National Board for Professional Teaching Standards and professional specialty association recommendations for advanced study.**

MAT: Mathematics faculty members are familiar with the standards of the National Council of Teachers of Mathematics (NCTM). These standards are discussed in Math 511, Trends in Mathematics Education, and are emphasized in the instruction that candidates receive in other courses.

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9.5.7.A.2 The program’s advanced content area specialization study provides for breadth in the field or for detailed study of one or more specialized aspect of the field, and for access to new research and developments. The program uses a variety of performance assessments of candidates’ understanding and ability to apply that knowledge.**

Candidates are required to take a breadth of courses in the MAT: Mathematics program. The required core courses include: Research in Mathematics/Mathematics Education, Fundamental Concepts of Advanced Mathematics, History of Mathematics, Trends in Mathematics Education, Probability and Statistics, Geometry, Calculus for Teachers, Algebra, and six semester hours of elective courses. Candidates complete a detailed study of at least one area of mathematics and/or mathematics education when they complete a two-credit formal writing project or thesis. The course, Trends in Mathematics Education, exposes candidates to new research, developments, and trends in mathematics education.

Once candidates have completed the required core of courses, they must pass an oral exam that encompasses the material of the required core courses. The thesis or formal writing projects has candidates research an area of mathematics and/or mathematics education, including its relevance to the teaching and learning of students of mathematics.

**Coverage of North Dakota Program Approval Standards for Advanced Programs for Teachers: Advanced Study in a Specialty Area-Master of Arts in Teaching: Mathematics at Minot State University**