**B.S.Ed with a major in Mathematics**

BSE in Mathematics requires 128 hours minimum

Credits are Semester Hours

**North Dakota State Standards 8.17 (Mathematics)**

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8.17.1 The program requires problem solving and mathematical reasoning. The program uses varied performance assessments of candidates’ understanding and abilities to apply that knowledge.**

Math 165 In Calculus I students are expected to solve a variety of problems, both abstract and applied, using symbolic, numeric, and graphic methods. Students are required to construct proofs of elementary theorems. Students’ ability to solve problems and write proofs is assessed using homework assignments, examinations, and in-class presentations.

Math 166 Students solve real world problems using techniques of integration and series representations of analytic functions. Students’ ability to solve problems is assessed using homework assignments, examinations, group discussion, and in-class presentations.

Math 205 Math Proof and Problem Solving provides a solid foundation for mathematical reasoning by requiring direct proofs, indirect proofs, proofs by contradiction, proofs by cases, and mathematical induction proofs. Students learn to think mathematically and to communicate mathematical arguments to others. The students’ problem solving and reasoning skills are assessed through class questions and discussion, homework, and examinations.

Math 265 Students solve real world problems using one and several variable calculus. Students are assessed through homework assignments, examinations, group discussion, and in-class presentations.

Math 305 In Linear Algebra students are expected to solve a variety of problems, both abstract and applied, using symbolic, graphic, and numeric methods. Students are required to construct proofs of problems to demonstrate their ability to reason mathematically. Techniques for proving theorems and proof writing style are an important part of the course. Students’ ability to solve problems and write proofs is assessed using homework assignments, examinations, and in-class presentations.

Math 320 Students are required to prove assertions both formally and informally. They are required to develop and investigate conjectures about properties of integers. They are required to demonstrate understanding of fundamental computational techniques such as calculation of greatest common divisor, testing for primality and finding a prime factorization, solving linear equations and inequalities, and calculating Legendre symbols. They investigate the application of number theory to cryptography and related issues of secure transmission of data. Assessment vehicles include examinations, homework with occasional informal solutions, and discussion of problems presented in class.

Math 330 In College Geometry, students are required to construct proofs of various theorems so as to demonstrate valid mathematical reasoning. Students’ ability to write proofs is assessed through homework assignments, examinations, and in-class presentations.

Math 445 Probability and Statistics in especially rich in problem solving. In order to solve a variety of probability problems, students are forced to apply their knowledge of probability distributions to new situations. Often they cannot simply find the right formula, but instead, must adapt their knowledge to new situations. This requires problem solving and mathematical reasoning. The students’ reasoning skills are assessed through in-class questions and discussion, homework, and examinations.

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8.17.2 The program includes the study of mathematical connections, communication and representation. The program uses varied performance assessments of candidates’ understanding and abilities to apply that knowledge.**

Math 165 In Calculus I, students study the interplay of algebra and geometry. They connect what they learn through applications to engineering, chemistry, physics, biology, economics, and other natural and behavior sciences. They are assessed using written examinations and homework assignments.

Math 166 In Calculus II students explain, verbally and in writing, the steps that they used to solve problems. Students are assessed through homework and peer assessment.

Math 205 Math Proof and Problem Solving makes mathematical connections between the dual systems of sets, logic, and Boolean arithmetic. For example, students often represent a set problem as a logic problem before completing the proof. The students’ use of connections and representations are assessed through class questions and discussion, homework, and examinations.

Math 265 In Calculus III students explain, verbally and in writing, the steps that they used to solve problems. Students are assessed through homework and peer assessment.

Math 305 In Linear Algebra, students learn to write proofs. They also learn applications to engineering, chemistry, physics, biology, economics, and other natural and behavioral sciences. Their ability to write proofs and solve applied problems is assessed using written tests and homework assignments.

Math 320 Students are encouraged to develop solutions to problems in self-selected groups. Some class time is devoted to discussion of problems and concepts using class and small group discussion. Assessment includes homework and examinations.

Math 330 In College Geometry, students outline and explain the proof processes that they use both verbally and in writing. Students construct a proof, write it on the front board, explain their proof to the rest of the class, and are then assessed by their peers. Some homework problems and exam questions require students to explain or outline a proof.

Math 380 In History of Mathematics students relate modern day concepts to ancient ideas. For example, completing the square and solving simple algebraic equations are demonstrated geometrically as it was done over 2000 years ago. Students are assessed through in-class questions, homework, and examinations.

Math 391 In Math 391 students spend quite a bit of time learning how to incorporate writing into the mathematics curriculum. Students learn how to use cooperative learning strategies to foster discourse between students in their mathematics classrooms.

In their lesson plans students are encouraged to find links to other disciplines and develop problems that illustrate the connections of mathematics to the other disciplines and to other topics in mathematics. They are assessed through in-class discussion, formal writing assignments, oral presentations, and evaluation of their lesson plans.

Math 445 Probability and Statistics requires students to connect the mathematics in other courses to the setting of probability and statistics and to connect mathematics to the real world. For example, with continuous distributions, calculus is connected to probability as a necessary tool. In statistics, sampling theory connects mathematics to the real world. The students’ skills are assessed through class questions and discussions, a project, homework, and examinations.

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8.17.3 The program requires candidates to demonstrate an understanding of the concepts of school mathematics including algebra and function, number and operation, geometry, statistics, probability, and measurement. The program uses varied performance assessments of the candidates’ understanding and abilities to apply that knowledge.**

Math 165 It is in calculus that students are expected to master the use of algebra and further develop the concept of function. In addition, algebraic geometry becomes an essential tool for students to fully comprehend calculus. Students are assessed through in-class questions, homework, and examinations.

Math 166 It is in calculus that students are expected to master the use of algebra and further develop the concept of function. In addition, algebraic geometry becomes an essential tool for students to fully comprehend calculus. Students are assessed through in-class questions, homework, and examinations.

Math 205 Math Proof and Problem Solving requires candidates to demonstrate an understanding of the concept of function. For example, the cardinality of sets requires that students find a one-to-one function between two sets in order to claim that they have the same cardinality. In Math Proof and Problem Solving, students must use the vocabulary of function and the concepts of one-to-one, onto, into, composite, and inverse functions. The students’ are assessed through class questions and discussion, homework, and examinations.

Math 265 It is in calculus that students are expected to master the use of algebra and further develop the concept of function. In addition, algebraic geometry becomes an essential tool for students to fully comprehend calculus. Students are assessed through in-class questions, homework, and examinations.

Math 320 Students study the fundamental properties of the integers, including unique factorization, the distribution of primes, and properties of congruence. Assessment includes homework and examinations.

Math 330 Students in College Geometry study the properties of lines and angles, parallel lines, triangles and congruence, quadrilaterals, similar triangles, circles, measurement, and area. They are assessed through in-class questions, homework, student construction of proofs on the front board of the classroom, examinations, and Geometer’s Sketchpad assignments.

Math 445 Probability and Statistics, as the name applies, requires candidates to demonstrate an understanding of the concepts of probability and statistics. Candidates demonstrate their knowledge both verbally and in writing. Other concepts reinforced in the course include algebra and function, number and operation, geometry, and measurement. For example, probability distributions are generally represented visually as well as verbally. The students’ skills are assessed through class questions and discussion, homework, and examinations.

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8.17.4 The program requires the study of the core mathematics content including calculus, axiomatic geometry, linear and abstract algebra, analysis, statistics, probability, and compute programming. The program uses varied performance assessments of students’ understanding and abilities to apply that knowledge.**

Math 165 In Calculus I students study limits, continuity, differentiation, the intermediate value and mean value theorems, indefinite integrals, and definite integrals. Students are assessed using written examinations and homework assignments.

Math 166 In Calculus II students study applications of the integral, methods of integration, polar equations, sequences, series, and power series. Students are assessed through homework and peer assessment.

Math 205 Math Proof and Problem Solving develops abstract algebra in the context of mathematical proofs. Students use their ability to write mathematical proofs to prove concepts of abstract mathematics. The students’ skills are assessed through in-class questions and discussion, homework, and examinations.

Math 265 In Calculus III students study functions of more than one variable, multiple integrals, line integrals, and Green’s and Stokes theorems. They use matrices and basic geometric ideas to simplify or formulate results obtained from the study of Calculus III. Students are assessed using homework assignments, in-class presentations, and examinations.

Math 305 In Linear Algebra students study vector spaces, subspaces, linear transformations, matrices, eigenvalues and eigenvectors, and vector geometry. They are assessed through homework, examinations, and in-class discussion.

Math 320 Students investigate ring and field properties of integers modulo n which are topics in abstract algebra. Students are assessed through in-class questions.

Math 330 In College Geometry students study traditional Euclidean geometry, area and volume relationships, and measurement. They are assessed through homework, examinations, Geometer’s Sketchpad assignments, and in-class questions.

Math 445 Probability and Statistics requires the study of the core mathematics content of probability and statistics. Multiple discrete and continuous probability distributions are studied. This knowledge is applied to statistical sampling and interpretation of results. The students’ skills are assessed through in-class questions and discussion, homework, and examinations.

Note: Students are required to take at least 3 credit hours of computer programming and are assessed through programming assignments, in-class discussion, and examinations.

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8.17.5 The program requires the study of the history and philosophy of mathematics. The program uses varied performance assessments of candidates’ understanding and abilities to apply that knowledge.**

Math 205 Students who complete Math Proof and Problem Solving investigate some of the famous (historical) mathematical proofs such as proving that is irrational. The students are assessed through in-class questions and discussion, homework, and examinations.

Math 330 In College Geometry, students study traditional Euclidean geometry. Ancient Greeks who contributed to the development of geometry are discussed during lecture and students view videos that reinforce this knowledge. Students are assessed through in-class discussion and examinations.

Math 380 Students in the History of Mathematics course write two papers. For the first paper they are asked to define mathematics and support this definition using historical evidence and philosophical viewpoints. This leads students to develop their own philosophy of mathematics. For the second paper students write about the life of a famous mathematician. Students must also outline and explain a famous theorem that was proven by the mathematician who they chose to write about. Students are assessed through writing assignments, oral presentations, in-class projects, and examinations.

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8.17.6 The program requires the appropriate use of technology. It requires the study, selection, and use of concrete materials to help students build understanding of mathematical concepts. The program uses varied performance assessments of candidates’ understanding and abilities to apply that knowledge.**

Math 165 Students learn to use the Texas Instruments TI-89 graphing calculator to help them understand calculus concepts through numeric, graphic, and symbolic representations. In addition, they use the calculator as a programmable computer. They are assessed through homework assignments and examinations.

Math 166 Students continue to use the Texas Instruments TI-89 graphing calculator in Calculus II to help them understand calculus concepts through numeric, graphic, and symbolic representations. Students also use the calculator as a programmable computer. They are indirectly assessed through their use of technology on homework assignments and examinations.

Math 265 Students learn to use the Texas Instrument TI-89 graphing calculator to graph functions in 3-D so that they can visualize concepts related to area and volume. With the help of the calculator, students can solve problems involving tedious differentiation and integration computations. They are indirectly assessed through their use of technology on homework assignments and in-class activities.

Math 330 Students learn to use the Geometer’s Sketchpad in College Geometry. At least once every other week they work on lab assignments using this software. The lab assignments are used to introduce students to theorems that they will prove in the near future. Students are assessed by observation them at work and through lab reports that they turn in on disk.

Math 391 In Math 391 students are introduced to MathType, an equation editor that works with word processing software. Students learn to use spreadsheets both for instruction and grade management. Other technology used in Math 391 includes graphing calculators, Geometer’s Sketchpad, calculator based lab equipment, the Texas Instruments Ranger, and the Internet. The students learn to use all of these technologies for instructional purposes. They are assessed through in class presentations, use of the technology in their teaching activities, and formal projects utilizing those technologies.

Math 445 For Probability and Statistics students are required to use the graphing calculator (TI-83) and computer (Minitab) as tools. With these tools real world data sets can be evaluated, rather than using simplified and/or fictitious data sets. The use of technology and real data results in the development of deeper conceptual understanding and the ability to apply this knowledge to the real world. The students’ skills with technology are indirectly assessed when students use technology on their homework and examinations.

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8.17.7 The program requires the study of a variety of teaching methods and strategies. The program uses varied performance assessments of candidates’ understanding and abilities to apply that knowledge.**

Math 391 Students are asked to use a variety of teaching strategies in the lesson that they present in class. Strategies used include lecture, cooperative learning, discussion, team teaching, peer tutoring, and writing to learn. Students learn about good questioning techniques, how to address various learning styles (including visual, auditory, and kinesthetic tasks), and how to engage their students in the learning process. Assessment tasks include teaching of lessons, writing of lesson plans, discussion of observation of other teachers in the practicum experiences.

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8.17.8 The program requires the study of formative and summative assessment strategies to determine students’ understanding of mathematics and to help candidates monitor their own teaching effectiveness. The program uses varied performance assessments of candidates’ understanding and abilities to apply that knowledge.**

Math 391 Formative assessment is examined as they write and teach their lesson plans in the classroom. Students are expected to walk around the classroom while their students are engaged in developmental activities to determine the level of proficiency obtained by each student. Students learn how to ask effective questions to ascertain the depth of understanding of a particular concept by a particular student. They learn how to incorporate higher level thinking activities in their lessons. For summative evaluation of student learning, the students learn how to write and use appropriate scoring rubrics for tests, homework, and projects. After teaching a lesson in class, feedback on the effectiveness of their teaching and the quality of the lesson is given by their peers and by the students who were brought in to be their students. Students examine and score 25 problems that are examples of student work. Scoring results are compared on each problem with their peers and their teacher and rationale for the scores is examined. During this activity the students begin to examine student error patterns and begin to decide what value they place on various types of errors. During this course students are taken to a professional development conference in mathematics where they have an opportunity to interact with practicing mathematics teachers. They also have an opportunity to learn about some good activities that can engage students in the learning process more effectively. Students are asked to read and report on four professional journal articles. These articles address various aspects of teaching, assessing, and engaging the students in mathematical endeavors.