Both of these courses are specifically designed for students planning to teach mathematics

• M360M: Mathematics as Problem Solving focuses on problem solving in subjects of secondary mathematics. Students solve non-routine problems, learn about heuristics for problem solving, and read and discuss parts of the Principles and Standards for School Mathematics. This is an honors course for future teachers. Students need permission of the instructor to enroll. The requirement is grades of B or better in both M404C and D or strong performance in math courses past calculus.
• M326K: Foundations of Number Systems is a course intended for elementary, middle grades, and secondary mathematics teachers. Topics are selected from place value, analysis of arithmetic operations and algorithms for computing them, historical development of numbers and algebra, prime factorization, rational, irrational and transcendental numbers, complex numbers. Emphasis is on conceptual understanding and developing ability to provide both formal proofs and informal explanations. Usually includes reading and discussing portions of the Principles and Standards for School Mathematics.

Both courses address the following parts of Standard II: Patterns and Algebra:

"The beginning teacher of mathematics is able to:

• (2.1s) use inductive reasoning to identify, extend, and create patterns using concrete models, figures, numbers, and algebraic expressions; …
• (2.5s) translate problem-solving situations into expressions and equations involving variables and unknowns;
• (2.6s) model and solve problems … using concrete, numeric, tabular, graphic, and algebraic methods and
• (2.7s) recognize misleading patterns." (p. 6)

Both of these courses (and especially M 360M) address the following items of the Logical Reasoning and Problem Solving parts of Standard V: Mathematical Processes:

"The beginning teacher of mathematics is able to:

• (5.1s) apply correct mathematical reasoning to derive valid conclusions from a set of premises;
• (5.2s) apply principles of inductive reasoning to make conjectures and use deductive methods to evaluate the validity of conjectures;
• (5.3s) use formal and informal reasoning to explore, investigate, and justify mathematical ideas;
• (5.4s) recognize examples of fallacious reasoning;
• (5.5s) evaluate mathematical arguments and proofs; and
• (5.6s) provide convincing arguments or proofs for mathematical theorems.
• (5.7s) recognize that a mathematical problem can be solved in a variety of ways, evaluate the appropriateness of various strategies, and select an appropriate strategy for a given problem;
• (5.8s) evaluate the reasonableness of a solution to a given problem;
• (5.9s) use physical and numerical models to represent a given problem or mathematical procedure;
• (5.10s) recognize that assumptions are made when solving problems and identify and evaluate those assumptions;
• (5.11s) investigate and explore problems that have multiple solutions;
• (5.12s) apply content knowledge to develop a mathematical model of a real-world situation and analyze and evaluate how well the model represents the situation; …" (p 17 - 18)

Both of these courses also address the following items of the Connections and Communication parts of Standard V:

"The beginning teacher of mathematics is able to:

• (5.15s) explore problems using verbal, graphical, numerical, physical, and algebraic representations;
• (5.16s) recognize and use multiple representations of a mathematical concept…
• (5.17s) apply mathematical methods to analyze practical situations; ...
• (5.21s) translate mathematical statements among developmentally appropriate language, standard English, mathematical language, and symbolic mathematics;
• (5.24s) use the language of mathematics as a precise means of expressing mathematical ideas." (pp. 19 - 20)

Since both courses include students planning to teach at a variety of grade levels and include reading for various grade levels from the Principles and Standards for School Mathematics, they contribute to portions of Standard IX: Professional Development:

"The beginning teacher of mathematics is able to:

• (9.2s) exchange information with mathematics teachers at lower and higher grade levels to ensure continuity in students' mathematics education; …
• (9.5s) select materials from appropriate publications produced by professional mathematics organizations to develop lesson plans, instructional activities, and assessments;
• (9.6s) use local organizations and electronic communities as a forum for exchanging, discussing, and evaluating ideas regarding mathematics and mathematical instruction, and as an opportunity for professional self-assessment; …" (p. 26)

The main content focus of M 326K is Standard I: Number Concepts: "The mathematics teacher understands and uses numbers, number systems and their structure, operations and algorithms, …" Click here to see details.

M 326K also addresses the following additional parts of Standard II: Patterns and Algebra and portions of Standard VI: Mathematical Perspectives:

"The beginning teacher of mathematics is able to:

• (2.13s) give appropriate justification of the manipulations of algebraic expressions … (p. 7)
• (2.22s) use deductive reasoning to simplify and justify algebraic processes… (p. , 8)
• (6.1s) use key events and knowledge of specific individuals throughout the history of mathematics to illustrate age-appropriate mathematical concepts; ..
• (6.3s) use historical developments of mathematical ideas to illustrate how mathematics progresses from concrete applications to abstract generalizations …" (p. 21)

M 360M: This course directly addresses the underlying themes of problem solving, language and communication, connections within and outside mathematics, reasoning, justification and proof, and multiple representations that are listed in the Basic Understandings for Algebra I, Geometry and Algebra II, and in the introductions to Precalculus and Mathematical Models with Applications.

M 326K: This course provides depth of mathematical background for teaching the Number, Operation, and Quantitative Reasoning content strand and parts of the Patterns, Relationships, and Algebraic Thinking strand for grades K - 8. It also focuses on the underlying processes of problem solving, communication, connections, and reasoning that run through grades K - 12.

How do these courses relate to the National Council of Teachers of Mathematics' Principles and Standards for School Mathematics?

M 360M includes a major focus on the Problem Solving, Reasoning and Proof, Communication, Connection, and Representation standards of the Principles and Standards.

M 326K includes a major focus on the Number and Operations Standard of the Principles and Standards, and may include reading from some of the other Standards as well.

Both courses can help prepare you for M341, M328K/M343K/M373K and M361K/M365C.

Here are some things to take into account in deciding which of these two courses to take:

• M 360M is recommended for students planning to teach Geometry, Algebra II, Precalculus or Calculus.
• M 326K is recommended for students planning to teach middle grades or Algebra I.
• M 360M has more stringent prerequisites than M 326K (See above).
• M 360M is offered only in the fall.
• M 326K is offered only in the spring.

If you are obtaining the BA, you can only count one of these courses toward your degree. If you are obtaining the BS, you can take both courses and count one toward your additional math hours.

• Remember that these courses are not taught by a lecture method; they require active participation on the part of the student.
• Take advantage of the discussion format of the class to practice your math communication skills.
• Take advantage of the discussion format of the class to listen to other students' ideas. This is a good opportunity to learn how other people learn and think.
• Take advantage of the range of grade level teaching interests in the class to become familiar with the math curriculum at grade levels different from the ones you plan to teach, so that you can teach in a manner that helps integrate math learning across the grades.