Course Syllabus

MATH 2000 Algebraic Reasoning with Modeling

Course Description

Algebraic Reasoning with modeling presents the basic ideas of sets and functions in the context of and motivated by modeling bivariate data. Some basic concepts of the course include the concept of basic set theory such as unions, intersections, Venn diagrams, etc. The course also addresses basic ideas and algebra of functions, including polynomial, exponential, and logarithmic functions. Other topics include basic combinatorics, counting principles, and arithmetic and geometric sequences. The course culminates in a pictorial introduction to the basic ideas of calculus presented with minimal computation.

Justification

Algebraic Reasoning with Modeling provides a synopsis of advanced mathematics for Elementary Education and Special Education majors.  Students learn about what happens in mathematics courses beyond what they would typically be teaching in their classrooms, empowering them to answer the question "what is this used for?" without going into full detail.

General Education Outcomes

1. A student who completes the GE curriculum has a fundamental knowledge of human cultures and the natural world. Mathematics is the language used by many fields and almost every culture to communicate about events and processes that occur in the natural world. Elementary Ed majors will deepen their knowledge of algebra relating to economic, financial, natural science systems, and/or engineering problems as well as other disciplines. This ability to problem-solve in the natural world may be assessed through homework, exams, quizzes, student projects or presentations, etc.
2. A student who completes the GE curriculum can read and research effectively within disciplines. In the field of Mathematics, students must be able to carefully examine a given problem then determine and execute a plan for solving the problem. Often the information given is presented using symbols and variables the student must be able to read and interpret mathematically within the context of the given problem. In addition to learning new concepts, Math 2000 students are encouraged to express their new understanding using various mathematical symbols and visual representations. This ability to read, retrieve, evaluate, interpret, and deliver mathematical information will be evaluated through homework, exams, and, at the instructor's discretion, quizzes, student projects or presentations, etc.
3. A student who completes the GE curriculum can draw from multiple disciplines to address complex problems. In this course, students are expected to develop their ability to analyze a problem, determine an appropriate approach to solve the problem, and then apply their approach to reach a reasonable solution. As they learn new skills to solve mathematical problems, they are also shown how those skills can be used to solve real life problems through a variety of application problems. Specifically in Math 2000 we also look to explore visual mathematics. Exposure to these problems allows students to see how math plays a part in everyday life within different disciplines. This ability to apply a mathematical solving process to solve a real world application problem involving multiple disciplines may be assessed through quizzes, homework, projects, or exams.
4. A student who completes the GE curriculum can reason analytically, critically, and creatively. To be able to solve a mathematical problem a student must first examine what information is given, determine what information is needed, decide what process will best fit the problem to arrive at a conclusion, and then finally decide if the answer reached is reasonable. Through this course students are taught to reason analytically, critically, visually and creatively about different math processes and facts. This ability to reason analytically, critically and creatively may be assessed through homework, exams, quizzes, student projects or presentations, etc.
5. A student who completes the GE curriculum can reason quantitatively.  A course of algebra, consisting of equations and math centered problems will present the student with multiple opportunities to practice and obtain the logical processes of solving and analyzing problems. The ability to reason logically and visually about quantitative values is important to this Math 2000 course. Students are taught to analyze the numerical results and visual information of the equations and application problems they solve. Students then decide if they violate any of the constraints of the problem as well as whether or not the answer is reasonably accurate in context of the application or visual. In addition, students can propose creative, new solutions. Proficiency of these skills may be assessed through homework, exams, and quizzes.

General Education Knowledge Area Outcomes

1. Multiple representations (visual, algebraic, graph, etc.) of information is presented to students in a Math 2000 course. Students are required to extract the information in order to explain the information within them. This ability to explain mathematical information in various forms may, at the instructor's discretion, be assessed through exams, homework, quizzes, student projects or presentations. Multiple representations (visual, algebraic, graph, etc.) of information is presented to students in a Math 2000 course. Students are required to extract the information in order to explain the information within them. This ability to explain mathematical information in various forms may, at the instructor's discretion, be assessed through exams, homework, quizzes, student projects or presentations.
2. Convert relevant information into various mathematical forms (e.g., equations, graphs, diagrams, and tables). Through the use of multiple representations (visual, algebraic, graph, etc.) students in a Math 2000 course practice moving seamlessly through a single problem and looking at all of its facets in equation, graph, diagram and table form. This ability to convert relevant mathematical information into various forms may, at the instructor's discretion, be assessed through exams, homework, quizzes, student projects or presentations.
3. Demonstrate the ability to successfully complete basic calculations to solve problems. An algebra course allows students an almost innumerable number of chances to solve problems using basic calculations. Math 2000 course allows students to take these basic calculations, see them visually, and use them to solve a variety of problems from basic set theory to the basic ideas of calculus. This ability to successfully complete basic calculations to solve problems may, at the instructor's discretion, be assessed through exams, homework, quizzes, student projects or presentations.
4. Demonstrate the ability to problem solve using quantitative literacy across multiple disciplines. Make judgments and draw appropriate conclusions based on quantitative analysis of data, recognizing the limits of this analysis. The algebra student derives many solutions as they solve equations. Math 2000 students will practice interpreting those answers in the context of the stories they are telling using other variables and non-variables as their evidence. This ability to problem-solve in the natural world may, at the instructor's discretion, be assessed through exams, homework, quizzes, student projects or presentations.
5.  Students will demonstrate their ability to express quantitative evidence in support of their conclusions to questions presented in this class by showing how their visual representations relate to step-by-step calculations used to solve given problems. This outcome may, at the instructor's discretion, be assessed through exams, homework, quizzes, and student projects.

Student Learning Outcomes

1. The student will model bivariate data when the relationship is linear and understand the importance and place modeling data has in society and science.
2. The student will use set theory and notation to classify and model collections of different types of data and to compute unions, intersections, and complements, draw and understand Venn diagrams, and represent data as a set.
3. The student will use functions to model the relationship between two sets of data, describe the properties of many different types of functions including polynomial, exponential, and logarithmic functions, manipulate such algebraic functions and expressions correctly, solve equations involving such functions, graph such functions and describe important graphical properties, and understand and use arithmetic and geometric sequences.
4. The student will describe the basic ideas of calculus graphically, including using tangent lines and derivatives to understand and model instantaneous rates of change, and using Riemann sums and integrals to compute areas and volumes.
5. The student will use appropriate technology and tools (e.g. manipulatives) to accomplish objectives 1 - 4.

Course Content

This course covers a number of advanced mathematics topics that elementary education majors may encounter. These topics may include but are not limited to:• problem solving using a variety of methods• computation, both written and mental• set theory and notation• polynomial, rational, exponential, and logarithmic functions• analyzing graphs• solving polynomial, exponential, and logarithmic equations• solving systems of equations and inequalities• using sequences and series• introduction to Calculus concepts