Syllabus: MATHS 207
Mathematics for the Teacher of the Exceptional Learner (4 hours)
1. Prerequisite: qualifying score on Gateway Examination and any of the following: qualifying ACT or SAT score, or appropriate score on the Mathematics Placement Test, or credit in MATHS 108, or permission of the department chairperson. Not open to students who have who have credit in MATHS 201, 202, or 203. Open only to special education majors.
2. Course Description: Development of concepts in number and operation, algebra, geometry, measurement, data analysis and probability needed by teachers of exceptional learners. Use of selected concrete manipulatives and technology is included.
3. Course Objectives: The course is designed to provide the mathematics foundation needed by teachers of exceptional learners. It provides an early opportunity for students to assess their interests, talents, and goals as prospective teachers. A further objective of this course is to provide basic academic and intellectual tools needed by effective teachers of mathematics. This foundation enables the students to communicate ideas and concepts using appropriate mathematical language.
MATHS 207 satisfies the University Core Curriculum requirement for mathematics. In particular, addressing the first Core Goal, the course provides for the development of foundational knowledge of both the content and discourse of mathematics. Students will develop knowledge of multiple representations of mathematical concepts and procedures, reason mathematically, solve problems, and communicate mathematics effectively at different levels of formality. Addressing the second Core Goal, the course provides students with a basic understanding of quantitative aspects of their civilization. Students will investigate and use historical and contemporary symbols, models, and tools of mathematical representation.
Additionally, MATHS 207 addresses the following Overall Goals:
1. Students will develop an ability to engage in life-long education. This includes learning to acquire knowledge and utilize it towards intelligent ends.
An ability to make mathematical connections, form mathematical generalizations, and justify mathematical reasoning.
2. Students will develop an ability to communicate at a level acceptable for college students.
An ability to use the language of mathematics (i.e., terminology, symbols, and notation) to express mathematical ideas at a level acceptable for college graduates.
3. Students will develop an ability to solve the common problems of living by drawing on a knowledge of historical and contemporary events and the elements of the cultural heritage related to those events.
An ability to solve both applied and abstract problems involving number, geometry, measurement, statistics, probability, functions, and the use of variables while developing perspectives on the nature of mathematics though a historical and cultural approach.
4. Students will develop an ability to work in concert with others in solving the common problems of living.
An ability to work collaboratively to solve both applied and abstract mathematical problems.
4. Course Rationale:
The course is designed to provide basic academic and intellectual tools of mathematics appropriate for prospective teachers of exceptional learners. The course provides a collegiate perspective of the foundations of number, geometry, measurement, statistics, probability, functions, and the use of variables that will help these students to become effective teachers of mathematics.
Problem-solving approaches are used throughout the course to study mathematical concepts and procedures. Through the use of various group formats, students learn to work in concert with others to solve problems and to communicate mathematics both verbally and in writing. Students learn techniques for logical reasoning to enhance their ability to engage in life-long learning. Historical, cultural, and mathematical connections permeate the course content.
The course is designed to prepare students to become effective teachers of mathematics. Students will gain an appreciation for mathematics and add to their procedural understanding by gaining conceptual understanding through the use of selected models, materials and problem solving situations. These components are critical to the university foundational goals of the University Core Curriculum.
5. Course Content:
Problem Solving (1 week)
• Explore and apply problem-solving strategies using Polya’s four-step process
Patterns, Functions, and Use of Variables (1 week)
• Develop mathematical language and symbolism
• Represent and solve problems requiring the use of variables to lay a foundation for the growth of mathematical ideas
• Represent functions verbally and in tabular, graphical, and symbolic formats
Sets (1 week)
• Develop set language and notation
• Explore relationships between and among sets, including the use of Venn diagrams in problem solving and deductive reasoning
Numeration Systems (1 week)
• Investigate the structure of ancient and present-day numeration systems to develop an appreciation of the contributions made by various cultures
• Gain an understanding of place value through the use of several number bases
Whole Numbers (2 weeks)
• Understand the use of whole number concepts, operations, and properties through the use of several number bases
• Apply a variety of mental and written whole number algorithms
Number Theory (1 week)
• Model primes, composites, factors, and multiples in a variety of ways
• Explore the relationships between GCF and LCM using several techniques such as the use of models or divisibility tests
Integers (1/2-1 week)
• Extend the number system from whole numbers to integers including the ordering of numbers and the extension of the number properties
• Explore basic concepts and operations of integers using a variety of physical models
Rational Numbers (2 weeks)
• Extend the number system from the integers to the rational numbers including the ordering, density, and operations of rational numbers as well as the extension of the number properties
• Develop a conceptual understanding of fractions, decimals, percents, ratios, and proportions through the use of physical models
• Explore relationships between and among different rational number representations
Geometry (2 weeks)
Basic Terms
• Develop geometric language and use basic geometric terms to appropriately communicate mathematical ideas.
• Include language of an informal deductive nature (all, some, none, if-then, what if).
Plane Figures
• Measure angles and explore relationships between sets of angles.
• Classify quadrilaterals using minimum characteristics and develop logical arguments about the properties.
• Classify triangles according to their sides and to their angles.
• Investigate the interior, exterior, and central angles of regular polygons. Look for generalizations.
• Use physical models to explore regular and semi-regular tessellations, and determine which regular polygons will tessellate.
• Use physical and visual models to explore reflection and rotation symmetry of plane figures.
• Construct plane figures using geometric tools (protractor, compass, mira, LOGO).
• Use physical and visual models to explore congruence and similarity.
• Formulate and solve problems whose solutions require two-dimensional spatial sense.
• Use physical and visual models to investigate transformations (slides, flips, and turns).
Space Figures
• Explore properties of polyhedra, prisms, pyramids, cylinders, cones, and spheres.
• Analyze and describe regular polyhedra. Look for generalizations.
• Explore reflection and rotation symmetry of space figures.
• Formulate and solve problems whose solutions require three-dimensional spatial sense.
Measurement (2 weeks)
Nonstandard and Standard Units of Length, Area, and Volume
• Develop ideas that units to record measure are different from the process of measurement itself.
• Use standard and nonstandard units to estimate and measure various attributes.
Customary and Metric Units
• Present measurement through its historical development.
• Provide a variety of experiences with the customary and metric systems.
Area and Perimeter (rectangles, squares, parallelograms, triangles, trapezoids, circles, and irregular polygons)
• Develop the formulas for area and perimeter through meaningful activities.
• Investigate relationships between area and perimeter.
• Formulate and solve problems whose solutions require two-dimensional spatial sense.
Volume and Surface Area (polyhedra, prisms, pyramids, spheres, cones)
• Develop the formulas for volume and surface area through meaningful activities.
• Investigate relationships between volume and surface area.
• Formulate and solve problems whose solutions require three-dimensional spatial sense.
Pythagorean Theorem
• Discover, generalize, and communicate conjectures which support the Pythagorean Theorem through the use of area models.
• Formulate and solve problems whose solutions require the Pythagorean Theorem.
Area Models of Probability
• Explore a variety of situations involving simple and compound events through the use of area models.
Statistics (1 week)
Measures of Central Tendency
• Investigate the measures of central tendency including mean, median, and mode, and explore the relationships among them.
Measures of Variation
• Investigate the measures of variation including range, variation, standard deviation, and outliers, and explore the relationships among them.
Graphical Representations
• Construct and interpret graphical representations of data including line plots, picture graphs, bar graphs, circle graphs, stem-and-leaf plots, box-and-whisker plots, and scatter plots.
Probability (if time)
• Explore probability through single and multi-stage experimentation and simulation activities
• Build an understanding of the relationship between empirical and theoretical probability
• Investigate odds and expected value as well as the probability of simple, compound, and complementary events
6. Course Format: Students work individually and in small groups to solve problems and participate in activities in class and to complete assignments outside of class. Faculty engage students in interactive lectures and whole-class discussions. Students use calculators and computers to solve problems and explore various representations of mathematical concepts. A TI-73 graphing calculator is required.
7. Methods for Evaluating Student Performance: Methods used for evaluating student performance may include but are not limited to the following: exams, quizzes, homework assignments, essays, journals, and projects. The evaluation and weight of these various components are at the discretion of the individual instructor.
Additionally, a set of common assessment instruments will be used in MATHS 207 in conjunction with MATHS 201 and 202. These will include the following: a gateway exam, individual problem-solving assignments, collaborative projects, and a set of common final exam questions.
8. Evaluation of the Course: The departmental Teacher Education Advisory Committee and Undergraduate Programs Committee periodically evaluate these courses. The instruction of the course is evaluated by departmental student evaluations and peer evaluations.
[Stump 4/02, revised by S. Kerlin 4/07]