MATHS 203: Data Analysis, Geometry, and Measurement for the Primary Grades Teacher (2)
Syllabus
1. Prerequisite: qualifying score on Gateway Examination and MATHS 201 with a C or better. Not open to students who have credit in MATHS 202.
2. Course Description: In-depth treatment of concepts underlying common topics in the elementary mathematics curriculum including selected concepts in data analysis, geometry, and measurement. Use of selected concrete manipulatives and technology is included.
3. Course Objectives: The course, in combination with MATHS 201, is designed to provide the mathematics foundation needed by teachers of primary grades. 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.
4. Course Rationale:
The course is designed to provide basic academic and intellectual tools of mathematics appropriate for prospective teachers of primary students. The course provides a collegiate perspective of the foundations of geometry and measurement that will help these students to become effective teachers of mathematics. Standards and recommendations for the mathematical content knowledge essential for preservice teachers made by the National Council of Teachers of Mathematics, the Mathematical Association of America, and the Indiana Professional Standards Board guide the selection of topics presented in this course. As a result of successfully completing the study of mathematical content in MATHS 201 and 202/203, these teaching majors are prepared to continue their educational studies in a mathematics methods course, where they learn how to teach these mathematical topics to children.
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:
Statistics (2-3 weeks)
Measures of Central Tendency
Investigate the measures of central tendency including mean, median, and mode, 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.
Geometry (7-8 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.
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.
Formulate and solve problems whose solutions require three-dimensional spatial sense.
Measurement (4-5 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.
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.
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.
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 MATHS 203 and all sections of MATHS 202. These will include the following: 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.
9. Addendum:
Recommended Textbook:
ODaffer, Charles, Cooney, Dossey, & Schielack. (2002). Mathematics for Elementary School Teachers (Second Edition). Boston: Addison-Wesley.
[Stump, Kitt, Toll, 1/