MATH 202: Data Analysis, Geometry, and Measurement for the ...

MATH 202: Data Analysis, Geometry, and Measurement for the Elementary Teacher (3 hours)Syllabus1. Prerequisite: MATH 201 with a C– or better.2. Course Description: In-depth treatment of concepts underlying common topics in the elementarymathematics curriculum including concepts in data analysis, geometry, and measurement. Use ofselected concrete materials and technology is included.3. Course Objectives: The course, in combination with MATH 201, is designed to provide the mathematicsfoundation needed by teachers of elementary students. It provides an early opportunity for students toassess their interests, talents, and goals as prospective teachers. A further objective of this course is toprovide basic academic and intellectual tools needed by effective teachers of mathematics. Thisfoundation enables the students to communicate ideas and concepts using appropriate mathematicallanguage.4. Course Rationale: The course is designed to provide basic academic and intellectual tools ofmathematics appropriate for prospective teachers of elementary students. The course provides acollegiate perspective of the foundations of geometry, measurement, and statistics that will help thesestudents to become effective teachers of mathematics. Standards and recommendations for themathematical content knowledge essential for preservice teachers made by the National Council ofTeachers of Mathematics, the Mathematical Association of America, and the Indiana ProfessionalStandards Board guide the selection of topics presented in this course. As a result of successfullycompleting the study of mathematical content in MATH 201 and 202/203, these teaching majors areprepared to continue their educational studies in a mathematics methods course, where they learn how toteach these mathematical topics to children.Problem-solving approaches are used throughout the course to study mathematical concepts andprocedures. Through the use of various group formats, students learn to work in concert with others tosolve problems and to communicate mathematics both verbally and in writing. Students learn techniquesfor logical reasoning to enhance their ability to engage in life-long learning. Historical, cultural, andmathematical connections permeate the course content.The course is designed to prepare students to become effective teachers of mathematics. Students willgain an appreciation for mathematics and add to their procedural understanding by gaining conceptualunderstanding through the use of selected models, materials and problem solving situations. Thesecomponents 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 therelationships 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, bargraphs, 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 communicatemathematical 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 theproperties.• 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 whichregular 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 prisms, pyramids, other polyhedra, 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 (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, 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 Theoremthrough the use of area models.• Formulate and solve problems whose solutions require the Pythagorean Theorem.6. Course Format: Students work individually and in small groups to solve problems and participate inactivities in class and to complete assignments outside of class. Faculty engages students in interactive

lectures and whole-class discussions. Students use calculators and computers to solve problems andexplore various representations of mathematical concepts. A TI-73 graphing calculator is required.Geometer’s Sketchpad is required.7. Methods for Evaluating Student Performance: Methods used for evaluating student performance mayinclude 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 theindividual instructor.Additionally, a set of common assessment instruments will be used in all sections of MATH 202. Thesewill include the following: a gateway exam, individual problem-solving assignments, collaborativeprojects, and a set of common final exam questions.8. Evaluation of the Course: The departmental Teacher Education Advisory Committee andUndergraduate Programs Committee periodically evaluate these courses. The instruction of the course isevaluated by departmental student evaluations and peer evaluations.[1/01, Stump; 12/02, E. Bremigan; 4/07, S. Kerlin; 11/10, Pierce; March 2013, UPC, Chair Pierce; Fall 2014,UPC, R. Pierce Chair]