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May 02, 2024
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MATH 2110 - Introductory Geometry for Middle School Teachers
This course prepares prospective teachers to teach mathematics to children in grades 4-9 and is appropriate for middle childhood education and other education majors. It focuses on the geometry and measurement topics covered in the Common Core State Standards for grades 4-9. The course also addresses how some of these topics develop in secondary grades to give prospective teachers a sense of the mathematics they will be preparing students to learn later. The course is taught through an inquiry approach that focuses on problem solving and discussion and is designed to encourage exploration and explanation of mathematical ideas. This course will cover visualization, angles, geometric shapes and three-dimensional figures and their properties, some constructions with straightedge and compass and with technology, transformational geometry, symmetry, congruence, similarity, measurement (especially length, area, and volume), converting measurements, principles underlying calculations of areas and volumes, why various area and volume formulas are valid, the behavior of area and volume under scaling, uses of right angle trigonometry and various technologies to aid in teaching geometry. Students will be expected to develop and prove or disprove conjectures about geometric figures. Construction of proofs will involve exploration, discovery, conjecture, and certification of reasoning. Topics will be addressed to develop a deep conceptual understanding of geometry and measurement needed for teaching this content to grades 4-9 students. Students will experience and grapple with how geometry can describe and interpret problems from various circumstances in the real world.
Requisites: (MATH 1300 or 1322 or 1350 or 2301 or Math placement level 3) and any education major.
Credit Hours: 3
Repeat/Retake Information: May be retaken two times excluding withdrawals, but only last course taken counts.
Lecture/Lab Hours: 3.0 lecture
Grades: Eligible Grades: A-F,WP,WF,WN,FN,AU,I
Learning Outcomes: - Students will be able to communicate their own and others¿ mathematical ideas clearly and precisely, both orally and in writing, and support those ideas logically with clear mathematical reasoning.
- Students will be able to solve routine and non-routine problems using clear mathematical reasoning and mathematical modeling.
- Students will be able to calculate and approximate measurements, including areas and volumes, and attend to precision of units.
- Students will be able to distinguish among the ways in which unknown measurements can be determined and analyzed through the use of mathematical relationships coupled with known attributes described by quantitative measures for two and three dimensions.
- Students will be able to derive and explain the rationale behind formulas for perimeter, area, surface area, and volume of these two and three-dimensional figures: square, rectangle, triangle, parallelogram, circle, regular polygon, trapezoid, prism, pyra
- Students will be able to describe the relationship between the circumference and diameter of a circle through hands-on investigation.
- Students will be able to construct and analyze geometry figures using tools (including dynamic geometry software).
- Students will be able to solve problems about angle relationships.
- Students will be able to describe geometric concepts of angle, parallel, and perpendicular, congruence, similarity and use them in describing and defining shapes and in solving problems.
- Students will be able to identify, classify, visualize and represents two- and three-dimensional objects (e.g, triangles, quadrilaterals, regular polygons, prisms, pyramids, cones, cylinders, and spheres)
- Students will be able to build, decompose, rearrange, compose, transform and examine cross-sections of 2D and 3D geometric objects (e.g., decompose a parallelogram into 2 triangles) and explain and justify properties of geometric objects.
- Students will be able to derive and explain formulas for distance, midpoint, and slope and use that information to classify figures and solve problems in the coordinate plane.
- Students will be able to transform geometric figures using dilations, translations, rotations, reflections, glide reflections and compositions of transformations.
- Students will be able to describe attributes of the figures that are preserved under different types of transformations.
- Students will be able to describe geometric transformations in terms of functions.
- Students will be able to construct and analyze tessellations in the plane
- Students will be able to describe symmetries of a figure as compositions of transformations and state when those symmetries will map a figure onto itself.
- Students will be able to prove geometric theorems using transformations, coordinates, algebra and deductive reasoning as appropriate.
- Students will be able to explain why the Pythagorean Theorem is valid in multiple ways, under what conditions it is valid and use the Pythagorean Theorem to solve problems.
- Students will be able to prove and explain theorems about angles, lines, triangles, quadrilaterals, and circles.
- Students will be to identify and use proportional relationships and scale factors to solve problems making comparisons between a known and similar object.
- Students will be able to use scale drawings of two-dimensional, real-world and mathematical problems to analyze figures and situations as well as to investigate the relationships between similar figures.
- Students will be able to identify and prove or disprove if figures are congruent or similar.
- Students will be able to use right triangle trigonometry to solve problems in a real-world context.
- Students will be able to describe the importance of similarity to the development of trigonometric ratios.
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