Mar 25, 2023
MATH 1102 - Elementary Topics in Mathematics II
This is a continuation of MATH 1101. Elementary Topics in Mathematics I and II develop mathematical topics usually taught in grades preK-5 to a depth required for future elementary and middle grades educators (and related fields) to establish professional expertise. The courses are taught through an inquiry approach that focuses on problem solving and discussion. Key themes include 1) explaining and justifying standard and nonstandard algorithms for basic arithmetic operations learned in grades preK-5; 2) students’ construction and critique of their own ideas and others’ ideas; and 3) using manipulatives to represent and justify algorithms. This emphasis on the standard algorithms for basic operations taught in K-8 mathematics and their comparison to children’s invented algorithms allows students to engage with the cultural aspects of mathematics and see how our approach to computation and teaching mathematics reflects our greater access to technology and our evolving values of broader society. The mathematical content is focused on topics of fundamental importance for understanding, reasoning about, interpreting, and constructing arguments with quantitative data. The specific topics include ratios and proportional reasoning, algebraic reasoning, functional and non-linear relationships, and measurement. Properties of two-dimensional and three-dimensional geometric objects are explored including area, congruence, similarity, symmetry and translations. Foundational ideas of probability and statistics are addressed including data displays, measure of central tendency, comparing populations and samples, experimental and theoretical probability, and relationships in bivariate data. Does not apply to Arts & Sciences Natural Science requirements.
Requisites: MATH 1101
Credit Hours: 4
OHIO BRICKS Arch: Constructed World
General Education Code (students who entered prior to Fall 2021-22): 1M
Repeat/Retake Information: May be retaken two times excluding withdrawals, but only last course taken counts.
Lecture/Lab Hours: 4.0 lecture
Grades: Eligible Grades: A-F,WP,WF,WN,FN,AU,I
Course Transferability: OTM course: TMM022 Mathematics in Elementary Education II
College Credit Plus: Level 1
- Students will be able to justify and explain the meaning of key concepts, and represent these concepts verbally, numerically, symbolically, graphically, and with concrete manipulatives.
- Students will be able to use and explain quantitative reasoning and relationships that include ratio, rate, direct proportion, inverse proportion, functional relationships, linear and non-linear relationships, and the use of units in problem situations.
- Students will be able to investigate and reason about functional relationships represented using data, tables, graphs, equations, and descriptions of functions in words.
- Students will be able to demonstrate proficiency in solving linear equations through both inverse operations and through alternative methods such as diagrams, and explain the relationships between these methods.
- Students will be able to use and convert between metric and U.S. customary units of measure of length, area, volume, weight, mass, and capacity, including choosing appropriate units for measurement, and describing the relationships between them.
- Students will be able to use and describe geometric measure in linear units, measures of area, surface area, volume, and additivity and invariance related to measurements.
- Students will be able to describe and use basic geometric objects in one, two, and three dimensions, such as line segments, lines, rays, angles, circles, arcs, polygons, polyhedral solids, cylinders, cones, and spheres.
- 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 classify shapes into categories and reason to explain relationships among the categories.
- Students will be able to decompose 2D and 3D geometric objects into parts (e.g., a parallelogram into 2 triangles) and explain and justify properties of geometric objects.
- 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.
- Students will be able to explain why the Pythagorean Theorem is valid and under what conditions it is valid and use the Pythagorean Theorem to solve problems.
- Students will be able to informally prove and explain theorems about angles and solve problems about angle relationships.
- Students will be able to use and describe a variety of transformations & their properties (translations, rotations, reflections, glide reflections, dilations, compositions) and will express symmetry, congruence, and regularity in terms of transformations.
- Students will be able to calculate theoretical and experimental probabilities of simple and compound events, and understand why their values may differ for a given event in a particular experimental situation.
- Students will be able to formulate a statistical question use reasoning about proportional relationships to make claims about a population based on a sample.
- Students will be able to select, create and interpret appropriate data displays for different types of data in order to ask and answer questions about data and to compare data sets.
- Students will be able to summarize, describe, and compare distributions of numerical data in terms of shape, measures of central tendency (e.g., mean, median), and spread (e.g., range, interquartile range).
- Students will be able to generate problem solving strategies collaboratively and respectfully share their thinking in small groups and whole class settings.
- Students will be able to respectfully question, justify, and evaluate their own and others’ ideas in small groups and whole class settings.
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