Foundations of Elementary Math I
Course Number: MTH 211
Transcript Title: Foundations of Elem Math I
Created: September 1, 2012
Updated: September 25, 2013
Total Credits: 4
Lecture Hours: 40
Lecture / Lab Hours: 0
Lab Hours: 0
Satisfies Cultural Literacy requirement: No
Satisfies General Education requirement: Yes
Grading options: A-F (default), P-NP, audit
Surveys mathematical topics for those interested in the presentation of mathematics at the K-9 levels. Topics emphasized are problem solving, patterns, sequences, set theory, logic, numeration systems, number bases, arithmetic operations, and number theory. Various manipulative and problem solving strategies are used. Prerequisite: MTH 95 or higher, and WR 115 and RD 115 or equivalent placement test scores. Audit available.
Upon successful completion students should be able to:
- Understand the theoretical foundations of mathematics focusing on whole number arithmetic as taught at the K-9 level in order to develop mathematical knowledge for teaching.
- Use various problem solving strategies and algebraic reasoning to create mathematical models, analyze real world scenarios, judge if the results are reasonable, and then interpret and clearly communicate the results.
- Participate in a teacher education program.
- Use appropriate mathematics, including correct mathematical terminology, notation, and symbolic processes, and use technology to explore the foundations of elementary mathematics.
Outcome Assessment Strategies
- At least two proctored examinations
- At least one writing assignment and
- At least two of the following additional measures:
- Take-home examinations
- Graded homework
- Individual/Group projects
- In-class activities
- Individual projects exploring the NCTM standards.
- Individual or team teaching demonstration(s).
- Field experience
- Service Learning
Course Activities and Design
In-class time is primarily activity/discussion or lecture/lab emphasizing the use of manipulatives and problem solving techniques. Activities will include group work, field experience, or teaching demonstrations.
Course Content (Themes, Concepts, Issues and Skills)
1.0 MATHEMATICS AND PROBLEM SOLVING
The instructional goal is to develop problem solving ability.
1.1 Utilize Polya's four-step problem solving process.
1.2 Develop problem solving strategies, including making a drawing, guessing and checking, making a table, using a model, and working backward.
1.3 Explore patterns and sequences, and their relationship to problem solving.
1.4 Use algebra and algebra manipulatives to problem solve.
1.5 Solve application problems utilizing functions and graphs.
2.0 SETS AND LOGIC
The instructional goal is to learn the fundamental concepts of set theory and logic.
2.1 Explore attributes and classification.
2.2 Use set theory symbolism.
2.3 Represent set concepts using Venn diagrams.
2.4 Understand and use the concepts of subset, intersection, union, and complement of a set.
2.5 Utilize set theory in application problems.
2.6 Apply deductive reasoning.
2.7 Use symbolic logic to explore premises, conclusions, and validity.
3.0 NUMERATION SYSTEMS AND WHOLE NUMBERS
The instructional goal is to develop an understanding of systems of numeration and the system of whole numbers.
3.1 Explore numeration systems of other cultures.
3.2 Define the set of whole numbers and their properties.
3.3 Model, compute, and investigate whole number operations in several bases.
3.4 Estimate and use mental arithmetic.
4.0 NUMBER THEORY
The instructional goal is to understand elementary concepts of number theory and how these concepts are used in the elementary curriculum.
4.1 Explore divisibility.
4.2 Identify prime and composite numbers.
4.3 Prime factor numbers and determine when numbers are "relatively prime".
4.4 Find the least common multiple (LCM) and the greatest common divisor/factor (GCD/F) of two or more numbers.
4.5 Use "clock arithmetic" and other simple modular arithmetic applications.
This is the first term of a three-term sequence (MTH 211, 212, and 213).
Foundations of Elementary Math I is intended to examine the conceptual basis of elementary mathematics and to provide students with opportunities to experience using manipulatives to model problem solving, computational operations with whole numbers, topics in number theory and set theory. The content and pedagogy is based on the NCTM standards. Emphasis is on why mathematics works as it does rather than on memorization of algorithms.