School

Science, Technology, Engineering & Math

Department

Mathematics

Academic Level

Undergraduate

Course Subject

Mathematics

Course Number

121

Course Title

Mathematics for Elementary Teachers I

Credit Hours

3.00

Instructor Contact Hours Per Semester

62.00 (for 15-week classes)

Student Contact Hours Per Semester

62.00 (for 15-week classes)

Grading Method

A-E

Pre-requisites

MATH-109 OR MATH-1094 OR MATH-110 with a C grade or better OR a satisfactory score on the placement test.

Co-requisites

Enrollment in ENG-131 or ENG-131 with a C grade or better

Catalog Course Description

For students who are involved in a curriculum for elementary teachers. Includes problem solving, an introduction to logic, set theory, number theory, numeration systems, whole numbers, and fractions. Addresses concept development, communication skills, both oral and written, and problem solving skills in accordance with the National Council of Teachers of Mathematics (NCTM) Standards. Course integrates topics in algebra throughout.

### Goals, Topics, and Objectives

Goal Statement

- To strengthen mathematical problem solving skills pertaining to curricular topics related to the preparation of future elementary school teachers.
- To strengthen communication skills, both written and oral, of mathematical ideas.
- To strengthen mathematical competence in logic, set theory, number theory, whole numbers, and fractions.

Core Course Topics

- Problem Solving
- Solve word problems using a variety of strategies.
- Solve word problems employing Polya’s four-step process.

- Logic
- Identify a statement as being a negation, conjunction, disjunction, implication, or one of the various forms of an implication.
- Translate statements of the above types from verbal form to symbolic and from symbolic to verbal form.
- Discern the truth value of the above types of statements, and combinations of them.
- Determine whether two statements are equivalent.

- Numeration Systems
- Identify the characteristics of tally and place-value numeration systems.
- Give examples of tally and place-value numeration systems.
- Convert between different numeration systems (including different base systems).
- Add, subtract and multiply in a variety of numeration systems.

- Set Theory
- Define: set, subset, proper subset, null/empty set, element, universal set, complement of a set.
- Demonstrate knowledge of element and subset relationships.
- Perform operations on sets (union, intersection, complement, set difference, cross product).
- Demonstrate knowledge of properties of set operations (commutativity, associativity, distributivity, identity).
- Use Venn Diagrams to verify set properties.
- Use Venn Diagrams to solve problems.

- Whole Numbers and Their Operations
- Use ordinal, cardinal, and nominal models to demonstrate whole numbers.
- Use the relations of <, > and = with whole numbers.
- Model and explain using manipulatives whole numbers operations.
- Demonstrate knowledge and understanding of the standard algorithms for whole number operations.
- Justify alternate algorithms for whole number operations.
- Demonstrate proficiency in using estimation techniques for whole number operations.
- Demonstrate proficiency in mental mathematics for whole number operations.
- Demonstrate knowledge of the properties of whole number operations.
- Solve problems involving whole numbers.

- Algebraic Reasoning
- Demonstrate an understanding of the concept of variable and apply this knowledge to problem solving.
- Demonstrate an understanding of equation solving and apply this knowledge to problem solving.

- Number Theory
- Define: the unit, prime number, composite number, even number, odd number, factor and multiple.
- Define and use the relation “divides”.
- Demonstrate an understanding of “greatest common factor” (GCF) using a variety of techniques.
- Demonstrate an understanding of “least common multiple” (LCM) using a variety of techniques.
- Solve problems involving the concepts described above.

- Fractions
- Model fractions using a variety of manipulatives and hand-drawn methods.
- Model fractions using a variety of mathematical concepts.
- Use the relations of <, >, and = with fractions.
- Model and explain using manipulatives fraction operations.
- Demonstrate proficiency in using estimation techniques for fraction operations.
- Demonstrate proficiency in mental mathematics for fraction operations.
- Demonstrate knowledge of the properties of fraction operations.
- Solve problems involving fractions.

- Proportional Reasoning
Demonstrate an understanding of proportional reasoning by using several different problem solving methods.

### Assessment and Requirements

Assessment of Academic Achievement

- Pre-Education students are required to create an e-portfolio as part of their academic work at HFC. Instructors must include a minimum of three e-portfolio assignments as part of course work. These assignments will be stored in each student's e-portfolio.
- All students will be required to complete a comprehensive final examination that assesses the learning of all course objectives. This exam must be weighted in a manner so that this exam score is worth a minimum of fifteen percent (15%) of the final course grade. In selected semesters this exam may be a common exam administered to all sections of Math-121.
- Additional assessment of student achievement may include assignments, quizzes, and exams.
- Application problems must not only be included on chapter exams but also on the final exam.

General Course Requirements and Recommendations

- Application problems must be covered in all mathematics courses. Every section in any course outline that includes application problems must be covered.
- A scientific calculator is required of each student.

### Outcomes

General Education Categories

- Mathematics

Institutional Outcomes

- Quantitative Literacy

### Approval Dates

Effective Term

Fall 2019