School

Science, Technology, Engineering and Math

Division

Mathematics

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-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, set theory, number theory, numeration systems, whole numbers, and fractions. Addresses two aspects of teaching children mathematics – content and pedagogy – focused on Michigan Department of Education Standards for the Preparation of Teachers of Lower Elementary (Pre-K – 3) and Upper Elementary (Grades 3 – 6). Also addresses concept development, algorithms, children’s mathematical work, and communication skills--both oral and written--important for teaching children.

## 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 fundamental set theory and numeration systems that undergird
- Whole-number concepts and operations and
- Number theory fundamental to fraction operations.

- To develop pedagogical skills consistent with MDE Core Teaching Practices that are used for teaching mathematics to children.

Core Course Topics

- Michigan Department of Education Core Practices
- Demonstrate knowledge of leading a group discussion.
- Demonstrate knowledge of explaining and modeling content, practices and strategies.
- Demonstrate knowledge of eliciting and interpreting individual students’ thinking.
- Demonstrate knowledge of implementing norms and routines for classroom discourse and work.

- Problem Solving (MDE Standards: B-K M.9)
- Solve word problems using a variety of strategies.
- Solve word problems employing Polya’s four-step process.

- Numeration Systems (MDE B-K; M. 13, M.15. Pre-K – 3: M.9, M.10, M.11, M.12. Grades 3-6: M.5, M.6)
- Identify the characteristics of tally and place-value numeration systems.
- Give examples of tally and place-value numeration systems.
- Represent Base 5 numerals using a variety of manipulatives.
- Convert between Base 5 and Base 10 numeration systems.
- Add, subtract and multiply in Base 5 numeration system.
- Compose and decompose Base 10 numbers in a variety of ways.
- Use a variety of manipulatives to represent Base 10 numbers.
- State benefits and limitations of a variety of manipulatives.

- 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).
- Demonstrate knowledge of properties of set operations (commutativity, associativity, distributivity, identity).
- Use Venn Diagrams to solve problems.

- Whole Numbers and Their Operations (MDE B-K; M.13, M.14, M.15. MDE Pre-K-3. MDE Grades 3–6: M.5, M. 6., M.7, M.8)
- Use ordinal, cardinal, and nominal models to demonstrate whole numbers.
- Compare whole numbers and develop the meaning 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 alternative algorithms for whole number operations.
- Make connections among whole number operation algorithms.
- 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.
- Respond to observations of children’s mathematical work.
- Develop sets of problems with varying degrees of difficulty

- Algebraic Reasoning (MDE B-K: M.10, M.11, M.12)
- 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.
- Apply knowledge of functions represented in a variety of forms.
- Solve problems requiring equations in two variables.

- Number Theory
- Define: the unit, prime number, composite number, even number, odd number, factor and multiple.
- 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 of GCF and LCM.

- Fractions (MDE: Pre-K-3: M.13, M.14, M.15, M.16. Grades 3 – 6: M.9, M.10, M.11, M.12)
- Model fractions using a variety of manipulatives and hand-drawn methods.
- Develop meaning of fraction using a variety of mathematical concepts.
- Define fraction.
- Compare fractions and develop the meaning of <, >, and = with fractions.
- Model and explain fraction operations using manipulatives.
- Demonstrate knowledge and understanding of standard algorithms for 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.
- Observe and respond to children’s mathematical work.
- Develop sets of problems with varying degrees of difficulty.

## 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.
- All students will be required to complete journal assignments.
- 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

MTA Categories

- Category 3: Mathematics (Quantitative Literacy Track)

Satisfies Wellness Requirement

No

Effective Term

Winter 2023