## Math for Elementary and Middle School Educators - MTH 120 at Southwest Virginia Community College

https://courses.vccs.edu/colleges/swcc/courses/MTH120-MathforElementaryandMiddleSchoolEducators

Effective: 2024-05-01

### Course Description

Provides a comprehensive and conceptual examination of fundamental mathematical concepts covered in VDOE K-8 Standards of Learning (SOLs). Designed for future K-8 mathematics educators. Emphasizes problem-solving, logical reasoning, the establishment of connections between mathematical concepts, effective communication of mathematical ideas, and the utilization of multiple representations. This is a cross-listed course with EDU 120.

Lecture 4 hours. Total 4 hours per week.

4 credits

The course outline below was developed as part of a statewide standardization process.

### General Course Purpose

The purpose of this course is to provide a comprehensive and conceptual understanding of fundamental mathematical concepts covered in VDOE K-8 mathematics Standards of Learning (SOLs). This course is intended to cover the content of the first semester of a two-course lower-level math for elementary educators sequence, with the second semester of the course taken at the four-year college after transfer.

### Course Objectives

- Quantitative Literacy
- Use problem-solving skills and quantitative reasoning to solve problems, explore new ideas, and improve your understanding of mathematics
- Critical Thinking
- Formulate multiple solution paths for mathematical problems and describe connections between and within these paths
- Written Communication
- Demonstrate proper use of terminology, notation, and/or written conventions used in the field of mathematics and mathematics education
- Professional Readiness
- Analyze and evaluate the mathematical thinking of K-8 students expressed in their oral and verbal reports, written work, and authentic representations
- Design strategies to develop positive math beliefs, including growth mindset, persistence in work, and productive student struggle

### Major Topics to be Included

- Problem Solving and Quantitative Reasoning Skills
- Identify connections between conceptual knowledge and standard algorithms
- Generate meaningful mathematical representations using algorithms, employing both written formats and physical manipulatives
- Counting and Number Systems
- Describe quantities across multiple number systems, encompassing natural numbers, whole numbers, integers, and rational numbers
- Establish connections between concepts such as place value and regrouping, explaining their relationship within the base-ten number system
- Analyze similarities and differences between the base-ten number system and numbers in alternative bases
- Integers and Rational Numbers
- Apply fundamental understanding of whole numbers to grasp integers and their associated operations
- Utilize core principles of number theory, such as prime factorization, divisibility, greatest common factors, least common multiples, etc., to examine the structure of integers
- Generate multiple representations for rational numbers and justify their equivalence in various forms
- Comparing Fractions and Arithmetic Operations
- Make valid comparisons between rational numbers and model arithmetic calculations with them
- Utilize various reasoning approaches to justify arithmetic operations involving whole numbers
- Develop standard and non-standard algorithms for addition, subtraction, multiplication, and division by drawing on principles of counting, place-value grouping, and partitioning
- Base Ten and Other Bases
- Exhibit adaptable and conceptual thinking while exploring numbers, operations, and their interconnections
- Investigate the concepts of place value and regrouping within the framework of the base-ten system and alternative numerical bases
- Addition and Subtraction
- Use, compare, and mathematically justify different strategies and representations to solve addition and subtraction problems
- Develop versatile computational skills across all number categories, using and articulating various methods for addition and subtraction
- Multiplication and Division
- Formulate multiple solution paths for multiplication and division problems and describe connections between and within these paths
- Assess and explain the mathematical ideas and reasoning used in multiplication and division
- Formulating Solution Paths and Beliefs about Mathematics
- Embrace a growth mindset to reflect on personal beliefs regarding mathematics and the teaching and learning processes, fostering an open exploration of mathematical concepts.
- Generate comprehensive mathematical representations for the course content, incorporating written formats (such as area models, number lines, scaled diagrams, strip diagrams, etc.) and tangible manipulative tools (like base-ten blocks, Cuisenaire rods, linking cubes, pattern blocks, etc.), to enhance understanding and engagement.