MA 226 - Teaching Counting and Whole Number Operations

Description
This is the first in a 2-course sequence for prospective elementary teachers. In-depth explorations will focus on whole number representations, counting, and operations. Pedagogy will focus on the development of students’ understanding, thinking processes, strategies, and problem solving. Clinical experience will include working with a local preschool or elementary school and/or studying student work, observing student-teacher interactions, and peer review.

Credit Hours: 4
Contact Hours: 4
Prerequisites/Other Requirements: C or Higher in one of the following courses: MA 107 OR MA 108 OR MA 110 OR MA 127 OR MA 129 OR MA 131 OR MA 133 OR MA 134 OR MA 245 OR MA 255 OR MA 257 or ALEKS score of 46 or Higher
English Prerequisite(s): None
Math Prerequisite(s): None
Course Corequisite(s): None
Academic Program Prerequisite: None
Consent to Enroll in Course: No Department Consent Required
Dual Enrollment Allowed?: Yes
Course Fees: $19.00
Number of Times Course can be taken for credit: 1
Programs Where This Course is a Requirement:
Pre-Elementary Education, A.A. (Ferris State University), Pre-Pedagogical Content Knowledge for Elementary Teaching + Educational Studies, A.A. (Grand Valley State Univ),

General Education Requirement:
None
General Education Learner Outcomes (GELO):
None
Course Learning Outcomes:

Demonstrate understanding of whole numbers and their operations, counting, and place-value.
Communicate strategies and thinking related to whole numbers, whole number operations, counting and place-value through models and physical representations.
Demonstrate an understanding of pedagological methods for helping develop competency, and fluency in whole numbers, whole number operations, counting and place-value in Pre-K through 6th grade students.
Apply current Grade PK-6 national and state teaching and learning recommendations to whole numbers and their operations, counting and place-value.
Demonstrate application of current mathematical pedagogy with Pre-K through Grade 6 students to facilitate communication of their thinking around whole numbers, counting and place-value.
Plan and facilitate instruction of whole number, counting and place-value concepts based on analysis of student thinking.

Course Outline:
I. Mathematics Pedagogy & Strategic Tasks of Mathematics Teaching

a. Leading a group discussion

b. Explaining and modeling content, practices, and strategies

c. Eliciting and analyzing children’s mathematical thinking

e. Building respectful relationships with students

II. Mathematical Content

A. Introduction to Whole Numbers, Counting, and Place -Value
1. One-to-one correspondence and cardinality

2. Subitizing

3. Conservation

4. Counting all, counting on, and counting back

5. Composition and decomposition of whole numbers

6. Place-Value

7. Multiple physical representations

8. Counting in bases other than ten

B. Operations with Whole Numbers

1. Addition and Subtraction

a. Meaning of Addition and Subtraction
b. Analyzing tasks which model addition and subtraction through manipulatives or other techniques.
c. Properties of addition and subtraction
d. Analyzing and justifying algorithms for multi-digit addition and subtraction.
e. Computation in bases other than ten
f. Identifying various mathematically consistent approaches to addition and subtraction including student generated methods and explanations.

2. Multiplication

a. Meaning of Multiplication
b. Analyzing tasks which model multipication through manipulatives and other techniques (repeated addition, skip counting, partial
products, …)
c. Properties of multiplication
d. Analyzing and justifying algorithms for multi-digit multiplication.
e. Identifying various mathematically consistent approaches to multiplication including student generated methods and explanations.

3. Division

a. Meaning of Division - sharing and measurement concepts

b. Analyzing tasks which model division using manipulatives.

c. Properties of division

d. Analyzing and justifying algorithms for multi-digit division.

e. Identifying various mathematically consistent approaches to division including student generated methods and explanations.

C. Building Fluency and Automaticity for Basic Number Facts

1. Number Fact Strategies

2. Whole number relationships

3. Composing and decomposing numbers

4. Basic number theory (divisibility, prime vs. composite, GCD/LCM)

5. Strategies for addition and subtraction

6. Strategies for multiplication and division

7. Whole number operations and early algebraic thinking.

D. Children’s Strategies

1. Analyze videos and/or classroom experiences and identify student thinking and processes

2. Analyze student work and identify student thinking and processes used.

3. Develop plans to respond to an advanced student thinking process and understanding

Approved for Online and Hybrid Delivery?:
Yes
Instructional Strategies:
Lecture: 0-60%

Facilitated Discussion: 10-60%

Collaborative Learning: 30-60%

Technology Supplemented Learning: 10-30%
Mandatory Course Components:
None.
Equivalent Courses:
None

Name of Industry Recognize Credentials: None

Course-Specific Placement Test: None
Course Aligned with ARW/IRW Pairing: NA

Mandatory Department Assessment Measures:
None.

Course Type:
Program Requirement- Offering designed to meet the learning needs of students in a specific GRCC program.
Course Format:
Lecture - 1:1
Total Lecture Hours Per Week: 4
People Soft Course ID Number: 105135
Course CIP Code: 27.01
Maximum Course Enrollment: 28
General Room Request: Math Teaching Room

High School Articulation Agreements exist?: No
Non-Credit GRCC Articulation Agreement With What Area: No
School: School of STEM
Department: Mathematics
Discipline: MA
First Term Valid: Fall 2022 (8/1/2022)
1st Catalog Year: 2022-2023
Name of Course Author:
Meghan VanderMale

Faculty Credential Requirements:
18 graduate credit hours in discipline being taught (HLC Requirement), Master’s Degree (GRCC general requirement), Other (list below)
Faculty Credential Requirement Details:
M.S., M.A. M.Ed., or PhD. in Mathematics or Mathematics Education with 18 graduate credit hours in mathematics. A background in Mathematics Education (or a demonstrated interest in professional development in elementary education) and a thorough knowledge of the current teaching techniques used in elementary schools is preferred.

Course Review & Revision Year: 2026-2027