MTH 226 - Teaching Counting and Whole Number Operations

Was previously MA 226

1. Explain and justify whole number concepts, including counting, place value, and operations, using multiple representations and reasoning strategies.
2. Communicate mathematical thinking related to whole numbers using accurate and precise language, models, multiple representations, and mathematical discourse.
3. Interpret and analyze Birth–6 student thinking related to whole number concepts using student work and classroom interaction evidence.
4. Apply current PK–6 state and national mathematics recommendations to the design and instruction of counting, place value, and whole number operations.
5. Use research-based pedagogical practices to support the development of students’ conceptual understanding, fluency, and communication of whole number ideas in Birth–6 learners.
6. Plan, facilitate, and reflect on standards-aligned instruction on whole number concepts that responds to and advances student thinking and incorporates formative assessment.

A. Core Teaching Practices

1. Lead whole-class and small-group mathematical discussions

2. Explain and model mathematical content, practices, and strategies

3. Build respectful and inclusive relationships with students

B. Elicit, Interpret, and Respond to Student Thinking

1. Elicit and analyze children’s mathematical thinking

2. Examine developmental progressions in children’s strategies

3. Use evidence of student thinking to inform instructional decisions

C. Children’s Strategies and Instructional Response

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

2. Analyze student work to identify strategies, misconceptions, and levels of understanding

3. Develop instructional plans that respond to and advance student thinking and understanding

II. Mathematical Content

A. Whole Numbers, Counting, and Place Value

1. Counting principles and early number concepts

a. One-to-one correspondence

b. Cardinality

c. Subitizing

d. Conservation of number

2.  Counting strategies and progressions

a. Counting all

b. Counting on

c. Counting back

d. Skip counting

3. Structure of whole numbers

a. Composition and decomposition of numbers

b. Place value and unitizing

c. Multiple physical and visual representations

4. Number systems

a. Count and represent numbers in bases other than ten

B. Operations with Whole Numbers

1. Addition and Subtraction

a. Meanings and problem structures for addition and subtraction (e.g., join, separate, part-part-whole, compare)

b. Analysis of tasks that model addition and subtraction using manipulatives and representations

c. Properties of addition and subtraction

d. Analysis and justification of algorithms for multi-digit addition and subtraction

e. Computations in bases other than ten

f. Student-generated strategies (e.g., split, jump, compensation) and mathematically consistent approaches

2. Multiplication

a. Meanings and problem structures of multiplication (e.g., equal groups, arrays, area, comparison)

b. Analysis of tasks that model multiplication using manipulatives and representations

c. Properties of multiplication

d. Analysis and justification of algorithms for multi-digit multiplication

e. Computations in bases other than ten

f. Student-generated strategies and mathematically consistent approaches

3. Division

a. Meanings and problem structures of division (e.g., partitive, measurement)

b. Analysis of tasks that model division using manipulatives and representations

c. Properties of division

d. Analysis and justification of algorithms for multi-digit division (partial quotients/scaffolding, standard, explicit-trade)

e. Computations in bases other than ten

f. Student-generated strategies and mathematically consistent approaches

C. Building Fluency and Automaticity for Basic Number Facts

1. Development of number fact strategies grounded in understanding

2. Whole number relationships and structures

3. Composing and decomposing numbers

4. Basic number theory

a. Divisibility

b. Prime and composite

c. GCF and LCM

5. Reasoning-based strategies for operations

6. Connections between whole number operations and early algebraic thinking

Facilitated Discussion: 10-60%

Collaborative Learning: 30-60%

Technology Supplemented Learning: 10-30%

Alternative grading will be used in this class.
Mandatory Course Components:
Math Play Activities
Equivalent Courses:
None