Lecture 10 Powerpoint

Course: TCHLRN 520 Developing Mathematical Thinking in Early Childhood
Materials: Nametag, handouts, supply box

Agenda

Learning Goals

Deepen understanding of the developmental phases of learning addition and subtraction to recognize how children progress in their mathematical thinking and problem-solving abilities.
Understand basic fact strategies for subtraction, focusing on techniques that enhance students' fluency and comprehension in basic arithmetic.
Leverage the Addition and Subtraction Learning Trajectory to guide instruction based on student needs and comprehension levels.
Develop an understanding of the Addition and Subtraction Story Situation Types, improving teachers' ability to create relatable and engaging mathematical contexts for students.

Phases of Student Learning

Definition: Children model the situation or action step-by-step using tangible objects (like blocks or counters) or visual aids (like drawings).
Technique: Count-count-count approach is employed to help children visualize their calculations thoroughly.
Example: Aiyisha has 13 shells, gives 7 away, and counts to find the remaining shells by organizing her counting process.
- Total: 13
- Giving Away: 7
- Remaining: 6
Equation: 13 - 7 = 6

Definition: Children visualize the quantities involved and apply counting-on or counting-back strategies to ascertain results without redundant counting of all objects.
Technique: Utilizing fingers or drawing to keep track of quantities during the counting process.
Back Counting Example: To solve for the remaining shells, start at 13 and count backward: 13, 12, 11, 10, 9, 8, 7, 6.
On Counting Example: Beginning at 7, counting up to reach 13, applying the counting-on strategy: 7 + 1 + 1 + 1 + 1 + 1 + 1 = 13.

Definition: Children begin to use number relationships and logical reasoning to work with quantities more strategically. They employ techniques such as decomposing numbers to simplify calculations.
Strategies:
- Think Subtraction: Decompose a number to make working with tens more manageable.
- Think Addition: Find ways to reach ten or identify pairs of numbers that can simplify addition or subtraction.
Example: To solve for 13 - 7, a child can decompose to: 13 - 3 - 4 = 6.
Explanation: “I took away 3 to reach 10 first, and then 4 more to find out that 6 are left.”

Subtraction Strategies for Basic Facts

Students should demonstrate understanding of mathematical operations, focusing on the notation for operations and algebraic thinking essential for grades K.OA and 1.OA clusters.

Types of Situations:
- Add To (join): Students learn to combine quantities.
- Take From (separate): Students learn to understand the concept of taking away from a quantity.
- Put Together or Take Apart (whole unknown): Challenges students to discover parts of a whole or a whole from its parts.
Examples of Context:
- Result Unknown: "Eight frogs sat on the grass… How many frogs are there now after some left?"
- Change Unknown: "Some frogs joined the group… What was the original number of frogs?"

Utilize Goal-Directed Tasks to identify levels of students’ understanding and strategies in problem-solving based on their experiences.
Key Levels: Direct Modeling, Counting On/Back, and Numerical Reasoning are critical stages in developing mathematical understanding.

Engage in discussions regarding partnerships and preparations for child interviews, focusing on reflective practices to address experiences, challenges, and potential questions that may arise during the interviews.

Fluency Practice: Assign exercises that build skills around modeling subtraction expressions through real-world scenarios.
Game Night: Recommend engaging mathematical games to solidify understanding of addition and subtraction strategies, fostering a playful learning environment.