Rethinking Addition and Subtraction

Gabr’l StackhouseApril 25, 2015

Purpose To strengthen the teaching and

learning of addition and subtraction word problems in kindergarten, first, and second grade classrooms.

Learning Goals To understand why students think

addition means “join together” and subtraction means “take away.”

Collaborative Norms Actively engage

Openly share

Provide honest, constructive feedback

Have fun

Introductions

Name

Position

Number of years as an educator

I Know . . . . I Wonder . . . .

Discuss in your groups how you teach students how to solve addition and subtraction word problems. What do you know ? What do you wonder?

Use a piece of chart in the middle of your table to create a T-chart and express your thoughts.

I Know . . . . I Wonder . . . .

Let’s Do Some Math

Select a math problem from the middle of your table.

Solve the problem using a piece of white paper.

What would a student need to know and

understand in order to solve your math problem?

Addition and Subtraction

Grade K

Addition and Subtraction

Grade 1

Addition and Subtraction

Grade 2

Addition and Subtraction

Understanding addition and subtractions sets the stage for understanding all other operations students will encounter throughout school.MultiplicationDivision

How is addition and subtraction related to

multiplication and division?

NCTM. (2011). Developing and essential understanding of addition and subtraction: Pre-k-grade2. Reston, VA: National Council for Teachers of Mathematics.

Representing Situations with Addition and Subtraction

Many different problem situations can be represented by part-part whole relationships and addition or subtraction.

To develop flexible thinking about part-part-whole relationships, students need to understand that numbers can be represented in many ways.PicturesWordsSymbolsNCTM. (2011). Developing and essential understanding of addition and subtraction: Pre-k-grade2. Reston, VA: National Council for Teachers of Mathematics.

Representing Situations with Addition and Subtraction

Part-part whole relationships show how two numbers are related to the whole.

WholePart ??

Part Part

Whole? Part

Whole? ?

NCTM. (2011). Developing and essential understanding of addition and subtraction: Pre-k-grade2. Reston, VA: National Council for Teachers of Mathematics.

Representing Situations with

Addition or Subtraction

Students demonstrate many misunderstandings about when to add and when to subtract in contextual situations.

Problem solving is more complex than extracting numbers from given problems.

Thinking is different from applying a “key word”.

NCTM. (2011). Developing and essential understanding of addition and subtraction: Pre-k-grade2. Reston, VA: National Council for Teachers of Mathematics.

Representing Situations with

Addition or Subtraction

The “key words” approach does not support students in the process of sense making

Students need to analyze the full problem, taking every word and the contextual information into consideration to build their understanding of the problem’s meaning

NCTM. (2011). Developing and essential understanding of addition and subtraction: Pre-k-grade2. Reston, VA: National Council for Teachers of Mathematics.

Working with Context in

Word Problems The context of a problem situation

and its interpretation can lead to different representations.

Many children think the equal sign always comes before the answer.

2 + 6 = + 4How might a child complete the number

sentence?

Working with Context in

Word Problems According to Fosnot and Dolk

(2000), context is essential to the development of understanding and should be used from the start as a means of “construction” rather than as a culminating or extending activity for application at the end of a unit.

Fosnot, C., Dolk, M. (2001). Young mathematicians at work: constructing number sense, addition, and subtraction. Portsmouth, NH: Heinemann.

Working with Context in

Word Problems Presenting students with a

situation provides the following: An opportunity for them to chart their

own path to a solutionAn opportunity for them to construct mathematical ideas rather than apply an algorithm

An opportunity for them to discuss and make sense of the situation rather than focusing on rules and proceduresNCTM. (2011). Developing and essential understanding of addition and subtraction: Pre-k-grade2. Reston, VA: National Council for Teachers of Mathematics.

Working with Context in

Word Problems

What role does context play when we are teaching students how to solve

addition and subtraction word problems?

Problem Type Group Activity

In your groups, read through each of word problems in the Problem Type envelope.

Sort each word problem on the Problem Type sorting mat.

Select one person from your group to share.

Representing Situations with Addition and Subtraction

Which problem types should students master at the end of

kindergarten, grade 1, and grade 2?

K

K

K

1

1

K

1

1

1

1

1

2

2

2

2

Standards Group Activity

Read through the standards for kindergarten, grade 1, and grade 2.

What is the major work for each grade level? How does the major work guide your instruction? Planning? Assessment?

What are students expected to know, understand, and do with addition and subtraction word problems for each grade level?

ResourcesCommon Core Standards Writing Team (2015, April 4). Progressions for the common core state standards in mathematics: K-5, Number and operations in base ten. Retrieved from: www.commoncoretools.wordpress.com.

Fosnot, C., Dolk, M. (2001). Young mathematicians at work: constructing number sense, addition, and subtraction. Portsmouth, NH: Heinemann.

NCTM. (2015, March 31). Position Statements. Retrieved from: http://www.nctm.org/Standards-andpositions/NCTM-Position-

Statements/

NCTM. (2000). Principles and standards for school mathematics. Reston, VA: National Council for Teachers of Mathematics.

NCTM. (2014). Putting essential understanding of addition and subtraction into practice. Reston, VA: National Council for Teachers of Mathematics.

Session Evaluation Reflect on the session today.

What is your biggest “ah-ha?”

What validated your current practice?

What do you know you will work on moving forward?

What support do you need?

Contact Information

Gabr’l StackhouseMath ConsultantCreative Minds ConsultingEmail: gabrl@mycreativemindsconsulting.com

Phone: 980.352.0218

Thank you for your participation

“I hear and I forget. I see and I remember. I do and I

understand.”

~ Chinese Proverb ~