Transcript The Value of Place Value - RESA 3 PRE K-12

Fluency is More Than a Race
Developing Fluency with Understanding
It is All About the Problem
Using Rich Problems to Develop Mathematical
Understanding
TERESA HAMMOND, WVDE
LYNN BAKER, NBCT
[email protected]
[email protected]
Session Goals
Share evidence of student understanding related to
place value.
Examine strategies to help students develop fluency
with basic facts and standard algorithms.
Review problems that engage students in the
problem solving experience.
Linda Gojack
Evidence of Student Learning
5 minutes/teacher
Summarize mathematical task
Share evidence of student learning
Seek input from fellow teachers
Respect student privacy
What is
Computational
Fluency?
Adding It Up
The National Academies Press
“Procedural Fluency-skill in
carrying out procedures flexibly,
accurately, efficiently, and
appropriately.”
Key Fluencies
Grade
K
1
Required Fluency
Add/subtract within 5
Add/subtract within 10
Add/subtract within 20
(using mental strategies)
2
(by end of Grade 2, know from memory all sums of two one-digit numbers)
Add/subtract within 100 (pencil and paper)
(using strategies based on place value, properties of operations and/or the relationship between
addition and subtraction)
Multiply/divide within 100
(using strategies such as the relationship between multiplication and division (e.g., knowing that 8
× 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations)
3
(by the end of Grade 3, know from memory all products of two one-digit numbers)
Add/subtract within 1000
(using strategies and algorithms based on place value, properties of operations and/or the
relationship between addition and subtraction)
4
5
Add/subtract within 1,000,000
(using the standard algorithm)
Multi-digit multiplication
(using standard algorithm)
Key Fluencies (6-8)
6
Multi-digit division
(using standards algorithm)
Multi-digit decimal operations
(add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each
operation)
7
Solve px + q = r, p(x + q) = r
8
Solve simple 22 systems by inspection
Developing Fluency
1. Help children develop a strong understanding of number
relationships of the operations
2. Develop efficient strategies for fact retrieval through
practice.
3. Then provide drill in the use and selection of those
strategies once they have been developed.
John A. Van de Walle & LouAnn H. Lovin
From Memory ≠ Memorize
Develop
Meaningful
Understanding
Practice
Fluency
Timed Tests and the Development of Math
Anxiety
By Jo Boaler
Group Discussion:
What challenges your thinking?
How will this article impact your thinking?
What questions did this article raise?
Strategy-Personalized Flashcards
Characteristics:
26 cards
10 cards that students know
8 cards that students know but need continued practice
8 cards that students need to learn:
4 cards related to one fact family
4 cards related to one fact family
Teaching Basic Facts
WHAT TO DO---
WHAT NOT TO DO---
Ask students to self-monitor
Don’t use lengthy timed tests
Focus on self-improvement
Don’t use public comparisons of
mastery
Drill in short time segments
Work on facts over time
Involve families
Make drill enjoyable
Use technology
Emphasize the importance of
quick recall of facts
Don’t proceed through all facts
all at once
Don’t move to memorization to
soon
Don’t use facts as a barrier to
good mathematics
Don’t use fact mastery as a
prerequisite for calculator use
Fluency-Standard Algorithms
Standard Algorithms in the Common Core
Karen C. Fuson & Sybilla Beckmann
Introduction
Strategy, Standard Algorithm, and Written
Method
Criteria for Emphasized Written Method
It is All About the Problem
Using Rich Problems to Develop Mathematical
Understanding
Kathy Seeley
Inside Mathematics
http://www.insidemathematics.org
Parking Cars
rd
(3
Grade
Illustrative Mathematics
http://www.illustrativemathematics.org
Next Steps
Focus on developing fluency and engaging students with
problems.
Bring evidence of student learning
Thursday, May 7, 2015—Fractions--More Than Apples
and Pizzas