Math Workshop for Second
Language Learners
WABE 2012
Dr. Kristin Percy Calaff
[email protected]
Workshop Agenda
Purpose: To develop effective instructional
strategies in order to build the mathematical
thinking of second language learners.
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Review effective ELL math instruction
Practice Singapore model drawing
Develop a math “workshop”
Effective Math Instruction
Explicit Purpose Statements
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Use a sentence frame
– The purpose of today’s lesson is to…
in order to…
– We will…so we can…
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Key Components
– What? (name the activity)
– Why? (link to long-term goal)
– How? (plan your assessment tool)
Effective Math Instruction
Input Strategies
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Cognitive Content Dictionary
Signal Words
Pictorials
Chants
Process Grid
CCD - Fractions
Word
Meaning
Example
numerator
number of pieces
3
4
denominator
names the size
or total
equivalents
different fractions
with equal values
5
8
1 = 3
2
6
multiples
counting by a
number
3, 6, 9, 12, 15…
factors
numbers you can
divide by evenly
FACTORS of 8
1, 2, 4, 8
(1x8) (2x4)
improper
fraction
top is bigger than
the bottom
17
12
mixed
number
a whole number
and a fraction
3½
Sketch
Pictorial - Addition
Addition
Add
Plus
Sum
Combine
Counting On
3+3=6
3 plus 3 equals 6
plus
3
+3
6
4+4=
4…5, 6, 7, 8
total
equals
How many?
Altogether
In all
Problem, Equation, Number
Sentence
4+4=8
Everett Public Schools
Operation
Vocabulary Key
Purple= Related to the
Symbol
Green= Related to word
problems
Red= Related to equations
Pink= numbers
The Mr. Four Bugaloo
I’m Mr. Four and I’m here to say
I count by 4’s almost every day.
4…8…12…16
I skip all the numbers in between.
Next I count 20, 24, and 28,
I’m almost there and I’m feeling great!
32, 36, and 40, woo-hoo!
Doing the Mr. Four Bugaloo!
Process Grid - Quadrilaterals
Quadrilateral
Angles
Congruent Sides
Parallel Sides
parallelogram
trapezoid
rectangle
rhombus
scalene
square
Everett Public Schools
Effective Math Instruction
Output Strategies
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Turn and talk / 10:2
Explain your thinking
– How did you get that?
– How do you know?
– I used the ______ strategy because…
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Group Work / Team Tasks
– Cooperative roles in math
– “Don’t touch their pencil.”
Singapore Problem-Solving
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1. UNDERSTAND
– Read the problem.
– Underline the important information.
(Who? What? How?)
– Write a “mmm” statement.
2. PLAN
– Draw a diagram.
– Label the parts.
– Put the ? in place.
3. SOLVE
– Do the math. (Choose a strategy.)
4. CHECK
– Fill in in your answer. (Does it make sense?)
Karen had $12 more than José. If José had
$23, how much did they have altogether?
Marisa and Lucas were giving out flyers to
advertise a car wash for their class. Marisa
gave out 3 times as many flyers as Lucas. If
Lucas gave out 6 flyers, how many did they
give out altogether?
Johnny had 30 candy bars to sell for his scout
troop. If he sold 3/5 of the candy bars on the
first day, how many did he have left to sell?
Why Math Workshop?
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Differentiated Instruction
Smaller groups = Individual attention
More effective use of Para support
Greater student ownership
Increased motivation
How Does It Work?
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2 or 3 flexible groups
Daily formative assessment
Teacher repeats/adjusts “mini-lesson”
Students practice independently
“Math Experts” assist peers
Students do extension/review activities
Two-Group Workshop Model
10:0010:20
Group 1 (Low/Mid)
HW
Review/Readiness
Activity/
Extension Activities*
Group 2 (Mid/High)
Mini-Lesson
w/Teacher
10:2010:40
Mini-Lesson
w/Teacher
Independent and/or
Group Practice*
(Math Experts Assist)
10:4011:00
Independent and/or
Group Practice
(Teacher Assists)
Extension Activities
OR More Practice*
* Para/Volunteer may assist, if available
Key Elements of Math Workshop
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Mini-Lessons
– Additional manipulatives
– High-level concepts, simple numbers
– Challenge problems
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Independent Practice
– Clear Expectations
– Math “Experts”
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Readiness/Extension Activities
– Readiness (from previous year)
– Games, Extensions
– Computer: Math Playground, Xtra Math
Three-Group Workshop Model
Group 1-Low
10:00- Readiness/
10:20 Extension
Activities*
Group 2-Mid
Mini-Lesson
w/Teacher
10:20- Mini-Lesson
10:40 w/Teacher
Independent
Practice*
(Math Experts)
10:40- Independent
Extension
11:00 Practice*
Activities OR
(Math Experts) More Practice
* Para/Volunteer assists
Group 3-High
Independent
Practice (from
previous day)
(Math Experts)
Extension
Activities
Mini-Lesson
w/Teacher
Plan Your Workshop
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How will you assess and group students?
What assistance do you have available?
Will you use a 2 or 3 group model?
What readiness activities do you need?
What extension activities will you use?
How will you teach expectations for student
ownership and independence?
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Overview of Assessment