Transcript PowerPoint - Camsp.net

Welcome
California Mathematics and Science
Partnership (CaMSP)
Year 2, Follow Up 3
January 22, 2011
Slide 1
Agenda: Making the Invisible
Visible
•
We will identify the language of explaining
quadratic equations to teach this language
effectively.
Slide 2
Essential Questions
•
•
How can we identify the language that we
need to teach our students so that they can
discuss quadratic equations?
What are effective instructional strategies
that help students learn this language?
Slide 3
Identifying Language to Teach
Step 1: Analyzing language
use to identify the many
features.
Step 2: Limiting the features to
a manageable number.
Slide 4
Identifying the language features
to teach entails language analysis
of texts—oral and written
Written – written explanations, e.g.,
from the students’ textbooks and other
resources
 Oral – transcribed language use –
usually of teachers and students

Slide 5
Handout
Let’s analyze how others describe
quadratic equations.
Student talk = output
Our talk to students = input
Language students read = input
Slide 6
We will be doing a task shortly
that requires you to use a
handout.
Handout : The Language Needed to
Explain Quadratic Equations
Slide 7
You need a handout that looks
like this one:
Slide 8
Stand up! Hand up! Pair up!
Slide 9
Steps

Read the handout on the language of
quadratic equations. Take at least five
minutes. Underline the language you might
use to explain quadratic equations. Write
down any additional language.
Slide 10
Steps





Stand up when you are done and find a partner across
the room.
Put your hand up, smile and establish eye contact with
someone else who has finished reading the handout.
Do a high five.
Partners interact for three minutes.
They discuss the answers to several questions.
Slide 11
Task—Answer these questions:
What language enables you to explain
quadratic equations?
 Would you use any of the language in
the handout?
 What additional language would you
use?

Slide 12
Would you use any additional
vocabulary?
Slide 13
What about prepositions?
Slide 14
Would anyone use the word
functions?
Would anyone say:
• Functions are rules that describe the
relationship between two variables. They
are commonly expressed as equations.
• Functions are often expressed as
equations that include two variables, as in
x+3=y.
Slide 15
What about function table?
Did anyone say:
• Function tables represent pairs of numbers
that follow a certain rule, or function.
Slide 16
Function Table (cont.)
Did anyone say?
 A function table for x+3=y would
include a column of corresponding
numbers for "x" and a column for "y" to
reveal a numerical pattern.
Slide 17
Would anyone give an example
of a function table?
y = 2x + 6
X
y
1
8
2
10
3
12
4
14
Slide 18
Column
a line of numbers or words written
under each other that goes down a
page
Slide 19
Row
a line of things or people next to each
other
Slide 20
In a row
One after another, consecutively
Slide 21
Would anyone use unknown
numbers or the word let?
Did anyone say:
 When you are looking for unknown
numbers, let a variable represent that
numbers?
Slide 22
What about the word
represent?
Slide 23
Timed Pair Share
1. Partners find a place to sit down. They decide who is Partner 1
and who is Partner 2.
2. Teacher describes the task. Partners will take turns explaining
what a quadratic equation is.
3. In pairs, Partner 1 explains a quadratic equation as Partner 2
listens and completes the graphic organizer.
4. Teacher calls “time”.
5. Partners switch roles. Partner 2 explains what a quadratic
equation is as Partner 1 listens and completes the graphic
organizer.
TASK: What language enables you
to explain quadratic equation?
First Partner: Explains quadratic equations.
 Second Partner: The partner completes the
graphic organizer, writing down the language
his/her partner has used.
 Both Partners: Discuss the language.

Next, partners switch roles.
Slide 25
Take a minute to prepare.
Slide 26
What language did you or your partner use to
explain quadratic equations?
Reminder: Complete the graphic organizer.
Slide 27
Identifying Language Features
to Teach

STEP TWO: Narrowing the language
features to a manageable number that
you want students to learn.
Slide 28
Step 2: Narrowing the List of Features:
Using the guiding questions below, determine what
manageable list of features you would choose to teach.
Guiding Questions
• Is the language feature unknown?
• Will it improve students’ ability to explain patterns?
• Will it increase students’ understanding of math?
• Will students use the feature in other math assignments?
• Will knowledge of the feature help to improve students’
knowledge of academic language and/or the language of
math?
Key Language Features
Task: Write 6 key features
of language you would
want to teach students
before asking them to
discuss or explain
quadratic equations in
partner activities.
Slide 30
Slide 31
Perfect Practice in Conversation
Each time a teacher gets a student to practice
a language feature correctly, it helps the student learn the feature!
That’s right!
Adapted from David Howe 2006
Slide 32
How Much Practice is Needed?
Number of correct repetitions in a row of a new
word needed to “automatize” the word - NICHD
Type of Learner
Number of
Repetitions
Most Able
1 or 2
Average
4-14
Least Able
20+ (?)
(R. Lyon, 1997)
Slide 33
What techniques can we use to
make sure students deliberately
practice using specific
language?
Does anyone suggest reading explanations aloud to
students, explaining the language in it and discussing it?
What about asking students to read it aloud afterwards?
Here are just a few (see handout
for other ideas):
Deliberate modeling and repetition – individual,
group and choral
Reading Aloud: Tables, equations, algebraic
expressions
Mathematically Speaking
Discussions and Analyses – e.g., of student
notes, textbook explanations, teacher
summaries…especially with word banks and/or
sentence stems!
Choral Repetition
Algebraic
Expression
Word Phrase
Operation
w+4
A number plus 4.
Addition
w–4
A number minus
4.
Subtraction
4 x w or 4w
4 times a number
Multiplication
w
4 divided by a
number
Division
4 or w/4
Choral Repetition
Repetition
2x2 + 3x + 1 = 0
x2 + x = 2x + 3
(x+2)(x+3) = 5
x2 - 6x + 2 = 0
Tips for Preparing Choral
Response Activities
Make sure to elicit at least four-six
sentences, phrases or words
 Try to make sure all sentences,
phrases or words are parallel in form

Slide 40
Choral Repetition for
Answering Questions
Listen -- Listen to the directions or prompt
Think--Think how you would respond.
Wait--Keep from blurting out the answer. Give everyone time to think.
Respond--When given the signal say or write your response.
Why should we use choral repetition?
Why is language use
important?
Kathryn Morgan Woodward, research associate Williams, T., Kirst, M.,
Haertel, E., et al. (2010). Gaining Ground in the Middle Grades: Why Some
Schools Do Better. Mountain View, CA: EdSource.
http://www.edsource.org/middle-grades-summary.html
Let’s look at the language in
the released word problems on
the California Standards Test
in Mathematics.
Slide 43
What makes these problems
difficult for English learners?
•
With your one or two partners, determine the
answers to the released algebra items.
•
List the language in the problem that could
be difficult for English learners to understand.
Decide how you could teach it to them.
Slide 44
Debrief
•
Share solutions.
•
Discuss language that could cause
English learners difficulties.
Slide 53
What the Research Says
Slide 54
Summary
•
•
How can we identify the language students
need to know to discuss patterns?
What are effective instructional strategies we
can use to help students use this language?
Slide 55
Take a Break
Slide 56