Reading Interactions That Unnecessarily Hinder Algebra Learning and Assessment. Carl Lager, PhD University of California, Santa Barbara [email protected] (805) 8937770. Overview. 1) ELs – The numbers 2) ELs – Engaging math items 3) ELs  Uncovering EL engagement
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Carl Lager, PhD
University of California, Santa Barbara
(805) 8937770
Carl Lager  May 16, 2008  [email protected]
1) ELs – The numbers
2) ELs – Engaging math items
3) ELs  Uncovering EL engagement
4) Treisman challenge
5) Adding it up (2001) application
6) What you can do to help ELs
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Who are California’s English learners? Learning and Assessment
19% 6  8, 19% 912
Carl Lager  May 16, 2008  [email protected]
Mathematics Achievement of California’s Middle School Students
20062007 EO/FEP CST mathematics results:
20062007 EL CST mathematics results:
Carl Lager  May 16, 2008  [email protected]
Mathematics Achievement of California’s Secondary Students Students
2006  2007 CAHSEEM
EOs – 80% passed
ELs  47% passed
IFEP – 85% passed
RFEP – 86% passed
Carl Lager  May 16, 2008  [email protected]
Mystery Quote – When/Who? Students
Raleigh Schorling, NCTM, 1926
“…our secondary schools are crowded with pupils who have little background and experience and less ability for mathematical training…Many come from ‘first generation homes.’ They do not even speak our language.
Every school subject now has unusual difficulties with the vocabulary of the subject…The language difficulties which the teacher confronts in instructing the children of recent immigrants,  a problem met in many high schools, is alone very great.”
Carl Lager  May 16, 2008  [email protected]
Equity strand, NCTM, 2000 Students
“Students who are not native speakers of English, for instance, may need special assistance to allow them to participate fully in classroom discussions.
Some of these students may also need assessment accommodations. If their understanding is assessed only in English, their mathematical proficiency may not be accurately evaluated.”
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]ion.ucsb.edu
Afterward, you will freewrite to specific questions and share out lessons learned.
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
The owner of an apple orchard ships apples in boxes that weigh 2 kilograms (kg) when empty. The average apple weighs 0.25 kg, and the total weight of a box filled with apples is 12 kg. How many apples are packed in each box?
A) 14 C) 48
B) 40 D) 56
Carl Lager  May 16, 2008  [email protected]
1) What specific meaningmaking strategies did you employ?
2) How effective were your strategies?
3) How confident were in your answers?
4) What “mental movies” were you generating? What were you seeing?
5) How did you feel?
Carl Lager  May 16, 2008  [email protected]
1) What specific meaningmaking strategies did you employ?
2) How effective were your strategies?
3) How confident were in your answers?
4) What “mental movies” were you generating? What were you seeing?
5) How did you feel?
Carl Lager  May 16, 2008  [email protected]
The owner of an apple orchard ships apples in boxes that weigh 2 kilograms (kg) when empty. The average apple weighs 0.25 kg, and the total weight of a box filled with apples is 12 kg. How many apples are packed in each box?
A) 14
B) 40
C) 48
D) 56
Carl Lager  May 16, 2008  [email protected]
The owner of an apple orchard ships apples in boxes that weigh 2 kilograms (kg) when empty.
Carl Lager  May 16, 2008  [email protected].ucsb.edu
The average apple….
When have you ever heard this phrase? Average as an adjective? An EL would expect red, juicy, ripe, etc. to describe the physical characteristics of the apple, not average.
The owner of an apple orchard ships apples…
Ships as a verb? What about ships on the water?
Carl Lager  May 16, 2008  [email protected]
How many apples are packed in each box?
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Reading Comprehesnion challenges
Carl Lager  May 16, 2008  [email protected]
…the process of simultaneously extracting and constructing meaning through interaction and involvement with written language. It consists of three elements: the reader, the text, and the activity or purpose for reading.
Carl Lager  May 16, 2008  [email protected]
…these elements interrelate in reading comprehension, an interrelationship that occurs within a larger sociocultural context that shapes and is shaped by the reader and that interacts with each of the elements iteratively throughout the process of reading.
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
The Study (Lager, 2006) challenges
Reading Interactions That Unnecessarily Hinder Algebra Learning and Assessment
Carl Lager  May 16, 2008  [email protected]
Research Question challenges
1) What are the specific language difficulties that hinder Spanishspeaking ELs in grades 6 and 8, from understanding one set of visualbased linear function activities?
Carl Lager  May 16, 2008  [email protected]
Design challenges


Carl Lager  May 16, 2008  [email protected]
Design challenges
60/40 split for 6th & 8th and EL/NonEL
Students worked silently, independently, and without notes
Carl Lager  May 16, 2008  [email protected]
Your turn (white sheets) challenges
Carl Lager  May 16, 2008  [email protected]
Overall Results – Correct Response challenges
Carl Lager  May 16, 2008  [email protected]
Lack of empty grid spaces!
Carl Lager  May 16, 2008  [email protected]
Example – Task 2 challenges
Figure number (N)
Number of blue squares (B)
1
3
2
5
3
7
Carl Lager  May 16, 2008  [email protected]
Example – Task 2 challenges
Figure number (N)
Number of blue squares (B)
1
3
2
5
4
3
9
7
Carl Lager  May 16, 2008  [email protected]
Mathematics Register challenges
Carl Lager  May 16, 2008  [email protected]
Figure Number (N) – Type II challenges
Carl Lager  May 16, 2008  [email protected]
Row Fallacy challenges
1
Figure 1
1
2
Figure 2
1
2
3
Figure 3
Carl Lager  May 16, 2008  [email protected]
Blue side fallacy challenges
1
1
Figure 1
1
1
2
2
Figure 2
1
1
2
2
3
3
Figure 3
Carl Lager  May 16, 2008  [email protected]
Yellow column height fallacy challenges
1
Figure 1
1
2
Figure 2
1
2
3
Figure 3
Carl Lager  May 16, 2008  [email protected]
Number of blue squares (B) challenges
0
Figure number (N)
Task 3Carl Lager  May 16, 2008  [email protected]
Number of blue squares (B) challenges
0
Figure number (N)
One possible correct scaling10
8
6
4
2
1
2
5
3
4
Carl Lager  May 16, 2008  [email protected]
Number of blue squares (B) challenges
0
Figure number (N)
Figure number scaling issue #110
8
6
4
2
1
2
3
4
5
Carl Lager  May 16, 2008  [email protected]
+1
+2
Number of blue squares (B) challenges
0
Figure number (N)
Figure number scaling issue #210
8
6
4
2
1
4
9
16
25
Carl Lager  May 16, 2008  [email protected]
Number of blue squares (B) challenges
0
Figure number (N)
Number of blue squares scaling issue11
9
7
5
+2
3
+3
1
2
5
3
4
Carl Lager  May 16, 2008  [email protected]
Research Questions challenges
2) What are the specific language difficulties that hinder Spanishspeaking ELs in grades 6 and 8, from communicating their mathematical understandings of one set of visualbased linear function activities?
Carl Lager  May 16, 2008  [email protected]
Did the students successfully express what they understood? challenges
Carl Lager  May 16, 2008  [email protected]
Precise challenges
Vague
Appropriate
“the blue squares change by 1”
“You add one square on each side.”
Inappropriate
“The blue squares can’t be added by 1 becouse then the figure would be different from the other figures.”
“Each time you add one blue square it’s going to make the triangle bigger because the numbers are mostly odd.”
Appropriate/Precision matrix
Carl Lager  May 16, 2008  [email protected]
“By 1” challenges
(e.g. 3, 5, 7, 9, 11)
– student successfullycommunicated his misunderstandingof the term change by
Carl Lager  May 16, 2008  [email protected]
“By 1” challenges
+1
+1
+1
+1
+1
+1
Carl Lager  May 16, 2008  [email protected]
“By 1” challenges
1
1
1
2
2
3
Carl Lager  May 16, 2008  [email protected]
“Two spaces” challenges
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
5) We will share out immediately afterward.
6) ARE YOU READY…..?!
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
W: What do I want to figure out, find out, or do?
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Unknown! challenges
Find the inferencesCarl Lager  May 16, 2008  [email protected]
Amount of money paid – Amount of change received = Total cost of stamps purchased
Carl Lager  May 16, 2008  [email protected]
x + y = 120
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
1) Activate related prior knowledge and experience.
2) Break down task into smaller chunks.
3) Use visual representations of realworld objects.
4) Predict the problem.
Let’s experience them as learners…use back of blue paper
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
b + t = 36
2b + 3t = 80
Carl Lager  May 16, 2008  [email protected]
What does b + t = 36 represent?
Carl Lager  May 16, 2008  [email protected]
What does b + t = 36 represent?
Carl Lager  May 16, 2008  [email protected]
b + t =36
What does b + t = 36 represent?
Number of bikes and tricycles
Number of bicycles and tricycles
Carl Lager  May 16, 2008  [email protected]
Number of bicycles and tricycles situation?
Number of bicycles and tricycles
Number of bicycles and tricycles
=
36
36
36
=
=
=
Number of bicycles (b) + number of tricycles (t)
b + t
Carl Lager  May 16, 2008  [email protected]
What does 2b + 3t = 80 represent?
Carl Lager  May 16, 2008  [email protected]
What does 2b + 3t = 80 represent?
Number of bicycle wheels and tricycle wheels
Number of wheels
Carl Lager  May 16, 2008  [email protected]
What does 2b + 3t = 80 represent?
Number of bicycle wheels and tricycle wheels
Number of bicycle wheels and tricycle wheels
Carl Lager  May 16, 2008  [email protected]
Bicycle wheels situation?
Tricycle wheels
Cognitive organizerNumber of wheels
Carl Lager  May 16, 2008  [email protected]
The overriding meaningmaking and meaningsharing challenges situation?
Carl Lager  May 16, 2008  [email protected]
Carl Lager  May 16, 2008  [email protected]
Thank you.
Carl Lager  May 16, 2008  [email protected]