Preparing for Success in Algebra
English Language Learners in Mathematics
A Collaboration among:
 LAUSD Local District 6
 UC San Diego
 San Diego State University
 UC Irvine
Partners
LAUSD Local District 6
UC San Diego
San Diego State University
UC Irvine
Who's Who?
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Grant Project Director – Open (Local District 6)
LD6 Transition Leadership Team – Sharon Sweet, Suyen
Moncada-Machado, Stephanie Flaxbeard, Brian Olona, Josie
Pajon
UCSD:
– Gretchen Laue, Director
– Dolly Casco, Associate Director
– Stephan Bera
SDSU:
– Dr. Rafaela Santa Cruz
– Dr. John Elwin
UCI – Robin Scarcella, Researcher
Why this grant?
What does the data tell us?
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In 2007-2008
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–
–
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Grade 5
Grade 6
Grade 7
Grade 8
Algebra
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Grade 7
Grade 8
45% Proficient or Advanced
27% Proficient or Advanced
23% Proficient or Advanced
9% Proficient or Advanced
44% Proficient or Advanced
17% Proficient or Advanced
Grant Goals
Research
 Effect of professional development on
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–
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Teacher knowledge
Instructional practices
Student achievement
How will we achieve this work?
Summer Institutes
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30 hours of mathematics content (2009 – 2011)
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Focus – Curriculum, Instruction, Assessment
40 hours of SB 472 (2009/2010)
36 hours of follow up and
research practicum
30 hours culminating
Research Institute (2011)
Academic Year
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24 hours of follow up
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Analyzing student data, adjusting instruction,
building on content knowledge
12 hours of research practicum
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Collaborate with university staff
Develop plan for action research
100 – 115 teachers, grades 5 – 8 (algebra)
Johnny Rivera, Southeast Middle School
Teacher Commitment
ACHER RESPONSIBILITIES
year participation at the same grade level
se instructional strategies specified at training
hare learning with PLC
ollaborate with administration on action research project
ork with director of the grant (observations, and coaching)
Yesenia Medrano, Southeast Middle School
Summer Institutes
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Dr. John Elwin
Dr. Rafaela Santa Cruz
Mini Lesson
Student from Local District 6
MATHEMATICS INSTRUCTIONAL GUIDES (MIG)
6th Grade
Unit 2, Concept 3 - Algebraic Thinking and Proportional
Reasoning
Standards:
AF2.2 Demonstrate an understanding that rate is a measure of one quantity per
unit value of another quantity.
AF2.3 Solve problems involving rates, average speed, distance, and time.
NS1.2 Interpret and use ratios in different contexts to show the relative sizes of
two quantities, using appropriate notations.
NS1.3 Use proportions to solve problems. Use cross-multiplication as a method for
solving such problems, understanding it as the multiplication of both sides of an equation
by a multiplicative inverse.
NS1.4 Calculate given percentages of quantities and solve problems involving discounts
at sales, interest earned, and tips.
MATHEMATICS INSTRUCTIONAL GUIDES (MIG)
6th Grade
Unit 3, Concept 3 -Statistics, Data and Probability
Standards:
SDAP1.1 Compute the range, mean, median, and mode of data sets.
SDAP1.3 Understand how the inclusion or exclusion of outliers affects measures of
central tendency.
SDAP1.4 Know why a specific measure of central tendency (mean, median, mode)
provides the most useful information in a given context.
SDAP2.3 Analyze data displays and explain why the way in which the question was
asked might have influenced the results obtained and why the way in which the results
were displayed might have influenced the conclusions reached.
SDAP2.5 Identify claims based on statistical data and, in simple cases, evaluate the
validity of the claims.
MATHEMATICS INSTRUCTIONAL GUIDES (MIG)
Algebra Readiness
Unit 2, Concept 1 -Decimals, Ratio and Proportions and
Percents
Standards:
7NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and
terminating decimals) and take positive rational numbers to whole-number powers.
7NS1.3 Convert fractions to decimals and percents and use these representations in
estimations, computations, and applications.
Jolly Ranchers/Jawbreakers (3)
5
JR 100


13 JB
JB
5  JB  13 100
1300
JB 
 260
5
Jolly Ranchers/Jawbreakers (4)
JB  JR  720
5  JB  13  (720  JB)
JR  720  JB
5 JR 720  JB


13 JB
JB
13  720
JB 
 520
18
5  JB  13  720  13  JB
JR  720  520  200
Estimating the number of fish
 Let L be the number of fish in the lake and
assume we have tagged 50 fish.
 Let b be the number of black beans and w
the number of white beans in our sample.
Then
b 50

w L
 is our proportion. Since we have computed
b and w, we can calculate L.
Proportional Reasoning
Estimating populations
One method of estimating the number of fish in a lake is to catch and tag a collection of
fish and then release them. At a later time we return and catch a sample of fish and
determine the proportion of tagged fish.We can then use that proportion to estimate
the total fish population in the lake. For example, suppose that we initially caught,
tagged and released a total of 50 fish. If we return later and catch a total of 60 fish, 18
of which were tagged, we can then estimate of the number of fish in the lake?
Let’s simulate this situation using a bag with an unknown number of white beans. For
this exercise, please work in pairs at your table of 4. Remove 50 white beans and
replace with 50 black beans (the tagged fish). Then using a scoop, have one partner
remove a sample from the bag, count the respective numbers of black and white beans
and return the sample to the bag. The other partner will then follow and do the same.
Each person at the table should collect a sample, count the respective numbers and
replace the sample. Let L denote the number of fish in the lake. Determine your estimate
for L by setting up and solving a proportion. When you have calculated your estimate,
please write your estimate on a dot and place the dot in the appropriate bin in the
histogram of results we are constructing.
ACCESS STRATEGIES
 Cooperative Learning Environment
 Instructional Conversations
 Academic Language Development
(ALD)
 Advanced Graphic Organizers
Workshop Guidelines
 Work in small groups (usually 4)
 Select rich problems with threads across
grades guided by ‘big mathematical ideas’
and the MIG
 Support and encourage participation in
existing PLC groups
 Foster a better understanding of issues
faced by those teaching at other grade
levels
Web Tool
The CaMSP Web Tool
will be available in June. It is
an online community space
for teachers to receive
updates, review video
examples, and share
instructional strategies.
Video
http://erickutner.com/staging/Tennis_v5.mov
Dinner
The Research
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Experimental Group/Control Group
Qualitative and Quantitative mixed methods
design
Getting into the research
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Pre and post test for teachers
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Given each year to teacher participants
Classroom Observations
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2 trained research associates will observe
teachers 3 times during the year with an
observation instrument
Grant director will observe and coach teachers
through the grant
Pre-Test
Calendar/Questions