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 6UC San DiegoSan Diego State UniversityUC Irvine

Who's Who?

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?

In 2007-2008– Grade 5 45% Proficient or Advanced– Grade 6 27% Proficient or Advanced– Grade 7 23% Proficient or Advanced– Grade 8 9% Proficient or Advanced– Algebra

Grade 7 44% Proficient or Advanced Grade 8 17% Proficient or Advanced

Grant Goals

Research Effect of professional development on

– Teacher knowledge– Instructional practices– Student achievement

How will we achieve this work?

Summer Institutes 30 hours of mathematics content (2009 – 2011)

– 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

24 hours of follow up– Analyzing student data, adjusting instruction,

building on content knowledge

12 hours of research practicum– Collaborate with university staff– Develop plan for action research

100 – 115 teachers, grades 5 – 8 (algebra)

Johnny Rivera, Southeast Middle School

Teacher Commitment

TEACHER RESPONSIBILITIES

•3 year participation at the same grade level•Use instructional strategies specified at training•Share learning with PLC•Collaborate with administration on action research project•Work with director of the grant (observations, and coaching)

Yesenia Medrano, Southeast Middle School

Summer Institutes

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.

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Estimating the number of fishEstimating the number of fish

Let L be the number of fish in the lake and Let L be the number of fish in the lake and assume we have tagged 50 fish.assume we have tagged 50 fish.

Let b be the number of black beans and w the Let b be the number of black beans and w the number of white beans in our sample. Thennumber of white beans in our sample. Then

is our proportion. Since we have computed b is our proportion. Since we have computed b

and w, we can calculate L.and w, we can calculate L.

Lw

b 50

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.

Proportional Reasoning

Estimating populations

ACCESS STRATEGIESACCESS STRATEGIES

Cooperative Learning EnvironmentCooperative Learning Environment

Instructional ConversationsInstructional Conversations

Academic Language Development (ALD)Academic Language Development (ALD)

Advanced Graphic OrganizersAdvanced Graphic Organizers

Workshop GuidelinesWorkshop Guidelines

Work in small groups (usually 4) Work in small groups (usually 4) Select rich problems with threads across Select rich problems with threads across

grades guided by ‘big mathematical ideas’ grades guided by ‘big mathematical ideas’ and the MIGand the MIG

Support and encourage participation in Support and encourage participation in existing PLC groups existing PLC groups

Foster a better understanding of issues Foster a better understanding of issues faced by those teaching at other grade faced by those teaching at other grade levels 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

Experimental Group/Control Group Qualitative and Quantitative mixed methods

design

Getting into the research

Pre and post test for teachers– Given each year to teacher participants

Classroom Observations– 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