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Preparing for Success in Algebra English Language Learners in Mathematics. A Collaboration between: Los Angeles Unified School District University of California, San Diego San Diego State University University of California, Irvine San Diego Mathematics Project. LANGUAGE. Follow-Up
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Preparing for Success in AlgebraEnglish Language Learners in Mathematics A Collaboration between: Los Angeles Unified School District University of California, San Diego San Diego State University University of California, Irvine San Diego Mathematics Project
LANGUAGE Follow-Up October 23, 2010
Yesenia Medrano, Southeast Middle School Teacher Commitment Descriptions and the Language of Mathematics
Agenda • We will all work to: • Learn to teach academic language and get our instruction to “stick” • Identify activities that provide good input and output to help students describe • Identify language challenges in the released word problems related to geometry and measurement
A Quick Review of the Research Stand up, Hand up, Pair up! What does the research say are effective practices for teaching English learners?
Measurement and Geometry 58% ⏎
Measurement and Geometry Set 1.0 Students understand and compute the volumes and areas of simple objects: 5MG1.1* Derive and use the formula for the area of a triangle and of a parallelogram by comparing it with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rectangle of the same area by cutting and pasting a right triangle on the parallelogram).
Set 1.0 Students understand and compute the volumes and areas of simple objects: 5MG1.2* Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area for these objects. 5MG1.3* Understand the concept of volume and use the appropriate units in common measuring systems (i.e., cubic centimeter [cm3], cubic meter [m3], cubic inch [in3], cubic yard [yd3]) to compute the volume of rectangular solids.
Set 1.0 Students understand and compute the volumes and areas of simple objects: 5MG1.4 Differentiate between, and use appropriate units of measures for, two- and three-dimensional objects (i.e., find perimeter, area, volume).
Standard Set 2.0 Students identify, describe, and classify the properties of, and the relationships between plane and solid geometric figures.
Standard Set 2.0 5MG2.1* Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software). 5MG2.2* Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360° and use this information to solve problems. 5MG2.3 Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids.
I do, we do, you do… helping students describe geometrical figures. Generalization – I do Congruent – we do Adjacent – you do
Key academic word: Generalization Step 1: Introduce the word. Say the word for students so that they can hear it clearly. Use the word in a sentence.
Generalization • Step 3: Students see the word and read it aloud. • Step 4: Students listen to you explain the word and use the word. Ask them to take notes. Step 2: Students pronounce the word.
Key Word: Generalization a statement about all the members of a group that may be true the process of coming up with a general idea about a group by identifying common properties
Generalization • Step 5: Use complete sentences to talk about the word. What generalizations can you make about these shapes? ★
Some Generalizations Squares have angles. Triangles have sides. Students have books.
Step 6: Talk about grammar and use. You can make/constructageneralization or generalizationsaboutsomething. You can make a sweepinggeneralization. You can justify your generalization with evidence. You can come up with a new generalization.
Over-Generalizations Boys with blue eyes can’t be trusted. Girls are bad at telling jokes. Boys are bad when it comes to asking for directions.
Velcro! • Step 7: Do something to help your students remember the word. Perhaps you could tell a story entailing the use of the word. Perhaps you could draw a picture the students could associate with the word.
Provide additional opportunities for students to use the word. Use it or lose it.
I do, we do, you do Congruent
Congruent Having the same size and shape Refers to triangles
Congruence We can talk about the congruence of two triangles.
Providing Input and Output Please look at the activities in your handout. Which one do you think best provides students with input for language development? Which one do you think best provides students with output for language development?
What to say when you.. compare & contrast They are similar because... Notice how the two compare… This is a lot like how… Zwiers, J. (2009)
compare & contrast The two differ because one…, while the other… On the other hand,… We can see that …. is different from… in the area of ______ They share the following traits: Zwiers, J. (2009)
Discussion: What’s challenging? Let’s talk about WXYZ and WXY. Let’s talk about the “figure below.”
The What Works Clearinghouse was established in 2002 by the U.S. Department of Education's Institute of Education Sciences to provide educators, policymakers, researchers, and the public with a central and trusted source of scientific evidence of what works in education. The What Works Clearinghouse (WWC) collects, screens, and identifies studies of effectiveness of educational interventions (programs, products, practices, and policies). http://ies.ed.gov/ncee/wwc/
http://www.centeroninstruction.org/ The Center on Instruction, a partnership of five organizations, provides resources and expertise to the Regional Comprehensive Centers in reading, mathematics, science, special education, and English language learners.
http://www.nctm.org/ NCTM is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. Founded in 1920, NCTM is the world’s largest mathematics education organization, with 100,000 members and 250 affiliates throughout the United States and Canada.
National Council of Teachers of Mathematics http://illuminations.nctm.org/
