scaffolding engageny mathematics for english learners
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Scaffolding EngageNY Mathematics for English Learners. Anita Bright, Ph.D. Portland State University Portland, Oregon February 4, 2014. Visit http://goo.gl/Ua0fcf to access the electronic version of this document. . Our Agenda. Looking at a lesson - PowerPoint PPT PresentationTRANSCRIPT
Scaffolding EngageNY
Mathematics for English Learners
Anita Bright, Ph.D.Portland State University
Portland, OregonFebruary 4, 2014
Visit http://goo.gl/Ua0fcf to access the electronic version of this document.
Our Agenda Looking at a lesson A few quick ways to scaffold INSTRUCTION Questions?
Visit http://goo.gl/Ua0fcf to access the electronic version of this document.
Let’s look at part of a lesson.
What do you notice that might be problematic for English learners?
What might you do to modify this lesson?
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How many 1 in x 1 in x 1 in cubes will fit in the following prism?
Have students discuss their solution with a partner. How many 1 in x 1 in x 1 in cubes would fit across the bottom of the rectangular prism? How did you determine this number?
How many layers of 1 in by 1 in by 1 in cubes would fit inside the prism?
If each cube represents dice that need to be shipped, how many 1 in x 1 in x 1 in dice will fit in the box?
How did you determine this number? How is the number of cubes or dice related
to the volume? What other ways can you determine the
volume of a rectangular prism?
Example 1 (5 minutes)1. The same package in the opening exercise will
be used to ship miniature dice whose side lengths have been cut in half. The dice are ½ in x ½ in x ½ in cubes. How many dice of this size can fit in the box?
How many cubes could we fit across the
length? The width? The height?
How many 1 in x 1 in x 1 in cubes will fit in the following prism?
Have students discuss their solution with a partner. How many 1 in x 1 in x 1 in cubes would fit across the bottom of the rectangular prism? How did you determine this number?
How many layers of 1 in x 1 in x 1 in cubes would fit inside the prism?
If each cube represents dice that need to be shipped, how many 1 in x 1 in x 1 in dice will fit in the box?
How did you determine this number? How is the number of cubes or dice related
to the volume? What other ways can you determine the
volume of a rectangular prism?
Example 1 (5 minutes)1. The same package in the opening exercise will
be used to ship miniature dice whose side lengths have been cut in half. The dice are ½ in x ½ in x ½ in cubes. How many dice of this size can fit in the box?
How many cubes could we fit across the length?
The width? The height?
3. A toy company is packaging its toys to be shipped. Some of the very small toys are placed inside a cube shaped box with side lengths of ½ in. These smaller boxes are then packed into a shipping box with dimensions of 12 in x 4 ½ in x 3 ½ in.
a. How many small toys can be packed into the larger box for shipping?
Here’s a re-wording: Original
A toy company is packaging its toys to be shipped. Some of the very small toys are placed inside a cube shaped box with side lengths of ½ in. These smaller boxes are then packed into a shipping box with dimensions of 12 in x 4 ½ in x 3 ½ in.
How many small toys can be packed into the larger box for shipping?
Scaffolded
A toy company puts small toys into boxes. The boxes are cubes with side length of ½ in.
These small boxes are put inside a bigger box with dimensions of 12 in. x 4 ½ in. x 3 ½ in.
How many toys can be put into the larger box?
Another note on this lesson
Words are used interchangeably: Long/ length High/ height (and sometimes deep/ depth) Width/ wide
Some words are have multiple meanings (like volume).
These relationships between these words need to be taught!
Three* big ideas:1. Amplify key language (to
increase accessibility).
2. Use graphic organizers (to help students focus on the big ideas).
3. Provide support for speaking and writing (to enrich their academic register).
*More big ideas at the end!
Amplify key language
Text is written in present tense and may be redundant for clarity.
Sentences are short with no or few clauses. (These may read awkwardly to fluent speakers of English.)
New sentences begin on a new line.
Contexts are familiar to students in school.
Names chosen for examples should not be similar to content (including names like Ray and Mark).
Pictures/ visuals/ illustrations are used to make content clearer.
Words with multiple meanings that might be confusing are not used (ie, a garden plot and the request to plot points on a coordinate plane).
Language is internally consistent (if practice problems ask students to solve, the assessments should use the same term). If language is not internally consistent, then different terms are highlighted and taught (add, plus, sum, combine, all mean the same thing).
A Standard Example (Lesson 8.1, p. 12)
Suppose a colony of bacteria doubles in size every 8 hours for a few days under tight laboratory conditions. If the initial size is , what 𝐵is the size of the colony after 2 days?
Scaffolded Example
A group of objects doubles every 8 hours.
Today there are B objects in the group.
How many objects are in the group after 2 days?
(There are 24 hours in one day.)
A Standard Example (Lesson 8.1, p. 12)
A rectangular area of land is being sold off in smaller pieces. The total area of the land is 𝟐𝟏𝟓 square miles. The pieces being sold are 𝟖 𝟑 square miles in size. How many smaller pieces of land can be sold at the stated size? Compute the actual number of pieces.
Scaffolded Example
Kim has a farm in the shape of a rectangle.
The area of Kim’s farm is 𝟐𝟏𝟓 square miles.
Kim divides her farm into pieces that are each 𝟖 𝟑square miles in size.
How many pieces does Kim make?
Provide side-by-side texts.
Look at how useful this is! (Google translate will even provide a read-aloud.)
(Note: This is best for students who are already highly LITERATE in their first language. Do not assume this is the case with all students.)
Provide step-by-step instructions in student-friendly language & use visuals.
From a lesson on translating one-step word problems to algebraic equations.
Directions:a) Define a variable for each problem. b) Write an equation to represent the information.c) Be sure the equation requires the use of one inverse operation to find the solution!d) Show a check for each solution.
2. Provide graphic organizers.
Non-verbal displays of relationships A way to visually organize thinking
Similarities and Differences
Concept: Conic Sections
parabola
hyperbolacircle
ellipse
Similarities and Differences
Concept: ____________
4xy
16 ( 1)2y x
2( 10)5 x y
7y
5x
Similarities and Differences
Concept: Which does not belong?
(Can you think of another term that would fit?)
acute
parallel
obtuse right
3. Provide support for speaking and
writing Each day needs structured opportunities for
students to speak and write in English.
Give concrete guidelines for speaking, reading, writing or listening.
“Turn to your neighbor and explain…”Write the day’s objective on the board and have students read it along with you. Point to each word as you read aloud.Provide sentence frames for anyone who may benefit. (“I know the area of parallelogram B is larger/ smaller ______ than the area of parallelogram A because _____.”)
(More advanced students might be ready for some transition language like this: http://writing2.richmond.edu/writing/wweb/trans1. html)
Sentence frames (perhaps with word banks) can support student
explanations. Visit this link for some elementary
examples from Justin Johnson.
See also page 24 of this fabulous document from Kate Kinsella.
“The volume of my prism is ___units cubed. I found this by ______.
“My idea is similar to _____’s because ____.”
“I know the answer is a fraction because_____”Word bank:
Added
Less than one
Combined
Whole number
Equal
Have students chorally repeat key vocabulary or phrases.
Have students chorally repeat the key term in creative ways.
(“The word is pronounced hypotenuse. Again, hypotenuse. Repeat after me: hypotenuse. Whisper it: hypotenuse. This side of the room only: hypotenuse. Everyone wearing jeans, hypotenuse.” )
Why? It lowers the affective filter since there are multiple voices speaking at once. It promotes fluency. It provides and accurate auditory imprint.
Be direct about language.
EXAMPLE OBJECTIVE FOR A LESSON:
Identify perfect squares; determine square roots.
Discuss the word square. Ask students to describe what a square is: a shape with 4 equal sides and 4 right angles. Have students point out objects in the room that are squares.
Introduce expressions with the word square that students will use in this lesson – square number, perfect square, squared, square root.
Explain to students that the word square can be a noun or a verb. In the expression “the square of a number…”, square is a noun. In the expression “if we square the number…”, square is a verb.
Tell students that we will be using the word root in the mathematical expression square root. Ask students if they know any other uses of the word root (roots of trees or plants, family roots). Point out to students that in these cases, the word root relates to the beginning or foundation for something.
Use online resources for key vocabulary.
How about a cool dictionary?
Or what about Google translate?
Provide word banks. These can provide
appropriate and relevant vocabulary to use in speaking or writing about the content.
Adjacent
Complementary
Congruent
Equal
Supplementary
Vertical
Use manipulatives! The more concrete and visual these ideas
can be, the better!
Remember this thing? Use something from the classroom instead!
Connect to the real lives of students. Use concrete
examples whenever possible. Example: The same shape can have multiple names. This is a picture of Dalia. She is:
A sister A student A cousin A daughter An accountant A friend A driver A winner
All at the same time!
In the same way, this slide can be seen as a closed figure, a parallelogram, a rectangle, a polygon…
Show finished examples and provide
a rubric for self-evaluation.
___ x 3 = ___
What factor can you use in this equation to make a product that is even and between 10 and 40? Show all possible solutions. Explain your strategy.
Name and notice• Look at this
mathematical writing
• Identify what qualities make this mathematical writing strong.
The Necessity of Language Instruction in Mathematics; Angela Alcantar, Sunshine Price, and Michelle Stroup English Language Acquisition Specialists, Salem-Keizer Public Schools. 2013.
Use quick, formative assessment to
establish background knowledge Teaching students how to find the mean and median? What do they need to know?
They must FIRST know how to:
Count Put numbers in order from smallest to
largest Add Divide
Incorporate interactive games.
These can explicitly include scripted speech. “When I substitute 8 for the variable c, my equation is equal to 3.
Replace obscure words or contexts with things from a
high-frequency word list. Students learn English beginning with
HIGH FREQUENCY words. Here’s one example of a list.
Try to choose SCHOOL contexts.
Allow students to show what they know
in different ways.
This includes allowing for students to share their thinking in their first languages.
CCSS.Math.Practice.MP4 Model with
mathematics
In each of the 16 houses in the neighborhood, there were 2 dogs.
How many dogs total lived in the neighborhood?
Say it with pictures.
Say it with numbers.
Say it with words.
Say it with numbers.how many dogs
how many houses
2 x 16 = 32
Total number of dogs
Say it with words.There were two dogs
at each house and 16 houses so I counted by 2’s sixteen times. I used my fingers to help me keep track.
The Necessity of Language Instruction in Mathematics; Angela Alcantar, Sunshine Price, and Michelle Stroup English Language Acquisition Specialists, Salem-Keizer Public Schools. 2013.
Mathematics is not a universal language MUCH of what we share with students is
embedded in language that is specific.
Example: Think of the similarities and differences between the words OF and OFF.
Example: Hypotenuse is the longest side of a right triangle. EVERYONE learns the word hypotenuse; ELs need to learn the word LONGEST.
Fractions may be especially challenging
The METRIC SYSTEM is used in pretty much the entire rest of the world.
We can’t assume literacy in L1.
Not all students have had access to ongoing formal education.
Students may have yet-undiagnosed learning differences.
Students learn casual language before academic language.
This means they may sound comfortable and fluent, but may need additional support in their writing and speaking in an academic register.
Communicating in a new language can be very stressful.
Above everything else, we need to prioritize the health and well-being of our students by ensuring our classrooms are safe and welcoming.
Thanks for your time!
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