Developing Thinking Skills in Deaf Learners: Strategies and Priorities for the Science and Mathematics Teacher Harry G. Lang Rachel C. Lewis National Technical.

Developing Thinking Skills in Deaf Learners: Strategies and Priorities for the Science and Mathematics Teacher

Harry G. LangRachel C. Lewis

National Technical Institute for the DeafRochester Institute of Technology

Objectives

At the end of this unit, the teacher will be able to:

• identify five target thinking skill areas which are in need of further emphasis in the instruction of deaf learners

• apply strategies for strengthening these skills in deaf learners

Five General Thinking Skills

• There are many different thinking skills that can be addressed during instruction in mathematics and science.

• Based on our review of the literature and discussions with teachers, we have selected five areas that are especially important.

Five General Thinking Skills

• Multi-dimensional problems

• Metacognition

• Semantic memory

• Hierarchical structure

• Cause-effect relationships

Multi-Dimensional Problems

• Research (Marschark, Lang & Albertini, 2002) has shown that deaf students struggle with problems that require them to consider more than one dimension, for instance considering both size and color.

• Some possible reasons:– less experience identifying multiple

dimensions in a task compared to hearing students

– differing level of motivation or threshold for frustration

Multi-Dimensional Problems

What can you do in your class to strengthen students’ skills in dealing with multi-dimensional problems?

Take 10 minutes and discuss your ideas with the group, or submit your ideas to the discussion board and see what other teachers have submitted.

Multi-Dimensional Problems

• Students need to have FREQUENT and VARIED exposure to such problems, including many activities throughout each course and grade level.

• Teachers should have dialogue with students about the different dimensions to be considered in a task or activity, and challenge the students’ thinking.

Multi-Dimensional Problems

Plan for it!For every course taught, you should

identify 5-10 deliberate activities aimed at strengthening students’ skills with “Multi-Dimensional Problems” for the specific course(s) you will teach.

As many of these activities as possible should be conducted during the elementary and middle school years.

What About TIME?

• Embedding thinking skills will NOT steal time away from teaching the content objectives in our lessons.

• Both the mathematics and science national standards strongly encourage an emphasis on process and thinking skills development.

Examples:

How many crescent moons do you see in this picture? How many are dark colors? How many are light colors?

Note: As always, key vocabulary should be taught before such an activity.

Multi-Dimensional Problems

Examples:

How many of these leaves have rounded leaflets?

How many of these leaves are ferns?

How many of these leaves have needle-like leaflets?

Multi-Dimensional Problems

Mathematics Example:

Consider the spinner shown to the right. If Alec spins it once, what is the probability that it will land on an odd factor of twelve? On an even multiple of 3?

Multi-Dimensional Problems

12

11

10

9

87 6

5

4

3

21

Multi-Dimensional Problems

Mathematics Example:

How many real numbers are in the figure?

How many odd numbers?

How many rational blue numbers?

Multi-Dimensional Problems

Other Suggestions:

• Hold chess tournaments

• Find games that include multiple dimensions, such as Sudoku or the card game SET.

Multi-Dimensional Problems

Film clip T1 demonstrates a game called SET, which is one of many activities teachers have available to challenge students’ thinking with multi-dimensional tasks.

Metacognitive Skills

Metacognition is basically “thinking about one’s own thinking.”

• Research shows that deaf learners are relatively lacking in metacognitive skills

• Possible reason:– teachers may take a more concrete, focused

approach, hoping students will have a clear understanding of a particular strategy

(Marschark, Lang & Albertini, 2002)

Metacognitive Skills

What can you do in your class to strengthen your students’ metacognitive skills?

Take 10 minutes and discuss your ideas with the group, or submit your ideas to the discussion board (“Thinking Skills Discussion Board”) and see what other teachers have submitted.

Metacognitive Skills

Plan for it!For every course taught, you should

identify 5-10 deliberate activities aimed at strengthening students’ “Metacognitive Skills” for the specific course(s) you will teach.

Many strategies should be utilized very often throughout the grade levels and throughout each course.

Metacognitive Skills

• First, establish a classroom environment in which it feels ‘safe’ to openly discuss one’s thoughts and reasoning.

• Model such discussions, and ask students how they should react if they don’t agree with or don’t understand a classmate.

Metacognitive Skills

• Present students with problems that are open to several methods of solving.

• Example: Emily has a one-pound bag of candy. Her brother takes 1/4 of the candy, and she gives 30% of what’s left to her friend. How much candy does Emily have left?

• This problem may be approached by converting to percents, converting to fractions, drawing a picture, etc.

Metacognitive Skills

• Encourage students to explain or narrate their thinking process as they work, in writing, to a partner or as a group.

• This should be a regular part of the learning process!

Metacognitive Skills

• In film clip T2, a student is “signing aloud” his thoughts about placing the number 2 in a Sudoku puzzle. The goal is to have each number from 1 to 9 show up only once in a row and once in a column in a given 3 x 3 box. Signing aloud allows the teacher to see the student’s thoughts as he progresses.

Metacognitive Skills

• Short translation: “Number 2 maybe goes here. I have to check this column. Yes. I see no other 2’s. Fine, but I need to check these other boxes. The problem is that I see a 2 already in this row, so I can’t have a 2 here. I have to move it here. Now it’s good!”

Metacognitive Skills

Example:Give a word problem in print. Have each

student write about the problem, how they would solve it, AND write down how they corrected their own thinking while reading the problem and solving it.

Teachers should model this by talking/signing their own way through the solution of a problem, including correcting their own thinking about the data or dimensions.

Metacognitive Skills

• Provide framework for practicing metacognition, asking why they did what they did, or why they chose not to do something.

• Example: In science class, make such questions a regular part of lab reports. Also, give students opportunities to question each other.

Metacognitive Skills

• Give students opportunities to actively examine their understanding of new concepts.

• Example: Creative Writing – (See PowerPoint Lesson on “Writing-to-Learn: Creative Piece”) After learning about the terms “vertebrate” & “invertebrate,” have students write a one-act play where a vertebrate meets an invertebrate and they discuss their similarities & differences.

Semantic Memory

• Deaf students sometimes lack flexibility in deciphering the meaning of a word, because they’ve had fewer experiences with multiple meanings.

• As a result, they have fewer meanings to retrieve from long-term memory when they see a word while reading.

Semantic Memoryand Multiple Meanings

Example: What does “table” mean?

• a flat-topped piece of furniture

• an arrangement of data in columns

• to postpone a discussion

• the flat surface of a gem

The number of meanings known depends on the students’ prior experiences with this word.

Semantic Memory

What can you do in your class to strengthen students’ semantic memory skills?

Discuss your ideas with the group, or submit your ideas to the discussion board and see what other teachers have submitted.

Semantic Memory

Plan for it!Work on strengthening your students’

“Semantic Memory” every chance you get, every time a word presents an opportunity.

One option: have students keep a log or journal of multiple meanings.

Semantic Memory

• In signing environments, be aware of sign selection.

Example: “the WILL to live”

If a student signs WILL as “future tense of ‘to be,’” do not quickly brush off the wrong sign and go on.

Rather, discuss the different meanings and the different signs in depth.

Ask the students to use each meaning in a different sentence.

Semantic Memory

Consider the word RUN.Discuss the appropriate sign to use in each

situation:

• Why does your nose RUN when you come in from the cold?

• When you RUN for a long time, what happens to your heart rate?

• Who wants to RUN for class representative?• Make sure you watch the gauge as you RUN the

machine.

Semantic Memory

• Be conscious of words with multiple meanings, and do not assume students will know the proper meaning for that context.

• Example: The word “function” has a very particular meaning in mathematics which is not clearly related to the everyday meaning of this term.

• What are some other words that come up in your subject area which have multiple meanings?

Semantic Memory

• When words with multiple meanings arise, discuss each possible meaning.

• See what they already know, and have them look up all meanings in a dictionary.

• Guide the students through determining which meaning makes sense in that situation.

Semantic Memory

• In film clip T3, a middle school math class is discussing rectangular prisms. The teacher asks students for possible meanings of the word “face” and they discuss the suitability of each.

• (View Film Clip T3)

Semantic Memory

• Another thing to look for is spelling errors. Sometimes, the spelling errors may indicate the student has not learned a new word as expected.

• For example, students who have learned to perform several TRIALS in a science experiment may spell this word as TRAIL.

• Make extra effort to be sure the students know the difference between these two terms.

Semantic Memory

• Watch for metaphorical or idiomatic uses of words. Deaf students may not have had the exposure to understand the meaning.

• Science Examples: “Mother Earth” or “I feel like a cloud in the air.”

• Mathematics Examples: “The negative three is like holes” or “Equations are balanced scales.”

Semantic Memory

• A useful practice to teach students is to watch for common roots, prefixes, or suffixes. Such fragments can serve as either cues or miscues, however.

• Examples: The ‘sub’ in submarine and submerge are clearly connected, but how do they relate to subtract?

• Millimeter and millennium both relate to an idea of “one thousand,” but ‘millimeter’ is actually one-thousandth of a meter while a ‘millennium’ is one thousand years.

Hierarchical Structure

• Deaf students may not automatically recognize a concept’s place in a hierarchical structure.– A Corvette is a type of car which is a type of

vehicle. A car is not a type of Corvette.– An apple is a type of fruit which is a type of

food. Food is not a type of apple.

• This is basically a function of prior experience (Marschark, Lang, and Albertini, 2002).

Hierarchical Structure

Chemistry example:

An electron is a component of an atom or molecule, which is matter.

Mathematics example:

A coefficient is part of a term, which is part of a polynomial, which is part of an equation.

Hierarchical Structure

• The very learning of mathematics is hierarchical. One must understand addition before multiplication, multiplying numbers before variables, monomials before binomials, and so on.

Hierarchical Structure

What can you do in your class to strengthen students’ understanding of hierarchical structures?

Discuss your ideas with the group, or submit your ideas to the discussion board and see what other teachers have submitted.

Hierarchical Structure

Plan for it!For every course taught, you should

identify 5-10 deliberate activities aimed at strengthening students’ skills in understanding and applying “Hierarchical Structures” for the specific course(s) you will teach.

As many of these activities as possible should be conducted during the elementary and middle school years.

Hierarchical Structure

• Provide a list of terms and have the students arrange them in hierarchical order.

• Science Example: organelle, cell, tissue, organ, organism

• Mathematics Example: real numbers, integers, rational numbers, natural numbers

Hierarchical Structure

• One way to facilitate an understanding of hierarchy is by using graphic organizers, which organize information visually. Some examples are concept maps and flow charts.

Hierarchical StructureWarning: Not all graphic organizers are

hierarchical. Compare the two following:

Linear Functions

steady increase/decre

asestraight line

y=mx+b

slope = rise-over-

run

positive slope: /

negative slope: \

y-y1 = m(x-x1)

Hierarchical StructureWarning: Not all graphic organizers are

hierarchical. Compare the two following:

Forces

Strong Electro-

magnetic

Weak Gravity

nucleus of atom

charges (+ and -)

like repel/

opposites attract

neutrinos

masses attract

Hierarchical Structure• This diagram is not hierarchical. All items relate

to the central topic, but there is no sense of order among the subtopics.

Linear Functions

steady increase/decre

asestraight line

y=mx+b

slope = rise-over-

run

positive slope: /

negative slope: \

y-y1 = m(x-x1)

Hierarchical Structure• This diagram is hierarchical. Each level

provides a detail related to the level immediately above.

Forces

Strong Electro-

magnetic

Weak Gravity

nucleus of atom

charges (+ and -)

like repel/

opposites attract

neutrinos

masses attract

Hierarchical Structure

• In film clip T4, a student is asked to group geometric shapes into hierarchical order. He makes a mistake, and the teacher discusses the meaning of “quadrilateral,” then asks the same student to revise his hierarchy.

Hierarchical Structure

• Science example: Provide an intentionally-incorrect hierarchy, such as the biological classification system (kingdom, phylum, class, etc.) – the order of the categories may be incorrect and/or groups may be placed under the wrong classification level. Challenge students to repair the hierarchy.

Hierarchical Structure

• Mathematics example: As students learn about new kinds of numbers, such as rational numbers (fractions, decimals, percents) or integers, they can be added to a chart showing how each set of numbers is a subgroup of a larger set. For example, integers include the set of natural numbers.

Cause-Effect Relationships

• Children in general often struggle with cause-effect relationships, incorrectly answering reading comprehension questions involving such relationships.

• Possible reason:– Younger children tend to focus on the

present, while cause and effect may be separated by time.

Cause-Effect Relationships

What can you do in your class to strengthen students’ understanding of cause-effect relationships?

Discuss your ideas with the group, or submit your ideas to the discussion board and see what other teachers have submitted.

Cause-Effect Relationships

Plan for it!For every course taught, a teacher should

identify 5-10 deliberate activities aimed at strengthening students’ understanding of “Cause-Effect Relationships” for the specific course(s) you will teach.

As many of these activities as possible should be conducted during the elementary and middle school years.

Cause-Effect Relationships

• In film clip T5, a math class plays a game called “Guess My Rule.” The teacher asks for numbers and she applies a rule and enters a second number in the adjacent column. The students are being encouraged to figure out the “cause” when she shows the “effect” of her rule.

Cause-Effect Relationships

• Various graphic organizers can be used to help students see cause-effect relationships, especially timelines and flow charts.

Cause-Effect Relationships

Flow Chart Example – Science:

Plant Seed

Water?

Plant Grows

No Plant

yes no

This simple example can be expanded to show the effects of different decisions – i.e., giving the plant light or not – or variations on a single decision, such as varying the amount of water.

Cause-Effect Relationships

• You can use activities that are already in your curriculum to teach cause and effect.

• Science example: Any experiment can be used to discuss cause and effect. In particular, help students understand the role of a control group and the importance of only changing one variable at a time – without those practices, you would see the effects without being able to isolate the cause.

Cause-Effect Relationships

• Mathematics examples: – Have students experiment with the

general form of an equation, such as y = ax2 + bx + c to determine the effects of changing the coefficients. After giving time for experimentation, show a particular graph and ask students if they can come up with the equation.

Cause-Effect Relationships

• Mathematics examples: – Story graphs: Draw a graph that represents distance

from home or money in a bank account, such as the one below, and ask students to explain what might be happening at different points on the graph.

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Cause-Effect Relationships

• Possible Story: – “Carin left to walk to the store for her mom, but after

she’d been walking five minutes, she realized she forgot the money, so she hurried home to get it. She started walking again, but ran into a friend, so she stopped and talked a while before continuing.

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It took her five minutes at the store to get what she needed, then she started home, not getting there until more than half an hour after she first left.”

Summary

Five General Thinking Skills

• Multi-dimensional problems

• Metacognition

• Semantic memory

• Hierarchical structure

• Cause-effect relationships

Summary

Teachers can make a difference by embedding these and other thinking skills activities throughout each and every course they teach.

The key is to be aware and prepared for opportunities to address these skills throughout each school year.