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

2. 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

3. 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.

4. Five General Thinking Skills Multi-dimensional problems Metacognition Semantic memory Hierarchical structure Cause-effect relationships

5. 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

6. 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.

7. 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.

8. 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.

9. 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.

10. 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

11. 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

12. 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

13. Mathematics Example: How many real numbers are in the figure? How many odd numbers? How many rational blue numbers?

14. Multi-Dimensional Problems Other Suggestions: Hold chess tournaments Find games that include multiple dimensions, such as Sudoku or the card game SET.

15. 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.T1

16. Metacognitive Skills Metacognition is basically thinking about ones 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)

17. 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.

18. 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.

19. Metacognitive Skills First, establish a classroom environment in which it feels safe to openly discuss ones thoughts and reasoning. Model such discussions, and ask students how they should react if they dont agree with or dont understand a classmate.

20. 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 whats 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.

21. 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!

22. 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 students thoughts as he progresses.T2

23. Metacognitive Skills Short translation: Number 2 maybe goes here. I have to check this column. Yes. I see no other 2s. Fine, but I need to check these other boxes. The problem is that I see a 2 already in this row, so I cant have a 2 here. I have to move it here. Now its good!

24. 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.

25. 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.

26. 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.

27. Semantic Memory Deaf students sometimes lack flexibility in deciphering the meaning of a word, because theyve 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.

28. Semantic Memory and 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.

29. 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.

30. 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.

31. 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.

32. 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.

33. 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?

34. 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.

35. 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.T3 (View Film Clip T3)T3

36. 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.

37. 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.

38. 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.

39. Hierarchical Structure Deaf students may not automatically recognize a concepts 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).

40. 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.

41. 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.

42. 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.

43. 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.

44. 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

45. 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.

46. Hierarchical Structure Warning: Not all graphic organizers are hierarchical. Compare the two following: Linear Functions steady increase/decrease straight line y=mx+b slope = rise- over-run positive slope: / negative slope: \ y-y 1 = m(x-x 1 )

47. Hierarchical Structure Warning: Not all graphic organizers are hierarchical. Compare the two following: Forces Strong Electro- magnetic WeakGravity nucleus of atom charges (+ and -) like repel/ opposites attract neutrinos masses attract

48. 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/decrease straight line y=mx+b slope = rise- over-run positive slope: / negative slope: \ y-y 1 = m(x-x 1 )

49. Hierarchical Structure This diagram is hierarchical. Each level provides a detail related to the level immediately above. Forces Strong Electro- magnetic WeakGravity nucleus of atom charges (+ and -) like repel/ opposites attract neutrinos masses attract

50. 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.T4

51. 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.

52. 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.

53. 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.

54. 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.

55. 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.

56. 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.T5

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

58. Cause-Effect Relationships Flow Chart Example – Science: Plant Seed Water? Plant Grows No Plant yesno 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.

59. 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.

60. Cause-Effect Relationships Mathematics examples: –Have students experiment with the general form of an equation, such as y = ax 2 + 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.

61. 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.

62. Cause-Effect Relationships Possible Story: –Carin left to walk to the store for her mom, but after shed 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. 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.

63. Summary Five General Thinking Skills Multi-dimensional problems Metacognition Semantic memory Hierarchical structure Cause-effect relationships

64. 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.