Introduction

Most people know, or are taught, at an early age, how to process information and develop an organized plan or strategy when confronted with a problem, whether that problem is social, academic, or job related. Others find this cognitive process quite difficult. Learning disabilities have only recently been recognized as disabilities, however, these students can be taught effective learning strategies that will help them approach tasks more effectively. (From: "Learning Strategies for Problem Learners", by Thomas Lombardi).

Teacher Presentation

1. Always ask questions in a clarifying manner, then have the students with learning disabilities describe his or her understanding of the questions.
2. Use an overhead projector with an outline of the lesson or unit of the day.
3. Provide clear photocopies of your notes and overhead transparencies.

4. Provide students with chapter outlines or study guides that cue them to key points in their readings.

5. Provide a detailed course syllabus before class begins at the beginning of the semester or quarter.

6. Ask questions in a way that helps the student gain confidence.

7. Keep oral instructions logical and concise. Reinforce them with a brief cue words.

8. Repeat or re-word complicated directions.

9. Frequently verbalize what is being written on the chalkboard.

10. Eliminate classroom distractions such as, excessive noise, flickering lights, etc.

11. Outline class presentations on the chalkboard or on an overhead transparency.

12. Outline material to be covered during each class period unit. (At the end of class, summarize the important segments of each presentation.)

13. Establish the clarity of understanding that the student has about the assignment.

14. Give assignments both in written and oral form.

15. Have more complex lessons recorded and available to the students with learning disabilities.

16. Have practice exercises available for lessons, in case the student has problems.

17. Have students with learning disabilities underline key words or directions on activity sheets (then review with them) .

18. Have a complex homework assignment due in two or three days rather than on the next day.

19. Pace instruction carefully to ensure clarity.

20. Present new and or technical vocabulary on the chalkboard.

21. Provide and teach memory associations (mnemonic strategies).

22. Support one modality of presentation by following it with instruction and then use another modality.

23. Talk distinctly and at a rate that the student with a learning disability can be follow.

24. Technical content should be presented in small incremental steps.

25. Use plenty of examples, oral or otherwise, in order to make topics more applied.

26. Use straight forward instructions with step-by-step unambiguous terms. (Preferably, presented one at a time).

27. Write legibly, use large type; do not clutter the blackboard with non-current / non-relevant information.

28. Use props to make narrative situations more vivid and clear.

29. Assist the student, if necessary, in borrowing classmates' notes.

30. Consider cross-age or peer tutoring if the student appears unable to keep up with the class pace or with complex subject matter. The more capable reader can help in summarizing the essential points of the reading or in establishing the main idea of the reading.

31. Use interesting problem situations within a child's experience.
32. Encourage and reinforce children's estimates, even if the answers are irrelevant.
33. Pose problems situations orally. This is very helpful for children who have difficulty in reading.
34. Develop their mental calculation skills at an early age. Help them by using rapidly flash pictures, numbers, or objects. Help them concentrate on remembering and recognizing what they saw first, second, and etc.
35. Encourage older students to use place value to find answers to larger computation problems mentally.
36. Do not use problems that students in class have solved. (The teacher may solve the problems, purposely making mistakes, and have students identify the problem).
37. Have them write mathematical sentences for problems without computing the answers. This emphasizes the importance of a procedure, rather than the correct answer.
38. Use problems containing too much or too little information. Teacher may ask students to identify what is still needed or what information is extra.
39. Teacher may encourage children to devise word problems or use manipulatives to describe computation problems. Problems should relate to situations that are part of their experiences.
40. Use problems with words such as some or many instead of numbers to check that students know when to use each operation. Encourage students to insert low numbers to help determine the operation.
41. Systematically introduce new mathematics vocabulary.
42. State a purpose for any independent reading.
43. Use colored highlighting pens to emphasize key information and get attentions.
44. Give verbal descriptions of each part of a multistep process or algorithm.
45. Encourage students to verbalize steps as they work problems.
46. Highlight operation signs in practice activities involving a mix of operations.
47. Provide a model problem and solution at the top of practice worksheets.
48. Many different words are used in mathematics to mean the same thing:
    • The term 'sum of' or the 'difference between' can be very confusing. Some may have problems with concepts of 'above' and 'below', 'higher' and 'lower', 'greater' and 'lesser', which lead to considerably difficulty in interpreting instructions or memorizing concepts.
    • Suggestions:
      • Addition can be: sum of, increase, +, plus, and, total, more than, add, altogether, greater than or count on.
      • Subtraction can be: less than, decrease, - , subtract, take away, difference, minus, count back, reduce, orÊ short of.
      • Multiplication can be: multiply, times, x, of, product, or double.
      • Division can be: share, split, group into, how many, divide, or (division sign).
    • Problem-Solving Process:
      1. Decision Making:
         • The decision-making process requires the ability to use abstract reasoning, to be able to both understand and express words in a meaningful way, to draw on previously learned concepts and skills, to distinguish among them, and to choose the concept or skill that is most appropriate in a given situation
      2. Rounding:
         • It is essential for students to understand the relationship between rounding isolated number and problem solving. Teacher may help them to understand that rounding a computation, is similar to what you might do if you want to make sure you have enough money with you to go to take a bus, buy a book, and have dinner.
      3. Choosing Efficient Methods:
         • Teacher may use an analog clock and ask students to time how long it takes to solve a problem mentally, compare the results when using calculator or paper and pencil.
         • Children with abstract-reasoning difficulties, may be able to punch the keys on a calculator quickly without understanding what is happening unless they have access to manipulatives or unless they imagine a picture.
      4. Predicting:
         • Create extensive activities work with blocks, coins, and other real life objects often helps children think about 'what might happen if we did this?' Spread some centimeter cubes out on the table and ask children what might happen if the cubes were all pushed together. Encourage different answers: "They'd be closer together." "I'd be able to carry them easier." This will help children to recognize different ways of thinking, and develop self-confidence.
      5. Introducing the Language of Estimation:
         • Help the students to understand the different meaning between such expectations as "I have 5 pencils" and "I have about 5 pencils."
      6. Estimating:
         • Plot the answers on a number line and about situations in which the different estimates would be acceptable. The goal is to develop comfort with estimates, as opposed to 'correct' estimates and computation.
      7. Working Backward:
         • This technique can be used when the answer or situation is known. This skill is useful in planning situations whenever the limits of cost, time, distance, and so on are known. With more complex problems, students are encouraged to write down the amounts or situations so they can be accounted for in an orderly fashion. This way, students won't become frustrated or lost in the process of working from the general to the specific.
         • Begin problem solving as part of the initial mathematics program. Do not wait.
         • Make problem solving the reason for computation.
         • Assist students with what they cannot do so that they can solve problems. If a student cannot read the problem, rewrite it. If the computation is too complex, break it down into smaller steps.
         • Ask students to write their own problems and to modify existing problems.
         • Monitor progress and modify problems as necessary.
      8. Determining the Correct Operation:
         • Typical Disabilities Affecting Progress: Difficulty with abstract reasoning, visual memory, receptive or expressive language, and nonverbal learning disabilities.
         • In the early stage, it is good to help students to develop reasoning skills by presenting problems with answers but without signs. Have students to supply the correct sign.
           
           Tips: Help them to verbalize that the answers to addition problem have to be larger than the addends involved. For subtraction, answer must be smaller than what you start with.
         • Do it with big numbers: When using large numbers, keep the pace fairly quick so the students do not have time to compute the answer. Make sure students can tell whether the answer will be larger or smaller than what you start with.
           
           Special Help: Prepare a strip that contains correct sign/ symbols to serve as a visual reminder of the association.
         • Do the easy one first: Older students who have learned when to use each of the four operation in situations involving whole numbers often have trouble with fractions and decimals when trying to recognize which operation to use and carry out the appropriate operation.
           
           [In this situation, it is helpful to parellel two problems that are solved similarly but involve different types of numbers].
      9. Determining Whether An Answer Is Reasonable:
         • Typical Disabilities Affecting Progress: Difficulty with abstract reasoning and closure.
         • Present questions and multiple-choice answers. Students are to select the most logic answer. Discuss and reason why other choices won't work.
         • Help them estimate answers by getting a "ballpark" answer.
         • Follow-up: Have students tell/show how they arrived at the ballpark answer.
         • Hearing/seeing how others derive estimates gives them ideas on how to proceed and makes them more confident about trying themselves.
      10. Computation: Choosing the calculation method
          • "Computation must be taught meaningfully. This means careful attention to underlying concepts and relationships. A conceptual approach to computation often prevents many of the problems children otherwise would experience in learning to compute" (Bley 53).
          • First do the "good" mental-calculation problems; do the rest using paper and pencil. Provide specific exercises using a mix of problems Ð some that lend themselves to quick mental calculation.
          • Build estimation skills. For example: Always ask students to take a minute before doing an exercise and identify sums (differences, products, or quotients) that are close to $10.00. Students need to estimate. Next, they are to use the calculator to check their thinking.
          • Emphasize situations where an estimate is good enough.
          • Foster a positive attitude. Hold back from labeling a response as 'right' or 'wrong'. Accept a broad range of answers and alternatives solutions. Guide the students to get closer to the answer when estimating.
      11. Make Good Use of Information
          • Typical Disabilities Affecting Process: Difficulty with long-term memory, abstract reasoning, and receptive and expressive language.
          • Have the students eliminate any information that is not needed. For younger students, teacher can help them to highlight the needed items.
          • Present short problems that do not ask a question but merely supply information. Then, have students tell the teacher what they understand from the small amount of information.
          • Number word to numeral. In the following question, students are asked to fill in the numeral names. Later, the appropriate operation can be determined and the computation carried out.
            
            Example: a) You work seven (__) days and you work eight (__)hours a day. How long do you work in all?
      12. Recognizing patterns:
          • This technique is applicable in numbers, words, letters, shapes, and forms such as 3,6,9É (Students can translate scrambled quotations from mathematics and science to develop skills in recognizing patterns. Patterns can also be found in animal and human footprints, geological formations, cloud arrangements, and outer coverings of living things.
      13. Drawing and modeling:
          • Drawing a picture or making a model helps students to visualize a situation, explain complex and abstract ideas, relate to hands-on activities illustrate relationships.
      14. Making a table or graph:
          • Students can organize and summarize both numerical and verbal data in order to draw inferences and make evaluations of past situations or projections for future actions. A graph or table can also be used to order data in difficult problems and as a tool to classify information.
      15. Acting it out and simulating:
          • Many students learn best when they can construct a kinesthetic understanding of a concept or fact. At the higher grade levels, students can make paper-and-pencil simulations by drawing a picture or making a table.
      16. Calculators and Computers:
          • Calculators and computer-based tools such as spreadsheets and graphing programs can empower students with learning disabilities to explore important mathematical relationships.
          • Graphing calculators provide students with a visual bridge between concrete and abstract mathematical concepts.
          • Spreadsheets can help students to learn about place value, decimals, making calculations, seeing relationships, understanding variables, and working with large numbers.
      17. Computerized information organizers:
          • Use information-organizing software such as 'electronic outlining' and 'concept-mapping' programs. (can create visual representations of the interrelationship of ideas. Require students to organize and synthesize information, reinforcing their learning. Ideally, outlining programs should be integrated with a graphics component (such as Inspiration Software, Inc.), enabling students to change outlines into diagrams and vice versa.
      18. Mapping and Directions:
          • Elemental Processing of Patterns Ð begin with the basic elements then connect the elements to complete the task.
          • Global Processing of Patterns Ð begin with the overall design then fill in the elements. Ex: 2+3=5, 2+( )=5, ( ) +3=5.
          • Sectional Processing of Patterns Ð complete the parts of the pattern or sequence that one remembers then try to figure out the rest.
          • Backward Processing of Patterns Ð start with the most recent information given and work backwards. Ex: If the sum is 6, what is a possible problem? (3+3, 4+2).
      19. Phrase Sequence:
          • Indexing Ð make up a story using the words or items to be remembered.
          • Chaining Ð think of the information to be remembered in the exact order (i.e., first..secondÉ). Remember the steps in the process, could use a mnemonic. Ex: Red Fred Dives = Reduce the fraction. Find the common factor. Divide the top and bottom numbers by the common factor.
      20. Operations:
          • Operation of Addition: Emphasize that adding and also plus means "putting together," whether it be chairs, people, or decimals. Stress that in the process of addition, the order in which the sets of objects or numbers are added is unimportant. Important vocabulary meanings are plus, sum, total, more than, and greater than.
          • Operation of Subtraction: Subtraction is the act of "taking away." The results will always represent the number of objects left. It is possible to 'cancel' any subtraction with corresponding addition of the same quantity. In subtraction, the order of operation is not reversible. Vocabulary distinctions include less than, subtracted from, and minus.
          • Operation of Multiplication: Multiplication is a series of addition; therefore, a firm knowledge of addition must precede. Since multiplication is an addition of equal groups, the order in which the numbers are multiplied is not important.
          • Operation of Division: Division can be viewed as a subtraction of equal groups. The students must understand the terms involved in division. 8Ö2 is not the same as 2Ö8.
          • Fractions: All students should be able to draw pictures to represent fractional portions. Their understanding should not be limited to the abstract.
          • Decimals: Decimals should not be attempted until fractional concepts are clear. Some students might be familiar with baseball averages using decimals, others with test grades, etc. Above all, it should be emphasized that decimals are an easier way of dealing with fractions.
          • Relationship between addition and multiplication: A multiplication problem might be presented and the student asked to express the same problem as an addition problem.
          • Relationship between subtraction and division is similar to the application above.
          • Relationship between addition and subtraction: Games of chance are good examples to use to demonstrate that addition and subtraction are reverse operations. If in flipping a coin, every time a head shows you win a penny (addition) and vice versa. Students should be asked to create their own examples to demonstrate their relationships.
          • Relationship between multiplication and division: (same as above). Good examples should first be presented by the teacher, then students should be asked for examples.
          • Relationship between whole numbers and fractions: The idea that all whole numbers can be expressed as fractions should be make clear. Any counting number over one can be placed into fraction form. For example: 6 = 6/1. The students should be helped to understand that as the numerators and denominators of fractions approach the same size, the fraction approaches 1. For example: 4/6 is less than 1. à 6/6 = 1.
          • Relationship between fractions and decimals: The actual conversion of fractions to decimals is not of primary interest here. What should be stressed are concrete relationships. For example: The teacher might present a fraction such as 2/5 and draws a glass of water 2/5 filled and then ask the students what decimal would express the glass as being filled with that much water. If they were to respond .5 instead of .4, they would be very close, whereas an answer like 2.5 would show that they do not have a substantial realization of decimals. (In this case, they would have to be taken back to fractions).

Recitation

1. Clearly label equipment, tools, and materials. Color code them for enhanced visual recognition.

2. Consider alternate activities/exercises that can be utilized with less difficulty for the student, but has the same or similar learning objectives.

3. Provide clear photocopies of your notes and overhead transparencies.

4. For students with learning disabilities, make available cue cards or labels designating the steps of a procedure to expedite the mastering.

5. Use an overhead projector with an outline of the lesson or unit of the day.

6. Allow extended time for responses and the preparation and delivery of reports.

7. In dealing with abstract concepts, use visual tools such as charts and graphs. Also, paraphrase and present them in specific terms, and illustrate them with concrete examples, personal experiences, or hands-on exercises.

8. To minimize student anxiety, provide an individual orientation to the laboratory and equipment and give extra practice with tasks and equipment.

9. Find areas of strength in the student's lab experiences and emphasize those as much as possible.

10. Allow the students with learning disabilities the use of computers and spell checking programs on assignments.

Reading

1. Announce readings as well as assignments well in advance.

2. Find materials paralleling the textbook, but written at a lower reading level. (Also, include activities that make the reading more relevant.)

3. Introduce simulations to make abstract content more concrete.

4. Make lists of required readings available early and arrange to obtain texts on tape from Recording for the Blind or a Reading/Taping Service.

5. Offer to read written material aloud, when necessary.

6. Read aloud material that is written on the chalkboard on the overhead transparencies.

7. Review relevant material, preview the material to be presented, present the new material then summarize the material just presented.

8. Suggest that the students use both visual and auditory senses when reading the text.

9. Rely less on textbooks. Reading for students with learning disabilities may be slow and deliberate, and comprehension may be impaired for the student , particularly when dealing with large quantities of material. Comprehension and speed usually dramatically increase with the addition of auditory input.

10. Spend more time on building background for the reading selections and creating a mental scheme for the organization of the text.

11. Encourage students to practice using technical words in exchanges among peers.

12. Choose books with a reduced number of difficult words, direct non convoluted syntax, and passages that deliver clear meaning. Also select readings that are organized by subheads because this aids in the flow of ideas.

13. When writing materials for reading by students with learning disabilities, some of the strategies referred to in the reading section of the hearing impaired presentation will be appropriate.

14. Allow student to use a tape recorder.
15. Auditory Digit Sequence:
    • Rehearsal Ð saying the numbers or items over to oneself, repeating pieces of information.
    • Chunking Ð grouping numbers or components to be recalled in pairs (i.e., 2-3-6-4-=23, 64)
    • Associating Ð connect or join together new information with known information
    • Elaborating Ð thinking of other things to go with the information to be remembered, linking information to aid recall (i.e., making up a rhyme).
16. Further Difficulties:
    • Require children to learn and repeat exactly the instructions for each stage of the sum. (They tend to forget the type of sum and symbol they are working with. They often find it difficult to recall basic number facts such as number bonds and multiplication tablets.
    • Encouraged to read a sum in its entirety before working out the answer and at the end, as themselves: "Does this make sense?' It might be helpful to teach them to rephrase the question to make sure that they have established the meaning.
17. Constant-Time Delay procedure:
    • Incorporated teacher-selected or student-selected prompts to ensure accuracy of response. The process involved showing the student a math problem on a flash card, waiting four seconds for the student to give the correct response then providing either a visual, verbal, or material prompt to ensure the correct answer. Students would then repeat the entire problem with the correct response.

Testing

1. Avoid overly complicated language in exam questions and clearly separate items when spacing them on the exam sheet. (Refer to writing for students with hearing impairments in the reading section.)

2. Consider other forms of testing (oral, hands-on demonstration, open-book etc.). Some students with learning disabilities find that large print helps their processing ability.

3. Consider the use of illustrations by the students with learning disabilities as an acceptable form of response to questions in lieu of written responses.

4. Eliminate distractions while taking exams.

5. For students with perceptual problems, for whom transferring answers is especially difficult, avoid answer sheets, especially computer forms. Allow them to write answers (check or circle) on the test (or even dictate their responses.)

6. Gradually increase expectations as the students with learning disabilities gains confidence.

7. Grant time extensions on exams and written assignments when there are significant demands on reading and writing skills.

8. If distractions are excessive, permit the students with learning disabilities to take examinations in a separate quiet room with a proctor.

9. Provide study questions for exams that demonstrate the format along with the content of the exam.

10. Review with the student how to proofread assignments and tests.

11. Do not test material just presented or outcomes just produced, since for the students with learning disabilities, additional time is generally required to assimilate new knowledge.

12. Permit the students with learning disabilities the use of a dictionary and/or thesaurus and a calculator during tests.

Last updated:
Semptember 20, 2002

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Ed Keller