Mathematical Errors of Visually Challenged and Strategies for Overcoming them

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1 WA 099 Mathematical Errors of Visually Challenged and Strategies for Overcoming them Joicey P. Manickam & P. Nagalakshmi Senior Lecturers Department of Rehabilitation Science Holy Cross College Triruchirapalli TamilNadu India Mathematics is intimately involved in every moment of everyone s life. A common man can get on quite well without learning how to read and write, but he can never manage without learning how to count and calculate. Nobody can live without mathematics for a single day. There is a definite need of mathematics in anybody s lifelong planning and day to day planning. Even the most ordinary citizen has to calculate his wages and buy things from the bazaar. Therefore there is no escape for any individual from mathematics in his livelihood. Mathematics is a subject of principal importance for a successful or school life experience. Many students have difficulty becoming proficient at Mathematics. They may have difficulty in acquiring computation skills or in understanding mathematical concepts or in applying their knowledge in solving mathematical problems. Studies have showed that visually challenged students do not perform as well as average sighted students in basic arithmetic, although their work in literary subjects is at about the same level. Therefore it is necessary to find out the areas of computational difficulty of visually challenged students. For this, error analysis in computation is necessary and important especially for students with sensory impairments because it is an additional handicap to them. They also need adapted methods and materials to learn computation. The present study ascertains the error scores of 24 visually challenged students from two different types of educational settings in the four areas of computation namely addition, subtraction, multiplication and division. 1

2 Review of related literature: Instructional Strategies In a standards based classroom four instructional strategies are key: Inquiry and problem solving Collaborative learning Assessment embedded in instruction Higher order questioning The Rochester Institute of Technology (2000) notes appropriate instructional strategies for visual, auditory, and kinesthetic learners. Visual learners appreciate lessons with graphics, illustrations, and demonstrations. Auditory learners might learn best from lectures and discussions. Kinesthetic learners process new information best when it can be touched or manipulated; thus, for this group of learners, written assignments, note taking, examination of objects, and participation in activities are valued strategies to consider. Differentiated Instruction Learning to teach in a flexible manner is a challenge. Carol Ann Tomlinson and Jay McTighe (2006) promote differentiated instruction, which is primarily an instructional design model that focuses on "whom we teach, where we teach, and how we teach" (p. 3). The goal is to ensure effective learning for all. Theroux (2004) addressed four ways to differentiate instruction: content (requires pretesting), process (leads to a variety of activities and strategies), product (complexity varies), and manipulating the environment or accommodating learning styles. Among strategies for implementing differentiated instruction, Tomlinson and McTighe (2006) suggest that teachers consider: Compacting giving students credit for what they already know; Negotiated delay of due dates and times for tasks; Varied homework; 2

3 Bookmarked Web sites on key topics in languages other than English to support English language learners; Video and audio clips to support multiple intelligences and varied learning styles and disabilities; Flexible grouping, "expert" groups, and interspersing lecture with group discussions; Guided peer review; Teaching with part to whole and whole to part emphasis; Tiered assignments used when all students need to know the same skill or concept; Learning contracts; Independent study/projects; WebQuests and Web inquiries; Learning centers primarily used in elementary grades; and Adjusting questions to accommodate levels in Bloom's Taxonomy. Bloom's Taxonomy which was revised in 2001, now has levels of remembering, understanding, applying, analyzing, evaluating, and creating (Forehand, 2005). Research Based Instructional Strategies Classroom Instruction that Works (2001) by Robert Marzano, Debra Pickering, and Jane Pollock includes nine research based instructional strategies that have a high probability of enhancing student achievement for all students in all subject areas at all grade levels: 3

4 Identifying similarities and differences Summarizing and note taking Reinforcing effort and providing recognition Homework and practice Nonlinguistic representation Cooperative learning Setting objectives and providing feedback Generating and testing hypotheses Cues, questions, and advance organizers The authors caution, however, that instructional strategies are only tools and "they should not be expected to work equally well in all situations." Instructional Strategies for Students with Visual Disabilities Visual impairment varies greatly. Persons who have low vision may rely on residual vision with the use of adaptive equipment. Persons who are totally blind may have visual memory, the utility of which varies depending on the age when vision was lost. Whatever the degree of impairment, students who are visually impaired should be expected to participate fully in classroom activities, such as discussions and group work. Strategies for totally blind students Adapted educational aids are a necessary component of any mathematics class. Math teachers need to verbalize everything they write on an overhead or blackboard and be precise with their language. If the Braille learner still has difficulty keeping up, the math teacher should give the student/vi teacher a copy of their overhead transparencies prior to class if pre prepared or immediately after. Another alternative might be for a classmate to make a copy of their notes to share. Math teachers need to give worksheets, tests, etc. to vi teachers to transcribe into Nemeth far enough in advance. Relate various mathematical applications to student activities enjoyed by blind students as well as the sighted students Math teachers need to realize that it is their job to teach the mathematical concepts to their students. This is not the job of the VI teacher. The vi teacher can be very helpful by insuring that all materials are in proper Nemeth code and all graphics are of good quality if the math teacher is able to supply these in print in a timely manner. 4

5 Blind students should not be excused from learning a math concept because they are blind: It is very important for all students (and especially for the VI student) to use as many senses as possible when learning a new math concept. There is an ongoing need for four way communication among the math teacher, the VI teacher, the family, and the student. For classroom test taking, the student should be given the test in Braille Strategies for students with low vision Reserving front row seats for low vision students; making sure seats are not near windows (glare can make it hard for a student to see the instructor or the board). Use printed material which provides good contrast and objects with a variety of textures. Do not sort by colour alone. Use touch as well as sight whenever possible. Give the child extra opportunities for real life experience. Use uncluttered, realistic pictures and real objects whenever possible. Encourage use of listening skills. Allow the child as close an approach to people and material as necessary. Allow the child to choose his/her own reading distance. Avoid print on coloured backgrounds and print which is widely scattered on the page. Use a line?on window maker, or a finger. NEVER USE FAINT DUPLICATED COPIES. The child must have adequate illumination without glare. Enlarging is not a panacea. NEVER SHARE BOOKS. Raising the height of work above desk level may help. Use clear diagrams whenever possible. Stress importance of layout, with partitioned HTU columns. Allow the child to change colour of pencil when working out examples. Decomposition can be very visually confusing, colour coding may help. Be aware that maths text books can be very difficult to read. Circle the number of the sum to separate it from the sum itself. Do not expect the child to copy from the blackboard. Use a soft pencil or a fine black felt?tipped pen. 5

6 It is essential to ensure that letters and numbers are correctly constructed. Always use lines to write on. The child will need individual demonstration and lots of practice. Copying must be done directly under the example, and not from a distance. Take account of restricted visual experience. The method of delivery may need to be adjusted. Equipment and teaching materials may need to be adapted or specially prepared. Methodology of The Present Study A diagnostic methodology was adopted in order to identify the pattern of errors made by visually challenged students at the primary level in integrated and residential programmes. Data were obtained by testing the students in the four areas of computation in whole numbers. The objectives of the study were to determine the relationship between the error scores of visually challenged students in the four areas of computation namely addition, subtraction, multiplication and division and to find the difference in: error scores of visually challenged boys and girls; error scores of visually challenged students of residential and integrated educational programmes; error scores of visually challenged students of standards IV and V; error scores of visually challenged students with an experience of one year and three years in integrated educational programmes; error scores of visually challenged students and their academic achievement; error scores of visually challenged students and their age group and the influence of failure strategies in computational achievement. Based on the objectives appropriate hypotheses were framed. Three schools having integrated educational programmes at primary level were randomly selected and cluster sampling method was adopted. Visually challenged students of standards III and IV (boys and girls) in the three schools who satisfy the criteria for selection were twelve in number. The sample size of the visually challenged students in residential programme was also twelve in number. Variables Age Gender Standard Academic Achievement Type of programme : Experience in integrated programme 6

7 Tools The main aim was to diagnose the error patterns of visually challenged students of standards III and IV in residential and integrated educational programmes in computation in whole numbers. The tools used were An inventory prepared by the researchers which had problems on addition, subtraction, multiplication and division. The tool consisted of 60 sums to be done by the students in all the four areas of computation, having 15 sums in each area. Each area consisted of problems ranging from one digit problems to four digit problems. The tool also had some questions for getting information such as age, gender, and number of years of experience in integrated programme and achievement of students in other academic subjects. This tool, compiled by the researchers was approved by an expert in the field of visually handicapped. Scoring Scoring of the responses was based on the failure strategies given by Roberts for the systematic analysis of errors. The failure strategies used were wrong operation, computational error, defective algorithm, random response and carelessness. The errors of each student were calculated and converted into percentages for each student. The data were collected by administering the inventory to the students and allowing a consistent length of time for them to finish the sixty problems. Additional information regarding their achievement in other subjects, age, and experience in the programme were got from their teachers. Analysis Table 1 Relationship of the Error Scores of the Four Areas of Computation No. Areas of Addition Subtraction Multiplication Division computation 1. Addition 2. Subtraction Multiplication Division

8 Table 2 Difference In Error Scores Of Visually Challenged In Computation Areas of Gender Standard Type of Experience in integrated computation programme programme t value Addition 0.8 NS 0.47 NS 0 NS 0.96 NS Subtraction 2.26 S 0.36 NS 3.16 S 3 S Multiplication 2.53 S 0.6 NS 1.36 NS 3.09 S Division 2.02 NS 2.3 S 3.2 S 1.4 NS NS Not Significant S Significant Findings The error scores of visually challenged students were less in addition and high in multiplication. Their error scores in subtraction and division were average. In computation, the error scores of boys were higher than that of girls. The visually challenged students of residential and integrated educational programmes were less in subtraction, multiplication and division when compared to the error scores of students in residential programme. There is no significant difference between the error scores of visually challenged students in standards IV and V at 0.05 level. The visually challenged students with an experience of three years in integrated educational programmes made fewer error scores than those visually challenged students with one year s experience in integrated educational programmes. The error scores of high achievers in academic subjects is less than the error scores of low achievers in academic subjects. The visually challenged students of age groups ten years and thirteen years do not have significant differences in their error scores. This shows that age does not have any influence on their computational achievement. The most common error pattern of visually challenged students was computational error (76%). Their error scores in other areas are : Wrong operation (0.3%) carelessness (5%), random response (5%) and defective algorithm (14%). This shows that visually challenged students have difficulty in understanding the basic facts in computation. 8

9 Recommendations Regular Assessment should be made to ascertain the mathematical ability of visually challenged students to find out their present mathematical levels. When error patterns are identified by the teacher, individualized remediation should follow immediately for each student. Drill is recommended for visually challenged students to understand concepts, principles and process. The visually challenged students in residential programmes should be motivated to work harder and given opportunities to compete with sighted students. The visually challenged students who have less years of experience in integrated programme should given more opportunities to give them experience in understanding concepts through tactile materials. Basic facts in computation should be taught to visually challenged students to enhance their achievement in computation. References: Cawley, J., Parmar, R., Yan, W., & Miller, J. (1998). Arithmetic computation performance of students with learning disabilities: Implications for curriculum. Learning Disabilities Research and Practice, 13, Forehand, M. (2005). Bloom's taxonomy: Original and revised. In M. Orey (Ed.), Emerging perspectives on learning, teaching, and technology. Available: Marzano, R. J., Pickering, D. J., & Pollock, J. E. (2001). Classroom instruction that works. Alexandria, VA: Association for Supervision and Curriculum Development. Ontario Association for Mathematics Education (2004). Think literacy: Mathematics approaches grades Available: Rochester Institute of Technology. (2000). Some characteristics of learners, with teaching implications. Available: Tomlinson, C., & McTighe, J. (2006). Integrating differentiated instruction with Understanding by Design. Alexandria, VA: Association for Supervision and Curriculum Development. 9

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