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The following report is going to look at the importance of instruction in the teaching of mathematical word problems to learners with learning difficulties. It focuses on 1 and 2 step mathematics computations. Most educationists consider diagrams a very good strategy that can be employed to make complex information simple and transform information that is abstract to something more real and concrete. Studies on whether the use of diagrams translates to an improvement in performance and the learners ability to relate problem-solving skills in math to the real-life situation are mixed with some indicating a positive correlation and other moderate effects.
Learners with LD have trouble arriving at a satisfying diagram of a problem, and there is a need for them to be taught specific strategies to help them solve mathematical problems (Goldman, 1989). In light of the fact that studies have given equivocal results on the effect of using diagrams to enhance problem-solving skills in learners with LD, it is important that future studies focus on a multifaceted approach in which more than two operation signs are used. Previous studies have relied on addition and subtraction only. Similarly, learners should be allowed to generate their own diagrams so that the task becomes more meaningful to them. Finally, the diagram instruction should be changed so as it is clearer.
The study sought to find out whether students with LD could: Improve in their diagram generating ability to present a mathematical word problem, boasts a performance by use of diagrams, transfer the skills to real-life situations, and his feedback on the suitability of the strategy instruction method. The study involved three students, two males and one female. They were given one and two steps of computational problems. The students, aged between 10 and 14, were LD as the criteria stipulated. There had a full-scale IQ of 85 or more as per the Wechsler Intelligence Scale for Children, had met the eligibility test for LD as per their district specifications, and were identified by their tutor as having challenges in mathematical word problem-solving instructions.
The study focuses on the instructional strategies that can be used to enhance the ability of learners with LD to solve mathematical word problems that require more than two operational computations. As stated earlier, previous reports have concentrated more on the subtraction and addition operations. The instructions were not very clear, sometimes requiring students only to draw, coupled with the fact that learners were not at liberty to generate their own drawings. Such studies hence indicated a moderate correlation between the uses of diagrams in mathematical word problems to enhanced performance.
This study is situated in the instruction effectiveness field of knowledge and seeks to prove that if learners with LD were taught specific and efficient methods, it would be easier for them to represent a mathematical problem diagrammatically and solve it. It is important to understand the following about learners with LD and their ability to use diagrams:
- Most learners with LD have a vague idea of what diagrams are.
- Learners with LD are mostly conversant with the pictorial images and not the schematic ones. In the pretests, all learners drew pictorial images.
- Previous studies have not employed more than two operation signs
- The study, therefore, takes into consideration the above-stated facts and seeks to change the approach so that the learner acquires effective strategies.
The research design was experimental and multifaceted. A pretest design was used prior to the test and a posttest design used after the test. The problems were selected randomly from 250 problems. It had word problem tests, and learners were evaluated on the diagram used, form of the diagram and performance. The students were afterwards served with questionnaires.
The learners were observed and a research assistant recorded the score of their test. For diagram use, students were scored out of 100%. They could also get the same for diagram form and between 0 to 8 for solution. Lastly, they were asked to give feedback as to whether they liked or disliked the method.
Prior to the pretest, only one student managed to draw the diagram and score 100%.After the posttest, all the students could draw and score 100%. The same results were replicated in the word test problems. In the questionnaire, learners rated the strategy highly and said that they would employ it in future.
The study indicated that learners improved in their ability to generate and use diagrams while solving mathematics word questions. Their ability to solve one and two-step computational word problem increased. Further, it became easier for them to transfer or generalize the problem solving skills acquired by generating diagram to solve other problems in the world. Lastly, the learners expressed satisfaction with the instruction and were keen to recommend it to other people.
Before the instruction strategy, the learners hardly used diagrams. In fact, they did not know what they are. After following the instructions, all the students used diagrams for most of the times in the course of measurement. The learners could categorize diagrams as pictorial or schematic, an indicator that the study was successful. They could solve a four operations and two step computational problem. Interestingly, the learners could generalize what they had learned to an activity that is not routine, quite unusual for learners with LD (Montague, 1997).
One of the limitations of the study is that it is difficult to distinguish accurately whether the improved performance is because of the use of diagrams alone or the integration of the strategy (Garderen, 2007). The corrective feedback may as well have contributed to better performance. Secondly, the instructions were given by a researcher; not by a teacher or in a classroom situation. It would be difficult to generalize it to a large group or a classroom. Lastly, no one had measured the performance of the non-routine activity mentioned earlier before the strategy was implemented. Reports that the learners’ performance improved may not be directly attributable to the programme.
Implication for practice
Diagrams are an important teaching aid especially for learners with LD. According to Garderen (2007) the instruction should be geared towards the understanding of the concept of diagrams, how to generate them and use them as a tool in problem solving. The acquired knowledge in diagrams can be transferred to other spheres of life. The study therefore proves that performance can be improved using instruction strategies. Teachers can therefore adopt the strategy in inclusive classes so that they take care of learners’ different abilities. It is learner-centered and learners are likely to participate than in other teaching methods.
Garderen, D. (2007). Teaching Students With LD to Use Diagrams to Solve Mathematical Word Problems.Journal of Learning Disabilities,40(60),540-553. Web.
Goldman, S. R. (1989). Strategy instruction in mathematics. Learning Disability Quarterly, 12, 43-55. Web.
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Montague, M. (1997). Cognitive strategy instruction in mathematics for students with learning Disabilities.Journal of Learning Disabilities,30,164-177. Web.