Improving mathematics performance in students with learning difficulties

Strategies to Improve Mathematics Performance for Children with Learning Difficulties and their Effectiveness Introduction
One of the basic requirements in life is to have an adequate aptitude in mathematics as this is crucial in carrying out everyday actions which include drawing up a budget for time and finances, playing with numbers and checking the time. Apart from these, proper knowledge of mathematics helps promote lasting cognitive, workplace, scholastic, and body-related well-being and all this combines to boost the economic standing of nations. From previous studies, it has been established that about a fifth of scholars have poor skills with numbers and a range of 4 to 14% have been diagnosed with problems in learning mathematics, with the range due to selected methods of grouping (Furlong et al., 2016). (For this paper, the word ‘students’ means kids below the age of eighteen who currently attend mathematics classes in a recognized school). With variations due to the mode of research i.e. intervention studies or mathematical cognition, students with these problems are said to be suffering from a mathematical disability, mathematical learning disabilities (MLD), mathematical learning difficulties or developmental dyscalculia.
Difficulties in understanding singular or a group of mathematical concepts bordering from simple number operations to more complex algebraic and geometric calculations are common symptoms of MLD. Till today, MLD researches have narrowed their scope to the reasons for problems in understanding the simple parts of mathematics and always leave out the complex parts (Fischer et al., 2013). Some of the simple mathematical skills are arithmetical strength and basic proficiency with numbers. Having problems with solving basic mathematics problems could be due to poor strength in estimating the quantity and in the application of the mental calculator; little understanding of the processes involving in counting or favoring ineffective counting processes or even both; problems in mastering the basics of the Base-10 system; challenges in relating analog measurements, numbers in numerals and in words and finally, problems with applying the results from a calculation to another. Arithmetical strength is the measure of a person’s base proficiency in number operations such as multiplication, division, addition, and subtraction as well as the person’s ability to bring out the meaning from word problems. Statement of the Problem It is no longer news that several scholars do not like mathematics and some in fact detest the subject (Marks, 2014). Severally, students skip math classes in schools and even a large number of those who don’t, do not listen whenever the lecture is on-going. Outside the classroom, it is rare to see a student working on mathematical problems or doing further reading on it. If possible, several students would gladly take the option of distancing themselves from mathematics (Sa’ad, Adamu & Sadiq, 2014). This trend has caused low grades in mathematics assessments. Thus, we can conclude that student-related learning problems are the major factors worsening this condition and the inherent dislike among students for mathematics is the main cause of low grades in its assessments. As a result of this and the importance of mathematics in enhancing the better quality of living, we need to implement mechanisms effected by our teachers which aims at increasing the love for the subject, an action which should cause a related improvement in student grades.

Guiding Questions What are the processes applied by teachers in improving the understanding of mathematics in students who find it difficult to learn?
Are the methods applied by teachers in improving the understanding of mathematics in students who have MLD effective? Literature Review Students with learning disabilities face several problems. More often than not, these students advanced approximately one academic year for every two academic years they attended school. Strategies employed by teachers can have a significant impact on enhancing this particular performance in all levels of schooling. The lack of comprehensive strategies and interventions students with mathematics disabilities end up considerably lagging behind compared to their peers. Statistics indicated that approximately 25 percent to 35 percent of students experience difficulty with math knowledge and application skills. Moreover, 5 to 8 percent of all students in school have such considerable deficits that influence their capability to solve computation problems (Sayeski and Paulsen, 2010). In accordance to Hott et al. (2014), strategy training has been beneficial to students with learning disability when learning math conceptions and practices. As presented in the article one of the strategies is RIDE, which was established by Mercer et al. (2011). This approach is used to help students with answering word problems. LD students that face problems with abstract reasoning, memory, reasoning and attention skills may mostly benefit from this strategy.
Teaching different strategies to children with disabilities assisted them in learning and retaining not just higher-order conceptions and problems, but also simple mathematical facts. In particular, automaticity, which is the capability to undertake tasks devoid of occupying the mind the low-level details necessitated, is deemed significant for further development and understanding in math for children with learning disabilities. In accordance to Tournaki (2003), automaticity in math is taught either using drill and practice or through the direct teaching of a strategy. The author's study showed that it was useful and constructive to teach basic facts about students with learning disabilities via drill and practice. Tournaki (2003) posits that when students with disabilities are taught strategies, they are handed routine and practical knowledge that can be utilized in solving problems. Especially, in the research study, the author employed the minimum added strategy. This takes into account students counting up from the higher added the number of units itemized by the lower added. This particular approach was taught to both the students with and without learning disabilities and subsequently comparisons were made to both the students with and without learning disabilities that were taught through drill and practice. The outcomes of the study by Tournaki (2003) established that students with learning disabilities significantly improved solely in the strategy condition in comparison to the control and drill and practice conditions. Nonetheless, the study showed that only students in the strategy condition came to be significantly more precise in transfer tasks, for students with and without learning disabilities (Tournaki, 2003).
Montague (2007) argued that students with learning disabilities show significant issues with memory, responsiveness, and self-regulation. As a result, this has a considerable adverse impact on their performance in both math and reading. According to Montague (2007), self-regulation is considered to be a metacognitive function that is fundamental to being successful in academic. Especially, students with learnings disabilities are mostly poor at self-regulation and therefore have to be taught unequivocally how not only to observe but also control their intellectual activities as they take part in academic tasks, for instance solving math problems. The author demonstrates that self-regulation strategies can be used to enhance the performance of students with learning disabilities with the math subject at the elementary, middle and secondary school levels (Montague, 2007).
Wisniewski and Smith (2002) present the touch math program, a series that accentuates the use of manipulatives and examine its efficacy. The authors elucidate that several students with disabilities face difficulties and challenges in employing manipulatives for the reason that they forget the amount already counted at the point where they are ready to transfer the solutions to their worksheet. However, with the touch math program, such students did not have to leave their question worksheets to record or write down their solutions. The students with a disability were taught that each integer, from 1 to 9 had touch point that signifies the value of each particular integer. Wisniewski and Smith (2002) outline that this particular program employed three distinctive modalities, which take into account auditory, visual and kinesthetic. Imperative, when the math teachers utilize approaches for all styles of learning, then the students with disability attain the capacity to learn through their main modality and at the same time firming up and supporting the others. The outcomes of the research study indicated that all students employing touch math substantially enhanced their performance in accuracy as well as speed based on the tests undertaken prior and subsequent to the program (Wisniewski and Smith, 2002).
Maag et al. (1993) study the impact of self-monitoring on task behavior, academic efficiency, and academic accurateness and precision with six elementary students that have learning disabilities. In the research study, the students were taught how to write down the distinctive and particular self-monitoring objective and were signaled by a tape-recorded sound to record solutions for the number of questions completed, the number of questions finished correctly, as well as task behavior. In particular, Maag et al. (1993) established that self-monitoring augmented both the precision and the number of questions successfully finished by students in the fourth grade. According to de Boer et al. (2012), numerous research studies have shown the efficacy of strategy instruction. The authors delineate that most effective strategies consist of the metacognitive strategies of monitoring and control and those of evaluation and prediction. The subsequent mostly utilized strategies were the metacognitive technique of assessment and reflection and the cognitive approach of elaboration. In comparison to the reading understanding and writing interventions, the mean number of strategies taught in the mathematics instructions was to some extent lower. De Boer et al. (2012) demonstrate that math interventions more often than not consisted of different amalgamations of learning strategies. The addition of the cognitive strategy ‘elaboration' had constructive impacts on the students' mathematics performance. Utilizing previous knowledge, enthusiastically making relations between new material and comprehensive knowledge and expounding the material so as to enable the storage of knowledge in the longstanding memory are all instances of effective ways to handle and resolve mathematical problems.
Xin et al. (2005) examine the impact of mathematical word problem-solving strategy and instruction on students in middle school with learning problems. In particular, the research study examined the degree of difference and the impacts of two problem-solving instructional strategies, which are the general strategy instruction (GSI) and the schema-based instruction (SBI). These strategies were examined about the performance of 22 middle school students with learning disabilities are at risk of failing in math on solving mathematical word problems. The outcomes of the study showed that the group that experienced the schema-based instruction had a significantly better performance in comparison to the group that experienced the general strategy instruction, with regard to instantaneous and delayed posttests in addition to the transfer test.
Identifying students who are at risk of academic difficulties and offering the students intervention during their early ages has been endorsed widely by many researchers. It has been noted that it is easy to identify the numeracy skills that prove problematic and resulting in mathematic difficulties for students (Bryant, Bryant, Gersten, Scammacca, & Chavez, 2008). There is numerous research carried out in early reading that could be replicated for the early identification and intervention for mathematics in order to prevent mathematics difficulties in students. By making use of Tier 2 interventions it is possible to improve the performance of students and result in reduced difficulties in mathematics. According to Bryant et al. (2008) tier 2 comprises of informed instructional decision-making, flexible groupings, and evidence-based interventions. These characteristics have been pointed out by other researchers to be effective in improving mathematics cognition, especially for the early ages. In a majority of the cases, student interventions only begin when the student is in the upper classes, and this might be too later. Therefore, there is need to have mathematics interventions starting at an early age. This will ensure that a student will learn and grow up without having any difficulties in mathematics. Bryant et al. (2008) have established that Tier 2 students demonstrated a positive effect in improving their performance.
Teaching cognitive strategies have been found to be more effective in improving problem-solving accuracy for children who have mathematics difficulties (Swanson, Moran, Bocian, Lussier, & Zheng, 2013). There are various studies that have been conducted and they have all demonstrated that making use of cognitive strategies has a positive effect on improving the student's ability to solve mathematics problems. The researchers studied the role of generative strategies and working memory capacity for children in Grade 3 (Swanson et al., 2013). All the children selected for the study had been identified as having mathematics difficulties and they had been randomly assigned to three different groups. The results confirmed that making use working memory capacity, it is possible to improve the problem-solving accuracy of the students. There was also an improvement in the posttest scores of the students when generative strategies had been employed. Generative training was found to be quite effective in improving the problem solving of the students with mathematics difficulties (Swanson et al., 2013). Making use of the generative strategy students were also able to transfer what they learned and they could easily apply it to other settings and solve the problems. Transferability of a strategy is vital because it allows a student to learn and apply the strategy to other problems.
The study by Zhang, Xin, Harris, and Ding (2014) aimed to determine if it is possible to improve the problem-solving accuracy of students with mathematics difficulties by upgrading their strategic developmental levels. This was a micro-genetic study that employed a trial-by-trial assessment for three third graders. This approach is beneficial because it allows the researchers to have a precise assessment of strategy learning. With every trial of the students' problem-solving ability, an observation is made of how the student is learning during the intervention. This is beneficial to the study because it allows for a dense observation to be made of the participant. Zhang et al. (2014) has noted that it is possible to improve the students’ problem-solving abilities by using strategic training, but they have also noted that this might not be effective in all cases for students with MD. Therefore, there is need to further carry out research in order to identify the different subtypes of students with MD. From the study, it is clear that ST is effective but the results could not be transferred by all the participants. It has also been suggested that mathematic textbook writers could design task presentation sequences to foster the students' strategic developmental trajectory (Zhang et al., 2014).
The purpose of this study was to establish if mathematics interventions for students were effective and determine how effective these interventions were (Kroesbergen & Van Luit, 2003). The article focused on other studies that had been carried out targeted towards identifying mathematics interventions. The authors conducted searches for empirical studies conducted between 1985 and 2000. It has been established that a majority of the studies examined were offering interventions within the domain of basic skills. The domain of basic math skills has been shown to be vital because this is what lays the foundation for later development of math skills. Without the basic skills, a student would find it hard to solve mathematical problems in the future and it is for this reason that most of the interventions identified for this meta-analysis have focused on basic math skills. According to Kroesbergen and Van Luit (2003) it is easier to teach students with special needs basic math skills than it is to teach them problem-solving skills. The authors have established that self-instruction and direct instruction are effective methods for teaching math to students with special needs. Direct instruction has been shown to be effective in learning basic math facts. Self-instruction is effective in learning problem-solving skills. The use of computers has been put to question and although CAI is effective the authors have discovered that a computer cannot remediate the basic difficulties encountered by a student (Kroesbergen & Van Luit, 2003). Therefore, traditional interventions that use teachers have been found to be most effective. Group setting has been shown to be ineffective especially for students with special needs.
The article investigates the effectiveness of using a computer-based instructional method in Primary Education. Lazakidou and Retalis (2010) argue that the thinking strategies that teachers should foster in their students are metacognitive and self-regulative strategies. Self-regulated strategies are the main focus of this article. Self-regulated strategies are the efforts that would facilitate the achievement of a newly developed goal. The efforts being mentioned refer to adjustments in the behavioral, personal, or environmental conditions. Self-regulative strategies can predict the future outcomes of a student. Lazakidou and Retalis (2010) posit that having a sequence of instruction like observation, collaboration, and semi-structured guidance is vital in the development of basic math skills and allows students to develop their problem-solving skills. This has been supported by other researchers who also established the same thing as the findings of this case study. Therefore, self-regulative strategies could be used to improve the problem-solving skills of students who have MD (Lazakidou & Retalis, 2010). This study is important because it presents a case that could be easily replicated and if the same principles are used for students with MD there is a possibility that they could improve and their mathematics ability would improve too. Summary of Findings The literature review findings show that if there is going to be an effective strategy for improving mathematics performance among students with LD then the strategy has to be implemented earlier on in the student’s life. Most of the strategies that have been implemented when the student is in the upper classes have resulted in less than expected results and in others total failure. The most effective strategy is teaching cognitive strategies. Numerous studies have shown the effectiveness of this strategy. We have also found that mathematics interventions are effective and students who undergo these interventions have improved their math problem-solving skills. Self-instruction and direct instruction have been found to be most effective when teaching math to students with special needs. The use of computers had been recommended, but we have established that CAI might be effective, it is not possible for the computer to remediate the difficulties that the students encounter. Traditional methods are still the most effective methods for teaching math to students with LD.