Challenges to Teaching Students Struggling with Mathematics in Primary School
Abstract
This literature review will reveal challenges to teaching students identified with a math learning disability or students demonstrating math difficulties in primary school. Through the identification of behaviors and factors of concern, regular education classroom teachers can begin to provide the best interventions. This literature review will explore problem solving strategies and the implications of technology as a supplement to teacher direct instruction to increase mathematics achievement. In light of providing the current research, this literature review will expose the gaps in research associated with teaching struggling math learners in the regular education classroom at the primary level.
Key Words: math learning disabilities, math difficulties, problem solving, primary education
Best Practices in Teaching Students Struggling with Mathematics in Primary School
The United States is failing to adequately prepare its students with the requisite mathematics knowledge to be successful in the 21st century working environment (Xin & Zhang, 2009). According to the most recent Programme for International Student Assessment (PISA) data, the United States mathematics performance has been stable since 2006; however, when compared with the 35 participating nations in the Organisation for Economic Co-operation and Development (OECD), the United States has and continues to consistently perform below average in the area of mathematics (OECD, 2016). The learners most at risk of poor performance in mathematics are those learners identified with a math learning disability (MLD) or other learners demonstrating math difficulties (MD). According to the United States Department of Education (2015), a mere 16% of fourth grade students identified with disabilities scored proficient or advanced on the National Assessment of Education Progress (NAPE) Testing in 2013.
This literature review seeks to reveal the challenges to teaching students who may have identified math learning disabilities (MLD) or students demonstrating math difficulties (MD) in primary school. Viewing these challenges through the lens of a regular education classroom teacher will inform the practice of primary school educators. According to Desoete and Stock (2013), “the term MLD refers to a significant degree of impairment in the mathematical skills (with substantially below mathematical performance)” (p. 17). Desoete and Stock (2013) further add that additional characteristics of MLD include lack of responsiveness to interventions. Additionally, according to Martin et al. (2013) math difficulties can be defined as students showing low academic achievement in math with no diagnosis of a math learning disability (as cited in Powell & Fuchs, 2014).
Furthermore, due to the federal regulations within the Individuals with Disabilities Education Act (IDEA), regular education teachers are at the forefront of helping to educate students with disabilities. According to the United States Department of Education’s IDEA, all children with disabilities between the ages of three and 21 are entitled to a free appropriate public education (United States Department of Education, 2015). Schools are required to ensure that children with disabilities are educated with their “non-disabled” peers within the least restrictive environment to the maximum extent possible (United States Department of Education, 2015). Furthermore, according to IDEA:
Special classes, separate schooling, or other removal of children with disabilities from the regular educational environment occurs only when the nature or severity of the disability of a child is such that the education in regular classes with the use of supplementary aids and services cannot be achieved satisfactorily. (United States Department of Education, 2015)
In light of the provisions within IDEA moving regular education classroom teachers to the forefront of providing quality education for students with MLDs and MDs, this literature review seeks to expose the gaps in research to support best practices for teaching this population of learners within the regular education classroom.
Challenge: Identifying Struggling Math Learners
Research indicates that to begin implementing the best teaching practices for struggling math learners, regular education classroom teachers must be able to first identify what behaviors of concern are specifically related to MLDs and MDs. For example, Bryant, Bryant, and Hammill (2000) sought to examine specific behaviors of students with mathematics learning disabilities and determine if these behaviors were predictive of mathematics weaknesses. The researchers created a Likert-type rating scale to assess a total of 33 mathematics weaknesses and ranked the behaviors based on prevalence with the top three behaviors of concern being difficulty with word problems, difficulty solving multi-step problems, and difficulty with the language of mathematics. Bryant, Bryant, and Hammill (2000) stated again that regular education classroom teachers need to not only provide explicit instruction, but they must provide task-analyzed instruction and cognitive strategies for struggling math learners. Any student who continues to have persistent mathematics difficulties despite individualized, remedial efforts would be a candidate for special education testing (Bryant, Bryant, & Hammill, 2000).
Furthermore, there are additional math behaviors that can be observed by the regular classroom teacher which point to deficits in cognitive processes. Deficits in cognitive processes can be associated with identifying MLDs (Watson & Gable, 2012). Watson and Gable (2012) use research to highlight the underlying cognitive process behind math learning disabilities (MLD) and the challenges with evaluating students demonstrating math difficulties for learning support services. The researchers cited multiple research studies to identify deficits in working memory as a huge contributing factor to MLDs (Andersson, 2007; Geary, 2003; Raghubar, Barnes, & Hecht, 2010; Rasmussen & Bisanz, 2005; Rosselli, Matute, Pinto, & Ardila, 2006; Swanson & Jerman, 2006; Swanson & Kim, 2007; Toll et al., 2011, as cited in Watson & Gable, 2012). Although there are many other cognitive deficits that can contribute to MLDs, working memory is the most prevalent because of its implications on learning (Watson & Gable, 2012). According to Cowan (2010), “working memory can be described as information available in an easily accessible state that assists in completion of cognitive tasks” (as cited in Watson & Gable, 2012, p. 179). For a regular classroom teacher, deficits in students’ working memory can manifest as struggles with counting procedures and problem solving (Watson & Gable, 2012).
Additionally, Watson and Gable (2012) noted that identification for learning support services could be inconsistent because there are many factors, such as developmental stages or environmental factors that can impact the assessment. The researchers support the idea of early identification of MLDs (Watson & Gable, 2012). Most students are referred for testing after the regular education teacher has identified a deficit in their learning. Early identification of struggling math learners and instructional interventions can help remediate these deficits. The researchers suggest the Response to Intervention model as a framework for providing these necessary interventions (Watson & Gable, 2012).
In light of identifying observable behaviors associated with identifying MLDs and MDs, deficits in number sense abilities can further indicate poor mathematics achievement. For example, Jordan, Kaplan, Locuniak, and Ramineni (2007) found that there is a strong correlation between number sense and math achievement at the end of first grade. The researchers tracked number sense abilities in 277 children from kindergarten through first grade from a school district in northern Delaware. The researchers define number sense as counting skill, number knowledge, and the ability to transform sets through addition and subtraction. The participants were given a number sense core battery six times during the study time frame. The research findings suggest that screening number sense achievement in kindergarten will be beneficial in identifying children who may face later learning difficulties and learning disabilities in the area of mathematics (Jordan, Kaplan, Locuniak, & Ramineni, 2007).
Similarly, counting abilities are considered part of number sense and can therefore contribute to the identifying learners with mathematics difficulties. Desoete and Stock (2013) found that it is possible to differentiate between children who were and were not at risk for math disabilities in elementary school based on procedural and conceptual knowledge of counting. A total of 423 students in kindergarten and first grade from Belgium participated in the research study (Desoete & Stock, 2013). The participants were administered math assessments to evaluate their understanding of linear and random number patterns, addition/subtraction equations, and procedural calculations. Desoete and Stock (2013) found that the better the children’s performance on the last counting test in kindergarten greatly increased their chances of math success in first grade supporting that counting abilities in kindergarten can predict later math achievement.
In continuing the conversation of the challenges in teaching struggling math learners, the socio-demographic complexities of learners, such as low socioeconomic status and poor parental education, have also been found to contribute to identification of math learning disabilities (MLDs) and math difficulties (MDs). Anders et al. (2011) aimed to investigate which child, family, and home factors could predict teachers’ identification of children’s special education needs (SEN) status as part of a larger longitudinal study (EPPE3–11) in England. The sample for this study included 2,509 children between the ages of three and 11 in the U.K. The researchers collected a wide range of data and background information through parent interviews, teacher interviews, and questionnaires. Anders et al. (2011) found that children who come from low socioeconomic backgrounds, parents with low income, and/or parents with lower education levels are more likely to be identified with SEN in reading or number work in later primary school. It was further concluded that children identified with these at risk factors should be provided with the appropriate programs and resources to target learning needs.
Additionally, Gorker, et al. (2017) sought to research the probable prevalence of specific learning disorders and the relationship between socio-demographic characteristics in 2,174 primary children in second, third and fourth grades. The study took place in the 2013–2014 academic year in Edirne City, Turkey (Gorker, et al., 2017). The parents and teachers of the participants completed a Specific Learning Difficulties Symptom Scale, Learning Disabilities Symptoms Checklist, and socio-demographic forms. The researchers found that 6.5% of participants had math difficulties. Furthermore, researchers found that the socio-demographics of the participants, such as parent history of learning difficulties, parent income level, and parent education level, increased the risk of specific learning disorders. The researchers asserted that a key implication of this study is that these socio-demographic implications can assist with early detection and intervention of SLDs (Gorker, et al., 2017).
In spite of the research presented to assist regular education classroom teachers in identifying students with MLDs and MDs, limitations exist within the present research. Although Bryant, Bryant, and Hammill (2000) presented sound research on specific behaviors exhibited by identified and non-identified struggling math learners, the researchers indicated that the teachers, clinicians, and therapists who elected to participate in the research study worked primarily in the area of learning disabilities. There is no indication that a regular classroom teacher or pre-service teacher had an understanding of how to identify these behaviors or what steps to take when these behaviors manifested themselves within the classroom. Additionally, Watson and Gable (2012) recommend that further research is needed to better understand how to identify MLDs. Watson and Gable (2012) furthermore indicate that more longitudinal studies at different grade levels are needed, as well as a focus on early prediction and intervention of MLDs and MDs. Similarly, Desoete and Stock (2013) indicated that MLDs should not be considered a homogenous disability and that many other important predictors, both math skills and socio-demographic factors, can impact counting abilities and according to this study early predication of MLDs and MDs.
Challenge: Identifying Best Instructional Practices
Research has identified best practices to use in regular primary school classrooms when teaching students identified with math learning disabilities (MLDs) and math difficulties (MDs). The best practices include explicit problem solving instruction, the relationship between problem solving and algebraic reasoning, and technology as a supplemental support tool. Further, gaps in research affecting the implementation of these practices in primary school classroom will be explored.
Explicit Problem Solving Instruction
The Common Core State Standards have created a shift in mathematics skills toward problem solving and conceptual thinking. Research has found that mathematics problem solving is a major stumbling block for students identified with MLDs and MDs. Garderen (2006), sought to investigate the relationship between spatial visualization, visual imagery usage, and performance on math problem solving. Specifically, the study compared differences between a total of 66 students identified with learning disabilities, average-achieving students, and students identified as gifted on a variety of assessments to measuring mathematics problem solving performance, visual imagery usage, and spatial visualization abilities. Garderen (2006) found that students with learning disabilities were outperformed by their gifted and average achieving counterparts supporting the idea that students identified with mathematics learning disabilities struggle with problem solving tasks and spatial abilities. Furthermore, Garderen (2006) found that the students who did perform well on the mathematics problem solving assessments also performed well on the assessments used to measure spatial visualization. This correlation is important because increased spatial visualization supports complex mathematics problem solving. Furthermore, the researcher asserted that teachers play a major role in development of problem solving skills in learners. If problem-solving skills are not taught explicitly and effectively, students will likely incur deficits in their problem solving abilities.
Further, Jitendra, Dupuis, and Zaslofsky (2014) sought to extend previous research on the use of curriculum-based measurement of word-problem solving (CBM-WPS) as a valid and reliable measure of performance and progress in the context of the standards-based math curriculum for 136 third-grade math students identified as at risk for math difficulties. In addition to being identified as at risk for math difficulties, these students were drawn from 12 elementary schools in a large urban school district in the Midwestern United States, with 70% minority students and 66% of the population qualifying for free and reduced lunch. This research by Jitendra, Dupuis, and Zaslofsky (2014) replicated and extended previous research strengthen the evidence of the validity and reliability of CBM-WPS as a progress-monitoring tool. The researchers found that the participants’ problem correct score grew 0.33 per week. This is a key implication because although 0.33 problems correct per week may seem low, for a complex skill like problem solving this at risk population still showed growth. Additionally, the use of CBM-WPS can provide educators with data to detect growth, identify students struggling with problem solving, and inform instruction/interventions (Jitendra, Dupuis, & Zaslofsky, 2014)
In like manner, Kong and Orosco (2016) identified the Dynamic Strategic Math strategy as beneficial in assisting students with problem solving. Eight third grade students at risk for MD participated in this study. Six of the students were from Hispanic decent, one of the students was African American, and one student was from two or more other races. These students were selected from two elementary classrooms in a school in southern California. Word problems were given to these students that were similar to what they would see in classroom instruction. There were a total of 20 probes. The students worked within their ZPD (Zone of Proximal Development) level. The researchers found that, to best instruct minority students at risk for MD, teachers must teach by pulling from their background knowledge and experiences, differentiate instruction to math learning levels, use peer collaborative activities, decrease cognitive demands for multi-step problem solving, provide language models and sentence frames to discuss math problem solving, and provide additional time and opportunities for practice (Kong & Orosco, 2016)
Problem Solving Instruction through Algebraic Reasoning
Additionally, Powell and Fuchs (2014) determined that there is an association between word problems and algebraic reasoning. Students with word problem difficulty struggle the most with algebraic concepts. In the fall, the researchers assessed 789 second grade students from 61 classrooms across 12 different schools. These students were assessed using the assessments Addition Facts and Story Problems. In the spring, the students were assessed using the Test of Pre-algebraic Reasoning. Powell and Fuchs (2014) found that students with MDs can solve some algebraic problems without prior instruction with examples on the assessment. This helps teachers and researchers to know that students as young as second grade can think and reason algebraically (Powell & Fuchs, 2014). The researchers asserted that with effective instruction MD students can learn to meet success with more challenging algebraic concepts in later grades. This could mean that through proper assessment students as young as second grade who struggle with solving word problems can be identified for math interventions that would also target and remediate difficulties in algebraic reasoning due to the nature of word problems (Powell & Fuchs, 2014).
Moreover, Xin and Zhang (2009) found that when considering the interventions based on the Conceptual Model-Based Problem Solving (COMPS) it can increase mathematics achievement. Three fourth and fifth grade students enrolled in an after-school program in a Midwest urban public school (Indiana) in the United States participated in this study. They were administered a criterion word-problem solving test, KeyMath Revised Normative Update, and a Pre-algebra test. The criterion word-problem solving test sets were designed for baseline data, intervention, and post-intervention data. The problem solving subset of the KeyMath Revised Normative Update was administered before and after the intervention. Xin and Zhang (2009) found that there is a benefit to interventions to increase achievement in problem solving. Additionally, this study supports other research findings regarding transfer of skills. Classroom implications include teachers teaching students with MLDs to transfer specific skills to a variety of word problems with different situations. Additionally, the COMPS method of problem solving builds algebraic concepts (Xin & Zhang, 2009).
The available research on best instructional practices mainly focuses on areas of problem solving. This may be due to problem solving being considered the number one struggle for students with MLDs and MDs (Bryant, Bryant, & Hammill, 2000). While this research is very beneficial to regular education primary teachers, it is important to note that there is limited research available on other skill deficits for students identified with MLDs and MDs. To ensure that the best possible education is provided to this population of learners, more research is needed to support other mathematics behaviors of concern that can contribute to poor mathematics achievement for students identified with MLDs and MDs.
Using Technology to Support Teacher Direct Instruction
Studies reveal that technology can provide support for students identified with MLDs and MDs. Research indicates when used as an instructional support to teacher direct instruction, technology can increase academic achievement for all students, including those with MLDs and MDs (Kaur, Koval, & Chaney, 2017; Zhang, Trussell, Gallegos, & Asam, 2015; Kaczorowski & Raimondi, 2014; Castro, Bissaco, Panccioni, Rodrigues, & Domingues, 2014; Crawford, Higgins, Huscroft-D’Angelo, & Hall, 2016).
For example, Kaur, Koval, and Chaney (2017) examined the potential use of iPads as a supplement to promote the conceptual understanding of math skills for students with learning disabilities in high poverty schools. The ten participants identified with learning disabilities used ten free math learning apps aligned to math content standards that matched students learning abilities (Kaur, Koval, & Chaney, 2017). The students received instruction on math skills using traditional teaching methods, followed by using the math learning apps on the iPad to supplement this instruction. Kaur, Koval, and Chaney (2017) found that iPads have the ability to assist students with learning disabilities to understand math content better when used in conjunction with traditional instructional methods. Kaur, Koval, and Chaney (2017) argue that iPads can be used to individualize instruction and develop mathematical understanding due to breaking down computational steps visually and providing an engaging way to receive instantaneous feedback.
Similarly, Zhang, Trussell, Gallegos, and Asam (2015) sought to explore whether math apps can improve student learning, specifically for struggling math learners. The study was conducted in an inclusive fourth grade classroom in a public elementary school in the southwestern United States. A total of 18 students from the same classroom participated in the research study. Approximately half of the participants were identified with at least one disability (autism, emotional disorder, dyslexia, and learning disability) or identified as “at risk” due to poor academic performance and behavior issues. The students used three math apps to supplement teacher directed instruction on mathematics skills including place value concepts and multi-digit multiplication. Zhang, Trussell, Gallegos, and Asam (2015) found that the students improved their scores on the post-tests throughout the research study.
Zhang, Trussell, Gallegos, and Asam (2015) argue that the use of math apps in the general education classroom as an instructional support benefits all learners including struggling mathematics learners. According to Zhang, Trussell, Gallegos, and Asam (2015), “the affordances of the math apps, such as self-pacing, immediate feedback, and breaking down complex processes into small steps, may be even more beneficial for struggling students” (p. 38). Additionally, Zheng, Trussell, Gallegos, and Asam (2015) found that the math apps were easy to use and more engaging for the participants. The research findings suggests that the significant amount of math problems solved and the attempts to continue to practice the math skills due to instantaneous feedback on the apps would not likely occur if students were using paper/pencil activities (Zheng, Trussell, Gallegos, & Asam, 2015).
Additionally, Kaczorowski and Raimondi (2014) explored the use of a math eWorkbook created by the lead researcher to address the growing field of learning analytics and the research gap of how technology can support elementary students with math learning disabilities. The eWorkbook created for this research study was an iPad-based interactive, multimedia math workbook. It included review videos, interactive math practice, virtual manipulatives, and instantaneous feedback questions along with other media tools. Four third grade students with learning disabilities used the eWorkbook during independent math practice time. Kaczorowski and Raimondi (2014) found that the students’ accuracy and independence increased by using the eWorkbook rather than using the paper and pencil worksheets provided by the math program. The findings suggest that the use of the interactive videos and instantaneous feedback questions within the eWorkbook provided the most success in accurate math computations. Kaczorowski and Raimondi (2014) did note that the students did not always use the virtual tools as intended, but the math processes that the students engaged in on their own using the tools still lead to increased computational accuracy.
To continue, Castro, Bissaco, Panccioni, Rodrigues, and Domingues (2014) sought to evaluate whether a fun, virtual learning environment could improve motivation and math proficiency levels in students with math difficulties, specifically students with dyscalculia or students with math learning disabilities. The virtual learning environment was comprised of math mini games that were either created or adapted by the researchers and cover a variety of math skills within number sense and the four mathematical operations. The 43 students selected to participate in the intervention portion of the research study were second graders ranging from ages seven through ten from a public primary school in the eastern region of Sao Paulo, Brazil. After the pre-test, the students participated in interventions in addition to their regular math classes. The control group received the traditional interventions with the teacher while the experimental group received the virtual learning environment as their intervention. After the intervention phase, both groups took a post-test to measure progress. Castro, Bissaco, Panccioni, Rodrigues, and Domingues (2014) found that the students in the experimental group significantly improved their scores on the post-test. These findings prove that the computer-based games stimulated the students’ growth in mathematics, as well as suggesting that student improvement in motivation and increased participation within the classroom was a result of the virtual learning environment intervention.
Additionally, Crawford, Higgins, Huscroft-D’Angelo, and Hall (2016) sought to examine how the use of electronic support tools, such as calculators or formula tools, can impact students’ achievement in mathematics. The researchers evaluated the electronic support tools in the Math Learning Companion (MLC), a computer-based instructional program used as a supplemental math curriculum for students with learning disabilities or other students performing below grade level standards. The program is online and consists of 73 lessons across seven modules. For the study, the researchers created two different curriculums from MLC with six lessons each containing different skills. A total of 77 fourth, fifth, and sixth grade students participated in the study. The students were selected from four schools in north central Texas. Crawford, Higgins, Huscroft-D’Angelo, and Hall (2016) found that there is a positive relationship between the students’ math performance and the use of electronic support tools.
While the research presented supports technology as a supplemental support tool in the regular primary classroom, gaps in the research are still evident. The participants within the presented research studies are in second through fourth grade. The current research is missing sufficient evidence to support technology as supplement to teacher direct instruction in kindergarten, first, fifth, and sixth grades. The reporting of only three grade levels does not give primary school teachers a enough of an indication that the presented technology increases academic achievement across all primary school grades. Additionally, out of the four research studies presented, three of the studies worked with less than 20 participants suggesting that the current research available may not be generalizable across larger populations. Furthermore, Kaur, Koval, and Chaney (2017), and Crawford, Higgins, Huscroft-D’Angelo, and Hall (2016) only included participants identified with learning disabilities and do not indicate implications for use in the regular primary classroom with struggling math learners. This further supports that more research is needed to continue to provide a quality education for students identified with math learning disabilities and mathematics difficulties in the regular primary classroom.
Conclusion and Implications for Professional Practice
In conclusion, regular classroom teachers are on the front line in providing quality education for students identified with math learning disabilities and math difficulties (United States Department of Education, 2015). The first step in providing quality education for this population of students is to understand the nature of math learning disabilities and math difficulties through identifying the specific behaviors and socio-demographic factors that these learners can demonstrate in the classroom. Through identification of these behaviors and factors, regular education classroom teachers can provide the best possible interventions and feel confident when recommending a learner for special education testing.
Problem solving can be considered a major struggle for students with MLDs and MDs (Bryant, Bryant, & Hammill, 2000). Specific and explicit problem solving instruction is necessary for this population of learners to make progress with this difficult skill. Additionally, problem-solving abilities can have implications on future algebraic reasoning skills (Powell & Fuchs, 2014). Furthermore, the use of technology to supplement teacher direct instruction can provide a layer of support for struggling math learners (Kaur, Koval, & Chaney, 2017; Zhang, Trussell, Gallegos, & Asam, 2015; Kaczorowski & Raimondi, 2014; Castro, Bissaco, Panccioni, Rodrigues, & Domingues, 2014; Crawford, Higgins, Huscroft-D’Angelo, & Hall, 2016). Through using technology to supplement direct teacher instruction, students with MLDs and MDs can demonstrate increased mathematics achievement.
While the current research provides positive implications for professional practice, there are still gaps in research. To better support regular education classroom teachers, more research on effective teaching strategies within the general education classroom is needed at the primary and pre-service levels. Through the additional research with larger longitudinal studies, regular education primary teachers can gain sound insight on what strategies should be used in the classroom that demonstrate mathematics achievement and growth over time for this unique population of learners.
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