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The purpose of this paper will be to determine if a proposed drill and practice method is an efficient method to teach multiplication to students with a specific learning disability in mathematical computation. As per the Individuals with Disabilities Education Improvement Act (IDEIA), a specific learning disability “means a disorder in one or more of the basic psychological processes involved in understanding or in using languages, spoken or written, that may manifest itself in an imperfect ability to listen, think, speak, read, write, spell, or to do mathematical calculations, including conditions such as perceptual disabilities, brain injury, minimal brain dysfunction, dyslexia, and developmental aphasia…. Specific learning disability does not include learning problems that are primarily the result of visual, hearing, or motor disabilities, of …. [intellectual disability], or emotional disturbance, or of environmental, cultural, or economic disadvantage.” (34 CFR § 300.8[c]).
About 6% of mathematically deficient students are identified as having a mathematical learning disability (MLD) (Shalev & Gross-Tsur, 2001). An MLD is an impairment effecting the area of mathematics despite average IQ and general schooling (American Psychiatric Association, 1994). De Visscher & Noel (2014) identified a specific type of MLD, dyscalculia, that results in difficulty recalling facts. Children with dyscalculia struggle with a recalling network and have difficulty going from physical actions (counting on fingers) to a more memory-based retrieval system such as knowing 3 x 4 instantly (De Smedt, Holloway& Ansari, 2011).
In the last twenty years, there has been an increased focus on academic achievement for students with disabilities. To address this need, educators have utilized evidence-based practices to support instruction within the classroom. The need for evidence-based solutions has been vital in addressing many academic deficits that are faced in mathematics.
(Satsangi, Hammer, & Hogan, 2018). Throughout the years, policies, laws, and research have developed that dictate the instruction and intervention provided by educators to help struggling students with a learning disability. (Pressley, Duke, & Boling, 2004). Regarding policies and law, both No Child Left Behind (NCLB) Act of 2001 and the Individuals with Disabilities Education Act (IDEA) ushered in new laws regarding instructional practices using evidence-based practices which are designed address the needs of students with disabilities. Instructional practices were affected due to schools using empirically validated programs and prove that interventions were used to prevent failure. (Pressley, Duke, & Boling, 2004). An example of an effective evidence-based practice would be checking for understanding (Gersten et al., 2009). However, according to a study conducted by (McKenna, Shin, Ciullo, 2015), it was infrequently incorporated into instruction. Utilizing checks for understanding help identify students’ misconceptions and errors, provide appropriate scaffolds, and reteach individual concepts and skills (Meadows Center for Preventing Educational Risk, 2011). Another example is the use of explicit instruction, which includes teacher-directed instruction and that results in practice of recently learned strategies (Gersten et al., 2009). It, too, was infrequently used despite the evidence proving its effectiveness (Bryant, Bryant, Williams, Kim, & Shin, 2012; Gersten et al., 2009).
While previous research found that drill and practice results in increased retention and learning (Nist and Joseph 2008), there is minimal research on the most effective and efficient ways to use it. In a separate study by Becker, McLaughlin, Weber, & Gower (2009), they found that daily drill and practice was beneficial in learning recently taught skills. Evidence suggests it was beneficial to all students, but those who were one or two years behind benefitted most. Burns (2005) did a study on a specific form of drill and practice known as incremental research and found it to be a useful intervention for multiplication with third graders identified with dyscalculia. Burns (2005) contends that it is an easily-implemented academic intervention that could assist in practice of unknown items and should be investigated further. Additional studies have found that, as students’ progress through school and acquire more math skills, they needed less repetition. Students tended to need more repetition on math facts such as 4-7 than they did on 1-3 (Burns, Ysseldyke, Nelson, Kanive, 2015). Yet, Burns agrees that additional research would allow for better instructional planning and generalization across different settings.
To further the literature on the field of research, I am proposing the following hypothesis: Do students with dyscalculia learn multiplication problems faster when they are presented with easier facts (1,2,5, 10, and 11) first and harder facts later (3, 4, 6, 7, 8, 9, 12) versus when a group learns them in traditional order (1,2,3,4, etc.)? In this proposal, the dependent variable is length of time to learn times tables. The independent variable is the way that the multiplication problems are grouped. Impacts of this research could be large for students with and without disabilities in 3rd and 4th grade. If the findings were consistent, it could change the way that multiplication is taught. If it’s learned faster, it would allow for more repetitions that would generalize into other areas such as division, volume, area, order of operations, solving equations, etc. On a grand scale, there is a chance that it could impact state scores, and, as a direct result, teacher evaluations.
- American Psychiatric Association. (1994). Diagnostic and statistical manual of mental disorders (4th ed.). Washington, DC: Author..
- Becker, A., McLaughlin, T., Weber, K. P., & Gower, J. (2009). The effects of copy, cover and compare with and without additional error drill on multiplication fact fluency and accuracy. Electronic Journal of Research in Educational Psychology, 7(2), 747–760. Retrieved from https://proxy-calu.klnpa.org/login?url=https://search-ebscohost-com.proxy-calu.klnpa.org/login.aspx?direct=true&db=eue&AN=44962255&site=eds-live&scope=site
- Bryant, D., Bryant, B., Williams, J., Kim, S., & Shin, M. (2012). Instructional practices for improving student outcomes in solving arithmetic combinations. In B. G. Cook & M. Tankersley (Eds.), Research-based practices in special education (pp. 61–72). Upper Saddle River, NJ: Pearson.
- Burns, M. K. (2005). Using incremental rehearsal to increase fluency of single-digit multiplication facts with children identified as learning disabled in mathematics computation. Education and Treatment of Children, (3), 237. Retrieved from https://proxy-calu.klnpa.org/login?url=https://search-ebscohost-com.proxy-calu.klnpa.org/login.aspx?direct=true&db=edsjsr&AN=edsjsr.42899847&site=eds-live&scope=site
- Burns, M. K., Ysseldyke, J., Nelson, P. M., & Kanive, R. (2015). Number of repetitions required to retain single-digit multiplication math facts for elementary students. School Psychology Quarterly, 30(3), 398–405. https://doi-org.proxy-calu.klnpa.org/10.1037/spq0000097
- Burns, M. K., Zaslofsky, A. F., Kanive, R., & Parker, D. C. (2012). Meta-analysis of incremental rehearsal: Using phi coefficients to compare single-case and group designs. Journal of Behavioral Education, 21, 185–202.
- Cates, G. L., Skinner, C. H., Watson, T. S., Meadows, T. J., Weaver, A., & Jackson, B. (2003). Instructional effectiveness and instructional efficiency as considerations for data-based decision making: An evaluation of interspersing procedures. School Psychology Review, 32, 601–616.
- De Smedt, B., Holloway, I.D., & Ansari, D. (2011). Effects of problem size and arithmetic operation on brain activation during calculation in children with varying levels of arithmetical fluency. NeuroImage, 57(3), 771–781.
- De Visscher, A., & Noël, M.-P. (2014). Arithmetic facts storage deficit: the hypersensitivity-to-interference in memory hypothesis. Developmental Science, 17(3), 434–442. https://doi-org.proxy-calu.klnpa.org/10.1111/desc.12135
- Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79, 1202–1242. doi:10.3102/0034654309334431
- Individuals with Disabilities Education Improvement Act of 2004, commonly referred to as “IDEIA” or simply “IDEA” (Pub. L. No. 108-446), 20 U.S.C. § 1400 et seq. Regulations appear at 34 CFR Part 300.
- McKenna, J. W., Shin, M., & Ciullo, S. (2015). Evaluating reading and mathematics instruction for students with learning disabilities. Learning Disability Quarterly, 38(4), 195–207. https://doi-org.proxy-calu.klnpa.org/10.1177/0731948714564576
- Meadows Center for Preventing Educational Risk. (2011). Secondary special education observation and intervention study: Technical report. Austin, TX: Author.
- Nist, L., & Joseph, L. M. (2008). Effectiveness and efficiency of flashcard drill instructional methods on urban first-graders’ word recognition, acquisition, maintenance, and generalization. School Psychology Review, 37, 294–308.
- Pressley, M., Duke, N. K., & Boling, E. C. (2004). The educational science and scientifically based instruction we need: Lessons from reading research and policymaking. Harvard Educational Review, 74(1), 30–61.
- Shalev, R. S., & Gross-Tsur, V. (2001). Developmental dyscalculia: Review article. Pediatric Neurology, 24, 337–342.
- Satsangi, R., Hammer, R., & Hogan, C. D. (2018). Studying virtual manipulatives paired with explicit instruction to teach algebraic equations to students with learning disabilities. Learning Disability Quarterly, 41(4), 227–242. https://doi-org.proxy-calu.klnpa.org/10.1177/0731948718769248
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