C225_Task_2

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Feb 20, 2024

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1 Literature Review- Task 2 Tia Martin Student ID: #000631149 Program Mentor: Michelle Corona Vass Assessment Code: C225 March 2022 Education-Related Research Topic
RUNNING HEAD: LITERATURE REVIEW 2 The topic of my research is in regards to students in third grade learning the foundational skills of multiplication and then being required to transfer that knowledge from conceptual to abstract within the span of one school year. Despite educators doing their best to ensure students understand the meaning of multiplication it is difficult to transition to the conceptual- representational and abstract methodology within a 180 of the school year. Students are unable to perform at grade level in fourth grade due to the sudden transition from learning the meaning of multiplication in third grade to then multiplying by two-digit by two-digit using the standard algorithm. Research Problem Statement Students in the third grade have difficulty learning their multiplication facts fluency by the end of this school year. This is a significant problem because students need to learn the meaning of multiplication, represent multiplication with arrays, equal groups, and properties of multiplication, and then abstractly be able to fluently recall facts 1-12. If students do not learn how to fluently multiply this will affect their learning of mathematics in the upper grades. One significant contribution to the problem of students learning to learn their fact fluency is that perhaps the curriculum being used does not incorporate a significant amount of fact fluency proactive. Perhaps a study that investigates the depth of why students in third grade are required to learn the meaning of multiplication, represent it and then abstractly memorize their fact fluency will remedy the situation. Literature Review
RUNNING HEAD: LITERATURE REVIEW 3 Third-grade students across the country are being asked to learn the meaning of multiplication and then transition that conceptual understanding to representational and abstract within one school year. The purpose of this study is to analyze which multiplication strategies are more effective in transitioning between conceptual learning of multiplication to abstract reasoning through fact fluency for students in the third grade. In addition, the purpose of this exploration of literature is to synthesize what research has already been explored when it comes to teaching effective multiplication strategies. Exploration of the literature associated with the analysis of the effectiveness of learning multiplication has concluded that students learn multiplication best when they are first taught to make meaning of the equation. The various studies generated multiple examples of common themes in their research such as the meaning of multiplication. When educators teach students what the factors mean, then students can better understand the process behind the meaning of multiplication. Another area of the research analyzed was the teaching of the various multiplication strategies and the efficacy of each strategy. Lastly, the research studies focused on the importance of automaticity of multiplication fact fluency, and the lack of retention of basic multiplication facts. Students must demonstrate mastery of multiplication fact fluency by the end of third grade but the retention of basic multiplication facts is problematic for many third grade students. Thus leaving educators and researchers to investigate where the discrepancy is between conceptual understanding, representational understanding, and abstract mastery of multiplication fact fluency. Teaching Multiplication Strategy Deficit
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RUNNING HEAD: LITERATURE REVIEW 4 Multiplication strategies are vital to the conceptual understanding of multiplication. They assist students with making meaning of what each factor means. With the assistance of the different strategies, students can begin to understand the foundational skill needed to build upon the Nevada Academic Content Standards mathematical domain operations of algebraic thinking. One significant contribution to the standards of mathematical practice is students modeling their mathematics. Students in third grade learn the basic foundational skills of multiplication through various strategies. According to Baker and Cuevas (2018), it is important to build learning of multiplication by using “multiple/diverse strategies” that gain weight from the learner. Their study suggests there is validity in using various concrete representations while learning the foundational skills of multiplication. However, the in-depth examination of which strategy is better at building the concrete representation is absent from the study. Thus, looking into the importance of identifying which strategy, to begin with, when building conceptual understanding will be a key component to research further. In another research study conducted by Milton, Flores, and Moore (2018), they wanted to discover if they could take students who were unable to memorize their fact fluency and introduce the DRAW strategy, which is to discover the sign, read the problem, answer, draw or check and then write the answer. Students in the study were taught to draw tally marks as a representational picture of what the multiplication problem represents. However, due to the nature in which the research was being conducted the researchers could not generalize their findings. Thus leaving speculation as to the depth and breadth in which this study could be generalized to a larger population.
RUNNING HEAD: LITERATURE REVIEW 5 The Nevada Academic Content Standards (NVACs) require third-grade students to build upon their conceptual knowledge of multiplication by using various strategies to demonstrate a representational model. Students are required to demonstrate their understanding using the distributive property, associative property, and communicative property of multiplication. The operations of algebraic thinking under the NVAC standards is a quite large domain full of complex reasoning in mathematics. Researcher Kaufmann (2019) examined an in-depth study on various strategies teachers use to teach multiplication to third graders. What Kaufmann (2019) found in his study is that “textbooks emphasize equal grouping” while other strategies were only “sporadically presented” in the curriculum. Educators must follow the NVACs and not necessarily follow a curriculum with fidelity. This is causing students to not fully engage with the area model of multiplication. Another example of a qualitative research study by Aylar (2020), interviewed teachers about strategies students' used to solve their single-digit multiplication tests. Teachers were presented with four different students' tests and strategies. The study found the teachers identified the students who used the algorithm as the most correct strategy to use. However, the educators overlooked the students who chose to use the array model to solve each problem correctly. Students who used the array model performed better on the assessment than those who used the algorithm. This is disconcerting that educators were unable to recognize that students that used the algorithm did not have a conceptual understanding. As an educator, it is vital that we first realize building a conceptual understanding of a mathematical equation is far more important than students being able to just rote memorize the answer. We must place value on the process and not the answer. Multiplication Strategies
RUNNING HEAD: LITERATURE REVIEW 6 Multiplication strategies are a vital part of the conceptual learning of multiplication. In the research conducted by Garcia (2020), the research strategy of teaching students that the multiplication table is a pattern. Part of his focus was to determine if decreasing the number of interference students experienced when learning the patterns on the multiplication table would assist them in understanding the concept. The action research determined this strategy only works after students initially understand the meaning of the factors. There is value in making sure students understand the meaning of multiplication before seeing if patterns on the multiplication table are an effective strategy. While teaching multiplication, educators are required according to the standards to teach the properties of multiplication to assist with solving problems. Hurst and Huntley (2020) determined in a qualitative study, “there must be explicit teaching of the many connections within the broad idea of multiplicative thinking to develop conceptual understanding.” Students must have access to a greater understanding to be able to explore the properties of multiplication. The study determined students who understood the area model when multiplying were able to better grasp the distributive property of multiplication. The study lacks a deeper understanding of how the other properties of multiplication play a part in a student's ability to fluently multiply if they know the properties of multiplication.
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RUNNING HEAD: LITERATURE REVIEW 7 Procedural understanding of multiplication is pertinent to fact fluency. The research case study conducted by Gotze (2019) looked at the deficits of multiplicative understanding in at-risk students. Gotze hypothesized at-risk students were lacking in a conceptual understanding of multiplication. What he found was students with deficits were taught to procedurally focus on solving multiplication problems and not being taught conceptual understanding with models. It is problematic to skip a very important step in building a student's understanding of multiplication. As educators, it is our responsibility to ensure we are teaching our students through a research- based instruction strategy of conceptual, representational to abstract concepts. Having a choice is always an integral part of students' success in mathematics. The Nevada Academic Content Standards (NVACs) were developed to incorporate many strategies for multiplication. The quantitative research study by Zhang, et al. (2017) examined the many strategies of multiplication and the choices students choose when faced with an unknown product. The study indicates that students’ first choice of strategy was the standard algorithm, however, when they struggled to determine the product of the equation they would resort to using other strategies such as groupings. It is important to remember that not all students in the study may have received the same instruction with similar strategies. Further research could examine what strategies students have learned before assessing the strategies they resort to when faced with an unknown. Automaticity with Multiplication Facts
RUNNING HEAD: LITERATURE REVIEW 8 Through the stages of learning multiplication, students journey through the concrete, representational, and then abstract. As students move into the abstract phase of their learning multiplication they are now working on fact fluency. Researchers Carter and Berrett (2019) explain in their study “fact fluency is foundational for later mathematics education.” Their study focused on a quantitative approach to determining if students would learn their multiplication facts faster if it was a computer-based program. The study determined students who tested performed better, however, the data is not completed because the assessments were only given one time and not repeated. If we are to study a computer-based fact fluency model then multiple measures need to be administered. Fact fluency is critical for students to find success in math. The research by Karnes and Grunke (2021), studied the effectiveness of peer tutoring on four elementary students in the third grade with the use of a game board race track. This study is limited in the outcomes due to utilizing four students and some participants did not function well together. The study did determine that students did slightly improve when working with their peer tutor on multiplication fluency. A study by Mann, et al. (2012) researchers focused on determining if repeated exposure to flashcards would increase a student's multiplication fluency. The researchers used only two students to direct instruction with a focus on fact fluency with flashcards. This action research uses an extrinsic reward to reward the two students for the increase in their test scores. This research does not go enough into depth to determine if flashcards are a useful strategy to ensure students will learn their multiplication fact fluency. While strategies such as flashcards are a vital part of rote memorization, there is not enough depth in this study to determine the outcome is sufficient.
RUNNING HEAD: LITERATURE REVIEW 9 Technology has changed the way we instruct our students in mathematics. With the use of technology, teachers can differentiate instruction more effectively. One research by Musti-Rao and Plati (2015) looked to see if a group of 21 third-grade students could increase their automaticity of multiplication by being allowed time on their iPad during math instruction. The action research determined that 66% of students were able to increase their multiplication fact fluency. The study was conducted in a highly affluent socioeconomic area where each student has 1:1 devices. While technology is an integral part of the 21st-century classroom, students across the country do not all use the same type of device or even all have a device. The device in this study was an iPad with access to a math drill app, not all schools are fortunate to have 1:1 technology. Lack of Retention of Basic Multiplication Facts As educators, we are plagued with the dilemma of not having enough time to teach all content with the depth and breadth our students need. Many studies have been conducted on the reasons why students are not fluent with their basic math facts. However, the action research by Hinton, Flores, and Strozier (2014), looked in-depth into why students are unable to learn their multiplication facts. They discovered that students unable to retain their basic facts also lacked an understanding of place value. The researcher's solution was to introduce the DRAW strategy. However, students that do not understand one-to-one correspondence will struggle to make equal groups.
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RUNNING HEAD: LITERATURE REVIEW 10 Multiplication fact fluency is an important part of a child’s mathematical learning. Students fluent in their math facts fare far better than their peers when learning new concepts. Researchers Nam and Spruill (2005), studied the effectiveness of the acquisition of math facts to advance students' skills in other math domains. The research utilized the strategy called see-say, hear-say to determine which channel students could perform better. Students would see an equation and then say the product other students would hear the equation and then say the product. It was determined that teachers should not just assume that all students can perform in one channel. One significant problem with this action research is that students were not required to write down the facts but just to recall them orally. Part of the fact fluency would be for all students to be able to fluently write their facts as well as orally say them. As educators, we know that all students learn at their own pace and that their brain connections are unique as their abilities. A qualitative study on the effects of a student's neural activation when students recall basic multiplication facts was conducted on a fourth-grade class of 26 students. Researchers Polspoel, et al (2017) studied the student's brains when they recalled basic multiplication facts. It was determined that parts of the temporal lobe in the brain activate at a quicker rate when asked to recall basic facts. Thus determined by researchers there is a greater need for more in-depth studies on various age ranges and not just fourth graders. While this research is vital to understanding a student's brain, as an educator this study does not give enough information to be able to determine what to do next with activating a student's temporal lobe when asked to recall information. When studies such as this are performed it would help greatly if the information could be synthesized on what it would look like in best practices while teaching basic multiplication facts. Purpose Statement of the Research Study
RUNNING HEAD: LITERATURE REVIEW 11 The purpose of this research study is to determine if implementing fact fluency practice every day will better assist students with memorization of their multiplication facts. In addition, there are many strategies for teaching multiplication, but what are the most effective strategies to build a student's conceptual understanding quickly before moving on to rote memorization of multiplication fluency. Open-Ended Research Questions 1. How does implementation of multiplication fact fluency practice into daily math instruction impact the math fact fluency retention of third-grade students? 2. What teaching strategies are the best practices to address the learning outcome of multiplication fact fluency with third-grade students? Justification of Research Approach for Each Research Question 1. My first research question will be analyzed by using timed fact fluency multiplication tests through a quantitative approach. 2. My next research question will take a more qualitative approach to the data. I plan on interviewing teachers and students on multiplication strategies they believe help students' success rate in fact fluency.
RUNNING HEAD: LITERATURE REVIEW 12 Resources Aylar Çankaya, E. (2020). Investigating flexibilities of the classroom teachers for four operations in the basis of different strategies. Kuramsal Eğitimbilim , 13 (4), 646–662. https://doi.org/10.30831/akukeg.646023 Baker, A. T., & Cuevas, J. (2018). The importance of automaticity development in Mathematics. Georgia Educational Researcher , 14 (2). https://doi.org/10.20429/ger.2018.140202 Berrett, A. N., & Carter, N. J. (2018). Imagine Math Facts Improves Multiplication Fact Fluency in Third-Grade Students. Journal of Behavioral Education , 27 (2), 223–239. https://doi.org/10.1007/s10864-017-9288-1 García-Orza, J., Álvarez-Montesinos, J. A., Luque, M. L., & Matas, A. (2021). The Moderating Role of Mathematical Skill Level when Using Curricular Methods to Learn Multiplication Tables. Psicologia Educativa , 27 (2), 123–133. https://doi.org/10.5093/psed2021a14 Götze, D. (2019). Language-Sensitive Support Of Multiplication Concepts Among At-Risk Children: A Qualitative Didactical Design Research Case Study. Learning Disabilities -- A Contemporary Journal , 17 (2), 165–182. https://search.ebscohost.com/login.aspx? direct=true&AuthType=sso&db=eue&AN=139929949&site=ehost- live&scope=site&custid=ns017578
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RUNNING HEAD: LITERATURE REVIEW 13 Hinton, V., Strozier, S. D., & Flores, M. M. (2014). Building mathematical fluency for students with disabilities or students at-risk for mathematics failure. International Journal of Education in Mathematics, Science and Technology , 2 (4), 257. https://search.ebscohost.com/login.aspx? direct=true&db=eric&AN=ED548269&site=eds- live&scope=site&authtype=sso&custid=ns017578 Hurst, C., & Huntley, R. (2020). Distributivity, partitioning, and the multiplication algorithm. JRAMathEdu (Journal of Research and Advances in Mathematics Education) , 5 (3), 231– 246. https://doi.org/10.23917/jramathedu.v5i3.10962 Karnes, J., & Grünke, M. (2021). The Effects of a Math Racetracks Intervention on the Single- Digit Multiplication Facts Fluency of Four Struggling Elementary School Students. Education Sciences , 11 (6), 265. https://doi.org/10.3390/educsci11060265 Kaufmann, O. T. (2019). Students´ reasoning on multiplication in primary school classroom context. Journal of Research in Mathematics Education , 8 (1), 6. https://doi.org/10.17583/redimat.2019.2822 Mann, Z., McLaughlin, T. F., & Williams, R. L. (2012, November). The Effects of Direct Instruction Flashcards and Rewards with Math Facts at School and in the Home: Acquisition and Maintenance. Retrieved March 20, 2022, from https://eric.ed.gov/? q=Multiplication+strategies&pr=on&ft=on&id=EJ1127792
RUNNING HEAD: LITERATURE REVIEW 14 Milton, J. H., Flores, M. M., Moore, A. J., Taylor, J. J., & Burton, M. E. (2019). Using the Concrete–Representational–Abstract Sequence to Teach Conceptual Understanding of Basic Multiplication and Division. Learning Disability Quarterly , 42 (1), 32–45. https://doi.org/10.1177/0731948718790089 Musti-Rao, S., & Plati, E. (2015). Comparing Two Classwide Interventions: Implications of Using Technology for Increasing Multiplication Fact Fluency. Journal of Behavioral Education , 24 (4), 418–437. https://doi.org/10.1007/s10864-015-9228-x Nam, S. S., & Spruill, M. (2005). Learning channel intervention to develop and generalize fluency in multiplication facts. Journal of Early and Intensive Behavior Intervention , 2 (2), 103–111. https://doi.org/10.1037/h0100305 Polspoel, B., Peters, L., Vandermosten, M., & De Smedt, B. (2017). Strategy over operation: neural activation in subtraction and multiplication during fact retrieval and procedural strategy use in children. Human Brain Mapping , 38 (9), 4657–4670. https://doi.org/10.1002/hbm.23691 Zhang, D., Ding, Y., Lee, S., & Chen, J. (2017). Strategic development of multiplication problem solving: Patterns of students’ strategy choices. Journal of Educational Research , 110 (2), 159–170. https://doi.org/10.1080/00220671.2015.1060928

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