C225_Task_1

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1 Annotated Bibliography- Task 1 Tia Martin Student ID: #000631149 Program Mentor: Michelle Corona Vass Assessment Code: C225 March 2022 Education Related Research Topic
RUNNING HEAD: ANNOTATED BIBLIOGRAPHY 2 The research topic I have decided to research is students in 3rd grade learning to build their conceptual understanding of multiplication through manipulatives and transitioning that learning into fact fluency. Teaching 3rd grade for eight years has taught me very few students can learn the conceptual meaning of multiplication means and then move to fact fluency within a school year. Relevant Keywords/ Search Phrases 1. multiplication 2. conceptual understanding of multiplication 3. Automaticity for math facts 4. fact fluency 5. multiplication strategies 6. multiplication fluency strategies 7. representational strategies for multiplication Additional Relevant Keywords/ Search Phrases 1. Effectively teach multiplication strategies 2. Building multiplication fluency Useful Relevant Keywords/ Search Phrases When doing my research by using keywords I discovered that the most useful keyword search that resulted in the most resources were “multiplication strategies” and “multiplication fact fluency.” Explanation of Usefulness The resources helped identify the most effective ways to teach multiplication and then transition that learning into automaticity of their multiplication facts. They were helpful mainly
RUNNING HEAD: ANNOTATED BIBLIOGRAPHY 3 because they led to many articles based upon research of students and fact fluency with multiplication that I then used in my annotated bibliography. Annotated Bibliography 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 This research study explores the effectiveness of a computerized curriculum on students mastering their multiplication facts before the end of third grade compared to rote memorization. The researchers chose a quantitative method of data collection from multiplication assessments from the two variable groups. The data explored the benefits of implementing a technology component into increasing students' retention of multiplication facts by the end of third grade. Through various timed multiplication tests, researchers hypothesized that increased access to an online fact fluency program would increase their controlled groups' memorization of multiplication facts. Researchers discovered that in the three randomly assigned groups students began the year relatively low on math fact fluency. The three groups received the math online fact fluency game. All groups improved, slowly they took away group 1’s access and math scores decreased. Group 2 and 3 continued to the maintenance phase of the study. It was determined that the maintenance phase and access to the online math game were instrumental in students' fluency increasing. One strength in this study was the researchers used random assignment of the groups. A weakness of this study is the program being researched was by researchers that worked for the company testing the validity of the online math fluency game.
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RUNNING HEAD: ANNOTATED BIBLIOGRAPHY 4 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 This research study approach compares rote memorization of multiplication facts versus the rules of multiplication. The research study uses the quantitative method approach and analyzes the experimental research data collected from a group of second graders. Data explored was based upon the assertion that students learn multiplication by either rote memorization or based upon the rules of multiplication. Through many variable manipulations of the groups, it was determined that students who have deficits in their mathematical understanding will do better with rote memorization of the multiplication answers. Whereas students who are high achievers at multiplication will achieve greater success in their multiplication skills by using rules of multiplication. A strength of this study is the research design. Student populations in the groups were random and included students of all socioeconomic backgrounds. The weakness of this research design is that eighteen students who had a diagnosed learning difficulty such as dyslexia or dyscalculia were excluded from the analysis. 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
RUNNING HEAD: ANNOTATED BIBLIOGRAPHY 5 This is an original case study that examines the support of multiplication concepts among children with learning difficulties. The case study was designed with a qualitative approach to examine the effectiveness of using language-sensitive support to teach conceptual understanding of multiplication. The research study was based upon two children, Ilyan and Leon who both are third graders that have never meant. Leon has a mathematical learning difficulty, while Ilyan is an average learner. Leon was only able to associate multiplication by saying “one times two.” Leon had no understanding of the meaning of multiplication and was instructed in building the conceptual understanding by using vocabulary to make meaning of a multiplication problem. Ilyan was already able to memorize his multiplication facts but had difficulty making sense of what a problem meant. Ilyan was instilled using the same lessons as Leon. Both Ilyan and Leon were able to increase their understanding of multiplication by learning to make meaning of the factors and product. The study concluded that at-risk children can learn the conceptual understanding of multiplication as long as the instruction included language-sensitive vocabulary. One weakness of this study is that only two participants were being compared to the country norms. A strength is that the study used the same lessons to collect the data on both Ilyan and Leon. 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://doi.org/10.18404/ijemst.69677
RUNNING HEAD: ANNOTATED BIBLIOGRAPHY 6 This research study was conducted to determine if students with a learning disability could increase their multiplication fluency with strategic intervention. The researchers used the design of descriptive research with a quantitative focus to analyze the results over the years of how interventions and students with disabilities correlate and then proceeded to design their own research based upon previous data. Researchers used previous knowledge of the concrete- representational- abstract (CRA) model to work with students with a learning disability to incorporate more kinesthetic learning in the concrete-representational part of CRA. Students were taught the mnemonic DRAW which means Discover, Read, Answer, Write. The results indicated that the computation scores increased from 49% accuracy to 90% accuracy in students with disabilities. One weakness of the study is that the researchers then applied the same knowledge to the students using addition, subtraction, and division. Students had already been taught the mnemonic. A strength of the study was that the researchers examined previous decades' worth of data to determine the most effective way for students with disabilities to learn their fact fluency. Building upon other researchers' mistakes and successes helped this study see a significant increase in scores. 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 This research study examines the relationship between fact fluency as it is based upon a conceptual understanding of arrays connected to multiplicative properties such as the distributive property. The research approach used by the author is qualitative. The author seeks to find a
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RUNNING HEAD: ANNOTATED BIBLIOGRAPHY 7 correlation between students who conceptually understand multiplication and students who procedurally understand multiplication. This particular paper is part of an ongoing study to determine the effectiveness of learning the properties of multiplication. In the two years that the researcher studied groups of students, they discovered that students who understood the properties of multiplication were better able to grasp multi-digit multiplication. For example in the first group of students over 87% of the students could solve the multiplication problems as opposed to the 51% from the group of students who received no instruction of multiplication properties. While this study provides educators with valuable information on the importance of teaching the multiplication properties, it does have a weakness. The study uses two different teachers, the first group of students were taught by a veteran teacher with 20 years of experience, and the other group was taught by a new teacher with 2 years of experience. The strength of the research is that the data supports the benefit of teaching the conceptual understanding of the properties of multiplication because students who were explicitly taught them were able to communicate their thinking versus students who only performed the standard algorithm were unable to describe their thinking. 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 This peer-reviewed article examines the action research of the critical role multiplication fluency plays on a student's trajectory in mathematical understanding. The action research uses a qualitative approach to study a group of 6 students pre-selected based upon a certain set of criteria established by the researcher. Students selected had a basic understanding of
RUNNING HEAD: ANNOTATED BIBLIOGRAPHY 8 multiplication but were unable to recall their fact fluency. The design of the study was to determine if with intervention if students could recall their multiplication fact fluency. After six weeks of intervention, researchers discovered that students were able to increase their recall of multiplication facts. A weakness of this study is that researchers did not include all multiplication factors, they excluded 0’s, 1’s, and 10’s. A strength is that the teachers were able to use their data to choose 12 students and then researchers narrowed the field down to 6. 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 The article explores the connection between the inverse operation and mastering the concrete-representational and abstract method for learning multiplication and division. The researchers chose to design the study with a mixed-method design and used qualitative research students' understanding of the operations and quantitative to score the assessments and analyze the data. Students with learning difficulties who had not mastered their multiplication and division were the focus of this study. The researchers used this study to qualitatively analyze a student's perception when using the concrete-representational abstract method to teach multiplication and division. Evidence shows throughout the interviews with the group of students that their understanding of procedural multiplication and division increased significantly when first beginning with the conceptual understanding. One weakness of this study is that the researchers solely focused on the conceptual-representational-abstract method and did not use another method to compare its effectiveness. A strength of the study is that the teacher delivering
RUNNING HEAD: ANNOTATED BIBLIOGRAPHY 9 the intervention was first given professional development on the expectation of the CRA model and how to effectively implement it in the classroom. 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 This research study solely focuses on how the brain shifts from procedural to fact fluency. The researchers used mixed methods to design this study. They used quantitatively to score the assessment answers and qualitative to analyze the student's verbal responses in the interviews. The study was analyzing at which point in the neural system does the brain transfer from procedural knowledge of a multiplication problem to the fact of fluency and basic recall of the product. When analyzing the student's explanation of the process of procedurally how they solved the equation the researchers were unable to determine where in the transfer of knowledge the brain moved into a basic recall. One weakness of the study is that they only focused on one small group of fourth-graders and the study suggests the same process be attempted in other grade levels. A strength of the study is the fourth graders being analyzed had already mastered their recall of basic multiplication facts. Reed, H. C., Gemmink, M., Broens-Paffen, M., Kirschner, P. A., & Jolles, J. (2015). Improving multiplication fact fluency by choosing between competing answers. Research in Mathematics Education , 17 (1), 1–19. https://doi.org/10.1080/14794802.2014.962074 This case study was conducted to determine the recall fluency accuracy when students are given a choice between two answers. The research design is with a quantitative focus and the
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RUNNING HEAD: ANNOTATED BIBLIOGRAPHY 10 independent variable is the curriculum in which the teacher is delivering. Grade levels 3 and 4 were each given the same test of facts for multiplication. One group was given tests based upon basic recall while the other was given the choice of products. Data of students who were administered the basic recall tests were better for students who were high achievers than students who struggled with basic facts. Students who were low achievers on the basic facts increased their fact fluency a great deal when given a choice format assessment. The weakness of this research study is that students did not have to state which strategy they used to solve the choice format. The strength of this case study is that the researcher allowed for students to determine the choice assessment or basic recall assessment, which allowed the participants to take ownership of learning their facts. 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 This research is an action research study that was designed based upon a school in the midwest of the United States. The researchers used third grade, fourth grade, and fifth-grade classes at one school to study if students were each taught a strategic strategy for their grade level if it would help to improve multiplication understanding. The action research study was conducted with a mixed-method design. The researchers asked students to solve ten multiplication problems using a quantitative research design to interpret the data. Students were then interviewed using a qualitative approach for how they solved each problem. The data was examined and the results concluded that students who were unable to explain their strategy received on average 50% of the problems correct. Students that could explain how they solved the equation were able to 70% of the time explain how they were able to solve the equation. One
RUNNING HEAD: ANNOTATED BIBLIOGRAPHY 11 weakness of this research is that it lacks data on the demographics of the students. A strength of this research is that it approaches the data through the lens of both quantitative and qualitative. The value in interviewing students to analyze their knowledge is important to the research. Research Problem Statement The state of Nevada has adopted the Nevada Academic Content Standards (NVACs) which are based upon the Common Core State Standards (CCSS). The NVACs require students in 3rd grade to learn the foundational skills of multiplication and division and then fluency master the facts by the end of 3rd grade. With this expectation comes great difficulty for students to understand the conceptual meaning of multiplication and then move to mastery of the facts in 180 days if problematic. This is where the research inquiry comes into play. Relation of Research Problem to Professional Setting The research problem is related to my research because after teaching 3rd grade for nearly 8 years I have come to determine it is nearly impossible for all students to master the conceptual meaning of multiplication and divisions and then move to fact fluency within the school year. To determine the best course of action to ensure all students master their multiplication facts would be beneficial to the students and to their academic success as they continue the mathematical path. The exploration of the literature on this subject has helped me as a researcher identify potential avenues to explore and learn from. Benefits of the Literature Search and Annotated Bibliography Completing a literature search and thus an annotated bibliography has helped to inform me of the previous research that has already been done on this topic. It was very informative to
RUNNING HEAD: ANNOTATED BIBLIOGRAPHY 12 see that other researchers share similar questions regarding the phenomena of the conceptual- representational-abstract meaning of multiplication and division within the intermediate elementary level. By going through the process of reading the various studies and the researchers' approach to their inquiry it was helpful in determining which pathway I will take as a researcher for my capstone project. Annotated Bibliography 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: ANNOTATED BIBLIOGRAPHY 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://doi.org/10.18404/ijemst.69677 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 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 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 Reed, H. C., Gemmink, M., Broens-Paffen, M., Kirschner, P. A., & Jolles, J. (2015). Improving multiplication fact fluency by choosing between competing answers. Research in Mathematics Education , 17 (1), 1–19. https://doi.org/10.1080/14794802.2014.962074
RUNNING HEAD: ANNOTATED BIBLIOGRAPHY 14 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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