Pedagogy of Math Fact Fluency On Performance

Abstract

The essay that follows explores the need for a pedagogical shift in mathematical instruction to improve the overall performance of the United States on standardized exams. Math fact fluency skills, or the ability to solve basic arithmetic equations, is at the heart of the issue due to the structuring and scaffolding performed by key components of the brain. Shin (n.d.) provided insight into the functionality of functional magnetic resonance imaging. Another source (“Basic skills”, (2013) showcased the correlation between early mathematical ability and performance on standardized tests. Desilver (2017) provided a statistical analysis that showcases the United States performance in the subject of mathematics. “How children’s” (2014) provided insight on how children’s brains develop over time, specifically involving the development of mathematical abilities. DiNapoli (2018) proposed a pedagogical shift that is required to improve the education of mathematics. In addition, the researcher provides key questions that could be utilized in further studies.

Pedagogical Shift Required to Improve Mathematical Performance While Children’s Brains Develop

In order to research the impact of basic arithmetic on long term mathematical performance, the researcher discovered how a child’s brain develops to discover correlations between pedagogical strategies and memory scaffolding of math fact fluency. First of all, to understand why mathematics is a topic of great concern, studies proved that mathematics is a major problem in the United States. Further studies proved that as children’s brains develop, there is a transfer of information that is scaffolded in the hippocampus. Lastly, studies showcased that a shift in current pedagogical methods is required as collaboration is, in many cases, inferior to the collaborative competition. To research this ongoing problem further, the researcher proposes essential questions that could be used for further studies.

Literature Review

Mathematics, especially math fact fluency is a source of ongoing research on long term performance for the development of the skills, such as in math classes or performance on standardized tests. One such study was conducted by researchers and published in Science Daily, at the University of Western Ontario who utilized functional magnetic resonance imaging (fMRI) to observe any correlations that existed between math fact fluency and performance on the standardized test known as the PSAT. Functional magnetic resonance imaging is a method of observing neural activity by observing the blood flow to different regions of the brain and observing changes in blood flow that indicate more or less activity in the region (Shin, n.d., para. 5). According to Ansari (2013), “There is a clear link between fluency and high level abilities — being fluent at basic math counts.” (Ansari as cited in “Basic math”, para. 5). To further emphasize his point, he explained that students whose scores were higher on the PSAT were observed to have had more activity in the supramarginal gyrus, a region in the left side of the brain that has been previously linked to math fact retrieval. On the other end of the spectrum, students whose scores where lower were observed to have greater concentrations of neural activity in the intraparietal sulcus, which is in the right portion of the brain, that is used to evaluate complicated mathematical problems and heavy arithmetic processing. In order to conclude his research, Ansari mentions that these findings should halt the endless discourse on what mathematical pedagogical strategy is superior as basic repetition of arithmetic is equally important to conceptual learning. Another study conducted on the importance of mathematics instruction has been conducted by Pew Research, although it is more of a statistical analysis. The main question that the author wished to answer was how the performance of the United States in mathematics compared to that of other countries; however, it can be noted that most of the findings are applicable to the topic of mathematical fluency on long term performance. For the first important piece of statistical information in the analysis, the author used an international standard test named the Programme for International Student Assessment (PISA). This test ranks countries in a variety of subjects, one of which is math, by testing 15-year-olds. The United States placed 38th out of the 71 participating countries in the subject of mathematics. For the second piece of statistical analysis, the National Assessment of Educational Progress (NAEP) is used as it showcases the mathematical skills of 4th, 8th, and 12th graders. According to DeSilver (2017), “[In] 2015 NAEP rated 40% of fourth-graders, 33% of eighth-graders and 25% of 12th-graders as “proficient” or “advanced” in math. While far fewer fourth- and eighth-graders now rate at “below basic,” the lowest performance level (18% and 29%, respectively, versus 50% and 48% in 1990)” (para. 6). Overall, the United States needs to focus on its mathematical ability as it underachieves compared to other countries, which can be addressed by improving math fact fluency.

When researching the topic of mathematics, especially math fact fluency, it became evident that further information on how a child’s brain develops to support new mathematical information was necessary. As it turned out, several studies had already been conducted on the development of children’s brains around mathematical performance. For instance, an article published in Science Daily showcased a study conducted by the Stanford University of Medical Care on how a child’s brain acclimates to new mathematical evaluation strategies that are learned over time and are more efficient. The study conducted consisted of children, ages 7-9, adolescents, ages 14-17, and adults, ages 19-22, all of whom received multiple basic mathematical equations of comparable difficulty that required evaluation. Due to the nature of the experiment, those with mathematical deficiencies or those with attention deficit hyperactivity disorder (ADHD) were excluded from participation, and all participants had average IQs. All of the age groups received brain scans, unfortunately the type of brain scan is not mentioned, and went on normally for another 1.2 years before receiving a second scan. As the children and adolescent age groups were still in school for the duration of the study, these two age groups received mathematical instruction; however, on the other hand, the adults received no instruction. After the 1.2 year break of the study, all subjects of the first brain scan returned to evaluate more equations, similar to those equations to those used in the first scan, while receiving a second scan. Researchers were intrigued by the discoveries made. Based on the first scan, the researchers discovered that the region in which children performed mathematical computation is different than the region that the adults used: children use their prefrontal cortex and hippocampus. When the second scan was performed, one of the preliminary observations of the researchers was the usage of the hippocampus greatly increasing in children’s brains after the 1.2 year time span; however, areas that are known to be used for counting, such as the prefrontal and parietal cortex, were used less often. It was noted that the hippocampus became more attached to regions related to counting, such as the aforementioned prefrontal cortex, anterior temporal cortex and the parietal cortex, which influenced the ability of each individual student’s math fact retrieval. These connections were developed from math fact fluency skills at a young age, which shows the importance of basic skills. Even though this began to show signs of development, the children had not fully developed their brain as the brain scans of the adults indicated the usage of the neocortex instead of the hippocampus. To build onto this information, the researchers realized that the hippocampus was providing a mathematical schema for children’s brains, or a “memory scaffold” (“How children’s”, 2014, para. 11). During the construction of information banks such as the neocortex, the hippocampus acts as a temporary bank of math fact fluency. Even though the adult’s brains used the more sophisticated neocortex as the bank of their math fact retrieval, the researchers noted how the hippocampus appeared to store a backup of math facts.

In order to discover if something could be done to improve the math fact fluency of students and children, the researcher searched for an improved pedagogical method for mathematical instruction. Joseph DiNapoli is a geometry teacher that sought a way to engage his students and promote mathematical discourse amongst his students. After attempting a pedagogical strategy of collaboration, DiNapoli made a shift to collaborative competition. According to DiNapoli (2018),

Thus, collaborative competition, or collaborating students competing against other collaborating students, might be just as effective as collaborative learning in some contexts. Groups of students are still working together toward a common goal, but they are also enticed to persevere amidst challenge to outperform opposing groups. Further, the concern of disengagement from students on losing teams is less pertinent because the entire team shares the burden of defeat, not an individual. Yet, the idea of using competition in any capacity to motivate student engagement seems to have lost favour in education research, and collaborative learning alone has become widely recognised as a pedagogical practice that can promote learning. (para. 3)

He also explained how class attendance and overall engagement of students improved when implementing a collaborative competitive approach to teaching. In addition to this, an anonymous survey that he conducted of his students stated that most of the students were not discouraged for losing, instead they looked forward to the next competition day.

Indications

Further research can still be conducted on the topic of mathematics to compound more information on the effectiveness of various strategies to influence math fact fluency development. The research could include multiple age groups to see which strategies become more or less useful over time, potentially with further information transfer in the brain. Additionally, comparing the results from ‘normal’ brain scans to those with disabilities and or deficiencies can help further research in that field similar to the proposition of the brain development researchers (“How children’s”, 2014, para. 11). In addition to the aforementioned propositions, additional research could be done on mathematical ability throughout older age groups as an experiment to see if the brain shifts its storage of math facts later on it life. Lastly, more research could be done to see if math fact fluency will help prevent dementia and other degenerative mental diseases. References

Basic math skills linked to PSAT math success. (2013, January 4). Retrieved from

https://www.sciencedaily.com/releases/2013/01/130104143617.htm

DeSilver, D. (2017, February 15). U.S. academic achievement lags that of many other countries.

Retrieved from https://www.pewresearch.org/fact-tank/2017/02/15/u-s-students-internationally-math-science/

DiNapoli, J. (2018). Leveraging collaborative competition in mathematics classrooms. Australian

Mathematics Teacher, 74(2), 10+. Retrieved from https://link.gale.com/apps/doc/A546025209/SUIC?u=va_s_128_9999&sid=SUIC&xid=e8a3306c

How children’s brains memorize math facts. (2014, August 17). Retrieved from

https://www.sciencedaily.com/releases/2014/08/140817220106.htm

Shin, David What is fMRI? (n.d.). Retrieved from

https://cfmriweb.ucsd.edu/Research/whatisfmri.html

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