Fractions can be a very tricky concept to teach students at any age. As a child, I can clearly remember struggling with learning fractions because procedures involved in any other mathematical idea did not apply whatsoever! Because of these bad experiences, I developed pre-conceived notions towards learning and teaching math. Furthermore, I believed that I was not “good” at fractions. I was able to solve the problems procedurally but unable to describe why or how the problems were solved in that way. As the fractional concepts became more challenging, I was unable to successfully continue learning because I had not developed an understanding of the meanings behind the procedures. This struggle is something that many parents, teachers, and current students face. One specific research summary, titled Mathematical Content Knowledge for Teaching Elementary Mathematics: A Focus on Fractions (2014), written by Dana Olanoff, Jane-Jane Lo, and Jennifer Tobias completed a study that examined 43 different articles on prospective elementary teachers’ fractional knowledge. This study found that “[prospective elementary teachers’] fraction knowledge is relatively strong when it comes to performing procedures, but they generally lack flexibility in moving away from procedures and using ‘fraction number sense’ and have trouble understanding the meanings behind the procedures or why the procedures work” (p. 267). Because of these negative experiences learning fractions, elementary teachers, and most likely parents as well, are unable to further educate, assist, or support their students in building positive and meaningful connections with fractional concepts because they have not developed a solid foundation of knowledge themselves.

 

Although difficult to find the desire and want to pick up a pencil and start working on fractions again in adulthood, the benefits of rewiring your brain to change any and all preconceived notions about learning fractions are insurmountable because it will lead to changing the future generation of students and their ideas of learning math! By changing our own opinions building a strong base of fractional knowledge, we will ultimately become better stewards for all students and children who have the same struggles. This idea sounds great, but how can it be done? From personal experience and after looking through various studies and articles, I have narrowed down the educational approaches and strategies that I believe will best help students learn fractions, while also developing personal connections and important intellectual skills. The first approach involves familiarizing students to fractions at a much earlier age than initially introduced through Common Core State Math Standards in the third grade. In the research study titled Teaching and Learning of Fractions in Elementary Grades: Let the Dialogue Begin (2015), written by Dittika Gupta and Trena Wilkerson, the “effects of early exposure” to fractions were examined. The study consisted of students in grades K-3 who were studied for four years as they were introduced and familiarized to fractions throughout the years before beginning to learn about them through the third-grade curriculum. Overall, the study found that “exposing students to fractions in early grades helped build conceptual understanding that could be instrumental in developing fractional concepts in later grades” (p. 41). Furthermore, the study found that, by familiarizing students with fractions at an earlier age, it helped them become more comfortable and aware of the concepts and more equipped to tackle harder fractional problems. The second approach involves using visuals and manipulatives to engage students and enhance their development of fractional knowledge. Although this study was conducted in pre-service elementary teachers in college, it can still be relevant towards helping younger students understand the same material. This research study, titled A Study of Visual Models on Mental Computation of Fractions for Pre-Service Elementary Teachers (2001), written by Elliot Oster, examined the “effects of utilizing visual models to assist in mental computations of fractions” by testing using a controlled group, which did not use visuals, and an experimental group, that did use visuals (p. 137). In the end, the study found that “the visual models” used in the lessons to teach fractions had a “positive effect on students’ ability to mentally compute simple fractions”, moreover stating that the “experimental group also completed the test faster than the control group, further indicating a positive effect” (p. 141). Using visuals and manipulatives when teaching fractions provide opportunities for differentiated thinking, hands-on engagement, and enhanced learning because students are able to develop more meaningful, memorable, and personal connections to the fractional concepts.

 

Moreover, the resources I have found and listed below connect with the approaches and strategies stated above. Although labeled into specific categories that dictate whether the resources should be used by parents and teachers or students, all of the resources can and should be used by any person wanting to learn more about fractional concepts. These resources can be used personally at home or with lessons in the classroom. I hope you enjoy using them as much as I have enjoyed finding and learning more about them!