Research behind Frax
National assessments consistently show that large numbers of students struggle with fractions from grade 3 onward, effectively reducing their academic and career opportunities. Fortunately, a growing body of academic research is starting to uncover strategies that actually work.
The following summarizes a review of studies on the difficulties with fractions by two leading researchers in the study of learning fractions in: Putting Fractions Together. Braithwaite, D. W., & Siegler, R. S. (2020, March 19). Journal of Educational Psychology.
The Research Behind Frax
Whole number bias
Numerous studies show that many students tend to think of fractions as two separate whole numbers rather than as a single number (Mack, 1995; Meert, Grégoire, & Noël, 2009; Ni & Zhou, 2005). This is called whole number bias and it leads to fundamental errors in comparing fractions, understanding fraction equivalence, and fraction arithmetic. It’s what causes students to claim that 2/9 > 1/2 because 2 > 1 and 9 > 2, that 9/18 is larger than 1/2, or that 3/5 +1/4 = 4/9. These and other difficulties with understanding individual fractions are why 50% of U.S. eighth graders were unable to put 5/9, 2/7, and 1/2 in order from least to greatest on a major national assessment (U.S. Department of Education, Institute of Education Sciences, 2007).
The centrality of magnitude
Vital to understanding fractions and fraction arithmetic is the ability to represent or reason about fraction magnitude (size). The previous examples of errors caused by whole number bias, such as 2/9 > 1/2 or 9/18 is larger than 1/2, are all also errors in understanding fraction magnitude. And an inaccurate understanding of individual fraction size hinders performance on fraction arithmetic by robbing the student of the ability to recognize unreasonable answers. For example, in one recent study (Braithwaite, Tian, & Siegler, 2018), U.S. middle school students asked to estimate sums of pairs of fractions on a number line were no more accurate than if they had simply marked the midpoint on the line for each answer. Even worse, a majority of answers were smaller than the student’s own estimates of one or both of the numbers being summed. These results illustrate that when students don’t understand fraction magnitude, they are unable to do even the most basic reasoning about addition, the simplest of arithmetic operations.
The Integrated Theory of Numerical Development
The Integrated Theory of Numerical Development holds that “numerical development involves increasingly precise representation of the magnitudes of increasing ranges and types of numbers, including whole numbers and fractions” (Braithwaite & Siegler, 2020, p. 568). One of the most important predictions of the theory is that understanding numerical magnitudes is closely related to understanding arithmetic. This prediction has been supported by multiple studies showing a strong correlation between understanding magnitude and arithmetic for both whole numbers and fractions (Booth & Siegler, 2008; Byrnes & Wasik, 1991; Fuchs et al., 2010 Siegler et al., 2011). It has been further supported by experimental studies showing that interventions with a strong focus on fraction magnitude improve fraction arithmetic performance compared to traditional methods (Dyson et al., 2018; Fuchs et al., 2013), even as less instructional time is focused on the learning and practicing of arithmetic.
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Frax was 3x more effective than the average educational intervention for 3rd graders and 5x more effective for 4th graders.
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Research shows Frax increases students’ fractions knowledge and confidence
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