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The Research Behind Frax
Fractions are numbers, too! Frax’s teaching strategies are based on the latest educational research proven to help students build a deep conceptual understanding of fractions.
Founded on the latest educational research
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 reveals strategies that actually work.
Focused on what works, a growing body of rigorous efficacy research shows that ExploreLearning Frax positively impacts student learning, and can build the foundational understanding of fractions students need for ongoing math success in just 13 hours.
Meet the Research Behind Frax
Adaptive and game-based, ExploreLearning Frax uses the latest evidence-based research and instructional methods to create a better way to learn fractions. Discover some of the innovative research behind Frax’s teaching methodology that helps increase student achievement and math confidence.
The Frax White Paper outlines the prominent keys to fractions mastery supported by research, including:
- Extensive work with length models, including partitioning and iteration
- Magnitude comparisons of fractions
- Equivalence practice, including work with fractions greater than 1 and mixed numbers
- Estimation of fractions on number lines
- Relating fraction arithmetic to measurement models and number lines
Discover how Frax’s adaptive and game-based platform guides students to fractions mastery.
What research says about fractions instruction
Explore some of the difficulties commonly associated with learning fractions in this summary from leading researchers in Putting Fractions Together (Braithwaite and Siegler. 2020, Journal of Educational Psychology).
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 students' 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. Due to these misconceptions, fractions are often where math “stops making sense” for students.
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.
The Frax Difference: Research-Based Teaching Strategies
Frax delivers the latest research-proven instructional strategies in an adaptive, game-based learning format to create a better way to learn fractions.
A few of the key factors in Frax that make a difference:
In Frax, fractions are numbers first.
Throughout Frax, students learn that fractions are just like other numbers—they have predictable names and locations on the number line, and they can be compared to each other. Frax helps students develop an understanding of fraction magnitude (size), which in turn allows them to reason with and about fractions in various contexts. Students work extensively with length models and number lines to interpret, represent, compare, order, and estimate fractions. In doing so they overcome whole number bias and develop a strong understanding of fraction magnitude.
Frax is adaptive and individualized.
Adaptive technology responds to individual student performance to provide the right amount of support and challenge on their fractions journey. Students of all ability levels have early and ongoing success. In addition, the Frax online learning system consistently rewards students for both their effort and progress. Students come to understand that if they are willing to put in the work, they really can succeed in learning fractions.
Frax is game-based.
Each Frax mission features space-themed activities, fun characters, music, and enticing visuals that help students stay engaged and build a strong conceptual understanding of fractions. Students are challenged to perform a variety of tasks that build their fractions skills in a wide range of engaging scenarios. The math games are supported by brief, just-in-time instruction, allowing students to learn largely by doing.
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