## 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.

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.

## Elementary students using Frax experienced significantly larger academic growth in math compared to non-users.

New research conducted by ExploreLearning, determined by an independent review to meet the Every Student Succeeds Act (ESSA) Tier 2 rating for evidence-based interventions, found that elementary students using Frax:

- Met or exceeded growth benchmarks at significantly higher rates
- Achieved a higher percentage of expected growth
- Were more likely to reach or exceed grade-level proficiency in the spring, regardless of fall achievement levels

**Frax was 3x more effective than the average educational intervention for 3rd graders and 5x more effective for 4th graders.**

99.7% of teachers see improvement in student learning with Frax

Research shows Frax increases students’ fractions knowledge and confidence

### ExploreLearning Frax—a better way to learn fractions

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.

Each has a specific magnitude (size) and position on the number line alongside whole numbers and other fractions. 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 demystifies fraction arithmetic.

When students understand fractions as numbers they also better understand the arithmetic. They learn how to make sense of fractions operations and can draw connections to their work with whole numbers (e.g. the sum of two fractions must be larger than each individual fraction and therefore the sum of 1/2 + 1/3 can’t be 2/5).

Frax is adaptive and individualized.

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.

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 rather than by watching and listening.

#### Everybody's Talking About Frax

“Frax is by far the best program I have seen for fractions. Even the kids who experience math challenges seem to ‘get’ fractions. Now, when any fraction related math comes up in our lessons, they all seem to know the correct answer!”

*- Frax Teacher, Cloquet Independent School District 94, MN*

"I use Frax in my classes. On our mid-year screener, my students outperformed the other 3rd grade classes that don’t use Frax. My two classes’ average point increase was double that of the other five classes."

*- Frax Teacher, Liberty Hill Independent School District, TX*

"My kids absolutely love Frax! Their abilities vary, but ALL my students feel success with Frax. They have a much better grasp on fractions overall and it has really made a difference in what we are able to do in class."

*- Frax Teacher, Redwood Preparatory Charter School, CA*

"My students are super sad that there are only 27 Frax missions. They are literally begging to do more fraction work! One student who usually struggles with math concepts completed all of the missions and is now getting A’s in math instead of C’s."

*- Frax Teacher, Greenville Co School District, SC*

"My students LOVE Frax! They now regularly say things like ‘Well I know that 1/4 + 1/4 = 1/2...’ or ‘I know that 3/6 = 1/2...’, which were not things they were saying before working on Frax. The improvement in their fraction fluency has been noticeable."

*- Frax Teacher, Governor Wentworth Regional School District, NH*

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