What the research says

The 2012 study, Early Predictors of High School Mathematics Achievement, was led by Robert Siegler, then at Carnegie Mellon University, and published in Psychological Science. The researchers looked for the types of elementary math knowledge that best predicted success in high school.

Fractions and division stood out. The research team concluded that children need to master both if high school algebra and math achievement are going to improve, and called for urgent changes to how these topics are taught.

The study built on an earlier national review. In 2008, the National Mathematics Advisory Panel, set up to advise the President and the U.S. Secretary of Education, identified whole numbers, fractions, and certain aspects of geometry and measurement as the foundations for algebra. Of those, it described knowledge of fractions as the most important foundational skill that American students were not developing.

The panel also surveyed more than 700 Algebra I teachers from a nationally representative sample. They rated their students as having very poor preparation in rational numbers and operations with fractions and decimals.

Why fractions are so important

Fractions are often the first time children meet numbers that don't behave like whole numbers. For years, children learn that bigger numbers mean bigger amounts. Then fractions arrive, and suddenly 1/8 is smaller than 1/4, even though 8 is bigger than 4.

Researchers call this "natural number bias": the tendency to apply whole-number thinking to fractions and decimals, which makes it hard to understand their size and how to calculate with them.

Once children understand fractions properly, a lot of later math opens up. The National Math Panel's definition of fractions includes decimals and percent, leading into ratio and proportion. Those ideas then run straight into middle school math and algebra: rates, proportional relationships, equations with fractional coefficients, slope, and probability. A child who is unsure with fractions in 5th grade often finds 7th grade ratios or 8th grade equations much harder than they need to be, even if the fractions gap was never obvious at the time.

The latest results from the Nation’s Report Card, the National Assessment of Educational Progress (NAEP), suggest this is where many students are getting stuck. In the 2026 Long-Term Trend results, 13-year-olds showed no significant change in math compared to 2023, and their average score is still down almost 10 points since the pandemic. In the 2024 main NAEP, nearly 40 percent of 8th graders scored below NAEP Basic in math. Middle school is exactly when fractions-based topics like ratios, proportions and equations take center stage, so gaps from earlier grades tend to show up here.

When children learn fractions

Under the Common Core State Standards, followed in some form by many U.S. schools, fraction learning builds over several grades.

• 3rd grade: Students start by developing an understanding of fractions as numbers and learning to place them on a number line.

• 4th grade: They extend their understanding of equivalent fractions and ordering, including comparing fractions with different numerators and denominators by finding common denominators or using benchmarks like 1/2.

• 5th grade: The focus moves to fluency with adding and subtracting fractions, and to understanding multiplication and division of fractions in limited cases.

Because each year builds on the last, a gap in 3rd or 4th grade can quietly carry through to middle school.

When extra support can help

Sometimes a fractions gap goes back further than parents or teachers realize, especially for children who are already in middle school. In that case, the fastest way forward is often to identify exactly where understanding broke down, fill that gap, and then build back up to grade level.

APLUS America’sonline math tutoring is built around that idea. The Irvine, California company provides personalized K-12 math support that follows Common Core Standards, and each new student begins with a diagnostic called the Math Doctor assessment. It shows which concepts your child has already mastered and which gaps, including ones from earlier grades, are making current work harder.

Those results shape a personalized learning plan that is refreshed every Monday. It works on earlier gaps first, then reinforces what’s being covered in class, and moves into new material once your child is ready. Lessons are bite-sized and interactive, with visuals, immediate feedback and fully worked solutions. The curriculum runs from kindergarten to AP Calculus and covers fractions and decimals in the elementary grades.

If your child hits a problem they can’t solve, they can phone a tutor, who uses screen sharing and an interactive whiteboard to work through it with them. That help is available Monday to Thursday after school, up to 10 hours a week, and is included in the weekly price. Parents get a progress report each week, and children collect points they can trade for gift cards.

Plans start at $24 a week, and new students get their first two weeks free.

Signs your child's fraction understanding may be shaky

You don't need to be a math expert to spot warning signs. Look out for a child who:

• Thinks a fraction with a bigger denominator is always bigger, for example that 1/10 is more than 1/5

• Adds fractions by adding the tops and the bottoms, so that 1/2 + 1/3 = 2/5

• Can't estimate whether an answer makes sense, for example whether 3/4 + 2/3 is more or less than 1

• Struggles to connect fractions, decimals and percentages, such as knowing that 1/4, 0.25 and 25% are the same amount

• Can follow the steps for a fraction problem but can't explain why they work

• Finds word problems with fractions much harder than bare calculations

If you notice these in a middle schooler, it's worth going back to basic fraction understanding rather than simply practicing the current topic harder.

How to build fraction skills at home

A few simple habits can make fractions feel more concrete and less intimidating.

• Cook together. Measuring cups and spoons are fractions in real life. Ask how many 1/4 cups make a whole cup, or what happens if you double a recipe that uses 3/4 cup of flour.

• Share food fairly. Cutting a pizza, a sandwich or a chocolate bar into equal parts is a natural way to talk about halves, thirds and eighths, and to compare which piece is bigger.

• Use a number line. Drawing fractions on a line between 0 and 1 helps children see fractions as numbers with a size, not just a pair of numbers stacked on top of each other.

• Connect to money. Quarters, dimes and dollars link fractions to decimals and percentages. A quarter is 1/4 of a dollar, 25 cents, and 25% of a dollar.

• Ask "does that make sense?" Encourage your child to estimate before calculating. It builds number sense and catches mistakes early.

• Keep it short and regular. About 20 minutes, a few times a week, works better than one long session. It also avoids turning math into a battle.