Math Tutoring in Sacramento for Kids Who Struggle With Numbers

Why a smart kid can work hard at math and still fall behind

When a child works hard at math and still falls behind, the missing piece is usually foundational number sense.

Number sense is the group of skills that let a person work with quantities: knowing that 8 is close to 10, that 7 + 3 and 3 + 7 represent the same amount, and that 40 + 60 works the same way 4 + 6 does. Understood defines number sense as this core set of quantity skills, and children with weak number sense struggle with basic arithmetic operations.

A child without number sense relies on rote memorization to get through math class. Memorizing math facts without understanding the quantities behind them only holds for a few days. A math fact that clicks during Tuesday night practice holds through Thursday’s quiz and disappears by the next Monday because no understanding of quantity is holding that fact in memory. Parents describe this pattern of forgetting math facts after a few days more than any other math struggle.

Six signs of a math learning gap parents see during homework

You can spot a math gap during homework before any formal testing happens. Cleveland Clinic links finger-counting, forgetting facts overnight, freezing on word problems, and missing number patterns to dyscalculia, while messy columns and meltdowns point just as often to ADHD or math anxiety.

• Counting on fingers for basic addition and subtraction past the age when most peers have stopped. Finger-counting is a physical backup for weak number sense. A child who can picture that 7 is three away from 10 does not need to count up one by one from 7, whereas a child who cannot picture quantities mentally has to count on fingers every time.
• Knowing a multiplication fact one evening and forgetting that same multiplication fact the next morning. A math fact memorized by rote without understanding the quantity behind the numbers has nothing holding the fact in long-term memory. The child memorized a string of sounds that fades overnight, whereas a student who understands that 6 x 7 means six groups of seven can rebuild the answer even after forgetting the memorized fact.
• Freezing when a math problem is written as words instead of numbers. Solving a math word problem requires a child to read the text, picture the relationship in the story, choose the right operation, and calculate the answer. A student with weak number sense or limited working memory may know how to calculate the numbers and still freeze when translating the written story into an equation.
• Not recognizing that 5 + 3 and 3 + 5 are the same math problem. Cleveland Clinic lists missing basic number relationships as a core sign of dyscalculia in school-age children. A child who does not see that 5 + 3 and 3 + 5 are equal is treating each equation as a separate fact to memorize instead of seeing one quantity of 8 arranged two ways.
• Lining up multi-digit numbers in the wrong columns, throwing the math answer off by a place value. Misaligned number columns during multi-digit addition, subtraction, or multiplication usually come from a working memory or visual-spatial bottleneck. A student with ADHD often understands the math operation out loud and loses track of where each digit belongs while holding multiple steps in mind, which is why graph paper helps keep place-value columns aligned.
• Tears, stalling, or a stomachache that shows up only when math homework comes out. Physical distress at homework time is a sign of math anxiety. Worry about failing math consumes the working memory a child needs to calculate, making the math worksheet harder to solve once the stress response starts.

Dyscalculia, ADHD, and math anxiety are three different problems

Three students can fail the same timed math test for three different reasons. Dyscalculia blocks number sense, ADHD drops steps from working memory, and math anxiety burns up working memory with worry.

Many struggling math students have two or all three of these conditions at the same time. The job of a first math tutoring session is to figure out whether weak number sense, working memory limits, or math anxiety is causing the breakdown.

Why homework help makes a math gap worse

Most standard math tutoring re-teaches the school classroom lesson at a slower pace. Slower homework review gets a child through tonight’s worksheet and Friday’s quiz, but for a student with a number sense gap, passing Friday’s quiz without understanding the quantities only pushes the math gap into next year.

Math tricks and shortcuts create the same problem as slow worksheet review. Phrases like “just carry the one” or “if the word problem says altogether, add” teach a child to memorize a rule instead of understanding the math operation, and the shortcut fails the first time a test problem looks different. The IES practice guide for math intervention tells teachers to avoid teaching key words in word problems because a key word lets the student skip reading the full problem and pick an operation that is often wrong.

Middle school is where getting by on rote memorization and math shortcuts collapses. Fractions, decimals, negative numbers, and pre-algebra all stack on top of place value and number sense. A student who survived elementary math by memorizing steps runs out of working memory once middle school equations require multiple steps. I wrote more in a separate post about why specialized tutoring beats homework help.

The kinds of math instruction that work for kids who struggle

Children who struggle with math need explicit, hands-on instruction instead of slower worksheet review. The methods that work move from physical blocks to pictures to numbers (CRA) and stay on one skill until it sticks.

Every method above shows up in the two programs READ Learning Center uses for math tutoring. Making Math Real and Math-U-See are both multisensory, both move from physical objects to pictures to written numbers, and both keep a child on a skill until it is mastered. The difference is how each one gets there.

At READ Learning Center, our math tutors teach with both programs to match how your child learns.

How a parent knows math tutoring is working

Parents will see progress from math tutoring during homework at home before seeing higher grades on a school report card.

In the first month of structured math tutoring, nightly homework gets shorter and quieter. The child begins using physical blocks or drawings on their own to work through problems, and finger-counting happens less often.

By the second month of math instruction, learned math facts survive the weekend. A multiplication fact the child knew on Friday is still in memory on Monday, and the child reads word problems all the way through instead of guessing at the operation.

By the third month of math tutoring, the child starts a math worksheet without stalling. Stomachaches and tears stop showing up at homework time, and the child talks about math without saying “I hate math.”

A good math tutor can show parents baseline data on where the child started and what skills the child has mastered now. If a tutor cannot show clear progress from the starting baseline, parents should ask why.