Why Is Math So Hard for Some Students?
Key takeaways:
- A biologically-based mathematical disability is called developmental dyscalculia
- A student with developmental dyscalculia may have other learning differences like a reading disability or ADHD
- Poor math performance may be due to outside factors such as absenteeism, changing schools, a language barrier, or something going on at home
- A child with math disabilities often has a poor sense of numbers, including with multiplications, fractions, and decimals
- A child with a math disability may experience delays in counting and procedure skills
- A child with a math disability may be slower to determine how many items are in a set
- A child with a math disability might use the same word for two different objects
- The most frequent difficulty relates to storing and retrieving math factsA child with dyscalculia often relies on counting on his or her fingers as a crutch
Most professions require at least a basic understanding of math, and math skills are required in everyday life. Math is also a key part of a STEM-focused curriculum. Calculating sums and figuring out formulas comes naturally for some, but many students struggle.
The Expert Speaker Series hosted by American Heritage Schools, attempts to answer the question of why students struggle with math. We hosted Dr. Daniel Berch, a cognitive and developmental psychologist who specializes in child development and behavior. His research has helped improve our knowledge of why students struggle to learn mathematics while offering ways teachers and parents can help.Choosing the right school for a child with APD
A Q&A follows with Dr. Berch below.
Q: An assessment of 12th graders was just released. What were the main outcomes for general students and those with learning differences?
Dr. Berch: First, the assessment looked at different types of math, including algebra, geometry, measurement, data analysis, statistics, and probability. Then, they assigned three levels of achievement in each type: basic, proficient, and advanced. The basic level represents partial mastery and fundamental skills.
The assessment also includes students who did not score high enough to meet even the basic level. Around a third (36%) of students in the general population scored below the basic level. However, 75% of students with scored below the basic level.
The lowest-scoring students performed more poorly across the board compared to 2015, as well.
Q: So, why is math so hard for some students? Is it related to a mathematical learning disability?
Dr. Berch: Well, a mathematical disability is also called “developmental dyscalculia.” It is a biologically-based learning disorder associated with impairments in number sense, memorization, math facts, calculation, and math reasoning. Around 3-7% of the population have dyscalculia. Several criteria must be met to be diagnosed with dyscalculia. However, it cannot be attributed to low intelligence, sensory impairment, or language impediments.
Many students who experience math difficulties also have other learning differences. Around 40% of students with math disabilities also have a reading disability, and around 25-42% have ADHD.
Of course, poor performance in math may be due to outside (extrinsic) factors. It might be a combination of new math concepts and procedures, which are hard for the student to grasp. There might also be factors such as missing school, changing schools, a move, societal or cultural factors, a language barrier, or something going on at home.
The students might also have a learning style that doesn’t match with the teacher’s methods. Students who have been dealing with virtual learning in the past year have struggled, as well.
Q: Well, that’s true. This year has been challenging for everyone, especially students with learning differences. What challenges do students with math disabilities face?
Dr. Berch: Students can exhibit a variety of math difficulties. Some may be obvious to parents and teachers, but others are fairly subtle and may only be revealed through tasks that measure accuracy or how quickly (or slowly) the child responds.
One specific assessment is called “task taps.” It measures the innate brain system that allows us to estimate and compare quantities. Students with dyscalculia tend to perform more poorly on task taps.
There is another test that measures the ability to rapidly and accurately judge a small number of items without counting them (supetize). Children with dyscalculia have a smaller supetizing supetize range or they might be slower in arriving at the answer.
Another example relates to the ability to translate numbers from a verbal form to a number form (numerical transcoding). For example, you hear the word “five” and then write down the number (5) or vice versa. Then you have multi-digit numbers, such as 207. When you say the word “two hundred seven,” the “zero” is missing, which makes transcoding multi-digit numbers more difficult. You need to understand multi-digit numbers, as well as the placement of digits.
Most students can transcode multi-digit numbers and numerals by the end of second or third grade. However, children with math disabilities are less accurate with transcoding.
Another sign relates to number line estimation. For example, a student is presented with a line of numbers, ranging from 0 to 100. The student is given a number, say 71, and asked to put a hash mark where they think 71 falls on the number line. Young children struggle with this skill but show more accuracy as they get older. By contrast, students with a math disability do not develop accuracy.
Q: Any other examples of difficulties these students face?
Dr. Berch: Yes, a couple more. Students with a math disability experience delays in counting and procedures skills. They are also slower to determine how many items are in a set. They might use the same count word for two different objects. For example, if there are four items in a row, they might count “one, two, three” and determine there are only three items. They don’t understand that you should only use one tag for each object. They also don’t realize they should come up with the same number of items, whether counting from the right or left.
Perhaps the most frequent difficulty relates to storing and retrieving math facts. Children with dyscalculia have trouble recalling math facts and rely on counting-based strategies (counting on their fingers) as a crutch.
Children with math disabilities will present with one or more of these impairments.
Q: What makes learning fractions and decimals difficult for these students?
Dr. Berch: Children with math disabilities often have a poor sense of numbers. They don’t understand that adding two numbers results in a larger number. They also don’t understand that multiplication is repeated addition (i.e., 5 x 6 is larger than 5 x 4). They don’t understand that one-quarter (1/4) is smaller than one-half (1/2). The lack of basic math facts makes it harder to tackle the abstract operations needed for higher-level math.
As for fractions, younger students tend to have what’s called a “whole number bias.” They look at both the numerator and denominator as individual whole numbers, rather than as a single number.
Fractions can also be difficult because they can be presented in multiple formats. You can see a fraction as 1/3, but also as a decimal (.333), which is also a single number. This can be confusing for children at first. Students with math disabilities struggle even more with these concepts.
Q: Can you address how the ability to pay attention affects math learning?
Dr. Berch: Attention is the first step in learning math. Students have to process information, visually and auditorily. They must also selectively attend to critical information in their immediate environment to learn and retain information. Thankfully, a child’s ability to focus increases through adolescence. We can also use proven educational practices to improve students’ ability to focus.
Q: How early can parents notice signs of a math disability?
Dr. Berch: Students with dyscalculia might exhibit several signs at various stages of education.
Preschool students have difficulty recognizing numbers and experience delays in learning to count. They also exhibit transcoding issues, have difficulty recognizing patterns, and placing things in the right order. They lose track when counting and require visual or manual aids, such as counting on their fingers. While this is normal for young very very young children, children with learning disabilities rely on it much longer than their peers.
Elementary students exhibit similar difficulties. They might also have difficulty telling time on an analog clock. They have trouble telling which number is larger, recognizing quantities without counting, and difficulties counting by twos or fives, etc. They might also have trouble spatially placing numbers and will often misplace digits when writing down numbers. Plus, they have trouble learning to calculate and remembering basic math facts.
Middle school students exhibit many of the same signs we see in elementary students. They also have difficulties interpreting graphs, learning and applying formulas, and remembering rules for solving problems. You may also notice they have problems keeping score when playing games and difficulties with money, such as making change and estimating how much something will cost.
Q: How can parents help a child who struggles with math?
Dr. Berch: It’s important to focus on specific areas of math where your child is struggling. You want to pay attention to the strategies he or she is they are using to solve math problems, along with signs that those strategies aren’t working. You can also ask your child about the challenges he or she is they are facing with math. The thing you don’t want to do is say, “I’m not good at math, either.” Instead, suggest that you and your child could both improve your math skills.
Q: What about hiring a math tutor?
Dr. Berch: Yes, this is a good idea, but you need to watch the tutor and see how they interacts with your child. Not all tutors understand the different types of learning differences students experience.
Listen to the full recording
We thank Dr. Berch for sharing his expertise and tips with parents. Be sure to listen to the complete recording for a more in-depth conversation.
Helping children who struggle with math
If your child struggles with math or has a diagnosed math disability, we can help. The American Academy Program at American Heritage Schools is a specialized program designed to teach students with learning differences. Along with math disabilities, we also help students who have been diagnosed with dyslexia, ADHD, or other learning challenges.
American Heritage Schools is a leader in private education, academic excellence, and innovation. With two 40 acre campuses, one in Broward County and the other in Palm Beach County, Florida, we serve 4,600 students grades Pre-K 3 through 12. American Heritage Schools was recently named the #1 Private School for academic success with the highest number of National Merit Scholars of all private schools in the nation. For over 55 years, our mission of knowledge, integrity, and compassion through developing the full potential of each child to be an active, intelligent, creative, and contributing member of society. Contact an admissions director for more information or sign up for a campus tour.