1St grader struggling with math

Child Struggling with Math? 12 Signs and 7 Ways to Help

Many parents around the world -- like yourself -- have a child struggling with math. Without proper resources or a solid support system, this reality can be daunting.

But, don’t worry because you’re not alone! One of the most common complaints among children who dislike math is it’s too difficult or that they’re not smart enough. Sadly, this belief is one that can severely impact any child’s success in mathematics.

Parents often remark the causes and symptoms can vary from child to child, which is why we’ll outline and help you understand:

What causes children to struggle with math
Common signs among children struggling with math
How parents and teachers can help a child struggling with math

Let's start helping your child succeed, instead of struggle, with math. 👇

3 Main causes of a child struggling with math

Math can be hard because it’s a cumulative subject — it builds upon itself year after year. This is why so many parents worry when their kids appear to get disengaged with or disconnected from math.

It’s vital for parents to know this doesn’t necessarily mean their child lacks intelligence or drive. Believe it or not, kids who have trouble understanding math are often putting in a great deal of effort — mentally and physically.

So, what exactly causes a child to struggle with math? Research has narrowed the answer down to three things:

Lacking building blocks

As mentioned earlier, math is cumulative, so learning and understanding the basics is a must. If a child falls behind in one area due to a lack of understanding, moving on to more advanced topics will remain a challenge.

For example, if a child doesn’t yet understand the foundational knowledge of addition, it will be very difficult for them to grasp the concept of multiplication.

In 2015, the University of Akron published a study called “The Importance of a Strong Mathematical Foundation”. Researchers tested 39 ninth and tenth graders on fractions, ratios, and proportions. Participants had to complete questions ranging from third to seventh grade.

Only seven participants were able to pass the assessment. Seeing these results, study author Jasmine Wriston wrote:

[Students] were simply being taught mathematics concepts correlating to their current grade level and not based on the current mathematical knowledge they brought to class. Due to this, students were not mastering each grade level standard before continuing onto higher level instruction. This lack of mastery creates huge gaps in student understanding, hindering students from making the necessary content connections and gaining conceptual understanding.

Math anxiety

In the midst of hardship, it’s easy to feel as though we’re the only ones going through a certain problem. For parents of a child struggling with math, it’s no different. And while alarming, we hope parents everywhere find comfort in knowing their child is not the only one who may experience anxiety when it comes to math.

A feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations.

In fact, our guide to overcoming math anxiety highlights that around 93% of adult Americans experience math anxiety to varying degrees while 17% of Americans overall suffer from high levels of math anxiety.

Symptoms of math anxiety can include:

Avoidance
Lack of response
Low achievement
Negative self-talk
Feeling of permanency
Intense emotional reactions
Physiological effects like nervousness, clammy hands, increased heart rate, upset stomach and lightheadedness

And, for this reason, children can struggle with math from childhood all the way into adulthood.

Learning difficulties

There are numerous mathematics learning disabilities, including one of the more common ones: dyscalculia. Other names for it include math or number dyslexia.

According to Dr. Daniel Ansari, a professor in developmental cognitive neuroscience at Canada’s Western University, children with dyscalculia:

Often struggle with working memory
Have trouble remembering math facts
May understand the logic behind math facts, but not how or when to apply their knowledge to solve problems
May not understand quantities or concepts like biggest versus smallest, or the difference between the word five and numeral 5

Researchers aren’t entirely sure what causes dyscalculia but suspect it’s linked to the brain’s structure and function. Because there can be various factors involved — like one’s development, environment, genetic makeup or injury — how the symptoms show will likely vary as no two children are the same.

2. Gets anxious around math

Be it during a class, a test or working on a homework assignment, your child grows increasingly anxious when it’s time to do math.

Even though they may understand the concepts, math anxiety results in them forgetting what they’ve learned or how to apply them when the time comes.

3. Grades that are lower in math but higher in other subjects

Whether you hear it from a teacher or see it on their report card, your child performs well in every subject — except math.

Lower math grades may lead them to focus on subjects they’re already succeeding in, and spend little time practicing or studying math.

4. Trouble connecting math families

As students learn more math facts, they should begin to see the relationship between certain numbers and equations.

Your child may be struggling with math if they do not see the connection between, for example, 2+3=5 and 5-3=2.

5. Difficulty managing time

Time management is difficult for many people, including adults, so this sign can seem somewhat vague. Pay attention to see if your child has any trouble judging increments of time, adhering to set schedules, or reading clocks — analog or digital.

6. Trouble applying math concepts to real-world problems

Your child may grasp math concepts, but have a hard time seeing how they apply to things outside of the classroom. For example:

Finding out how many days remain until their birthday
Calculating the cost of something and how much change they should get back
Determining how much of a certain ingredient to use when helping you prepare food

P.S. Did you know that Prodigy Math features over 50,000 teacher-made questions that include real-world problems?

7. Mental math difficulty

While it can be helpful in early years, working out math problems using fingers to count could be a sign your child is struggling with math.

This is because as children get older, they’ll encounter bigger numbers and more advanced equations that require mental math practices — something that finger counting can discourage.

8.

Doesn’t try to find alternative approaches to problems

The moment a roadblock arises when tackling a math problem, your child may get discouraged and move on before thinking about — or trying — another potential solution.

9. Trouble with basic math concepts and fact recall

Memory could have a significant impact on thinking with numbers. Despite having been taught foundational math concepts and facts in the past, your child has trouble remembering and applying them appropriately.

10. Trouble learning advanced math concepts and facts

Due to mathematics’ cumulative nature, making connections between prior and new lessons is key.

Having difficulty when building upon earlier math concepts will limit a child’s ability to anchor new math skills in a meaningful, long-lasting way.

11. Difficulty paying attention

Every child learns differently — some can sit down at a desk and complete certain tasks, while others benefit from a more active, hands-on output.

If your child gets fidgety, loses their place in a problem, or seems mentally tired when doing math, they may be struggling with (the particular way they’re doing) math.

12. Not hitting milestones

Generally, children hit certain math milestones around the same age — but sometimes, they have trouble developing these skills at the same rate and fall behind.

Students in 1st and 2nd grade, for example, may struggle as they move on from counting by ones to twos, fives, and tens, while others pick it up with ease.

Tip: Use Prodigy's free parent account to get monthly reports about your child's math progress as they play Prodigy Math. See how it works here!

Check out the infographic below outlining math milestones and what you can expect at different ages!

Click to expand

How to help a child struggling with math (in 7 ways)

As a parent, one of your biggest goals is to help your child succeed. It’s important to remember, however, that the first step to solving a problem is identifying it.

Having awareness of the signs above will help you identify any problems your child may be experiencing with math.

And to take it a step further, we’ve outlined seven tips you can use at home to help transform math into a subject your child loves instead of fears!

Make math fun

For some children, all it takes is a change in perspective to transform math from something feared into something loved. A traditional pen-and-paper approach won’t always work and that’s when you need to get creative.

Tip: Consider reintroducing math to your child through a game-based lens. This can take on many forms like word problems, math books, math apps and more.

Or, try Prodigy Math — the engaging, curriculum-aligned math app used by over 100 million students and teachers. All in-game educational content is free and accessible at home or in class.

🌟 Plus, there are Membership plans available to maximize math practice and help you support your child's learning journey with ease. Becoming a member will unlock extra in-game rewards for your child and give you access to new parent features like Goals and Rewards, Practice Areas and Practice Sheets.

Find your Membership here

Find daily applications

Math is all around us and exists in our everyday lives, but do your children know that? Incorporating math into their day-to-day routine can help them understand — and appreciate — its relevance.

So, what are you waiting for? Start learning by doing!

Tip: Involve your child when it comes to activities like shopping, cooking, or gardening! Each of these real world applications involve numbers, facts, and concepts which can help solidify knowledge and understanding, as well as enjoyment in math.

Practice with your child daily

On the surface, this tip may seem as simple as sitting beside your child while they do homework and ensuring they complete it. But, involvement in your child’s education has many benefits.

According to author and developmental psychologist Rebecca Fraser-Thill, parental involvement fosters academic achievement, improves social skills, and can increase self-esteem.

Tip: Set aside time to practice math for as little as 10 minutes each night. This will help reinforce what they’re learning in class and keep foundational concepts front-of-mind as teachers introduce them to more advanced concepts in class. Even if your child doesn’t have any math homework, try our free, colorful and printable worksheets:

20 Telling Time Worksheets
20 Addition Worksheets
20 Long Division Worksheets
20 Multiplication Worksheets
19 Order of Operations Worksheets

Identify problem areas

If you can identify them yourself, amazing! If not, get in touch with your child’s teacher for a more intimate and accurate idea of how you can help increase your child’s ability to succeed.

Tip: Working with your child’s teacher, come up with an at-home action plan. This is also an excellent opportunity to share the types of learning that works best for your child at home — something their teacher may not know.

Adopt a positive attitude

While children can have negative attitudes toward math, your attitude toward the subject may need to change first. A 2017 study in School Science and Mathematics found that parents’ attitude toward mathematics can significantly predict students’ attitudes toward mathematics.

Most of the time, the negative attitude is simply because the students have told themselves they cannot do mathematics; they are never going to use it anyways; and so forth. School-based factors are compounded when they are reinforced at home, such as parents’ negative attitudes toward mathematics.

Tip: Even if you find math tricky, try your best to maintain a positive mindset about it around your child. Encourage your child when they get stuck and attempt to work through the problem together until you arrive at a solution! By practicing this, parents can become a positive inﬂuence on their child’s attitude toward math. As a result, this can increase children’s overall achievement and interest in math well into adulthood.

Get a tutor

Some parents have been out of school for a long time and are unfamiliar with certain teaching strategies. Others simply don’t feel comfortable being the “teacher” at home. This is why some parents consider going the online tutoring route.

Math Geek Mama outlines some helpful ways to find a math tutor for your child!

Word of mouth from friends or family
Check library or community centre bulletin boards
Ask your child’s teacher or school counselor
Find a local or online tutor using websites

Tip: A great way to make tutoring go further is to set learning goals and rewards with your child. If your child has a Prodigy Math Membership, you can set learning goals for them to achieve in our fun, engaging math game. When they successfully complete a goal, they'll receive in-game reward of your choice!

Find your Membership

Look into potential learning disabilities

If your child does have a learning disability, the sooner you seek help the better!

It can be challenging to address and diagnose but, in the long run, receiving prompt and appropriate support can help ensure the best educational journey possible for your child.

Tip: If you haven’t already been contacted, connect with your child’s teacher or school administrator(s) to discuss how they can help. As learning disabilities tend to be identified in school, they may use a process called response to intervention to help pinpoint whether or not a child has a learning disability.

Final thoughts: Is your child struggling with math?

Struggling with math can make children feel like they’re not smart and affect their self-esteem. However, this is a common struggle.

What’s more, there are practical ways to help as you can see!One of the greatest things you can do today is to let them know that everyone struggles — even you — and that everyone also has strengths!

Share a personal example of a time you struggled with math and, if possible, how you overcame it. Then, try incorporating some of the helpful tips listed above.

Math may be a struggle, but going on this journey together will help increase your child’s confidence and motivate them to keep trying!

You want your child to succeed in math. We can help.

Yes, Prodigy Math Game is a curriculum-aligned, fantasy-inspired platform used by many kids. But it also comes with incredibly valuable tools and features for parents like you. Watch the one-minute video below:

Ready to motivate your and help support them along the way?

Create your free parent account today!

Is Your First Grade Student Struggling with Math?

First grade is a big time of transition for your child. Their schoolwork has become more challenging and more demanding of their time. Their day has also probably become a lot longer. For a lot of children, this transition can be tough, especially for the new work they have to do in math class.

By age 6, when your child is most likely entering first grade, they can already do simple addition and subtraction with numbers up to 10. This is also the time when they are figuring out how to answer simple word problems. They are also learning about fractions, especially halves, thirds, and quarters.

Common struggles for first grade students can often be a result of children developing at different rates. A lot of development is happening between ages 6 and 7, and not all children have an understanding of these concepts at the same time. Your child can struggle with anything from fractions to telling time to subtraction.

How to Tell Your Child Is Struggling

An easy way to tell if your child is struggling in math is to look at their grades. If they are doing well in other subjects but not in math, that can be a sign that you need to address their math skills and not something else like vision changes or learning differences. It is also helpful to talk to your child’s teacher since they will likely know what specific concepts your child needs help with.

It is also important to ask your child directly what they think about math. This shouldn’t be about asking what went wrong with a test or assignment or how they got the wrong answers, but instead asking them about how they feel about math. Are they struggling with something specific, like word problems, or is it math as a whole? Are they feeling anxious about their tests? Pinning down the problem is the most important part of finding the solution.

How to Help Your Child in Math

The best way you can help your child when they’re struggling is to enroll in Math Genie. The teachers at Math Genie are kind, helpful, and responsive to students at all levels of ability. They can address specific problems as well as help your child feel more confident about their budding math skills.

You can also help your child at home. Have your child get involved with you in activities where math is used naturally, like cooking, baking, and shopping. It can be a big confidence boost for your child to help you with grown-up things and gives them a chance to practice math in a real-world setting. For example, have them help you bake cookies but double or halve the recipe so they have to tell you how much of each ingredient to put in.

You should also make sure to reassure them that math is important to learn and will get easier as they practice. Don’t tell them things like how math is hard or boring; math is fun and important! Also, try to take some pressure off of them if they are having any test anxieties. Let them know you love them and they are smart no matter how they do on any test.

First grade is a challenging time for any child, but learning math doesn’t have to be hard. Exploring the subject at Math Genie leads to a lot of success, and they will find out how fun math can really be!

Source: https://www.verywellfamily.com/how-to-help-a-child-in-first-grade-with-math-3895753

How to Solve Math Problems

141,058

Parents Interview

Key Ideas

Difficulties in learning math are familiar to many children.
Their abilities have nothing to do with it: psychological reasons hinder mastering this science.
Beauty and logic - only they will help to understand and love this subject.

“We only teach this mathematics! complains Irina, mother of 11-year-old Alice. - The daughter seems to know the formula, but still stumbles at every step. Sometimes it solves a difficult problem, but not a simple one. Controls are horror for the whole family. The child is all on his nerves, my husband and I have a headache. You never know if she will write for four or bring a deuce. Studying all weekend and no progress!”

I understand Alice very well. I remember how melancholy all these equations, functions and tangents evoked in me at school. Even the unloved chemistry and physics were closer to me: I could somehow correlate them with my own experience. But "a plus b divided by c" was infinitely far from my life.

Alice and I cannot be called an exception. In every class there are children for whom mathematics is a complete torment. And their parents are tormented by questions about how to relate to this and how they can help.

Do children need math?

These problems are everywhere. In 2012, The New York Times began a discussion about whether children need algebra if one in four students in the United States does not graduate from school due to problems with this subject.

And in France, the former Minister of Education and Science, Claude Allegre, himself a geophysicist, seriously discussed the abolition of the teaching of mathematics in schools, since many children cannot cope even with elementary tasks.

Do all children need mathematics? Or can someone do without it?

“No, my daughter is not, she is a humanist, like me, she will go to the philological faculty,” says 36-year-old Marina. “The main thing for us is that in literature, Russian, history there are fives, and in mathematics - if only not a deuce.”

“This is a painful question: how deep do you need to know mathematics for those who do not seem to need it? — reflects the writer and mathematician Leonid Kostyukov. But who are the humanists? One-tenth - people of art, and nine-tenths - people of culture.

People of art (artist, poet, actor) probably do not need mathematics for creativity. But people of culture — a historian, a philologist, an editor, a publisher, a journalist — cannot do without systems thinking. Namely, mathematics educates, disciplines the mind.

For the first time, I wondered if I hadn't neglected mathematics when I started writing my dissertation. The topic was purely philological - but what anguish it cost me to organize all the huge factual material and convincingly substantiate my concept! Logical thinking was the problem. But since I nevertheless managed to complete my dissertation, then maybe I'm not so hopeless in terms of logic, as it once seemed to me and my parents?

The most difficult subject?

If a child has difficulty with mathematics, we always have an answer ready: it means that there is no mathematical ability. And with that, we kind of close the topic: no, there is no trial. In other words, we easily agree: mathematics is so difficult that not everyone can cope with it. And we console ourselves with the fact that in other disciplines our child is quite (or perfectly) in time.

Leonid Kostyukov, an experienced tutor, is sure that he teaches one of the easiest subjects: “The mathematics course is incredibly elegant, beautiful, and logical. Very little needs to be learned, much more needs to be understood. If I don't remember the formula, but I remember where it comes from, I can quickly deduce it. There is no such possibility in any other school sciences.”

In his opinion, if a child does well in other subjects, there is no reason for him not to cope with mathematics. “If, for example, he is good at English, it means that everything is in order with his logic, because the English language is arranged very logically. Moreover, objectively it is more complicated than the language of school mathematics. This means that this child should be able to do well in mathematics.” So why is this not the case in practice?

When problems grow like a snowball

"Mathematics provides the purest and most direct experience of truth," said the German physicist and Nobel Prize winner Max Laue in his book Landau's Life Pages. And in every class there are children who are familiar with this experience, who experience pleasure, for example, from a beautiful solution to a problem.

What distinguishes students who do well in mathematics?

“As a rule, these children are active, curious, ready to take risks, they are not afraid of problem situations, they love to make discoveries,” says child psychologist Elena Morozova. - And children who are afraid of mathematics often do not rely on themselves, they are too dependent on the opinion of their parents (teachers, classmates), they are not confident in themselves, they easily believe that they are slow-witted.

Any task brings such a child into a stupor: he is afraid of the very expectation that now it will be difficult and he will be untenable. Fear can cause failure in other subjects as well.”

It grows gradually, like a snowball. For example, the child psychologist recalls, in the first grades, not all children still read well “and the condition of the problem may simply not be understood. In addition, they have not yet developed abstract thinking, it is difficult for them to imagine a picture: here is a train leaving point A, and here is another train leaving point B, here they meet. And the child deliberately refuses to delve into the problem: I won’t even try to do something about it.”

What is left out in primary school will be reflected later, as in no other subject. Precisely because everything in mathematics is logically connected

“If I missed Griboedov in literature, this will not prevent me from studying Turgenev,” notes Leonid Kostyukov. - But if I missed something in algebra, then I will have systemic problems. Other subjects represent a specific set of topics. Mathematics, by and large, is the development of one topic. But sometimes it turns out that not all older students know even the multiplication table for sure.

The reason is not math

“She has a bad relationship with the teacher”, “classmates laugh at him”, “she is worried that her father left the family” — there can be many reasons for poor performance in any subject. But are there reasons that cause difficulties with mathematics?

Educational psychologist Ann Sieti is convinced that mathematical concepts can awaken the deepest feelings. “Condition”, “required”, “prove”, “necessary, but not enough” - all these words can unconsciously be associated with internal problems.

“What is worth only the notorious “X” - an unknown, behind which lies an unknown what,” she says. - Or another example: one of my students did not put brackets in her equations, forgetting to separate some numbers from others. And then it turned out that at home it was difficult for her to be alone in her room - that is, to perceive herself separately from other family members.

A child's problems with mathematics are not connected with his intellectual abilities, but with something inside him that prevents him from thinking clearly and understanding the teacher. That's why there are so many disturbing emotions that block the mind.

Not to learn, but to understand

Let's face it: very often school failures piss off parents. We get angry, indignant and criticize a child who "does not try", "does not want to understand" and in general "does not think well". And experts are unanimous: the main task of parents is just the opposite - to reduce his stress and worries.

“A child should not be fixated on failures at all,” emphasizes Elena Morozova. “It’s better to say: yes, it’s not working yet, let’s think about how to help you.”

However, this does not mean “helping learn”, as parents sometimes think

“Mathematics needs to be understood, to feel its wholeness, unity. If you just cram, it will only be an extremely tiring and, most importantly, meaningless training for memory, ”warns Leonid Kostyukov.

“It is necessary not to hammer in, but to consistently lead the child to an independent decision,” continues Elena Morozova. - And when this insight happens, the child is amazed: “Wow, I could!” It turned out once, twice, a third - and gradually he begins to get carried away, to feel his worth.

Of course, the best help here is a specialist - a teacher who can be asked for additional classes, or an experienced tutor. But parents themselves can try to make these discoveries together with the child.

Not necessarily after that the student will shine in the classroom and bring fives. Although grades do get better if you don't focus on them, Ann Sieti notes: “After all, everyone has their own goals. For one, it is important not to be the worst in the class. Another dreams of becoming a veterinarian. The main thing is that children begin to feel better, get rid of anxiety and fear, and begin to enjoy doing math.”

“Mathematics should be taught as a special theory of beauty”

Psychologies: Why do many children find mathematics bored, afraid, disgusted?

Alexander Lobok, psychologist: This means only one thing: it is fundamentally wrong for this child to be taught at school. Many children experience the humiliation of mathematics. For long school years, they experience a feeling of their impenetrable mathematical stupidity, and the teacher supports this feeling either in a sparing form (“What can you do, he has humanitarian brains!”), Or in a cynical and malicious (“Well, you are stupid!”).

Many teachers are convinced that mathematical abilities are “from God” and that the reason for the “insanity” of millions of children who do not understand mathematics is their natural limitations. Whereas the task of the school is to help each child feel mathematical excitement and desire to study. If this interest and love arise, the child will be much more successful - including in traditional mathematical education.

Most often, problems arise in children of a humanitarian nature. How to awaken this excitement in them?

It is important for children in the humanities to feel the meaning. And the traditional school curriculum quite often offers mathematics as a set of abstract “digits”, without even trying to explain to students that mathematics is primarily a philosophy that allows you to take a completely new look at the world around you. If children open the door to the meanings of what mathematics does, they will have excitement and interest.

For example, when you explain and show that mathematics is such a special magic that allows you to calculate the whole world. And that means finding something fundamentally common throughout the world. For example, everything can be weighed, measured - on this basis, compare the boy Petya, his beloved cat and his father's car. And in general, it turns out that everything in the Universe can be compared!

Also, children do not suspect that mathematics is filled with inner beauty - no one tells them about it either. But any sequence of ornaments or a game of architectural forms is mathematics. And if children are taught mathematics as a special theory of beauty, it can really hook them.

Does this mean that every child can master the school mathematics course?

In the form in which it exists today, of course not. Yes, this is not necessary. But to comprehend the aesthetic and philosophical foundations of mathematics is within the power and everyone needs. Thanks to this, interest in mathematics - and in the most traditional one - arises in every child. Including those who have hated this subject all their lives and considered themselves incapable.

But what about parents whose children study in a traditional school and do not cope with mathematics?

This is always a deeply individual problem. But the general recommendation can be this: you need to find a teacher who is truly passionate about both mathematics and children.

About the expert

Alexander Lobok — psychologist, author of the book “Another Mathematics”.

Text: Galina Chermenskaya Photo Source: Getty Images

New on site

Prostitution in the past and in the 21st century: mutually beneficial enterprise or violence?

Panel of anger: what kind of noise from neighbors irritates the residents of high-rise buildings the most?

Guest marriage: what are the advantages and disadvantages - find out if such a relationship suits you

“I can't look people in the eye. What to do?”: 3 simple tips

“I hate to chat on the Internet, I ignore friends' messages for hours. What happened with me?"

How to love yourself? 7 steps to a healthy relationship with yourself

“Sorry, but it’s not my fault”: 4 mistakes in apologizing – ask for forgiveness correctly

“Godfather pester me and jokingly offers sex, but my husband never stands up for me”

7 ways to help a junior student with mathematics

Let's assume that mathematics already in the elementary school of the child is slow, with a creak. Difficult and boring to add and subtract, not to mention something more complex. New topics do not want to fit in the head. Writer and mother of three children Ksenia Buksha tells, based on her own experience, how to help a child master mathematics.

Putting difficulties on the shelves

At the level of 1-5th grade, there are no children incapable of mathematics. But there are children with specific difficulties that can and should be overcome. Let's think about why it is difficult for a child with mathematics.

Here are the options or combinations.

Poor counting, no counting skills. Not very familiar with numbers.
Cannot grasp the essence of the task, hardly understands what needs to be done. Tries all options (“So wrong? Then I’ll try to divide”, “Three times more - do you need a plus or a minus here?”).
Assimilates a template solution, but cannot refine it. Faced with the slightest change in conditions, he falls into a stupor.
Cannot read complex texts. As a result, he does not understand either the description of the rules or the text of the task. If you explain on your fingers what needs to be done, he immediately decides normally.
The concepts do not fit in my head. He understands them with difficulty and quickly forgets them. Such a child can hear an explanation of what x (unknown) is a hundred times, but never understand.
Visualization skill not developed. Cannot imagine, draw a schematic picture, "see in the mind".
Short attention: understands everything, but makes a lot of mistakes, especially in long complex examples.

As you can see, mathematics is decomposed into many different skills. When we figured out what the problem is, we can solve it. I apologize in advance to teachers and methodologists: I am just a parent, and my thoughts on this matter are just a private opinion, although I try to substantiate it.

We are waiting for the ability to think abstractly

The brain of a neurotypical child does not mature to abstraction and generalization far from immediately. For some it happens sooner, for others later. For example, not all children can match number and quantity. For very many, even in the 2nd or 3rd grade, there are only "15 apples", but simply "15" is not.

At the same time, they somehow get used to operating with numbers, and the gap in the basic understanding is not very noticeable until it comes to slightly more complex things. For example, it is difficult for them to understand why there cannot be “one and a half” in the answer to the question “how many diggers?”. And when percentages or tasks for speed and distance begin, it becomes quite difficult.

It's worth going back to the specifics. Perhaps, in order to understand fractions, for now it is necessary to pronounce “watermelons in the numerator, boys in the denominator; 21 watermelons went to 42 boys, each with half a watermelon.” Even in the fifth grade, almost all concepts can still be grounded to the point.

Developing counting skills

Just learning to count is boring. All sorts of games with numbers will help us. For starters, complicated walkers with 2-3 dice (when in one move the maximum is 18 points, not 6), then various dice games where you need to count points.

The simplest game is known to me as "one": players take turns rolling one die (or two, or three), trying to get to a hundred points. The series is interrupted when the player has at least one one: in this case, the points for this series burn out, and you need to be able to stop on time.

I highly recommend dice poker. In this game, there are a number of combinations, each of which must be thrown in three attempts. These attempts can be saved. Players take turns making moves, the one who completes all the combinations first wins. In addition to the simple skill of adding points, poker gradually develops a fine understanding of randomness and probability, calculated risk and odds. Even a six- or seven-year-old can learn to play such poker.

To practice division and multiplication, my daughter and I talked about numbers as "relatives". For example, the number 72 has a very large "family": he has "children" 24 and 36, there are "grandchildren" - 2, 3, 4, 6, 12, 18. But the number 37 did not get himself any "family", it is simple. But if you "marry" him with another "loner" - 41, they will get 78 together, now you can "have children and grandchildren." This helps a lot to navigate the multiplication table.

Learning to see and visually generalize the problem

In order to schematize well, one must be able to highlight exactly what is important for the condition of the problem, and schematically depict it in the picture. First, we learn to highlight the main thing. These are the famous “what is superfluous?” games, in which there may be several answers. Watermelon, stork, apricot, grapes - what is superfluous? Depending on what sign.

Peterson's textbook has wonderful problems cluttered with a bunch of unnecessary data or lacking necessary conditions. In the task, the author asks to find and highlight only those conditions that are needed for the solution, and if they are not there, to indicate what is missing. Having learned to see the task, you can move on to schematization.

Many children do not understand at all why drawing diagrams for tasks and why it is easier. This is because these schemes are ready-made. But on what basis are they built? Why, for example, does it matter how long the train itself is if it travels from A to B? How to draw "3 o'clock"? And "all the pears planted by boys"?

You can draw diagrams of different tasks together, and then invite your child to come up with similar ones. There are such tasks in textbooks, but there are few of them. For some, this difficulty generally determines all relations with mathematics, and indeed with the ordering of data, abstraction, generalization, and the search for a solution.

Sharpening logic

Logic is one of the tools that everyone needs. There are no people who would not be inclined to logic, there are those who have it "not set". It's like the ability to wield a screwdriver: anyone who has hands can learn. You can judge for yourself how iron-clad your logic is. I really love this wonderful test.

A person with logic cannot be confused by any propaganda or advertising, he will not be confused by an unscrupulous bank, he is much better oriented in the world around him.

With children, you can start with simple syllogisms that sometimes sound funny but lead to understanding of very important things. For example, after hearing from someone the maxim “boys don’t cry,” a child may clarify: “some or all?”

If the children do not go through the concept of a set, it is worth at least a little bit to draw "circles" with it (it is not necessary to immediately introduce all the concepts) and solve the corresponding problems: here are the boys, here are the cats, and here are those whose name is Vasya. Where are the boys whose name is not Vasya? And where are the girls? Where is Barsik the cat?

Imagination development

Imagination is necessary for everything related to mathematics and logic. (I don't even write "strange as it may seem" because it's not at all strange.) Especially the ability to think in images.

I really like the game in which the parent and the child take turns asking each other "graphic riddles" that do not have an exact answer. Each draws a series of incomprehensible geometric shapes or combinations thereof (a point in a triangle, a lightning bolt and a circle, several circles, tangents ...), and the other draws them in such a way that a picture is obtained. The smarter the solution, the more fun both players get.

There are many ancient and new games in which you need to add patterns from the details and fragments of an egg (Columbian egg), a square, differently colored faces of a cube (“Fold a pattern”). There are also three-dimensional sets, for example, "Pentamino". It's not about completing tasks, although all these sets can be used that way, but it's about creativity from the available details and the ability to see the image.

You can also cut out snowflakes, draw symmetrical butterflies and little men, invent ciphers, draw labyrinths and maps. All this is the development of mathematical imagination.

Teaching a child to isolate what specifically he does not understand (metacognition)

I have written about it more than once — both in connection with mathematics and in connection with essays. Briefly, metacognition is the ability to "understand how I think", "know what exactly I do not know", awareness of one's thought process. This is what is almost never taught in school, and sometimes even spoil the already developed ability. After all, it is assumed that there are simple and complex ways to solve a particular problem. Often this is the case, but sometimes it is much more valuable to be able to go on your own and check yourself step by step: “Is it necessary to do this? I'm right?"

Joint reasoning (and I'm not talking about mathematics) is valuable both because it brings the child and the parent closer, and because we show how the thinking process goes.