Foundations of Learning >> Cognitive Micro-Skills >> Core Skills of Math >> Number Sense
Unlocking Math: A Parent’s Guide to Number Sense
Has your child been wrestling with math for a while? Are you feeling frustrated or even helpless as you watch your child struggle with math? It’s tough to see them facing challenges, especially when those challenges come in the form of numbers and equations that make little sense. You’re not alone in this journey; many parents share the same concerns and frustrations when helping their children with math.
But take heart—there’s a light at the end of the tunnel, and it starts with understanding something called “number sense.”
Why Math Seems Hard
: If your child struggles with math, knowing they’re not alone is important. Many kids find math challenging, not because they can’t do it, but because they might not have fully developed what we call “Math Sense” or “number sense.”
What is Number Sense?
It’s like having a good sense of direction in the world of numbers. It’s not just about memorizing facts or following rules; it’s about deeply understanding numbers. Imagine being able to look at a handful of marbles and know how many there are without counting them one by one. That’s part of number sense! With a strong number sense, math doesn’t feel like a mysterious puzzle but more like an adventure with tools and maps to guide the way. This guide is here to help you understand how these fundamental skills can transform your child’s experience with math, making it more approachable and even fun.
Develop Your Child’s Number Sense by starting a free trial of the Brain Bloom System
Number Sense – The Underlying Cognitive Skills Needed to Develop Math Skills
These underlying cognitive skills are the foundational blocks of number sense. They relate to how we perceive, recognize, and interact with numbers in our minds. Before diving into formal math education, children need these skills to intuitively make sense of numbers. Think of them as the “alphabet” of math; without a good grasp of them, learning math becomes like trying to read without knowing letters.
Building these skills will improve math skills because they make thinking about math more efficient. We usually don’t even realize we are doing these things, which is why they go undetected and generally don’t get practiced.
1. Subitizing:
- What it is: The ability to instantly recognize how many objects are in a small group without counting.
- Example: When you show your child three cookies, they can immediately say, “There are three,” without counting each one.
- Importance: This skill lays the groundwork for quick number comprehension, which is crucial for developing an intuitive grasp of quantities.
2. Magnitude Comparison:
- What it is: Understanding which numbers are larger, smaller, or about the same.
- For example, If You Ask your child if 7 is more or less than 5, they can confidently say, “7 is more than 5.”
- Importance: It helps children conceptualize numbers as having size and position relative to each other, which is fundamental for all numerical reasoning.
3. Number Identification:
- What it is: Recognizing numbers in various representations (digits, words, symbols).
- Example: Your child can identify “8” whether written as “eight,” “8,” or “VIII.”
- Importance: Essential for reading and understanding math problems, setting the stage for all subsequent math learning.
4. Estimation:
- What it is: Making educated guesses about quantities or outcomes without exact calculation.
- Example: Your child guesses that there are about 20 jellybeans in a jar when there are 22, showing they understand quantities practically.
- Importance: Estimation fosters number sense by encouraging children to think about numbers in context, promoting flexibility and practical application of math.
The Brain Bloom System helps you build up “Number Sense.”. Start a Free Trial
Math Skills
These are the actual math skills that children will use in their academic and daily lives. They are built upon cognitive skills (number sense); without a strong foundation in subitizing, magnitude comparison, number identification, and estimation, they can be much harder to master.
Teachers excel in this area, which mostly involves teaching math. However, without students having basic number sense, it is far more difficult for teachers to do their jobs.
Parents play a crucial role in helping their children approach math with a natural understanding. By focusing on developing these underlying cognitive abilities, parents can make the transition to more complex skills smoother and more intuitive. This approach significantly reduces frustration and increases success in math learning, empowering parents to be more involved in their child’s learning journey.
Counting:
- What it is: The ability to count objects sequentially.
- Example: Your child can count the steps from the door to the car, understanding one-to-one correspondence.
- How it builds on cognitive skills: Counting applies subitizing and number identification in a sequential, practical manner.
Arithmetic Fluency:
- What it is: Quick and accurate performance of basic arithmetic operations.
- Example: Your child can quickly say that 3 + 4 equals 7 without needing to count on their fingers.
- How it builds on cognitive skills: This relies on understanding magnitude, estimation, and number identification to perform calculations swiftly.
Decomposition and Composition of Numbers:
- What it is: Breaking numbers down into parts or combining them to form new numbers.
- Example: Your child realizes that 15 can be seen as 10 + 5, making addition and subtraction easier.
- How it builds on cognitive skills: Uses subitizing and magnitude comparison to understand part-whole relationships.
Number Line Concept:
- What it is: Visualizing and understanding numbers on a continuum.
- Example: Your child can place numbers in order on a number line, understanding why 6 comes after 5 but before 7.
- How it builds on cognitive skills: Magnitude comparison and number identification help in placing numbers correctly on a line.
Mental Computation:
- What it is: Performing calculations mentally.
- Example: Your child can imagine that if they share seven candies with a friend, they’ll each get three candies, with one left over.
- How it builds on cognitive skills: It’s an extension of arithmetic fluency, estimation, and number sense for quick problem-solving.
Understanding of Number Properties:
- What it is: Grasping concepts like even/odd, primes, and properties of operations.
- Example: Your child understands why 2 is prime, but 4 is not, or that 5 + 4 is the same as 4 + 5.
- How it builds on cognitive skills: Requires a solid foundation in all the mental skills to see patterns and generalizations.
Benchmarking:
- What it is: Using known numbers to estimate or compare others.
- Example: When estimating a larger number, your child might say, “That’s about 50 because it’s close to half of 100. “
- How it builds on cognitive skills: Estimation and magnitude comparison are key here.
Proportional Reasoning:
- What it is: Understanding ratios, proportions, and percentages.
- Example: If one cookie costs $2, your child can calculate the cost of three cookies by saying, “Three times $2 is $6.”
- How it builds on cognitive skills: It builds on estimation, magnitude comparison, and number identification for scaling concepts.
Sense of Operations:
- What it is: Intuitive understanding of how arithmetic operations affect numbers.
- Example: Your child knows multiplication will make numbers bigger and division smaller, so they can predict outcomes without calculation.
- How it builds on cognitive skills: Relies on all cognitive skills to predict outcomes of operations.
Flexibility with Numbers:
- What it is: Using different strategies to solve problems.
- Example: To solve 9 + 7, your child might add 1 to 9 to make 10, then add 6 more, showing they can manipulate numbers in different ways.
- How it builds on cognitive skills: Combines all cognitive skills for adaptable problem-solving.
If you help your child build up number sense, math skills will be much easier. You are making teachers’ jobs easier and helping your child succeed and gain confidence.
Why Number Sense Matters
Real-World Relevance: Number sense isn’t just for the classroom; it’s crucial in everyday life. Think about shopping: understanding if you have enough money to buy something or if you’re getting a fair amount for what you’re paying. Cooking? It’s all about measuring and adjusting ingredients. Even in sports, knowing scores, times, or distances involves number sense. These skills make daily tasks less daunting and more manageable.
Academic Impact: A strong number sense lays the groundwork for all other math concepts in school. When children can intuitively grasp numbers, complex topics like fractions, algebra, or even geometry become less intimidating. They start to see patterns and relationships, boosting their math grades and confidence in tackling new mathematical challenges. Math becomes a puzzle they can solve, not a wall they can’t climb.
By fostering these skills, you’re not just helping your children with math homework but equipping them with life-long tools for problem-solving, critical thinking, and decision-making in a world that increasingly revolves around numbers and data.
How Parents Can Help
Games and Activities:
- Board Games: Games like “Chutes and Ladders” or “Yahtzee” involve counting, adding, and basic strategy, all enhancing number sense.
- Card Games: Simple games like “Go Fish” teach counting, matching, and basic arithmetic in a fun way.
- Number Puzzles: Sudoku for kids or jigsaw puzzles with numbers can be great for pattern recognition and spatial understanding.
Daily Life Integration:
- Cooking Together: Measure ingredients, double recipes, or halve them. Discuss quantities: “We need 2 cups of flour. How much is that if we only need half?”
- Counting in Routine: Count steps when going up or down stairs or cars when going for a walk.
- Shopping: Let your child handle money, calculate change, or compare prices. “Which cereal gives you more for the same price?”
Patience and Encouragement:
- Celebrate Small Wins: Every correct answer or improved estimation should be celebrated. “Wow, you guessed almost exactly how many apples we needed!”
- Encourage Effort, Not Just Results: Praise the effort in trying new math problems, not just the correct answers. “I can see you’re really thinking about how to solve this!”
- Be Patient: Learning number sense doesn’t happen overnight. It’s a journey with ups and downs. Show patience and provide a supportive environment where mistakes are learning opportunities.
By incorporating these activities into your daily routine, you’ll help your child with math and strengthen your bond through shared experiences. Remember, it’s about fostering a love for learning numbers in a way that feels natural and fun rather than like a chore or a test.
Are you looking for a structured way to improve number sense? The Brain Bloom System is what you are looking for.
Signs of Improvement
What to Look For:
- Faster Responses: Your child begins to answer math questions more quickly, indicating they’re gaining confidence and fluency with numbers.
- Improved Estimation: They get better at guessing quantities or outcomes without precise calculation. For instance, they might accurately estimate how many candies are in a jar or how long a trip will take.
- Increased Confidence: Notice if your child is more eager to participate in math activities or games and shows less hesitation or fear when numbers are involved.
- Pattern Recognition: Students start to see and describe patterns in numbers or sequences, such as the fact that adding two odd numbers always makes an even number.
- Problem-Solving: Your child might approach problems with a strategy, showing they’re thinking about numbers in different ways, not just following a rote procedure.
- Engagement with Numbers: Look for signs that they’re engaging with numbers outside of schoolwork, such as counting, sorting, or playing with number-based toys or apps.
- Better Understanding of Magnitude: They can compare numbers more effectively, understanding concepts like “more than,” “less than,” or “about the same.”
- Flexibility in Math: They can solve the same problem in different ways, showing they understand numbers at a deeper level rather than just memorizing steps.
- Asking Math-Related Questions: When children start asking questions about numbers or how things work mathematically, it’s a sign they’re curious and engaging with math concepts.
Remember, improvement might come in small steps and might not be uniform across all areas of number sense. Celebrate each of these developments, as they are all steps toward a stronger foundation in math. If you see consistent improvement in these areas, it’s a good indication that your child’s number sense is growing, making math less of a challenge and more of an exploration.
Empower Your Child
Understanding math sense is the first step toward empowering both you and your child in the world of mathematics. With patience, practice, and the right approach, you can turn math from a struggle into a journey of discovery. Every small step your child takes towards better number sense is a victory, not just in math class but in life.
Remember, you’re not just helping with homework; you’re nurturing a mindset that will benefit your child in countless ways. As your child develops these skills, they’ll find that numbers become friends rather than foes, making math an exciting part of their daily lives. As a parent, you can make math easier, enjoyable, and rewarding.
Brain Bloom Educational Therapy
At-Home Educational Therapy program. A general program that covers all of the foundations of learning
- Foundations of Learning
- Improve Grades
- Improve Confidence
- Restore the Love of Learning
Monthly
$49
7 Day Free Trial
SALE!
Regularly $69/month
Save $20/month
Yearly
$297
7 Day Free Trial
Sale!
Regularly $397
Save $531
over regular monthly Price
Attentive Ear Auditory Processing Program
At-Home Auditory Processing Program. Auditory processing is often at the core of learning struggles.
Improve:
- Focus
- Following Directions
- Listening Skills
Monthly
$49
Yearly
$297
5-Minute Reading Fix
Phonetic and image-based reading system. Creates word readers, NOT word guessers. Easy and takes only 5 minutes per day
Improve:
- Reading Fluency
- Reading Speed
- Reading Comprehension
Monthly
$39
Yearly
$199
All Access Plan – Save $793
Huge Savings!
Get all of our programs at an extremely reduced price. Also includes special All Access Members Only courses
Includes:
- Brain Bloom System
- 5-Minute Reading Fix
- Attentive Ear Program
- Extra Bonus Courses
Monthly
$69
7 Day Free Trial
SALE!
Regularly $99/month
Save $30/month
Yearly
$397
7 Day Free Trial
Sale!
Regularly $599
Save $202
Research
Understanding the cognitive skills contributing to mathematical abilities—such as subitizing, magnitude comparison, number identification, and estimation—is essential for grasping how individuals develop numerical competence. Below is a curated list of notable studies that explore these foundational skills, detailing their methodologies and findings:
- “Impaired Large Numerosity Estimation and Intact Subitizing in Developmental Dyscalculia”
- Authors: Not specified in the provided excerpt.
- Conducted at: Not specified.
- Published in: Frontiers in Human Neuroscience, 2021.
- Description and Findings: This study examined children with developmental dyscalculia (DD), a learning disability affecting numerical and calculation skills. The researchers found that while these children had impairments in estimating large numerosities, their ability to subitize (rapidly and accurately identify small quantities) remained intact. This suggests that large number estimation and small number quantification involve distinct cognitive processes, with the former being more affected by DD.
- “Subitizing but Not Estimation of Numerosity Requires Attentional Resources”
- Authors: Not specified in the provided excerpt.
- Conducted at: Not specified.
- Published in: Journal of Vision, 2014.
- Description and Findings: This study investigated whether subitizing and estimation rely on different cognitive processes. Participants were asked to enumerate items under varying attentional loads. The results indicated that subitizing (for small numbers of items) requires attentional resources, whereas estimating larger quantities does not, supporting the idea that separate mechanisms mediate these two tasks.
- “Grouping Strategies in Number Estimation Extend the Subitizing Range”
- Authors: Not specified in the provided excerpt.
- Conducted at: Not specified.
- Published in: Scientific Reports, 2020.
- Description and Findings: The researchers explored how grouping strategies affect number estimation and subitizing. They found that when individuals used grouping strategies, their subitizing range extended beyond the typical limit of four items. This suggests that cognitive strategies can enhance basic numerical processing abilities.
- “Magnitude Knowledge: The Common Core of Numerical Development”
- Authors: Robert S. Siegler and Hugues Lortie-Forgues.
- Conducted at: Not specified.
- Published in: Developmental Science, 2016.
- Description and Findings: This review identifies substantial commonalities in various aspects of numerical development, emphasizing the role of magnitude knowledge—understanding numerical value and size—as a foundational element in learning both whole and rational numbers. The authors argue that a strong grasp of numerical magnitudes is crucial for the development of mathematical proficiency.
- “The Relationship Between Numerical Magnitude Processing and Mathematics Achievement: The Role of Math Anxiety”
- Authors: Not specified in the provided excerpt.
- Conducted at: Not specified.
- Published in: Cognitive Processing, 2024.
- Description and Findings: This study examined how math anxiety relates to numerical magnitude processing and overall math achievement. The findings suggest that math anxiety is associated with deficits in processing numerical magnitudes, which in turn compromises the development of advanced math skills. Addressing math anxiety may, therefore, be important for improving numerical processing abilities and math performance.
- “The Componential Nature of Arithmetical Cognition: Some Important Variables and Their Interrelations”
- Authors: Not specified in the provided excerpt.
- Conducted at: Not specified.
- Published in: Frontiers in Psychology, 2023.
- Description and Findings: This article discusses the various components that contribute to arithmetical cognition, including subitizing, and their interrelations. The authors highlight that while subitizing is linked to mathematical ability, it is just one of several factors that collectively influence arithmetic skills.
These studies collectively underscore the complexity of numerical cognition and highlight the distinct yet interconnected roles of various cognitive skills in mathematical development.