Top Studies on Number Sense and Problem Solving

Strong number sense is the key to success in math - and life. Research shows that early math skills predict academic achievement better than early reading skills[1]. Here’s what you need to know:

• What is Number Sense? It’s understanding how numbers work, relate, and represent the world. Skills include subitizing (instantly recognizing small quantities), estimation, and recognizing number relationships.

• Why It Matters: Early number sense predicts future academic success. Weaknesses in this area can lead to lifelong math struggles.

• How It Helps Problem Solving: Kids with strong number sense can break down problems, spot patterns, and think flexibly - skills that apply to reading, science, and everyday challenges.

• Barriers to Development: Math anxiety, poor teaching methods, and socioeconomic factors can hinder number sense growth.

• Solutions That Work: Hands-on learning, reasoning-based teaching, and digital tools like the Funexpected Math app help kids build strong foundations.

Bottom Line: Early intervention and effective teaching methods can transform how children approach math, giving them the skills they need to succeed academically and beyond.

Why Some Children Seem to Have a Natural Math Sense, and Others Don’t

What Number Sense and Problem-Solving Skills Mean

Developing mathematical thinking starts with a strong sense of numbers, which forms the backbone of effective problem-solving. Let’s take a closer look at what number sense entails and how children use it to approach challenges.

Number Sense Basics

Number sense isn’t just about memorizing facts or formulas. It’s about understanding numbers on a deeper level - how they work, relate to one another, and represent the world around us [2].

At its core, number sense is built on several interconnected skills. Counting is the first step, but true understanding goes beyond reciting numbers. For example, subitizing, or instantly recognizing small quantities without counting, begins as early as age two [3]. Think of it as the ability to glance at a group of three apples and immediately know there are three, without needing to count them individually.

Another key aspect is recognizing relationships between numbers. A child with strong number sense understands that 5 is one more than 4, that 10 can be split into 6 and 4, or that 15 is closer to 20 than 10. This kind of flexibility with numbers is what drives mathematical thinking [4].

Estimation is another important element. When a child looks at a jar of marbles and guesses "about 30" instead of counting each one, they’re practicing estimation. This skill is especially useful in real-life situations where exact numbers aren’t necessary, helping build confidence in working with numbers [5].

"It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms." – Howden [6]

This type of mental flexibility allows children to break down problems into smaller, manageable parts. For instance, solving 8 + 5 might involve thinking, "8 + 2 equals 10, and 10 + 3 equals 13." These skills not only make math easier but also open the door to creative problem-solving.

How Children Solve Problems

When young children approach problems, their methods may look different from how adults solve math, but they follow logical patterns. They explore, test their ideas, and refine their strategies as they go [5].

Recognizing patterns is a big part of this process. Children begin to notice that adding makes numbers grow, that shapes can combine to form new ones, and that different problems may require different approaches. These discoveries form the basis of their problem-solving toolkit.

As they grow, children start using multiple strategies to solve problems. For example, they might count to solve a simple addition problem, draw pictures to work through a word problem, or break larger numbers into smaller chunks to make them easier to handle.

"Students come to understand that numbers are meaningful and outcomes are sensible and expected." – Marilyn Burns [5]

Reasoning skills also come into play as children learn to explain their thought processes and check their answers. This self-verification strengthens their confidence and sharpens their ability to think critically [5].

Research shows that a child’s mathematical knowledge when they start school is one of the strongest indicators of their future success - not just in math, but across other academic areas[7]. Why? Because the same reasoning skills used to solve math problems also apply to reading comprehension and scientific exploration, making math a foundation for broader learning.

Research Studies on Number Sense and Problem Solving

The link between number sense and problem-solving skills has been explored in depth, revealing how early math understanding can shape future academic success. These studies highlight not only the importance of number sense but also the critical periods and methods for its development.

Studies Showing the Connection

Evidence strongly supports the connection between number sense and advanced problem-solving abilities. This relationship is not just theoretical - it’s observable across different age groups and learning settings.

For example, a study published in Developmental Psychology found that early math skills at kindergarten entry are among the most reliable predictors of later academic success. Interestingly, these skills were shown to be even more predictive than early reading abilities, underscoring the foundational role of number sense [8].

Another study revealed that mathematical abilities at age 4 are closely tied to early numerosity perception at just 12 months old [9]. This suggests that the roots of mathematical thinking begin forming much earlier than many might expect.

Dr. Elizabeth Brannon, a Professor of Psychology and Neuroscience, explains this process:

"When children are acquiring the symbolic system for representing numbers and learning about math in school, they're tapping into this primitive number sense. It's the conceptual building block upon which mathematical ability is built." [10]

Her research further demonstrated that numerical preference scores at 6 months of age correlated with standardized math test results and nonsymbolic number comparison scores at 3.5 years old [11]. These findings illustrate how number sense evolves continuously from infancy through childhood, helping to forecast academic performance.

Early Number Sense Predicts Later Math Success

The predictive power of early number sense is well-documented. Studies show that kindergarten-level number sense strongly correlates with math achievement throughout elementary school [12]. Different aspects of number sense also play distinct roles in predicting future success. For instance:

• Early number sense is especially important for children with low and intermediate performance levels.

• Number relations skills predict success across all performance levels.

• Number operations skills are more predictive for children with intermediate and high performance [13].

The SENS (Screener for Early Number Sense) has proven to be an effective tool in identifying future math abilities in pre-K, kindergarten, and first-grade students [10].

Ben Clarke, an expert in early math and head of the Department of Special Education and Clinical Sciences at the University of Oregon, highlights this foundational role:

"For kids that have a fundamental weakness in mathematics, 80 percent or 90 percent of the time that's going to be linked to a lack of understanding numbers. If we want students to be able to access other pieces of mathematics that are really important, then they need to build this foundational understanding of numbers." [14]

The way children approach problems can also reveal their level of number sense. Doug Clements, the Kennedy Endowed Chair in Early Childhood Learning at the University of Denver, offers an example:

"Children who see 98 plus 99 and line them up vertically, draw a bar underneath with an addition sign, then sum the eight and the nine, carry the one and so forth - they are not showing relational thinking. Children who immediately say, 'That's 200 take away three, so 197,' are showing number sense." [14]

This flexibility in thinking is a hallmark of strong number sense and can be nurtured through effective teaching methods.

Common Problems Found in Research

Despite the benefits of robust number sense, research also identifies obstacles that hinder its development. Three key factors contributing to poor problem-solving skills include a lack of number sense, limited language proficiency, and math anxiety [15].

Math anxiety is particularly widespread, affecting 93% of American adults to some degree, with 17% experiencing severe anxiety [16]. This often begins in elementary school and can persist throughout life, making early intervention crucial.

The 2024 National Assessment of Educational Progress revealed that nearly 25% of fourth graders and 39% of eighth graders scored "below basic" in math [17]. Additionally, learning challenges are common. For example, about 10% of students are diagnosed with a math-related learning disability during their school years [13], and dyscalculia is estimated to affect 3% to 7% of the global population [7]. Children with dyscalculia often struggle with numerical knowledge, relationships, and operations [13].

Socioeconomic factors also play a role. One study found that higher-income students in kindergarten and first grade were more likely to use advanced problem-solving strategies, while lower-income students relied more on basic counting methods [14]. Classroom challenges such as difficulty connecting math concepts to practical problems, trouble finding alternative approaches, and struggles with basic math fact recall further complicate learning [16]. Often, these issues stem from teaching methods that prioritize memorization over understanding.

The good news? Early number sense skills are highly teachable. With the right interventions, even children at high risk for math difficulties can develop a strong foundation for future success [10]. This offers a clear path forward for educators and parents aiming to support young learners.

Proven Methods for Teaching Number Sense and Problem Solving

There’s a strong connection between early number sense and problem-solving skills, and tapping into this relationship can lead to more effective math instruction. Research highlights several strategies that cater to different learning styles and developmental stages. Here are three tried-and-true methods to help young learners build number sense and improve their problem-solving abilities.

Hands-On Learning Methods

When it comes to teaching math, nothing beats hands-on experiences. Kids grasp abstract math concepts more easily when they can physically interact with objects. Everyday items, number lines, tape diagrams, and manipulatives like blocks or counters make concepts like one-to-one correspondence, estimation, and pattern recognition more accessible. Activities like measuring with familiar objects also bring math to life[19][21].

The numbers back this up: students who use visual tools like number lines, tape diagrams, and graphs are six times more likely to solve problems correctly[19]. These tools not only make math more tangible but also help children visualize and understand relationships between numbers.

Teaching Through Exploration and Reasoning

Reasoning isn’t just a bonus in math - it’s a core part of learning. Research shows that weaving reasoning into every activity leads to deeper understanding[20]. According to the National Council of Teachers of Mathematics, children thrive when they engage in tasks that challenge them to think critically and reason at a high level[20].

Reasoning typically develops in stages: describing, explaining, convincing, justifying, and proving[20]. You can encourage this by incorporating play-based and inquiry-driven activities. For example, use colorful characters or hands-on experiments to make abstract ideas more relatable. Open-ended questions that prompt kids to explain their thinking not only enhance understanding but also build their confidence[20][21].

Direct Teaching and Step-by-Step Methods

For many students, especially those who struggle or have special needs, direct instruction provides the structure they need to succeed. This method involves teaching specific skills in a clear, step-by-step manner[23]. Research shows that direct instruction improves outcomes in reading, math, and spelling, and is particularly effective for students who need extra support[23][25].

Direct instruction often includes worked examples and guided practice. Teachers might model a problem, pause to reflect, and then assign similar tasks to reinforce learning[24]. Combining this structured approach with inquiry-based activities creates a balanced learning environment that strengthens both foundational skills and creative problem-solving[22]. By asking targeted questions and encouraging applied learning, direct instruction becomes an engaging and effective tool for teaching math.

Digital Tools for Number Sense Development

Digital tools are transforming how math is taught, complementing traditional methods with interactive and personalized experiences. When designed thoughtfully, these tools engage young learners while offering the structure and customization proven to enhance learning. One example of this evolution in digital education is Funexpected Math, a platform that combines research-backed methods with engaging interactivity.

How Funexpected Math Builds Math Skills

Funexpected Math blends innovative digital experiences with proven teaching strategies. The app features a library of tasks spanning over 50 topics across six learning tracks, tailored for young learners.

One standout feature is its personalized digital tutor, which adapts to each child's learning pace and style. Instead of a uniform approach, the app adjusts difficulty levels and provides targeted guidance where needed.

This mirrors the benefits of direct instruction by offering step-by-step support while keeping the experience interactive and engaging.

The curriculum focuses on foundational number sense skills - like counting, pattern recognition, and basic operations - while also introducing logic, early coding, and spatial reasoning. Each activity builds on prior knowledge, reinforcing core skills and encouraging critical thinking.

With support for 16 languages, Funexpected Math caters to diverse classrooms, including English language learners and multilingual families. For educators, the platform offers classroom management tools, simple rostering, and detailed progress tracking, making it easier to deliver structured and effective math lessons.

Why Interactive Learning Works for Young Children

The interactive design of Funexpected Math showcases why digital tools are reshaping early math education. By combining play with academic challenges, these tools align with how children naturally learn - actively, socially, and through exploration. Research supports this approach, showing that guided play helps children develop vocabulary and spatial skills more effectively than free play or direct instruction [26].

Guided play also fosters discovery-based learning, allowing children to explore new ideas within a structured framework. Digital tools like Funexpected Math excel in creating these supportive environments, encouraging students to think critically and experiment with mathematical concepts in meaningful ways [27]. Unlike traditional worksheets, these platforms present math through multiple representations, helping children visualize relationships and explore different problem-solving strategies.

Additionally, studies highlight that playful learning boosts problem-solving, communication, decision-making, and creativity, while also building resilience [28]. By making math enjoyable and engaging, digital tools ensure that every child has the opportunity to develop a strong foundation in number sense and become confident problem solvers.

Conclusion

Research highlights that number sense is the cornerstone of mathematical success and a critical skill that supports problem-solving abilities throughout life. Ben Clarke, an early math researcher and department head of special education and clinical sciences at the University of Oregon, underscores this point:

"If we want students to be able to access other pieces of mathematics that are really important, then they need to build this foundational understanding of numbers" [16].

A 2022 study in the Journal of Neuroscience shows that strong number sense in early childhood often predicts academic success, while weaknesses in this area can persist, leading to lifelong struggles with math [2]. Similarly, research in Developmental Psychology found that early math skills at kindergarten entry are among the strongest predictors of future academic performance - surpassing even early reading skills [14]. These findings emphasize the importance of prioritizing early math education, as outlined in the teaching strategies discussed later.

The consequences of neglecting early number sense are significant. Children who struggle with math in elementary school are 13 percentage points less likely to graduate high school and 29 percentage points less likely to attend college [30]. Alarmingly, recent data from the 2024 National Assessment of Educational Progress shows that nearly 1 in 4 fourth graders and 39% of eighth graders scored "below basic" in math [16]. This underscores the urgency of addressing early math education gaps.

Fortunately, research demonstrates that early intervention can dramatically improve outcomes. Children with strong number sense develop flexibility with numbers, confidence in problem-solving, and the ability to grasp mathematical concepts that benefit them across all areas of learning [4]. These skills enhance cognitive development, logical reasoning, and the confidence to tackle complex challenges in both academics and everyday life [14][29].

FAQs

How can I help young children overcome math anxiety?

Helping young children tackle math anxiety begins with fostering a supportive and encouraging learning environment. Emphasize effort over results to nurture a growth mindset, and guide kids to use positive self-talk to build their confidence.

Here are some practical ways to make math less intimidating and more enjoyable:

• Incorporate math practice into fun, interactive activities.

• Teach relaxation techniques, like deep breathing, to help manage stress.

• Celebrate small victories to keep motivation high and ease frustration.

By cultivating a positive relationship with math, kids can gain confidence and strengthen the problem-solving skills they’ll rely on in the future.

How does Funexpected Math help children build number sense and problem-solving skills?

Funexpected Math helps kids build a strong number sense through interactive, hands-on activities that make learning math both engaging and enjoyable. With personalized lessons and playful challenges, children can explore numbers, patterns, and relationships in a way that feels intuitive and exciting.

The app also boosts problem-solving skills by offering puzzles, coding exercises, and logic-based games. These activities inspire critical thinking, creativity, and strategic reasoning, empowering kids to tackle challenges with confidence. By adjusting to each child's learning pace, Funexpected Math delivers a customized experience that strengthens both their understanding of numbers and their ability to solve problems.