Why Children Learn Differently—and What Maths Teachers Can Do About It
We all have the experience of giving a very well crafted, very clear, very structured explanation of some mathematical idea, whether it's adding fractions with different denominators or whatever, and then gazing out at the classroom.
Some pencils are already clicking, hands are already nodding, pupils are prepped and ready for the next challenge! A large middle group grasps the concept, but requires coaching to do the steps accurately. Then a few students have looks of quiet panic staring at the board, not knowing where to start.
How can the same explanation have such a diverse impact in a space of 25 kids?
For years, mainstream education has attempted to provide an easy solution to the question: "Learning styles.The mainstream education has been attempting for years to answer the question with a simple solution: “Learning styles”. Teachers are informed that Child A was a visual learner, Child B is an auditory learner and Child C is a kinaesthetic learner. The reality is quite different, however, in the light of modern cognitive science and experience in the classroom.
Kids aren't packaged into pre-defined learning categories. Rather, they bring to class their own learning styles and different levels of background knowledge, processing speed, and emotional reactions to math.
It is important to be aware of these, if you want to teach maths to different learners. Instead of labelling children, effective maths teacher strategies involve flexible teaching approaches so that all children can learn mathematics at a pace which is suitable for them.
How is it that the same maths lesson is not suitable for every child?
If a maths lesson fails to go well with some pupils, it's not because they're not clever enough. Mathematics is a cumulative subject; new concepts build on top of old concepts.
Children are not starting from the same background in the classroom and so their mathematics starting points will rarely be the same.
Different Starting Points
What one child knows in a grade 4 classroom can be a world away from another child's knowledge. One child may know all the place value facts and have a secure understanding of basic multiplication facts, while another may be struggling to compose and decompose numbers mentally. As soon as you introduce long division, the first child has only to learn the new algorithm, but the second child has to keep up with the new algorithm and the basic subtraction facts at the same time, forcing his/her cognitive ability to the breaking point.
Different Learning Speeds
Some kids learn numbers quickly, and go directly from numbers to abstract concepts. Others need more time, physical models or several iterations of a concept before it "clicks. Often speed is interpreted as mathematical skill; however, processing speed is just a cognitive trait and not a measure of mathematical depth.
A variety of confidence levels are available.
A student who feels like “I am not good at maths” will solve maths problems in a high stress, low risk-tolerance manner. They give up or get stymied too quickly. On the contrary, the healthy attitude of a confident student is thinking about the difficult problem as a puzzle to be solved, which means that he is more persistent and curious.
Different Experiences With Mathematics
Children bring a variety of experiences with mathematics. A student who has been exposed to problem-solving using their home and/or co-curricular, play-based math scaffolding will approach problem-solving with the familiar mental tools. Some students have limited experience with math and have been subjected to a high-stakes math test culture, and may feel anxious and rigid about the subject.
So what is "Children Learn Differently"?
The introduction of the term 'cognitive diversity' is a step towards a more child-centred approach to maths teaching, but we need to work through what this means in the classroom. We know that children learn differently, which we are witnessing are cognitive, emotional, and physical differences:
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Differences in Prior Knowledge
One best predictor of mathematics learning success is prior knowledge. If the student has not developed proficiency in basic place value, then expecting him/her to comprehend decimal numbers and percentage conversions immediately overloads the brain. One of the ways people learn is through "learning style difference" but this is often only when they lack the necessary preknowledge.
- 2
Learning Pace Differences
The way that humans consolidate abstract ideas varies. A child can learn a math concept in 5 minutes, another in 3 days, depending on the variety of exposures and applications, and quiet time for reflection. It is natural to learn at your own pace; forced pacing is one of the main reasons for math anxiety.
- 3
Confidence and Maths Anxiety differences
Math anxiety is a scientifically studied mental state which actually negatively affects working memory. If a child is stressed while doing a maths problem, cortisol is released, which takes up some of the working memory and impairs the ability to solve the problem. Learners with high anxiety need to know they're in a safe environment, have less at stake at the beginning, and have confidence-building steps made explicit.
- 4
Differences in Attention and Working Memory
Working memory is the temporary memory holding arena in which information is temporarily stored and processed. The capacity of working memory is highly individual and children have widely different amounts. One student may have no problem with the multi-step word problem, which requires holding three numbers, doing two operations, and keeping track of the units; but another student's working memory may be completely exhausted by the multi-step word problem.
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Variability in Children's Problem engagement
Some students must have to do something with an object or draw a diagram in order to grasp an idea. Some like solving the problem by visual patterns, verbalizing their reasoning to another student, or systematically breaking down written rules. The following are not permanent characteristics but different ways of thinking about abstract concepts.
Why do teachers need to not place children in fixed learning-style boxes!
Popular education theory for decades has held that it is important to recognize a learner as a "visual," "auditory or kinaesthetic" learner, and to tailor teaching to that sense alone.
This is a strict model for which cognitive psychology studies have proved false. It can stifle a child's growth to say that they are a "visual learner" or "kinaesthetic learner.
The limits of sensory labels
If we label a pupil a ‘visual learner' we may be neglecting his/her ability to reason verbally and abstract numerically. In addition, mathematics is multimodal in nature. Visual diagrams alone do not provide enough insight into fractions; later on it is necessary to link the diagrams to symbolism, verbal descriptions and logical proofs.
Engage in Flexible Teaching Methods.
Don't classify students into types and focus on multi-sensory teaching for everyone, i.e. differentiated instruction for all students.
A mathematical concept presented multiple ways is beneficial to all children. The shift is from “How do I teach this visual child?” to “How do I represent this mathematical concept visually, concretely and symbolically so that all children understand it deeply?”
7 Ways Maths Teachers Can Adapt Their Teaching?
Differentiated instruction in a busy classroom doesn't mean that each class will have 25 different lesson plans. Rather, it is based on flexible teaching maths strategies, which incorporate flexibility into your current curriculum.
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Start by Identifying What the Child Already Knows
Run a short 3 minute diagnostic check or ask a diagnostic question prior to beginning a new unit. Knowing entry points helps you to see what has to be pre-taught to students who are struggling, and what extensions to provide for students who are ready for advanced work.
- 2
Explain the Same Concept in More Than One Way
Follow Concrete, Pictorial, Abstract (CPA) approach. In dealing with the concept of multiplication:
- Use visual models to represent: Draw arrays, area models, or number lines on the board.
- Clear verbal explanation: explain multiplication clearly, using the language of "equal groups" or "addition repeated.
- Demonstration & Concrete tools: Counters, base ten tools, or Abacus frame.
- Guided Practice: Lead students in Problem Solving in Pairs with Symbolic Notation.
Multiple accesses provide an opportunity for all learners to engage the concept in a manner they can do at that time.
- 3
Low floor, high ceiling (Difficulty Level)
Set up design challenges with a "low floor and a high ceiling. A low floor task is a task that is available for all students, even those with little prior knowledge; a high ceiling task is a task that allows advanced students to extend their thinking.
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Provide children with varying amounts of practice.
Some children learn to speak more quickly than others. If a student has learned to add two numbers that are ten or less, giving him/her fifty repetitions of the same set of numbers will bore him/her and make him/her feel unmotivated. On the other hand, if a student is rushed into more difficult word problems before he or she has a firm grasp on basic arithmetical facts, it causes anxiety. Adjust the amount of practice based on evidence of mastery, rather than on a random class timer.
- 5
Ask Questions, Don't Say All of the Answers
Avoid giving a student the next step in the problem right away when the student says "I'm stuck. Pose questioning, metacognitive questions:
- What does this question tell us to do?
- This is a question that is frequently asked.A common question is "Can you draw a quick sketch of what is going on in this problem?
- “What is a simplified version of this problem that is smaller and simpler that we can solve first?”
This strategy supports thinking, but not remove the productive struggle, which cultivates problem solving resilience.
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Don't make children feel "slow" by giving extra support.
Don't create permanent ability groups, such as "slow" and "fast" groups. Rather, adopt a flexible approach to grouping according to the learning needs of the day. Encourage the use of support materials throughout the classroom so that the use of a visual guide, number line or Abacus is seen as a good strategy, not a weakness.
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Gradually Increase Independence
Apply the “I Do, We Do, You Do” model (Gradual Release of Responsibility).
I Do
Show the thinking process in an out loud manner.
We Do
Work as a class, discuss with peers to solve problems.
You Do
Provide independent practice after students are ready, guided practice in small groups for those students requiring additional guided intervention.
How can Abacus Learning meet the needs of different learners?
For finding structured methodologies that support personalized maths teaching, specialized mental arithmetic tools, such as the Abacus, are excellent support for various learning styles.
The Abacus has been proven to be an effective learning aid for addressing multiple learning styles:
Concrete number representation
Abstract place value turns into concrete beads. A child who is having trouble with the digits on a page can physically touch, move and count units, tens and hundreds.
Progressive learning
Abacus training is a step-by-step learning process, physical operation to visual mental (vital) image to abstract calculation. This orderly process allows for different speeds of processing.
Repeated practice
Multi-sensory feedback of moving beads, to reinforce spatial memory and number sense.
The transition of physical beads to visualization
Children move from physical beads to visualizing the tool over time. This bridge directly enhances the capacity of working memory and spatial visualization.
At IIVA, all children are taught place value and mental calculation with the help of the Abacus before they are introduced to abstract algebraic notation.
How Vedic Maths Can Be Adapted for Different Learners
For older primary and secondary students who require flexible arithmetic techniques, Vedic Maths offers a powerful framework for differentiated instruction.
Traditional mathematics algorithms taught in schools are usually rigid—there is often only one standard way to multiply or divide. Vedic Maths, by contrast, introduces mental shortcuts and alternative techniques based on natural patterns.
| Learning Need | Traditional Approach | Vedic Maths Adaptation | Benefit for the Learner |
|---|---|---|---|
| High Maths Anxiety | Rigid, multi-step algorithms where one error ruins the problem | Flexible mental methods (e.g., base multiplication methods) | Reduces working memory overload and builds early success |
| Fast Processors / Advanced | Standard repetitive practice sheets | Cross-multiplication and general mental shortcuts | Challenge and deepens pattern recognition |
| Visual / Pattern Seekers | Abstract symbolic procedures | Dot-based subtraction and sutra-based visual patterns | Connects computation to spatial relationships |
Some important factors to keep in mind while applying Vedic Maths to various learners:
Use suitable techniques first
Use simple techniques, such as, "All from 9 and the last from 10" for subtraction questions before progressing to complex multiplication questions.
Emphasis on understanding not speed
Show the beauty of mathematics and alternative routes using the Vedic methods, not just speed.
Give students an opportunity to describe their strategy
Encourage students to speak about the strategy that was easiest for them to use and the reasons for this, fostering metacognition and active involvement with mathematical concepts.
Teachers are trained through IIVA, which will enable them to integrate the Vedic Maths techniques into their regular classroom methods and provide students with a toolbox of techniques, instead of a required procedure.
There are many other items teachers need to monitor besides the marks.
While timed tests and numerical marks are easy to score mathematically, we fail to capture important aspects of student growth if we do not consider them. To encourage a growth attitude, monitor a wider range of indicators:
Proficiency over "speed"
A child who works carefully and deliberately to accurately solve three math word problems is demonstrating deeper mathematical thinking than a child who guesses through ten word problems quickly.
Confidence and emotional safety
will the child attempt a difficult problem without taking immediate help? Do they raise their hand even if they don't know?
Active involvement
Monitoring active involvement in pairs work and class discussion gives an indication of students' level of comfort.
Problem-solving approach
Does a student draw a model, try different strategies, or try to find alternative patterns if stuck? Considering the selection of strategy provides a glimpse into their thinking.
Progress over time
assess a child's achievement against their previous work instead of progress against class standards.
Explain reasoning
Can the child give reasoning for the answer? Correct symbolic answers are not sufficient, a verbal/visual explanation of the concept is more accurate.
A Simple Differentiated Maths Lesson Framework
To put these principles into daily classroom practice, use this 7-step lesson framework designed for diverse learning needs:
- 1
Check Prior Understanding
3–5 minutes.Start with a quick warm-up question to assess prerequisite skills. Identify immediately which students need scaffolded support and which are ready for a challenge.
- 2
Introduce the Concept
5–7 minutes.Present the new mathematical idea using the Concrete-Pictorial-Abstract (CPA) approach. Combine a visual diagram or real-world object with explicit verbal explanation.
- 3
Demonstrate
5 minutes.Model the problem-solving process out loud ("I Do"). Demonstrate not just how to find the right answer, but how to handle mistakes or unexpected roadblocks along the way.
- 4
Guided Practice
8–10 minutes.Work through 2–3 problems together as a class ("We Do"). Have students use whiteboards or talk through steps with a peer to build confidence without individual risk.
- 5
Individual Practice
10–15 minutes.Assign differentiated task sets ("You Do"). Offer tiered options:
- Tier 1 (Foundation): Core skill reinforcement with visual aids or concrete tools.
- Tier 2 (Standard): Standard grade-level application problems.
- Tier 3 (Extension): Open-ended reasoning and complex problem-solving.
- 6
Targeted Support & Challenge
Ongoing during practice.Circulate through the room to pull a small, flexible intervention group to the teacher's desk for scaffolded assistance, while advanced learners tackle high-ceiling extension problems independently.
- 7
Quick Assessment
3–5 minutes.Conclude with an exit ticket or reflection question ("Explain in one sentence how you solved Problem 2"). Use this quick check to plan tomorrow's entry point.
Final Takeaway for Maths Teachers
There is a wide range of mathematical thinkers in each classroom. The idea that children's brains are "not wired for math" is false, and hinders learning from the very start.The notion that children's brains are "not wired for math" is a falsehood that impedes learning from the outset. When they are not being taught in a way that corresponds to their prior knowledge, confidence or learning rate, they get stuck.
By avoiding the labeling of "visual" or "auditory" learners and proactively, and in a flexible way, introducing differentiated mathematics instruction, we can open the doors of mathematics success for ALL!
Teachers, using multi-sensory teaching methods, changing levels of challenge dynamically, monitoring progress through more than just test scores, and utilising structured approaches such as Abacus and Vedic Maths, can take a small step at a time towards developing mathematical confidence in all children.
The goal of IIVA is to provide teachers with effective and flexible instruction that will transform a heterogeneous classroom into a vibrant space for mathematical inquiry.
