Why the CRA Math Approach Isn’t Working for Your Child—And What Educators Keep Getting Wrong
- Susan Ardila
- Jun 30
- 22 min read
Updated: Sep 12
Your Child's Math Tutor Is Doing CRA Wrong—And Why This Changes Everything
If your child’s math tutor is still making them “graduate” from manipulatives to worksheets, they’re stuck in 1990s thinking—and your child is paying the price.
The Shocking Truth About How Most Educators Butcher CRA
The Linear Lie That's Sabotaging Your Child's Math Understanding
Imagine this:Your daughter finally understands fractions using those colorful fraction circles. She’s building them, touching them, seeing how 1/2 + 1/4 actually works. Then her tutor smiles and says,
“Great! You don’t need these anymore. Let’s move to the worksheet.”
Two weeks later? She’s in tears, staring at 3/8 + 5/12, completely lost.
Sound familiar?
What just happened is one of the most common—and most damaging—mistakes in math education.Her tutor treated the CRA approach (Concrete–Representational–Abstract) like a ladder: climb it, then leave the lower rungs behind. But CRA was never meant to be linear. It’s not a staircase.
It’s a team. And it works best when all three parts are on the field at the same time.
“My son’s tutor said he had ‘outgrown’ base-ten blocks,” one frustrated mom told me.“Two weeks later, he was in tears over regrouping problems he’d been solving perfectly with the blocks.”
This isn’t just ineffective. It’s mathematically backwards.
Most educators—and yes, many well-meaning tutors—treat CRA like a sequence of developmental stages: first the blocks, then the drawings, finally the symbols. They’re essentially saying,
“Forget the tools that helped you understand. Now memorize the rules instead.”
But here’s the kicker: CRA approach math was never supposed to work this way.
The research is crystal clear—students who keep access to all three representations simultaneously don’t just perform better… they develop something far more powerful:
representational flexibility—the ability to choose the strategy or model that makes the most sense for them.
It’s what professional mathematicians do. And it’s exactly what most kids never get a chance to learn.
Meanwhile, walk into a classroom—or tutoring session—and what do you see?
Manipulatives stashed away the moment a student can write an equation. Tutors proudly announcing:
“You’re too old for blocks now.”
“Real math doesn’t use pictures.”
“Smart kids should be able to do this in their heads.”
This approach is sabotaging your child’s math understanding—and it’s happening in plain sight.
The tragic irony?
These educators think they’re helping. They believe they’re advancing students toward “real” math.Instead, they’re creating the very math anxiety, confusion, and memorization traps they’re trying to prevent.
Because when you strip away the concrete connections that made the concept click, all that’s left is a sea of meaningless symbols.
No wonder so many kids think math is just a random set of rules to memorize.
CRA isn’t the problem. The way it’s taught is.
What CRA Actually Is (And Why Bruner Would Be Rolling in His Grave)
The Constructivist Framework They're Ignoring
Here’s what most educators don’t realize:
Jerome Bruner—the cognitive psychologist who inspired the CRA approach—never intended his three modes of representation to be used in sequence and abandoned.
Let me say that louder for the tutors in the back:
Never.
Bruner’s original framework described three ways humans naturally process information:
Enactive – learning through action, touch, and movement
Iconic – learning through images and visual models
Symbolic – learning through language and abstract symbols
Now, notice what’s not there?
Any mention of “graduating” from one mode to the next.
Bruner understood what too many modern educators have forgotten:
These modes are meant to coexist, not compete.
They’re interdependent tools that students should use fluidly—not stepping stones to toss aside once they've “leveled up.”
Think of CRA not as a staircase to climb, but as a three-lane highway.
Students need the flexibility to switch lanes depending on what helps them reach understanding the fastest—and safest.
Let’s be real:
When a professional mathematician is working through a problem, do they stop using visuals just because they know how to write equations?
Of course not. They sketch. They model. They visualize. And yes, they write symbols. Often all within the same session.
They don’t limit themselves to one mode—they use whatever representation best serves the math.
So why are we teaching kids that using manipulatives is somehow “less than” working abstractly?
Why are we acting like real understanding has an expiration date?
The answer reveals a fundamental misunderstanding of how mathematical thinking actually works.
At the heart of effective math instruction—especially for neurodivergent learners—is constructivist learning theory.
This theory tells us students don’t just absorb math like a sponge. They construct understanding by making connections between what they can touch, see, and symbolize.
This is especially critical for students with learning differences like dyscalculia—something I dive into more deeply in this blog about what dyscalculia really looks like and how to support it.
When we force them to abandon the concrete and visual representations that helped it all make sense, we’re asking them to do the academic equivalent of this:
Tear down the foundation while they’re still building the house.
And here’s what the research actually shows:
🔬 The Evidence Behind Integrated CRA
🧠 Neuroscience Research:
When students encode math concepts through multiple sensory channels simultaneously, the brain forms stronger, more durable neural pathways. These connections are more easily retrieved, especially under stress.
🌍 International Comparisons:
High-performing countries don’t treat manipulatives like training wheels—they use concrete and visual models throughout both elementary and secondary education. They don’t rush to abstract instruction. They build understanding deeply and keep the tools that support it.
🎯 Special Education Research:
Students with learning disabilities—including dyscalculia, ADHD, and autism—consistently perform better when they retain access to manipulatives and visual supports, even well beyond early instruction.
The conclusion is clear:Integrated CRA isn't just more effective—it's how mathematical thinking naturally develops.
And yet, we’ve somehow built an educational culture that treats moving away from hands-on models as “progress” and sticking with them as “remedial.”
That’s not just outdated.
It’s backwards—and it’s hurting kids.
The Research That Proves Integration Beats Isolation
What Happens When Students See the Whole Picture
We’ve made the case. Now let’s back it up.
The last few decades of educational and cognitive research don’t just support integrated CRA—they make a crystal-clear case that it’s essential.
Study after study confirms what we’ve seen firsthand at MindBridge Math Mastery:
Students who learn using all three representations at once—not one at a time—don’t just perform better. They become confident, capable mathematical thinkers.
🧠 The Neuroscience Is Crystal Clear
When students engage multiple sensory pathways simultaneously—touching manipulatives, seeing visual models, and hearing or verbalizing mathematical language—their brains form stronger, more durable neural connections.
A landmark cognitive neuroscience study found that multisensory instruction creates redundant neural pathways.
Translation? If one route gets blocked (hello, test anxiety), the brain has backup routes to retrieve the same concept.
This is especially critical for neurodivergent learners.
Students with ADHD, autism, or dyscalculia process information differently.Integrated CRA offers multiple access points—not one "right" way to learn math, but their way.
🌍 International Evidence: What High-Performing Countries Do Differently
Let’s zoom out.
In countries like Singapore, Finland, and Japan—nations consistently leading the world in math performance—students continue using concrete models and visuals well into secondary school.
They don’t view manipulatives as “training wheels” or rush to abstraction.
Instead, they use hands-on tools to build such a deep, intuitive understanding that when students eventually solve problems abstractly, they can still see what the symbols mean.
Meanwhile, here in the U.S., we pack away base-ten blocks in second grade—then wonder why kids are still shaky on place value by middle school.
🎯 The Special Education Research That Changes Everything
Now let’s get personal.
For students with math learning disabilities, integrated CRA isn’t just helpful—it’s transformative.
Multiple studies on dyscalculia tutoring methods show a consistent pattern:When students continue using concrete tools alongside visuals and symbols, they don’t just improve… they often surpass peers taught using traditional, linear approaches.
One powerful longitudinal study found that students with math learning disabilities who received integrated CRA instruction saw:
✅ 67% greater gains in problem-solving skills
✅ 45% reduction in math anxiety
✅ Lasting retention even after instruction ended
And students in the sequential CRA group?Their progress plateaued after just six months.
📊 The Meta-Analysis That Should End the Debate
A comprehensive meta-analysis of 47 studies on CRA instruction confirmed the trend:
“Students benefit most when concrete, representational, and abstract modes are presented simultaneously rather than sequentially, allowing learners to make explicit connections between representations.”
In other words, the most effective math instruction teaches students to see the throughline—how blocks, pictures, and equations all show the same mathematical idea.
This is how they develop representational flexibility:The ability to choose the best tool, strategy, or model for the task at hand.
Not just for tests. For life.
🔍 What This Means for Your Child
If your child is getting specialized math tutoring, dyscalculia support, or help with math anxiety, this research matters more than ever.
They shouldn’t be:
Told they’ve “outgrown” manipulatives
Rushed into procedures they don’t understand
Memorizing rules they can’t explain
They should be:
Building a flexible, personalized math toolkit
Seeing how visual models connect to equations
Feeling empowered to use the strategies that make sense to them
Because CRA works best when it works together.And anything less? Isn’t just outdated—it’s educational malpractice.
The Hidden Cost of Linear CRA
What’s Really Happening to Your Child
Here’s the heartbreaking reality I witness in my tutoring sessions every single week:
Bright, capable kids—kids with so much potential—reduced to rule-followers.
Students who can recite steps like robots but have no idea why those steps work.
Children who once loved learning, now frozen by panic at the sight of a word problem.
And the cause?In far too many cases, it’s the same educational crime:
Severing the connection between concrete understanding and abstract symbols.
🔄 The Fragmentation Problem
When educators rush students through the linear CRA sequence, they create what I call mathematical amnesia—a sudden and disorienting loss of meaning.
Here’s how it usually plays out:
Weeks 1–3: Your child is thriving. Fractions finally make sense. They’re combining colorful pie pieces, seeing how 1/2 + 1/4 = 3/4 right in front of them.
Week 4: The manipulatives are packed away. “You don’t need these anymore—we’re ready for numbers.”
Week 6: Your child stares blankly at 3/8 + 5/12, completely lost. The connection between the symbols and their meaning? Gone.
Month 2: The story shifts: “I’m just not a math person.”
This isn’t a learning disability.
This is an instructional disability.
🌐 The Real-World Disconnect
When we strip away the tools that made math meaningful, we turn it into a foreign language—one with no translation guide.
Before Integrated CRA:
Fraction division = “flip and multiply” (a rule with no logic)
Area = “length times width” (memorized, not understood)
Negative numbers = “two negatives make a positive” (math-as-magic)
After Integrated CRA Math Approach:
Fraction division = “How many one-thirds fit in 2 wholes?” (visual, grounded, clear)
Area = “How many unit squares fit in this rectangle?” (buildable, spatial, real)
Negative numbers = movement on a number line (intuitive, connected)
One approach creates rule-followers.
The other creates mathematical thinkers.
⚠️ The Anxiety Spiral
When students lose access to the tools that once helped them understand, here’s what I often see:
Confusion → “I don’t get this anymore.”Self-doubt → “Maybe I’m not smart enough.”Avoidance → “I hate math.”Panic → Physical symptoms during math timeShutdown → “I can’t do this.”
I’ve seen this spiral dismantle confident learners in a matter of weeks.
And the worst part?
It’s completely preventable.
This disconnect can also lead to math anxiety and shutdowns—especially for neurodiverse students. I explore that emotional impact more deeply in this blog about how math anxiety shows up and how to ease it.
🧠 The Neurodivergent Impact
For students with dyscalculia, ADHD, or autism, the stakes are even higher.
These learners often depend on concrete and visual supports to organize and process mathematical information. When those supports are pulled away prematurely, it’s not just confusing—it can feel like cognitive whiplash.
As one of my ADHD students put it:“When you took away the blocks, it felt like someone turned off the lights in my brain.”
That’s not dramatic—it’s neurologically accurate.
Students with executive function challenges need external structures to think clearly.
Students with processing differences need multiple ways in.
Students with attention differences need multisensory input to stay engaged.
And yet, linear CRA removes all of that—right when they need it most.
⏳ The Long-Term Cost
The damage doesn’t stop in elementary school. It compounds over time.
Students who never develop deep conceptual understanding eventually struggle with:
Algebra – because they never truly understood how numbers work
Geometry – because shapes were never connected to spatial reasoning
Statistics – because quantities never held real meaning
Advanced math – because the entire structure was built on a hollow foundation
This isn’t just about second grade anymore. This is about your child’s confidence, capability, and future opportunities.
💡 A Different Story
But here’s what happens when we do it right.
Last month, I watched a 7th grader with dyscalculia solve a multi-step algebraic equation—on her own.
She started with algebra tiles. Then drew a model. Then wrote symbolic steps. Then circled back to the tiles to check her work.
Her mom turned to me, stunned:
“She’s never been this confident in math.”
That’s what happens when students aren’t forced to abandon what works.
That’s what happens when CRA isn’t treated like a staircase—but like a team.
They don’t just gain procedural fluency.They gain something far more valuable:
Mathematical courage.
The MindBridge Method: CRA as a Dynamic Team
How I Do It Differently (And Why It Works)
At MindBridge Math Mastery, I don’t just talk about integrated CRA—
I live it.
Every session. Every concept. Every breakthrough happens because I treat concrete, representational, and abstract not as separate steps, but as three lenses through which we understand the same mathematical truth.
🔧 What Integrated CRA Actually Looks Like
Let me paint you a picture of a typical session.
Sarah, a 6th grader with ADHD, is learning how to solve equations.But instead of the tired, step-by-step “manipulatives first, then worksheets” approach, here’s what her lesson looks like:
Minute 1: She builds the equation 2x + 3 = 11 using algebra tiles—physically placing two variable tiles and three units on one side, eleven units on the other.
Minute 2: While her hands are still on the tiles, she draws what she’s building in her notebook—rectangles for variables, squares for units.
Minute 3: As she manipulates the tiles to isolate the variable, she writes each step symbolically: Subtract 3 from both sides: 2x = 8
Minute 4: She checks her answer by substituting back into the original equation and by rebuilding it with tiles.
The result?
Sarah doesn’t just know that x = 4.
She understands why.She can explain it, visualize it, and verify it—with confidence.
And more importantly?She trusts herself to solve the next equation—because she has multiple ways to check her thinking.
This kind of multisensory math instruction is the cornerstone of how I teach—and I explain exactly why it works in this post.
🧰 The “Mathematical Toolkit” Approach
Here’s what makes my method different:
Manipulatives never disappear.
Every student has consistent access to what I call their mathematical toolkit—concrete materials, visual models, and symbolic representations working together in every session.
It’s not because they “need” the blocks.
It’s because mathematical thinking is richer when students have choices.
Professional mathematicians use graphs, symbols, drawings, models—whatever gets the job done.Why shouldn’t kids?
💡 Real Results from Real Students
The transformation? It’s often dramatic.
Emma (age 10, dyscalculia)
After two years of traditional instruction, she still couldn’t grasp place value.After six weeks of integrated CRA? She was confidently comparing decimals—and could explain why 0.3 is greater than 0.25 using base-ten blocks, number lines, and symbols.
Marcus (age 13, ADHD)
Fraction panic was his default. He’d shut down at the sight of a numerator.With multisensory fraction strips, visuals, and symbolic work layered together, he went from math meltdowns to “I’ve got this” in just eight sessions.
Zoe (age 8, gifted with autism)
She was bored with worksheets but couldn’t explain her thinking.Integrated CRA gave her the tools and language to articulate her ideas—and her problem-solving score jumped 30 points.
🧠 The Neurodivergent Advantage
Here’s what most educators miss:
Neurodivergent learners aren’t broken versions of neurotypical learners.They’re different kinds of thinkers who need different kinds of bridges.
My approach honors that difference:
🌀 ADHD brains crave movement and variety—so they get kinesthetic work alongside visuals and symbols.
🧩 Autistic thinkers often thrive with patterns and logic—so they see how models and equations connect.
🔢 Dyscalculic students need number sense built from the ground up—so they get multiple sensory pathways to access meaning.
🎓 Twice-exceptional learners crave complexity but need scaffolding—so they get both challenge and support, in every session.
Integrated CRA isn’t just effective for neurodivergent learners—
It was made for them.
🔁 The Session Structure That Changes Everything
Every MindBridge session follows what I call the “Triple Exposure” method:
Introduce concepts through all three modes—concrete, visual, symbolic
Practice by moving fluidly between them
Assess understanding across formats—not just with equations
Let’s say we’re working on fraction addition:
🍕 Students combine fraction pieces (concrete)
✏️ Draw pictures of their combinations (representational)
🧮 Write the equations (abstract)
💬 Talk through how they’re connected
It’s not three activities. It’s one experience that makes the math real, not just memorizable.
🔍 Why This Works (The Science Behind the Method)
My approach isn’t just intuitive—it’s backed by decades of research:
Cognitive Load Theory → Presenting ideas across multiple channels reduces overwhelm and improves connection-making
Transfer Theory → Students are more likely to apply what they’ve learned in new situations when they’ve seen it in multiple formats
Self-Efficacy Research → When students have tools they trust, they’re more likely to believe they can solve problems on their own
In other words:
When students feel empowered, they perform better. Period.
❤️ The Parent Difference
Here’s what parents tell me again and again:
“For the first time, my daughter can explain why her answer is right—not just how she got it.”“My son actually wants to do his math homework now.”“The meltdowns stopped. Math isn’t scary anymore—because she knows she has tools.”
That’s the power of true integrated CRA.
When students aren’t forced to abandon what works...When they can think visually, symbolically, and physically all at once...
They walk away not just knowing the steps—but knowing they can figure it out. That’s confidence. That’s ownership. That’s what sticks.
Red Flags: How to Spot If Your Child’s Math Support Is Stuck in the Past
The Warning Signs Every Parent Should Know
You're paying good money for your child’s math support.
You deserve to know whether you're getting research-backed instruction—or 1990s methods in a modern disguise.
Let’s break it down.
🚩 Red Flag num 1: The “Graduation” Mentality
What you hear:
“Great! You don’t need manipulatives anymore.”
“You’re too old for blocks now.”
“Real math doesn’t use pictures.”
“Smart kids should be able to do this in their heads.”
What it really means:
Your child’s tutor sees concrete materials as training wheels to be removed—not tools for understanding.
The truth?
Professional mathematicians use visual models, physical tools, and symbols interchangeably.Your child should be allowed to do the same.
🚩 Red Flag num 2: Procedure Over Understanding
What you see:
Your child can follow steps but can’t explain why they work
They panic when problems are slightly different
They’ve memorized rules like “flip and multiply” but don’t know what division means
They succeed on homework—but bomb the test
What this reveals:
Linear CRA creates rule followers—not mathematical thinkers.
🚩 Red Flag num 3: The Manipulative Shame Game
What happens:
Manipulatives are only brought out for “struggling” kids
Your child feels embarrassed to ask for tools
Hands-on materials are framed as a “crutch” instead of a valid strategy
Advanced learners are discouraged from using visuals
Why it matters:This creates a toxic hierarchy where abstract = smart and concrete = remedial.
That’s not just outdated. It’s emotionally harmful.
🚩 Red Flag num 4: One-Size-Fits-All Progression
What you notice:
Every student moves through CRA at the same pace
No accommodations for different learning needs
Dyscalculic students rushed into abstraction
ADHD learners expected to sit still and stay focused without support
Autistic students not given time to notice and process patterns
What’s missing:
Recognition that different brains need different bridges.
🚩 Red Flag num 5: Math Anxiety Ignored or Dismissed
Warning signs:
“Just practice more” is the only advice given
Meltdowns are dismissed as “drama”
No strategies to manage anxiety
All the focus is on getting correct answers—not building confidence
The truth:
Math anxiety is often the result of instruction that disconnects meaning from procedure.
Integrated CRA prevents this by keeping understanding front and center.
🚩 Red Flag num 6: Assessment Mismatch
What happens:
Students are only assessed on abstract work
No credit for correct reasoning with the “wrong” answer
Visual models and hands-on solutions are undervalued
One right way = the only way
Why it’s a problem:
This contradicts everything we know about how math understanding develops.
And it penalizes students for thinking differently—even when their thinking is correct.
✅ Green Flags: What High-Quality Integrated CRA Math Approach Looks Like
Here’s what effective, research-aligned math support actually looks like:
Manipulatives are available in every session—not just at the beginning
Students are encouraged to explain their thinking across representations
Confidence builds alongside skills
Tools are normalized—not stigmatized
Sessions adapt to your child’s learning profile
Math anxiety is addressed within instruction—not treated as a separate issue
❓Questions to Ask Your Child’s Tutor
Not sure where your tutor stands? These questions will tell you everything:
“Will my child always have access to manipulatives, or do you ‘graduate’ them away?”
✅ Green flag answer: “Students always have access to tools. We want them to choose what supports their thinking best.”
“How do you help students see connections between manipulatives, pictures, and symbols?”
✅ Green flag answer: “We use all three simultaneously so students understand they’re just different ways to show the same concept.”
“What if my child still prefers using manipulatives on ‘advanced’ topics?”
✅ Green flag answer: “That shows mathematical maturity. Using tools strategically is what real mathematicians do.”
“How do you support students with math anxiety?”
✅ Green flag answer: “We prevent anxiety by keeping meaning connected to procedures. When students understand why something works, they stop feeling afraid of it.”
🧭 The Bottom Line
Your child deserves instruction that honors how their brain actually learns.
If their current support is showing red flags, it’s not your child who needs to change—it’s the approach.
You have every right to ask for better.
And if you’re not getting it?
It might be time to find someone who understands that CRA isn’t a ladder to climb—it’s a toolkit to master.
The Neurodivergent Advantage
Why This Matters Even More for Your Child
Here’s something most educators still don’t understand:
Your neurodivergent child isn’t a broken version of a neurotypical learner.
They’re a different kind of mathematical thinker—and they need different kinds of bridges to understanding.
And when those bridges are built correctly?They don’t just catch up.
They often soar past their peers.
💥 The ADHD Mathematical Mind
Students with ADHD are often labeled “distractible” or “impulsive” in math class.But here’s what I see in my sessions:
ADHD brains are pattern-seeking, connection-making, big-picture thinkers.
They need movement, variety, and multisensory input to stay engaged.Linear CRA—where the end goal is stillness and abstraction—is like asking a race car to drive in first gear.
Take Marcus.
His previous tutor removed all manipulatives because they were “too distracting.” He was told he had math processing issues.
But within three sessions of integrated CRA, Marcus was confidently solving multi-step equations. Why?
Because he could:
Move algebra tiles while thinking (kinesthetic input)
See the patterns in his drawings (spatial processing)
Talk through his reasoning out loud (auditory processing)
Record each step symbolically (abstract reasoning)
His brain wasn’t broken.His instruction was.
🧠 The Dyscalculic Advantage
Students with dyscalculia often struggle with number sense—but many have exceptional strengths in spatial reasoning, pattern recognition, and creative problem-solving.
Traditional instruction strips away those strengths.
Linear CRA forces them into symbols too soon—before they’ve built a meaningful foundation.
Emma had been in traditional math support for two years with minimal progress. Her parents were told she “just wasn’t a math person.”
But with integrated CRA, everything changed.
Her visual-spatial strengths became her superpowers. She could:
Visualize fraction relationships using area models
Spot geometric patterns that unlocked algebra
Use her strong visual memory to connect hands-on experiences with abstract symbols
The key? I never took her tools away.
I built on her strengths while supporting her challenges.
🔍 The Autistic Mathematical Brain
Autistic learners often think in systems, patterns, and logical sequences.They crave understanding the why behind math—not just the how.
Linear CRA’s “just memorize the rule” approach is painful for brains wired to seek logic.
Zoe was gifted in math, but struggled to express her thinking.
Traditional instruction focused on fast, correct answers. She was frustrated and misunderstood.
With integrated CRA, she was able to:
Build and test mathematical theories using manipulatives
Create detailed visual models to represent her logic
Develop the language to explain her insights
See and celebrate the patterns that connect math concepts
Her autism wasn’t a barrier.
It was her pathway to mathematical brilliance.
🎓 The Twice-Exceptional Learner
These are the students who are both gifted and have learning differences.And they’re often the most underserved.
They’re too advanced for remediation—but still need support for how they process information.
Linear CRA fails them entirely, because it assumes everyone learns the same way.
Jake, for example, was doing calculus in his head—but couldn’t show his work due to dyslexia and ADHD.His school wanted to place him in remedial math.
But with integrated CRA, he finally had:
Concrete models to externalize his abstract thinking
Visuals to organize his complex ideas
Multiple formats to demonstrate his understanding
Tools to communicate what had previously stayed locked in his head
He didn’t need less challenge.
He needed more support.
🧬 The Research That Changes Everything
Study after study confirms what I see in practice:
🧠 Neuroscience: Many neurodivergent learners have heightened abilities in spatial reasoning, creative problem-solving, and pattern recognition—all of which are developed through integrated CRA.
📊 Educational Research: Students with learning differences show 67% greater improvement when they maintain access to multisensory supports.
🎯 Long-Term Studies: Neurodivergent students who receive integrated CRA often exceed grade-level expectations within two years—and retain those gains.
💔 The Emotional Truth
But beyond the data, here’s what truly matters:
Your child’s brain isn’t broken. Their instruction might be.
When instruction honors the way neurodivergent minds actually work—when the right supports are built in, not bolted on—something beautiful happens.
They don’t just learn math.
They fall in love with their own thinking.
🧠 What This Means for Your Family
If your neurodivergent child is struggling with math, ask yourself:
Are they being rushed through concrete learning toward abstraction?
Are their strengths being recognized—or ignored?
Do they have access to the sensory supports their brain needs to learn?
Is the instruction working with their brain—or against it?
The right approach doesn’t just build math skills.
It changes how your child sees themselves as a learner.
🔁 The MindBridge Difference
At MindBridge Math Mastery, I don’t see neurodivergence as something to overcome.
I see it as a different kind of mathematical brilliance—one that simply needs the right environment to thrive.
Every session is designed around your child’s unique neurological profile, learning strengths, and support needs.
Because when the bridges are built the right way?Neurodivergent learners don’t just succeed in math.
They redefine what it means to be a mathematical thinker.
Your child’s different brain isn’t the problem.
It might just be the solution.
Making the Switch: What the Integrated CRA Math Approach Looks Like in Practice
From Fragmented to Fluid: A New Way Forward
You’ve seen the research. You’ve spotted the red flags. You understand why your child’s math success depends on getting CRA right.
So now what?
🔎 What to Look for in a Quality Integrated CRA Session
In a truly integrated CRA tutoring session, you should see:
Manipulatives available from start to finish—not packed away after an “intro lesson”
Fluid movement between concrete, visual, and symbolic work within the same problem
Clear, explicit connections: “See how these three tiles represent the number 3 in the equation?”
Multiple solution pathways encouraged—not just one “right” way
Your child explaining their thinking using the mode that makes the most sense to them
Confidence growing alongside skills
You should also start to notice real change in your child’s thinking and attitude:
They can tell you why their answer makes sense—not just how they got it
Math anxiety fades; curiosity takes its place
Strategies learned in one area start transferring to others
They begin advocating for themselves: “Can I use the tiles?” or “Let me draw this out first.”
They approach unfamiliar problems with calm—not panic
❓Questions to Ask Any Potential Tutor
You’re allowed to ask hard questions—because you’re your child’s best advocate.
Here’s what to ask when considering math support:
“How do you introduce a concept like fraction multiplication?”
🚩 Red flag: “First we use manipulatives, then pictures, then move to the algorithm.”
✅ Green flag: “I teach all three modes together—hands-on tools, visuals, and equations—so the student sees how they’re all connected.”
“What if my middle schooler still prefers using manipulatives for algebra?”
🚩 Red flag: “By that age, they should be working abstractly.”
✅ Green flag: “Many of my most successful students use algebra tiles to deepen their understanding. I encourage strategic tool use at every level.”
“How do you support students with learning differences?”
🚩 Red flag: “We slow down and give more practice.”
✅ Green flag: “I tailor instruction to their profile and provide multiple ways in. Their neurodivergent thinking often leads to incredible mathematical insight.”
🏫 Advocating at School
If your child’s teacher doesn’t use integrated CRA, that doesn’t mean you’re out of options. Here’s how to open the conversation:
📧 Email template:
“Hi [Teacher’s Name], I’ve been learning more about CRA instruction and was wondering if we could talk about how [Child’s Name] might benefit from continued access to manipulatives alongside symbolic work. I’d love to share a few resources that explain how this approach can support learners with [learning profile]. Could we schedule a quick meeting?”
📋 Bring to the conversation:
This blog post (seriously—share it!)
A few examples of how your child learns best
Key research or observations from tutoring
A collaborative attitude: “How can we support them together?”
🏠 Supporting CRA at Home
You don’t need to be a math teacher to reinforce CRA principles:
Keep tools like base-ten blocks, fraction strips, and algebra tiles accessible
Ask process questions: “Can you show me that with a drawing?”
Celebrate multiple strategies: “I love that you checked it with blocks!”
Normalize using tools: “Engineers sketch diagrams. Smart people use what works.”
🚨 When to Make the Switch
If your child is:
Memorizing steps but can’t explain them
Becoming more anxious with every math assignment
Saying, “I’m just not a math person”Don’t wait.
Every day of fragmented instruction deepens those cracks.
It’s not too late—but rebuilding takes the right foundation.
The MindBridge Math Mastery Difference
At MindBridge Math Mastery, integrated CRA isn’t just a method.
It’s the mission.
Every session is personalized to your child’s learning profile, using multisensory, research-backed, and brain-aligned strategies that help math finally make sense.
I don’t “graduate” students away from tools.I help them build a toolkit that grows with them—even into advanced math.
And the results?
My students don’t just improve their grades.
They transform their relationship with math.
🎯 Your Next Step
Ready to see what integrated CRA can do for your child?
📞 Book a free consultation to:
Assess your child’s math understanding across all three CRA modes
Identify gaps caused by linear instruction
Create a personalized plan that builds on their strengths
Show you exactly what integrated CRA looks like in action
Because your child deserves instruction that actually honors how they learn.
👉 Book Your Free Consultation Now
✅ The Bottom Line
CRA isn’t broken.
The way it’s being implemented is.
Your child shouldn’t have to choose between understanding and achievement…Between tools and abstract thinking…Between neurodivergence and success.
They need instruction that sees these things as partners—not problems.
They need bridges, not barriers.
They need CRA that works.
And they need it now.
Ms, Susan, M.Ed. is a Certified Teacher, Educational Therapist, and founder of MindBridge Math Mastery, where she helps students—from struggling learners to gifted thinkers—actually understand math, not just memorize it. With over a decade of experience and a fierce passion for neurodiverse learners, Susan specializes in using integrated, multisensory methods like CRA the right way. When she’s not transforming math anxiety into math confidence, you’ll find her listening to her husband play guitar or happily nerding out over curriculum design.
References
Edutopia. (2024, March 5). Using the CRA Framework in Elementary Math. Edutopia.
Third Space Learning. (2025, March 31). Concrete Representational Abstract: What It Is And How To Use It.
Witzel, B. S. (2005). Using CRA to Teach Algebra to Students with Math Difficulties in Middle School. Learning Disabilities: A Contemporary Journal, 3(2), 49–60.
Accelerate Learning. (2025, January 1). Constructivist Teaching.
Khan, S. A. (2021). Concrete-Representational-Abstract and Multisensory Strategies: An Inclusive Approach to Mathematics. Asia Pacific Journal of Developmental Differences, 8(2).
Pennsylvania Training and Technical Assistance Network (PaTTAN). (2017). Concrete-Representational-Abstract: Instructional Sequence for Math.
PMC (PubMed Central). (2023, February 17). Using the concrete–representational–abstract sequence to teach mathematics.
Biswal, K., et al. (2020). Efficacy of Concrete Representational Abstract Approach in Early Mathematics Education.
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