The Simple Nearpoint Reference That Transformed My Student’s Math Confidence
- Susan Ardila
- Sep 1
- 11 min read
After 15 years of teaching math to neurodiverse learners, I thought I’d seen it all. My toolkit was bursting with research-backed strategies. I had my trusty manipulatives, my number lines, and my hot air balloon analogy that had never failed to make integer operations click.
So when 7th-grader Emma walked into our virtual session—dyscalculia, ADHD, several years behind in math—I was confident. This was going to be another success story.
Three weeks later, I was questioning everything I knew about math instruction.
If you’ve ever sat at the kitchen table watching your child cry over math homework, wondering if anything will ever click—you’re not alone. If you’ve tried every tutor, every app, every “proven” method only to watch your brilliant child shut down at the sight of numbers—I see you. I’ve sat in that helpless silence with countless families. And now, I was sitting in it with Emma.
Here’s the twist: sometimes the biggest breakthroughs don’t come from the shiny tools or the complicated strategies. They come from something so simple you almost miss it. In Emma’s case? Circles. Plain, hand-drawn circles on a sheet of paper. A nearpoint reference so basic most teachers would’ve tossed it aside. Yet those circles transformed not just her math skills, but her confidence, her focus, her belief in herself.
When Every “Proven” Strategy Falls Flat
Let me paint you a picture of those three weeks that nearly broke me.
I started with my hot air balloon analogy—the one that usually works like magic. “Positives make the balloon rise. Negatives make it sink.” Most kids light up at this visual. Emma stared at me like I was speaking another language.
So I pivoted. Thermometers. Number lines. Then open number lines for flexibility. Nothing.
Next up: two-color counters. Red for negatives. Yellow for positives. Zero pairs—the gold standard for teaching integer operations. Still nothing.
Fine. Virtual manipulatives then. Maybe digital interactivity would grab her ADHD brain. Nope.
I dug deep into metaphors. Different visuals. Different approaches. Finally, I stripped it down to the rules: “When the signs are the same, you add. When they’re different, you subtract.”
And yet—Nothing.Was.Working.
ADHD made it worse. Every lesson felt like pushing a boulder uphill. She’d fidget, glance away, lose track mid-problem. The more I tried, the more I saw it—the frustration building behind her eyes, that quiet belief whispering “I can’t do this.”
By week three, I wasn’t just doubting my methods. I was doubting myself. If I couldn’t help Emma, who could I help?
Here was this brilliant kid who could devour novels and solve puzzles most adults would struggle with—yet integers might as well have been written in hieroglyphics.
Sound familiar?
Maybe you’ve been there too—watching your smart, capable child slam into an invisible wall every time math shows up. You’ve bought the apps. Hired the tutors. Ordered the workbooks. And still, each day chips away at their confidence—and yours.
One mom once told me, “I started dreading 3 PM because I knew homework time was coming. I felt like I was failing her every single day.”
I knew exactly what she meant. It’s the same helplessness I felt staring at Emma’s blank face across the Zoom screen.
And parents, hear me: this is not your fault. And it’s not your child’s fault either.
When traditional methods don’t work, it doesn’t mean your child isn’t capable. It doesn’t mean you haven’t tried hard enough. It doesn’t mean they’re “just not a math person.”
It means the key is still out there. Sometimes, it’s not the complex, glittery tool we expect. Sometimes, it’s the simplest solution hiding in plain sight.
After three weeks of throwing everything in my arsenal at Emma’s integer struggles, I was left with a humbling truth:
Nothing. Was. Working.
What I didn’t know? The breakthrough was sitting just one algebra lesson away.
Sometimes the Answer Comes from an Unexpected Place
The breakthrough didn’t come during Emma’s session. It came with Jake, one of my high school algebra students.
Jake was brilliant but scattered—classic ADHD. He’d start strong, then halfway through a problem it was like his brain just… wandered off. He’d forget where he was, what came next, and the whole problem would unravel.
Sound familiar?
So I built him a tool. Not an app. Not a complicated chart. Just a plain checklist—a nearpoint reference he could touch and follow step by step:
First, distribute.
Then, combine like terms.
Then, isolate the variable.
Jake traced each step with his finger. And just like that, he wasn’t getting lost anymore. He had a roadmap.
That’s when it hit me.
Emma didn’t need another picture of integers. She didn’t need counters or number lines showing her what numbers looked like. She needed a pathway—a decision-making flow she could physically touch, follow, and own.
So I grabbed a sheet of paper and drew six circles. That was it.
A nearpoint reference so simple it almost felt silly. But it was exactly what her brain needed.
Here’s what we created together:
For Adding Integers
Circle 1: Look at the signs. Same or different?
If SAME → Follow the “S” path → ADD.
If DIFFERENT → Follow the “D” path → SUBTRACT.
Final circle: Who wins? (Same signs: keep the sign. Different signs: whichever sign there’s more of.)
For Subtracting Integers
Circle 1: ADD THE OPPOSITE (change subtraction to addition, flip the second number’s sign).
Then follow the same addition pathway.
Six hand-drawn circles. A flowchart Emma could touch with her finger.
And then the magic happened.
Emma touched the first circle: “Different signs, so I go to D.”
She touched the next: “D means subtract.”
Another circle: “More negatives, so my answer is negative.”
She worked through the entire problem—independently. No prompting. No reminders. No tears. Just Emma and her circles.
When she finished, she looked up at me with a smile so wide I still see it in my mind. “Wait—that’s it? I actually got it right?”
The relief in her voice still gives me chills.
And here’s the part that blew me away: all the manipulatives in the world couldn’t do what six little circles did. Not the research-backed two-color counters. Not the flashy virtual tools. Not even my beloved hot air balloon analogy that had worked for hundreds of other students.
Six. Hand-drawn. Circles.
Nothing polished. Nothing fancy. Just circles on paper. But it changed everything.
Why? Because Emma wasn’t passively looking at something I gave her. She was actively navigating a pathway her brain could understand. The circles gave her ADHD brain something concrete to focus on, gave her working memory a place to rest, and gave her confidence a foundation to stand on.
For the first time in weeks, Emma wasn’t drowning in the math. She was steering it.
It’s Not Magic — It’s Neuroscience
I know what you’re thinking: “Susan… circles? Really? How could something so simple work when all those research-backed tools didn’t?”
Here’s the thing: it’s not magic. It’s neuroscience.
Emma’s brain needed three things that traditional manipulatives couldn’t deliver—and her six little circles gave her all three.
1. Working Memory Support
Think about it. When you drive somewhere new, do you memorize every single turn before leaving the driveway? Of course not—you use GPS.
Emma’s circles worked the same way. Instead of cramming all the integer rules into her already overloaded working memory, she could offload that burden onto the flowchart. Her brain was finally free to focus on solving the math, not on remembering what came next.
2. Executive Function Support for ADHD
ADHD brains crave structure, but they also demand flexibility. Emma’s flowchart gave her both. The pathway was predictable (she always knew what circle came next), but she had to make an active decision at each step. No passive listening. No juggling multiple steps in her head. Just one circle. One decision. One success at a time.
3. Kinesthetic Input Through Embodied Learning
Here’s the secret sauce: Emma wasn’t just seeing the process—she was feeling it. Touching each circle anchored the learning in her body, giving her brain a sensory “hook” that a number line or counters simply couldn’t provide.
Think of it like GPS for the brain—one turn at a time instead of memorizing the whole map.
And here’s where most parents get tripped up: “But we tried visuals before, and they didn’t work.”
You’re right. You probably did try visuals. But here’s the difference:
A number line shows what integers look like.
Emma’s flowchart showed her how to think through integers.
Completely different cognitive demands.
And here’s the kicker: Emma could recreate this tool herself. Lost the paper? No problem. Six quick circles, and she had her pathway back in under a minute. That ownership—that ability to rebuild her own support—was where her confidence truly lived.
Here’s what the research (and real life) tell us happens when kids get tools like this:
Reduced cognitive load → less exhaustion, more energy for actual learning.
Increased independence → confidence grows faster than any sticker chart ever could.
Built-in self-regulation → kids learn to monitor their own thinking, a skill that carries far beyond math class.
Predictable success → the brain rewires itself. “I can’t do this” transforms into “I know how to figure this out.”
And let me be crystal clear: this isn’t about making math “easy.”
Emma’s flowchart didn’t water down the math. Integers didn’t magically become simple. What changed was her access. The work was still complex, but now she had a clear pathway through the complexity instead of getting lost inside it.
That’s the difference.
And that’s when everything shifted—not just for integers, but for Emma’s entire relationship with learning.
Customizing Support for Your Child’s Unique Brain
Emma’s flowchart was perfect for her. But here’s what most parents don’t realize: your child might need something completely different.
The magic wasn’t in those six circles. The magic was in understanding what Emma’s brain craved:
a clear decision tree,
tactile engagement,
and intentional language.
That’s the formula. But the application? That’s where creativity comes in.
For Visual Learners
Color becomes their compass. Maybe red circles signal “stop and think,” while green means “go ahead and solve.” Graphic organizers that map connections. Timelines that show steps in sequence. For these kids, the pathway has to be seen to be believed.
For Kinesthetic Learners
Think touch + movement. Some kids need to trace shapes, tap rhythms, or literally move pieces around as they work. Others thrive with textured “touch points” like Emma’s circles. The key is making the thinking process something they can physically interact with.
For Auditory Learners
Words matter. These students need chants, cues, or whispers they repeat to themselves. “Same signs add, different signs subtract” becomes a rhythm or song. The sound anchors the math.
For Executive Function Support
Structure is survival. Flowcharts and checklists aren’t just helpful—they’re lifelines. These kids need every step mapped out, with clear decision points and built-in “what if” branches for when they hit a snag.
And age matters too:
Elementary: Picture-based supports with simple language. Instead of “check the signs,” it might be “look for the happy face or sad face.” Big visuals. Lots of space.
Middle School: Ready for more independence. This is the perfect stage to involve them in designing their own nearpoint references—planting the seeds of self-advocacy.
High School: Now it’s about complex problem-solving. Nearpoint references evolve into formula decision trees, word-problem “detective pathways,” and even test-taking strategy guides.
And the applications? Endless.
Fractions → their own flowchart.
Multi-step equations → a checklist.
Word problems → a detective map for sorting clues from distractions.
Test strategies → visual reminders for pacing and anxiety management.
But here’s where the real transformation happens: when students learn to create their own nearpoint references.
Emma now designs her own flowcharts for every new math topic. She’s no longer waiting for someone to hand her the tool—she’s building the bridge herself.
She didn’t become confident because the work got easier. She became confident because she learned how to navigate complexity.
That’s the real magic. Not the circles. Not the charts. But the moment a child realizes: “I can create my own way through this.”
Is Your Child Struggling Despite Your Best Efforts?
You already know your child is brilliant. You’ve watched them master complex video games, build Lego creations with an engineer’s precision, or dive so deep into their favorite topic you can barely keep up.
So why does math feel like slamming into a brick wall?
If any of these sound familiar, your child may be sending a loud, clear signal that they need a different kind of support:
Steps vanish overnight. Yesterday they “had it.” Today it’s like they’ve never seen the concept before. You’re not imagining things—the process just won’t stick, no matter how many times you review it.
Math homework ends in tears. Not just frustration—real tears. The emotional reaction is bigger than the worksheet, and you can see their confidence cracking a little more each time.
Constant reminders. “What’s the next step?” becomes the soundtrack of homework time. No matter how patient you are, they just can’t internalize the sequence.
They shine everywhere else—except in math. Reading? Brilliant. Science? They light up. Art? Pure talent. But math? It’s like watching a different child—one who suddenly believes they’re “stupid.”
Accommodations aren’t enough. Extra time helps them finish, but it doesn’t help them understand. The IEP or 504 feels more like a band-aid than a solution.
Here’s what’s really happening: your child likely has dyscalculia or a related learning difference that changes the way their brain processes numbers.
And here’s the truth most educators won’t say out loud: “just practice more” is not the answer.
Practice without the right pathway doesn’t build mastery—it just reinforces confusion. It’s like asking someone to practice driving without ever giving them a map.
So if you’re nodding along to three or more of these signs, hear me clearly: your child isn’t struggling because they’re “not a math person.” They’re struggling because no one has shown them their math language yet.
The good news? Once they find it—like Emma found hers—everything changes.
And you don’t have to figure that language out alone.
Simple Steps to Transform Your Child’s Math Experience
Ready to create your own breakthrough moment? Here’s how to build a nearpoint reference that actually works for your child’s unique brain:
Step 1: Identify the decision points.
Where does your child get stuck? Remembering which operation to use? Deciding if the answer is positive or negative? Figuring out the order of steps? Pinpoint the exact friction points—specificity is everything.
Step 2: Map the pathway.
Break the thinking process into bite-sized decisions. Not the math steps—the thinking steps. “Do I add or subtract?” comes before “What’s 7 + (-3)?”
Step 3: Make it touchable.
This is the game-changer. Draw circles, squares, or arrows—whatever works. Your child needs something they can physically touch as they think through the process.
Step 4: Use intentional language.
Every word matters. “Add the opposite” works better than “change the sign and add” because it separates the actions into two crystal-clear steps. The right words create “aha” moments.
Step 5: Test for independence.
Can your child follow it without you hovering? Can they recreate it if they misplace it? If not, simplify until they can. Ownership is the goal.
What you need: paper and a marker. That’s it. (Index cards or sheet protectors if you want to get fancy.)
💡 Want to skip the trial and error? I’ve created a free Confidence Kit that includes Emma’s exact integer flowchart plus four other proven templates for different math concepts. These aren’t just worksheets—they’re confidence-building tools designed for kids who think differently.
👉 Download the free Confidence Kit here.
But remember—the real magic isn’t in my templates. It’s when your child learns to create their own. That’s when confidence explodes.
You Don’t Have to Figure This Out Alone
Here’s what I need you to know: if your child is struggling with math, it’s not because they’re lazy. It’s not because you haven’t tried hard enough. And it’s definitely not because they’re “just not a math person.”
I’ve seen too many brilliant kids convinced they’re “stupid” at math when really, they just needed someone who understood how their brain works.
After 15 years of experience and specialized training in multisensory math instruction, dyscalculia intervention, and educational therapy, here’s what I’ve learned: knowing which tool unlocks the door for each child is both an art and a science. It takes expertise to recognize when a student needs Emma’s tactile flowchart, another needs a visual organizer, and another thrives with auditory cues.
Parents—you shouldn’t have to become a cognitive scientist to help your child succeed. You shouldn’t spend every evening Googling “math strategies for ADHD” or second-guessing yourself.
That’s exactly where I come in.
Spending another school year watching your child’s confidence crumble isn’t an option. Not when there are tools that can turn everything around.
That free 20-minute consultation? It’s not just another meeting. It’s a chance to exhale. To sit across from someone who’s been exactly where you are—and knows the way out.
Together, we’ll identify your child’s unique math language and build a plan that works with their brilliant brain, not against it.
Because every child deserves to feel confident in math.
Even yours. Especially yours.
👩🏫 About the Author
Susan Ardila is a certified teacher, trained educational therapist, and the founder of MindBridge Math Mastery. With over 15 years of experience working with students who have dyscalculia, ADHD, and other learning differences, she specializes in turning math frustration into confidence through multisensory strategies and custom near-point references. Susan’s passion is helping every child discover that math is not only possible—but within their reach.
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