The Pedagogy-First Mindset

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As a Tech TOSA, teachers often come to me when they have a spark of an idea and need the right tool to bring it to life. Sometimes, they just need a reliable replacement for a tool they loved, like finding a new home for video discussions after Flip changed. My role isn’t to audit what’s in their “digital closet,” but to offer support and guidance as we navigate the “energy” of our classrooms together.

With the growing conversation around screen-time limits in districts like LA Unified, we have to be honest about what that energy looks like. When we stand side-by-side in a classroom where students are on a mandate for 90 minutes of adaptive software each week (45 minutes for math and 45 minutes for ELA), the room is often stagnant. It’s quiet, but is it the silence of deep thought or the silence of digital compliance?

The person who is doing the work is doing the learning.

The “Work” Litmus Test

I have a quote I live by in my own classroom: “The person who is doing the work is doing the learning.”

When we look at tech tools, the question isn’t “is this high-tech?” but “who is doing the heavy lifting?”

  • Compliance Tech: The software handles the logic and sorts the levels. The student is a passenger.
  • Creation Tech: Tools like Canva or Snorkl (which now hosts MathReps!) require students to be the drivers. In Snorkl, there is no passive learning; the student must articulate their thinking and record their process. That is the kind of “work” that leads to true learning.

The “Fluff” Tax vs. The Power of Fun

We all need to break the monotony sometimes. A fast-moving game like 99math or Wayground can be a fantastic way to build the fluency and basic facts students need before they can perform complex math. That “sprint” of excitement is a bridge to the next level of mastery.

The “fluff” tax happens when the game mechanics (like 20 minutes of boss battles in Prodigy) take up more brain space than the actual math. If the stimulation is a barrier to the standard rather than a bridge, it’s worth asking if it’s truly propelling them forward.

Making the Most of Mandated Minutes

We know the reality: many districts mandate 90 minutes a week for math and reading software. As a coach, I’m not there to push back on district policy, but to support teachers in navigating it. When I stand side-by-side with a teacher in a “stagnant” room, I like to ask four gentle, clarifying questions:

  1. Is the tool giving accurate information? Does the data on the screen reflect the growth (or struggle) you are seeing in the classroom?
  2. How do you know they are learning the material? If we closed the laptop right now, could they explain the “why”?
  3. Is this propelling them forward? Is this tool helping them master a Priority Standard, or just helping them finish a level?
  4. Who is doing the thinking?

Everyone will have a different take on it, and that’s okay. Some tools work better for some than others.

Final Thought

The goal of looking at pedagogy first isn’t to add a burden to the teacher. It’s to ensure that when we do use screens, whether it’s for a mandated block or a creative EduProtocol, the tech is helping them think, not just helping them finish.

Join the Conversation

How do you balance the “stagnant” mandated minutes with the “energetic buzz” of creation-based learning? Have you found a tool that actually reflects the growth you see in your small groups? Let’s talk about it in the comments.

Embracing Vulnerability in Math Education

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There is a heavy myth in education that once we step into the classroom, we are supposed to be the “Expert in the Room.” For many elementary teachers, this is especially daunting in math. Many don’t see themselves as “math people” and might even joke about it to cover up a deeper insecurity regarding the conceptual methods we use today.

It is terrifying to feel you have to teach something you don’t fully understand. But after years, I’ve realized something: The most powerful words you can say to a student are “I don’t know. Let’s find out”.

Modeling the Struggle

When we admit we don’t know something in the classroom, we are being instructionally agile. Admitting the struggle allows students to be vulnerable themselves. If they see that their teacher has to work at things, it gives them the silent permission to be okay with the struggle, too.

I’m not advocating for being unprepared. But when a student makes an observation you hadn’t thought of, saying, “I don’t know, let’s check it out,” or “Tell me more,” allows the students to become owners of the learning process and cultivates critical thinking. It turns math from a performance into a side-by-side discovery.

Confessions of a Coach

I’ve found that the most effective support I can offer teachers isn’t when I show up with all the answers, it’s when I model that I’m still a learner, too. For a long time, the area model for division was my personal “wall.” I understood the theory, but the mechanics just wouldn’t stick.

Instead of hiding that, I approached a 4th-grade teacher who was a master of the method and asked if I could come in, watch her, and record her lesson so I could watch it until it finally clicked.

Breaking the “Math Person” Trap

When I share this story with teachers who are hesitant to try a new method, the energy shifts. They see that:

  • The Struggle is Universal: If a coach has to “rep” a 4th-grade standard multiple times to learn it, it’s okay if they do, too.
  • The Method is a Conversation: By asking a colleague for help, I turned our relationship into a partnership. I wasn’t a coach; I was a learner benefiting from her expertise.
  • Persistence Pays Off: Just like we tell students that the Mastery Loop requires repetition, we need to give ourselves the same grace to grow.

The standard is the goal, but the method is the conversation.

Creating Space for “Cultural Wealth”

When we step aside as the “source of all knowledge,” we create space for students to be the teachers. I remember a year we were learning division, and a student showed the class a method her immigrant parents had taught her. We celebrated that. We all learned something new because we were open to the idea that there isn’t just one “right” way to get to the answer.

The standard is the goal, but the method is the conversation. By signing our own “permission slip” to not know everything, we empower every student in the room to finally feel like a “Math Person”.

Join the Conversation

When was the last time a student, or a colleague, taught you something in the middle of a math lesson? How did that shift the energy in your room? Let’s talk about the power of being the “Lead Learner” in the comments.

The MathReps Manifesto: Ending the “Rent-a-Concept” Cycle in Math

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For years, I followed the “Trimester Trap.”

In Trimester 1, we did the heavy lifting: number sense, multiplication, and long division. By Trimester 2, we moved on to “All Things Fractions.” By Trimester 3, we were classifying polygons and plotting data, all while keeping one eye on the looming state test.

But then, the “April Epiphany” hit. When I circled back to prepare for testing, I realized my students didn’t own the math from Trimester 1. They had merely “rented” it for the unit test and returned it.

The math was gone.

I knew I had to stop teaching in silos. I needed a way to keep every Priority Standard “warm” year-round.

The Inspiration: From Grammar to Graphs

The spark came from Jon Corippo’s 8 p*ARTS of Speech. I saw how a simple, repeatable routine could solidify complex grammar, and I thought: Why aren’t we doing this with Math?

When I sat down to create the very first template back in 2016, I called it Place Value Basics. I’ll be honest: I explicitly wrote in that blog post that what I came up with “isn’t nearly as fun” as Jon’s version. But the core mechanism, squeezing 9 to 11 different standards onto a single page and hitting them daily, was there.

The results in my 5th-grade classroom weren’t just “better”, they were transformative. What started as a personal survival strategy quickly spiraled. A friend in 1st grade asked for a version. Then 3rd grade. Then Kinder. Suddenly, we weren’t just doing “reps”, we were building a movement.

Why Repetition Isn’t a Dirty Word

There is a common fear in modern education that any form of repetition is “drill and kill” – a soul-crushing exercise in flashcards that kills a student’s love for math.

But true MathReps are the exact opposite of a drill sheet.

  • Drill and Kill is 50 problems of the exact same skill, practiced in a vacuum until the brain shuts off.
  • MathReps is one number or set of numbers, run through 10 different connecting skills, practiced daily until the brain turns on.

We aren’t asking students to do the same thing over and over to get “fast.” We are giving them a predictable routine so their cognitive load is reduced. When they don’t have to worry about the format or “What do I do next?”, they finally have the mental space to notice patterns and ask “Why does this work?”

The Accidental Algorithm

I watched this play out beautifully with a 5th grader working on a MathRep that included the area model for division. In our conceptual progression, we weren’t teaching the traditional algorithm yet (that’s a 6th-grade standard); we were focusing on the “why” of place value blocks and area.

Day after day, this student engaged with the routine. Because he knew the structure inside and out, he stopped worrying about the instructions and started noticing patterns. One afternoon, he called me over, and I noticed his paper and inquired about his use of the algorithm.

“I saw that when I was doing it the other way, I could just figure out how many groups I needed from each place.”

Without a single direct instruction lesson, he had inherently figured out the traditional long division algorithm. He didn’t find it because he memorized an abstract chant or an acronym. He found it because the daily, low-stakes repetition of the area model allowed him to see the mathematical patterns so clearly that the traditional algorithm became the next logical step.

That is exactly how math is supposed to work: naturally, through curiosity and pattern-finding.

Rooted in the Classroom, Not a Boardroom

One thing that makes MathReps different is that it’s grassroots. This isn’t a framework developed by a textbook company or a corporate suite; it’s an educator-owned project born directly from the needs of real students in a real classroom. It’s built by teachers, for teachers, and refined by the feedback of the thousands of you who use it every day.

We now know the cognitive science backs this up. The 10-Minute Mastery Loop proves that daily mixed spaced retrieval beats the weekly review cycle every single time. If you only teach fractions in January and February, the brain flags that information as “temporary.” But if you touch a fraction every morning, the brain recognizes it as “essential.”

Where We Are Going Next

MathReps is no longer just a collection of legacy slides. As we look forward, our focus is on:

  • Universal Access: Expanding the searchable directory so you can find the exact standard you need in seconds.
  • Student Agency: Using the Number Menu to let kids bring their own real-world numbers into the math routine.
  • Sustainability: Keeping the “low-prep, high-impact” promise that makes this routine actually doable on a rainy Tuesday in February.

The “Manifesto” is this: Every student deserves to feel like a “Math Person.” By giving them a consistent routine to practice the Priority Standards of their grade level, we move math from short-term memory to long-term mastery.

Join the Conversation

We’ve all seen the “Trimester Trap” in action.

Which specific standard or concept do your students always seem to “return to the rental shop” by the time spring testing rolls around? Drop it in the comments, and let’s look at which MathRep can help you keep it warm!

The Power of the “Number Menu” in MathReps

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We’ve all been there. It’s your math block, and you’re asking students to run a Place Value MathRep. You need a number to work with. You could ask a student for a random number, and depending on your class, that could be dangerous. 6-7 anyone?

But what if we gave them a Menu instead?

The Number Menu is a simple, low-prep strategy to turn a standard MathRep into a high-interest, culturally relevant experience. By providing a curated list of 5–10 real-world numbers, you give students agency, choice, and a reason to care.

Why it Works

  • Natural Differentiation: Include a “Mild, Medium, and Spicy” option. A teacher can put a 2-digit, 4-digit, and 7-digit number on the same menu, allowing students to self-select their challenge level.
  • Connection: It bridges the gap between the classroom and the community.

Build Your Menu: 5 Categories to Get Started

You don’t need to reinvent the wheel every day. Pick a few categories, update the numbers once a week, and post them in a dedicated corner of your whiteboard.

1. The “Home Base” (Local Landmarks)

Perfect for place value, rounding, and measurement.

  • The School’s Address: Use the street number of your building or a famous local landmark (local library, coffee shop, or grocery store).
  • Local Elevation: What is the altitude of your town? A nearby town? (Great for comparing numbers!) You could even do the population!
  • The Distance: How many miles is it from your classroom to the nearest State Capital? Or city hall?

2. The “Scoreboard” (Sports Stats)

Sports are a universal language for engagement.

  • The Box Score: Points scored, total rushing yards, or the attendance at last night’s local or national game.
  • Jersey Math: Use the numbers of local high school stars or professional athletes. This is perfect for the 4 operations with double-digit numbers.
  • Pro-Tip: Don’t be afraid to be a “homer”! Why not use at least one Detroit Lions stat on the menu? What a great way to engage in math! Not a Lions fan? (Why not? – don’t answer that), Use a favorite team of yours or your students.

3. The “Main Street” (Community Math)

Connecting math to the economy that students see every day.

  • Price Points: The current cost of a gallon of gas or a local favorite “Happy Meal.”
  • Elapsed Time: If the local library opens at 10:00 AM and closes at 6:00 PM, how many minutes is it open?
  • Historical Age: The year your town was founded vs. the current year.

4. The “Trend” Report (Pop Culture & Digital)

Meeting students where they live—online.

  • The Viral Count: Use the view count (in the millions!) of a trending (and school-appropriate) video or song.
  • Gaming Stats: The current “active player” count for games like Minecraft.
  • The Countdown: How many days/hours until the next big movie release? Or a local event like the Salinas Valley Fair?

5. The “Wildcard” (Nature & Science)

For the kids who love the “did you know” facts. I love this idea. So many random

  • The Weather: Today’s high and low temperatures (perfect for introducing negative numbers).
  • Animal Facts: The weight of a local species vs. an exotic one (e.g., a Black Bear vs. a Blue Whale).

Keep it Simple

The goal of MathReps is to keep the routine stable so the thinking can be deep. You don’t need a fancy tech integration for this. A simple “Weekly High Five” list on the board is all it takes to transform a routine repetition into a meaningful conversation.

When you bring the world into your MathReps, you aren’t just teaching place value—you’re showing students that math is happening all around them.

What numbers or topics are on your menu this week?

Poster Template

Math in the Valley: Making Reps Relevant

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In our rural communities, math isn’t just in a textbook; it’s on the side of every tractor, it’s in the dimensions of the fairgrounds, and it’s in the literal soil of the Salinas Valley.

This week, King City is buzzing. It’s Salinas Valley Fair week, and for our community, that’s not just an event; it’s a whole vibe. Between the FFA projects, 4-H exhibits, the animals, school projects, and local farmers showing their best, the town completely revolves around those 31 acres on Division Street.

When we use local data, we aren’t just teaching math; we’re validating the expertise our students and their families bring to the classroom every single day. We make it relevant, tangible, and relatable.

The “Acreage & Arena” Rep

Geometry and measurement feel different when you’re talking about the Stampede Arena.

  • The Data: The Salinas Valley Fairgrounds spans 31.4 acres. The Stampede Arena is exactly 180ft x 300ft (54,000 sq. ft.).
  • The Rep: Instead of finding the area of a generic rectangle, have students use the Stampede Arena dimensions. How many “arenas” fit into the 31.4 total acres?

The “Mustang Stadium” Comparison

To help students visualize magnitude, use a landmark they know well: War Memorial Stadium at King City High. * The Comparison: A football field is roughly 1.3 acres.

  • The Challenge: If our high school stadium is 1.3 acres, and the Fairgrounds is 31 acres, how many Mustang Stadiums could we fit inside the Fairgrounds? (Spoiler: It’s about 24!)

The “Salinas Valley Reach” (Fractions & Percentages)

We live in the “Salad Bowl of the World,” and the percentages are staggering. It’s also Steinbeck Country, so ELA EduProtocols fit well in our area.

  • The Data: The Salinas Valley grows 92% of the nation’s broccoli and 76% of its head lettuce.
  • The Rep: Use these high-leverage percentages in a fraction or decimal MathRep. This transforms a standard problem into a point of community pride.

Step-by-Step: How to Create a “Homegrown” Map Rep

Creating a MathRep that is relevant to your community is easy. You just need Google Maps and a curiosity about your community.

  • Find Your Landmark: Open Google Maps in Satellite View and find a spot your students know (like the Fairgrounds or the High School).
  • Use the “Measure Distance” Tool: Right-click on one corner of the property. Select “Measure distance.” Click the other corners to close the shape.
  • Bridge to the MathRep: Use the Total Area and Perimeter Google provides to fill in your MathRep frames.

The “Community Data Walk”

As we walk the fairgrounds this week, we’ll look at the exhibits through a mathematical lens. Every 4-H weight chart, every FFA livestock pen dimension, and every ag display is a MathRep waiting to happen.

By using the Fair as our “anchor,” we eliminate the “When will I ever use this?” question. The answer is: You’re using it right now, right here in King City. What will be your anchor?

Time Saver Toolkit: 3 Google Features for May Sanity

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When I think about classrooms this time of year, I’m thinking of the workflow. This time of year is jam-packed with activities, final checks, and state testing. We don’t have time to waste. That’s why it’s important to reclaim your time.

If you want to survive May with your sanity intact, here are three features you should be leaning on:

1. Rubrics in Google Classroom (The “State Test” Hack)

Many teachers don’t realize they can import or build rubrics directly into their Google Classroom assignments.

  • The Pro Move: Take the actual writing rubrics from our state testing and build them into your final writing assignments.
  • The Benefit: When you grade, you just click the level (1, 2, 3, or 4), and Google does the math for you. More importantly, the students see exactly where they stand against the state standard before the test starts.

2. Google Forms as the “Automated Exit Ticket”

Stop collecting 30 slips of paper at the door. A simple 2-question Google Form can be your diagnostic “Biopsy” for the next day’s lesson.

  • The Pro Move: Use “Quiz Mode” with answer keys for multiple-choice questions.
  • The Benefit: You get a pie chart of student understanding before the kids even leave the room. If 70% of the class missed the question on fractions, you know exactly what your MathRep warm-up needs to be tomorrow.

3. The “Schedule” Button (Mental Health Move)

The Feature: Instead of hitting “Post” on an assignment, click the arrow next to it and select “Schedule.”

Why it helps: You can batch-plan your entire next week on Sunday night (or during a prep period) and have assignments drop exactly when class starts. No more fumbling with the “Create” button while 30 kids are waiting.

Bonus May Helper

Version History in Docs/Slides

  • The Feature: File > Version History > See version history.
  • Why it helps: In May, students sometimes “accidentally” delete their entire project or claim they “worked on it for hours” when they didn’t. Version History shows you exactly who wrote what and when. No more “he-said, she-said” during grading, just pure data.

The Spring Lifeline: Zero-Prep, High-Impact Math Review

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It’s the end of April. If you’re like most teachers, you’re spent. Your students are spent. But the learning doesn’t stop just because the calendar flipped.

How do we keep the “polish” on our math skills without adding more prep to an already overflowing plate?

The “Assign and Go” Solution

I am thrilled to share that MathReps are live and pre-made inside the Snorkl library. No more standing at the copier. No more hunting for the right PDF. You can quite literally “Assign and Go.” Whether you need to sharpen the 4 operations or dive deep into fraction models, the heavy lifting is already done for you. And what a relief that is!

Why This is a Game-Changer Right Now:

  1. Zero Prep: Navigate to the Snorkl Library, click “EduProtocols,” and select “MathReps.” Everything from Kinder to 4th Grade (with 5th Grade coming soon!) is ready to push out to your students instantly.
  2. The AI Co-Teacher: At this point in the year, you don’t have the bandwidth to listen to 30 individual explanations. Snorkl’s AI does it for you. It listens to the student’s logic, catches the “Instructional Debt” (like that hidden skip-counting), and provides immediate feedback. Although you may have to remind the students to review the feedback, I’m finding that in some younger grades.
  3. Consistency Over Novelty: Since these are based on the MathReps your students already know, you aren’t teaching a new tool; you’re just using a better engine to run the routine.

How to Find Them:

It couldn’t be easier.

  • Log into Snorkl.
  • Navigate to the Library.
  • Look for the EduProtocols section.
  • Select MathReps.

A Quick Update for 5th Grade

I know my 5th-grade teachers are waiting. I’m currently getting those frames ready for you! Stay tuned; they’ll be live in the library soon to help you finish the year strong.

The Bottom Line: You don’t have to choose between your sanity and your students’ growth. Let Snorkl handle the prep and the feedback so you can focus on being the human connection your students need as we close out the year.

Lessons in Kindness from the Big Sur Marathon

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This post is a deviation from my normal writing. I was inspired and needed to share the goodness.

This past weekend, I ran the 11-miler at the Big Sur International Marathon. It was a perfect running day, but the most beautiful thing I saw had nothing to do with the scenery. It happened about a quarter-mile from the finish line.

My running partner, Karen, and I came across a marathoner who was in serious trouble. He was unstable, stumbling from side to side, veering off into the grass. He was physically spent, his body giving out just yards from the goal.

What happened next is something I’ll never forget. And yes, there were some tears.

The “Helper” Runners

One runner stopped to check on him. The young man tried to snap out of it, insisting he was “okay,” but he clearly wasn’t. Then, two other runners did something incredible. They didn’t just ask if he was fine; they stepped in. One put the man’s arm around his neck. Then a second helper joined on the other side.

The marathoner was essentially dead weight; hunched over, barely able to move his legs. These two strangers took on his burden. Karen and I knew we couldn’t physically carry him as he was much taller and completely out of it, but we knew we couldn’t leave. We initially stayed right by the marathoner, watching until the two strangers stepped in to help.

The Trio at the Finish

By the time they reached the end, two medics took over, basically carrying the man across the finish line and straight to the medical tent.

To witness that level of kindness and selflessness was overwhelming. Karen and I both welled up in the moment, and honestly, as I write this, I’m welling up again.

Why This Matters (Beyond the Race)

We spend so much time debating: pedagogy, politics, the “right” way to do things. But in that moment, none of that mattered. What mattered was a human being in need and others who were willing to sacrifice their own time to ensure a stranger made it home.

This is how we should be at all times. Whether it’s in our classrooms, our district offices, or our communities:

  • See the struggle: Don’t just take “I’m okay” for an answer when someone is clearly stumbling.
  • Shoulder the weight: Be the person who stops to put an arm around a colleague or a student who is “dead weight” in that moment.
  • Watch the back: Even if you can’t carry the load, stay behind. Watch out for each other until help arrives.

At the end of the day, we’re all just trying to get across the finish line. It’s a lot easier, and a lot more meaningful, when we do it together.

15-Day Routine for Math Test Confidence

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In the sports world, athletes don’t spend the week before a championship learning new plays. They spend it “polishing”, perfecting their form, sharpening their reaction time, and ensuring their fundamentals are second nature. However, as a lifelong Detroit Lions fan, I’m not sure this analogy is always accurate. While I love my Lions, there have been plenty of games where it looked like they just learned the plays in the huddle! But all joking aside, as educators, we are preparing our students for life skills, not just a state test.

The Problem: The “Skill Blur”

When students are sitting at a computer, facing math problems one after another, cognitive overload is a real threat. The “how and when” of the four operations can easily get jumbled with fraction rules, and suddenly, all that geometry vocabulary becomes one big ole mess in their heads. This can be frustrating for both students and teachers.

It’s not that they didn’t learn the material; it’s that the retrieval is getting blocked by the sheer volume of information and tasks that need to be completed.

The Solution: MathReps as a Tactical Warm-Up

MathReps lower the affective filter by repeatedly practicing these core skills. I remember a year when my students didn’t just “do a unit” on decimals; we consistently spiraled decimal practice into our MathReps alongside other skills.

Because it was part of their regular routine, when they eventually faced a screen with decimal problems and tasks at the end of the year, they didn’t panic. The decimal didn’t throw them because it wasn’t a “guest star” in the curriculum; it was a familiar friend. By using MathReps as a 10-minute daily “Tactical Warm-Up,” we help students:

  1. Filter out the Format: They’ve seen the area model and the number line hundreds of times. The “test screen” is just another canvas for their existing skills.
  2. Sharpen the Fundamentals: We move from “manual labor” math to automaticity.

The 15-Day “Polishing” Routine

If you have 15 days left before the test, don’t reach for a packet. Reach for a Routine or EduProtocol.

  • The Selection: Pick the MathRep that addresses the skill your students find the weakest. If they are tripping over the arithmetic, use an Operations Frame (like the giraffe example below).
  • The Routine: Use the same MathRep at the beginning of your math period for at least one week. Consistency beats variety here. On Day 1, they are reacquainting themselves with the procedures; by Day 5, they are mastering the logic.
  • The Pivot: After 5 days, if you’re feeling good, move to another high-leverage frame. Or, cycle back to a different MathRep you used earlier in the year to keep those older skills from getting lost in the sauce.

The Bottom Line

We aren’t “cramming” for a test; we are clearing the fog. When we polish these skills through MathReps, we give students the confidence to show what they actually know, rather than getting lost in the “mess” of a testing interface and the information overload that bogs them down.

The Importance of Learning Progressions in Math Education

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As an instructional coach in a district that recently began Standards-Based Learning in math, I hear similar concerns across the district, especially this time of year. The pressure to have mastery of all the Priority Standards before the year ends. (It’s important to note that all the standards are being taught. There are Priority Standards and supporting standards. The supporting standards do just that: support. They are the prerequisites, if you will, to the Priority Standards.)

But there is a hidden “Instructional Debt” that makes these standards feel like an uphill battle. If we want our students to succeed at high-level problem solving, we have to talk about the one thing that has become a bit of a “taboo” word in modern math: Memorization. Okay, the act of memorization isn’t taboo; some of the old methods are no longer supported by current research. It’s a frustration for all K-12 math teachers. So let’s talk about it and how we can help students master facts using current research.

The “Cognitive RAM” Problem

Every student has a finite amount of mental energy (let’s call it “Cognitive RAM”). I can hear you all now, “So do the teachers!” When we ask a student to solve a multi-step word problem, that task requires a massive amount of RAM for reading comprehension, translation, planning, and strategic persistence.

If that student hasn’t memorized their basic addition, subtraction, or multiplication facts, they are forced to use their limited RAM for “manual labor”: counting on fingers, drawing tally marks, drawing, modeling, or skip-counting. By the time they get to the actual logic of the problem, they’ve run out of “mental memory.” The whole task seems insurmountable.

The truth is: Memorization is Creative Freedom. When the facts are automatic, the brain is finally free to be creative in the approach to solving the problem. It breaks down a barrier. Think about it. If you are trying to solve a problem and realize you need to multiply 376 by 48, but you don’t have your facts memorized, this task just became a slow, muddy drudge. However, if you know you will need to multiply 376 by 48 AND you know your facts, the hard part is behind you once you know what to do. Suddenly, things don’t feel so unattainable.

The Progression is Non-Negotiable

To be clear: I am not advocating for “rote memorization” without understanding. Memorization is the final step of this Learning Progression. It only works if it is built on a solid foundation:

  1. Concrete: Manipulating base ten blocks and counters.
  2. Representational: Drawing tape diagrams, number paths, and arrays.
  3. Abstract (The Goal): Automaticity, mental fluency, and algorithms.

If we jump straight to memorization, we build a house of cards. But if we stay in the “Representational” phase forever, allowing students to rely on skip-counting patterns or finger-counting, we are capping their growth. We are asking them to do “back-breaking” math every single day. We do need to nudge them to move beyond the Representational model and help them see/understand that they are ready for the abstract and that the abstract is, in fact, your friend.

The Three Gaps Holding Students Back

When I listen to teachers discuss where students are “stuck” on a standard, they usually find that there is a gap in one of these three essential progressions:

1. The Missing Floor (Addition & Subtraction Facts)
If a fourth grader is still “counting on” to solve 14 + 6, they aren’t just slow, they are overloaded. Mental math strategies like “Make a 10” are the building blocks for every standard that follows.

2. The Fluency Wall (Multiplication & Division)
Skip-counting (7, 14, 21, 28…) and arrays are beautiful ways to learn multiplication, but it’s a weight around a student’s neck during long division. We have to move them across the bridge to automaticity.

3. The Magnitude Gap (Flexible Thinking)
When a student looks at 1/4 and 5/6, do they see numbers to crunch or magnitudes to visualize? Flexible thinking means knowing that 1/4 is “a little bit” and 5/6 is “almost a whole.” If they can’t visualize this, they aren’t ready for the standard of comparing fractions.

Bridging the Gap with MathReps

This is exactly why the MathReps framework exists. We don’t just “hope” kids learn their facts or develop flexible thinking. We build consistent, high-frequency opportunities to practice these skills alongside the priority standards.

A MathRep ensures that students touch the concrete and/or representational models every single day until those skills settle into the abstract. It allows us to pay off the “Instructional Debt” in small, daily installments so that when students are expected to solve two-step word problems with multiple operations, our students have the mental capital to win.

The Bottom Line: Don’t be afraid to slow down and build the floor. You aren’t “behind” on the pacing if you are busy building the progressions that make those standards possible.