Tag Archives: Technology

Moving Beyond ‘The Things’ in Math Class

I’ve always had such an appreciation for curriculum materials. I genuinely don’t know where I would have been as a new teacher without the Investigations curriculum. Those materials shaped my vision for math instruction and influenced not only my teaching, but my curriculum writing at Illustrative Mathematics as well. In all of my work, I continually advocate for the use of high-quality instructional materials.

At the same time, I’m not naïve enough to believe that any single curriculum—no matter how well designed—can meet the needs of every teacher or every group of students in any context. That tension is exactly why I care so deeply about adaptation.

For some curriculum publishers ‘adaptation‘ is treated as a dangerous word because it doesn’t align with the curriculum developers beliefs about how their curriculum should be used. Some worry that acknowledging the need for flexibility somehow sends the “wrong message” about the quality of the product.

What those organizations need to honor is what teachers know: their students, their prior knowledge, the ways they engage with content, and the day-to-day realities of a classroom. Pretending a curriculum is so perfect that it must be used exactly as written may keep a marketing narrative tidy, but it doesn’t support the humans doing the teaching, or the kids doing the learning.

Adaptations: The What and Why

Sometimes adaptation means shifting pedagogy.
Sometimes it means bringing in a strategically chosen resource.
Sometimes it means adjusting a task to better elicit the mathematical ideas at the heart of the lesson.

At its best, adaptation is about eliciting, honoring, and leveraging students’ ideas, curiosities, strengths, and mathematical understandings. It’s about making intentional choices that build from what students can do rather than from assumptions about what they can’t or won’t.

But over the years, I’ve noticed a pattern that feels impossible to ignore: instead of investing in thoughtful adaptation, math education has become (or always has been?) obsessed with quick fixes and flashy things.

We try them. We buy them. We’re promised they’ll solve our most persistent instructional challenges.

You’ve probably heard versions of this:

  • Students are ‘falling behind’ in grade level content → Purchase an RTI program.
  • Students aren’t being challenged → Create an accelerated track.
  • Students aren’t engaged → Make flashy digital lessons. 
  • Students still aren’t engaged → Find “fun” activities on the internet. 
  • Students aren’t writing explanations → Buy math journals.
  • Teachers don’t believe all students can learn → Hand them a book on growth mindset.
  • Teachers still don’t believe all students can learn → Hire a ‘big-name’ math ed keynoter.
  • Teachers can’t meet every student’s needs → Send them research on differentiation. 
  • Teachers don’t trust their curriculum → Replace it with a collection of random tasks.
  • Districts don’t trust any curriculum → Throw out the textbook altogether.

These moves usually come from care and urgency. When something isn’t working, it’s natural to want to fix it and in many cases, we can learn a lot from trying new things. I know I have learned a ton from the #mtbos days of old.

But these are not challenges for quick fixes. They are ‘easier said than done’ pain points. So, it’s worth pausing to ask: If these solutions are meant to produce consistent, measurable, and sustainable change…why are we still looking for solutions for the same problem?

The answer might lie in how we think about mathematics itself.

Math Is a Story. Quick Fixes Are Commercials.

When we see mathematics as a coherent story, one that builds, connects, and makes sense over time, each lesson is a chapter. New ideas grow out of previous ones. Students should feel the mathematics unfolding, connecting, and extending their thinking.

That story is already written into high-quality curriculum materials. Our role as teachers is to bring it to life, making adaptations that strengthen the narrative without breaking it.

Quick fixes, however, often come with their own storyline: their own logic, pacing, and purpose. When we drop them into instruction without careful consideration, they interrupt the mathematical story already in progress.

They become commercials.

And even when the commercial is fun, flashy, or well-intentioned, it still disrupts coherence and the learning experience. It’s unlikely, certainly not guaranteed to lead to lasting changes in teacher practice or student learning.

When teaching and learning are treated as a continuous, interconnected narrative, commercial breaks can add noise, not clarity. They leave students experiencing math as a series of disconnected activities rather than as a meaningful, connected discipline.

Thoughtful adaptation preserves the story. Quick fixes interrupt it. I even gave a talk on this exact idea at CMC-S many years ago. (minute 9:00)

The Things Aren’t the Problem , Our Lens Is

Once you start seeing instruction this way, it becomes easier to spot where coherence is preserved and where it gets disrupted. One of the clearest examples of this tension shows up in how we use math routines.

There is no shortage of powerful routines in math classrooms:

  • Number Talks
  • Which One Doesn’t Belong
  • Notice/Wonder
  • 3-Act Tasks
  • Visual Patterns
  • Counting Collections
  • Choral Counting
  • Sometimes/Always/Never
  • Talking Points
  • Open Middle

I LOVE these routines. I’ve used them in my own teaching, coaching, and curriculum writing because I deeply understand their value. Each one holds enormous potential and I have learned so much by using them. They invite reasoning, elevate student voice, and cultivate important mathematical habits of mind.

But their impact doesn’t come from the routine itself—the thing.

It comes from the things about the thing:

  • its mathematical purpose
  • how it positions students as thinkers
  • the teacher’s stance and what they notice and respond to
  • how it connects to what came before
  • how it advances what comes next
  • the opportunities it creates for sense-making

When a strong routine, activity, or other pain point solution is dropped in at random, it becomes just another commercial, well-produced and engaging, but disconnected from the larger story of the mathematics.

When that same routine (or other solution) is used with intention, grounded in the curriculum and responsive to students, it becomes part of the narrative and an agent for sustainable change.

How to Shift Our Lens

Shifting our lens doesn’t mean rejecting new ideas, routines, or resources. In fact, it requires the opposite. We try things. We study them. We learn from what happens when they meet real students in real classrooms. But instead of treating those things as replacements or fixes, we treat them as opportunities to better understand our students and the mathematics, and then adapt with intention.

This is where adaptation becomes the missing piece in effective and sustainable math instruction. Without adaptation, we swing between rigid fidelity (“just follow the program”) and disconnected add-ons (“just try this new thing”). Adaptation offers a third path: staying grounded in the curriculum’s design while making informed, purposeful decisions that support coherence and respond to students’ thinking. It asks not What can I insert? but How does this choice strengthen the mathematical story students are already experiencing?

Importantly, adaptation is not a free-for-all. As Remillard (2005) reminds us, “It would be inaccurate and irresponsible to conclude that all interpretations of a written curriculum are equally valid.” Some changes preserve the integrity of the mathematics; others unintentionally distort or fragment it. The work, then, is not simply to adapt but to learn how to distinguish between reasonable and unreasonable variations, especially those tied to the most central features of a curriculum’s design (pp. 239–240).

When we shift our lens in this way, trying something new is no longer the end goal, it’s part of a learning cycle. We try a routine, task, or approach. We notice how students engage with the mathematics. We reflect on what it revealed, what it obscured, and how it connected to what came before and what comes next. Then we adapt, not to chase novelty or flashy, fun options, but to better position students as sense-makers within a coherent mathematical storyline.

This kind of adaptation doesn’t promise instant results. But it does something far more powerful: it builds teacher knowledge, strengthens instructional decision-making, and supports math learning that is connected, meaningful, and sustainable over time.

So Where Do We Go From Here?

We don’t need to jump to new things to solve curriculum implementation challenges.
And we certainly don’t need more silver bullets.

What we need is coherence.
We need connectedness.
We need to treat mathematics as the coherent story it truly is and learn to adapt materials in ways that honor and strengthen that story.

That also means being more intentional about the curriculum partners we choose. We should be asking whether a curriculum acknowledges the professional judgment of teachers, reflects the complexity of classrooms, and explicitly supports thoughtful adaptation. The goal is not permission to change things at will, but guidance for how to adapt in ways that preserve the mathematical integrity and coherence of the design. Organizations that condemn teachers for adaptation, or frames it as a failure of implementation, misses a fundamental truth: no written curriculum can anticipate every learner, every context, or every instructional moment.

Choosing adaptations, then, requires looking beyond the thing itself and toward the things about the thing that make instruction sustainable, purposeful, and responsive to teachers and students. One way to begin is by grounding adaptations in a small set of guiding questions and principles.

First, adapt with the mathematical purpose in mind.
Before changing a task, routine, or lesson, be clear about the mathematics it is designed to surface. Strong adaptations clarify or sharpen that purpose; weaker ones obscure it. Sometimes that sharpening means being more explicit, naming an idea directly, modeling a strategy, or slowing down to highlight structure so students can actually see the mathematics you want them to see. If an adaptation makes the mathematics less visible, dilutes the focus, or shifts attention away from key ideas, it’s worth reconsidering.

Second, protect the coherence of the learning.
Ask yourself how the adaptation connects to what students have already experienced and how it sets them up for what comes next. Reasonable adaptations strengthen the storyline, helping ideas build, connect, and deepen over time. When an adaptation stands alone or introduces a competing logic, it risks becoming a commercial rather than a chapter.

Third, attend to how students are positioned.
Effective adaptations expand access to the mathematics without lowering the cognitive demand. They position students as thinkers, sense-makers, and contributors, not just followers of procedures. The question is not Is this easier or harder? but What opportunities does this create for students to reason?

Fourth, treat adaptation as learning, not fixing.
Adaptations work best when they are tried, studied, and revised. What did students understand more deeply? What surprised us? What might we adjust next time? This stance shifts adaptation from a reactive move to an ongoing professional practice.

When we adapt with these elements in mind, every instructional choice becomes part of a larger narrative: what students understand, who they are becoming as mathematicians, and how they make sense of the world.

And when we stop interrupting the story with commercials, the learning becomes clearer and the thinking becomes deeper.

Now if we revisit our initial list and reflect on the things about the thing, we move from quick fixes to thoughtful considerations. 

  • Students are ‘falling behind’ in grade level content → How is the RTI program connected to our curriculum materials? How does the program position students as knowers and doers of mathematics? How does the program build on what students know?
  • Students aren’t being challenged →What does it look like to extend student thinking? How does our current curriculum support extensions? How can we adapt our current curriculum materials and instruction to extend student thinking? How are teachers supported to address all students needs’ in the classroom? 
  • Students aren’t engaged →Why would a digital activity be more engaging? Why would the digital activity be better than a pencil/paper experience? How does it impact students collaboration? What is the cost/benefit of putting students on a device during math class?
  • Students still aren’t engaged → How do the ‘fun’ activities connect to what students are currently learning? What aspects of that activity make it fun? Which of those aspects could be implemented in our current lessons to increase engagement? Does fun= meaningful learning?
  • Students aren’t writing explanations → How do students view writing in math class? What do we do with their written explanations? How do I need to manage the journal to encourage students to write more? 
  • Teachers don’t believe all students can learn → How can we find out why teachers believe this? How can we adapt our curriculum materials to elevate student ideas to show all of the amazing things students know?
  • Teachers still don’t believe all students can learn → How can we collaborate as colleagues to learn more about how students feel about themselves as mathematicians? How can we leverage what we learn to adapt our instruction to elevate all of the knowledge students are building on.
  • Teachers can’t meet every student’s needs → What does it mean to differentiate? What are in the moment strategies we can use? How can we make the most out of any small group time we have? How can we leverage collaboration in the classroom to support differentiation?
  • Teachers don’t trust their curriculum → How can we find out why teachers don’t trust the curriculum? How can support teachers in adapting the curriculum in meaningful ways to gain trust?
  • Districts don’t trust any curriculum → What are the implications if we don’t have a scope and sequence? How does just pulling tasks aligned to standards impact student’s learning experience?

Final Thoughts

In the end, thoughtful adaptation is not about changing for the sake of change, it’s about honoring the complexity of teaching and the brilliance students bring to mathematics. High‑quality materials give us the storyline; our professional judgment brings that story to life. And that work becomes even stronger when it’s supported by curriculum partners who believe this too–partners who trust teachers, understand the realities of classrooms, and design materials that are meant to be adapted rather than protected with rigidity.When we adapt with purpose, protect coherence, and remain responsive to the learners in front of us, we create classrooms where mathematics makes sense, ideas build, and students see themselves reflected as capable thinkers. That’s the work that lasts. That’s the work that matters. And that’s the work worth investing in, not because it’s easy, but because our students deserve instruction rooted in meaning rather than momentum, in coherence rather than commercials, and in teaching that grows stronger, deeper, and more human over time.

Related posts on adapting:

Adapting Lessons Part 1: Launching an Activity

As a math teacher and coach, I’ve always adapted curriculum materials. I am sure we all have—it’s part of knowing our students and wanting to provide them with access to the math in ways that make sense to them. And while we have the best of intentions, sometimes the choices we make can unintentionally take the math out of students’ hands, disconnect from what they already know, or even reflect assumptions and expectations we didn’t realize we were holding.

Adapting activities is challenging for many reasons: some decisions require extensive prep, others happen in the moment, and all of them must be balanced with the pressure to keep pace while still giving students the time and space to share the incredible ideas, experiences, and mathematical thinking they bring into the classroom. I also found it difficult at times to know exactly what to look or listen for mathematically, and I sometimes interpreted students’ responses through my own assumptions and expectations. While a high-quality curriculum can provide problems that elicit student thinking, the deeper work of examining what we notice, what we value, and how we interpret and leverage students’ ideas extends far beyond even the most comprehensive teacher guide.

While thoughtful planning ahead of time is ideal, we all know it isn’t always possible. Because so much can get in the way of planning and prep time, I think a lot about how to make quick, in-the-moment adaptations based on what students are saying and doing—and on what I still need to learn about their thinking. I often wonder: What if our adaptations did more than simply “fix” a lesson? What if they opened space for deeper student thinking, a stronger sense of community, and richer mathematical understanding?

These questions keep pushing me to look closely at the flow of a typical lesson and identify the moments where even small adaptations can make a big difference. I’ve found that there are five points in a lesson where a few quick, minor changes can have a big impact:

  • Launching an activity
  • Working in small groups
  • Engaging with contexts
  • Sharing ideas
  • Synthesizing the lesson.

While it would be wonderful to have a single “right” adaptation for each of these, the reality is that different classrooms and moments call for different routines or structures. In the next series of posts, we’ll take a closer look at each of these opportunities and explore practical, in-the-moment ways to adapt them.

Ultimately, the goal of these small adaptations isn’t just to adjust an activity or lesson; they’re meant to open up richer mathematical experiences for students and provide increased insight for teachers. My hope is that these structures encourage sense-making and increase access to the mathematics; provide every student opportunities to share the amazing ideas they bring; create space for questions about one’s own or others’ thinking; build a stronger mathematical community; and support teachers in reflecting on why they’re adapting an activity and how those choices best serve students.

In this post, I’ll outline a few alternate ways to launch a lesson, and in subsequent posts, I’ll explore each of the other lesson moments listed above.

Alternate Ways to Launch a Lesson

Instructional Goal: Provide students with an entry point into the activity. 

When deciding which adaptation to use, it is helpful to think about what aspect(s) of the task might make it inaccessible to your students. For example:

  • If the context or representation of the problem might be unfamiliar to students, you could use the Tell a Story, What Questions, or Making Connections routine.
  • If the activity relies on a prior knowledge from earlier in the year or prior grade levels, it might make sense to use the What Questions or Making Connections routine.
  • If the language (including math language) adds a layer of complexity to the activity, you could use the Word Splash routine.

Try it!

There isn’t one “right” adaptation for any classroom scenario; each is an opportunity to learn more about your students. In the end, it’s not the routine itself that matters as much as what the routine affords—the ways it reveals student thinking, provides an entry point, and supports problem solving. The only way to figure out what works best is to try these structures out! Fortunately, they require little materials prep. All you need is a piece of chart paper or whiteboard and an image from the problem students will be solving.

In your next PLC or planning session, review the activities in an upcoming lesson. As you read through each problem, discuss:

  • What knowledge and experiences are your students bringing to the problem?
  • Is there an activity where students might not have access to the problem? If so, what specifically is inaccessible and why?
  • Which of the four routines will you use to launch the activity?*

*If you’re planning with your grade-level team, each person can try a different routine and then compare the affordances of each one. I’d love to see what you try! Share your ideas in the comments or on IG (@kgraymath)!

Part 2: Supporting student learning as they work in small groups

Math in a Movie Trailer

Last Wednesday at a PLC meeting, our district instructional technology specialist did a presentation on Blended Learning.  She did a beautiful job of demonstrating apps and web-based activities at various entry levels, so each teacher could participate. One of the fourth grade teachers expressed an interest, and a bit of fear, in trying to use ipads as part of her classroom routines. Since I had been in her room doing some math coaching the previous week, I offered to help her design an activity and give her a hand in the classroom with the ipad piece if she was not comfortable.

We met the next day to start our planning! She was just ending her 3D math unit in which students had been identifying 3D shapes by their silhouettes and attributes and finding volume of a rectangular prism. As a culminating activity, we decided to have the students create a movie trailer in iMovie that “told a story” about the unit. I sent the teacher home with one of the ipads to “play around” with iMovie, since she was not very familiar (or comfortable) with it.  I was so excited to come in the next day to see a trailer she had created at home that night! I LOVE when people jump right in!

This is how our lesson played out over the next two days…

– We created a room in “Todays Meet” on their ipads and had students go in and do a test post.

– We posted the question, “What is the purpose of a movie trailer?” in the TM room and let them type as we showed two movie trailers (Percy Jackson 2 and Despicable Me) on the SMARTBoard. When the trailers were over, we switched back to TodaysMeet on the SMARTBoard to go through their comments and have them expand on them. Here is a clip of the conversation:

TodaysMeet– Next we asked them to continue chatting about things they learned during this math unit. We noticed they were just writing one or two word things so we asked them to expand a bit and use more of their 140 characters. Sample clip:

TodaysMeet2– As a class we scrolled back through and had them stop and ask questions of each other if they didn’t understand what someone had posted. They were so engaged and they all kept asking if they could do this at home?!? YES! Next time I will leave the room open for a longer time frame so students can post as they think of things at home! What a great way to open class the following day!

– We took them through a brief “tour” of iMovie and let them move to a place in the room to look through the themes and storyboards and start brainstorming ideas for their trailer.

– To help them organize their thoughts, I had put a template of the storyboards: http://tinyurl.com/c3g5r2e in the Dropbox that was on each ipad. The students exported the PDF to UPad Lite: Upad

and let them play around with how to write on the document with pen width and different colors.

– The following day, students got in their groups (of 2-3 students) to plan out their storyboard and decide on pictures they need for their trailer.

When we meet on Monday, we are taking them around the school and outside to take pictures they need for their trailer. They are working this week finishing up the project, so this story will have  To Be Continued…

Mathematically Yours,

Kristin