November 3, 2023 7:00 am

The Science of Math Instruction: Incorporating Research-Based Instruction into Technology

Everyone’s talking about the science of reading, but what about mathematics? Take a look at agreed-upon best practices called cognitively-guided instruction, as well as technology that puts it into practice.

Teaching mathematics means more than introducing algorithms and procedures to students. Research shows that effective instruction also involves the development of a student’s conceptual understanding, mathematical reasoning, and problem-solving skills.

One research-based approach to mathematics instruction is Cognitively Guided Instruction (CGI), as described in Children’s Mathematics: Cognitively Guided Instruction (Carpenter et al., 2014). CGI shifts an educator’s focus away from direct instruction and toward understanding an individual student’s mathematical thinking. The teacher then leverages this understanding as the foundation to guide the student toward increasingly complex concepts.

Now, as online programs gain popularity in today’s classrooms, schools have the opportunity to choose technology that not only supports students’ procedural fluency but also aligns with research-based principles to develop students’ conceptual understanding. By evaluating the technology we bring to students through the lens of a framework such as CGI, we can help ensure that students have the opportunity to develop the skills they need to succeed beyond memorization.

What is Cognitively Guided Instruction (CGI)?

CGI is an approach to teaching mathematics that focuses on students’ critical thinking and problem-solving. Instead of just showing students how to solve a problem, teachers guide students to explore strategies and approaches that make sense from their unique understanding of a situation. The following are just some of the principles of CGI, as highlighted in Children’s Mathematics (Carpenter et al., 2014).   

  • Problem Solving: Students are encouraged to tackle problems using critical thinking and creativity before receiving direct instruction. Given a story problem anchored in a real-world context familiar to students (such as sharing a food item among friends), students reason using a strategy of their choice.
  • Teacher as a Facilitator: Teachers transition away from the role of traditional instructors and toward the role of facilitators. They listen to students’ strategies, pose thought-provoking questions, and steer discussions while providing opportunities for students to learn from their peers’ thought processes.
  • Building on Prior Knowledge: Students bring their experiences and understandings into the classroom. Teachers leverage each student’s prior knowledge as a foundation and layer new concepts on top of the ideas that students have already grasped.
student solving math equation

Applying CGI to Online Learning

When designed with research-based principles in mind, online programs have the ability to increase accessibility to effective instruction. For example, the following characteristics of various online programs provide the flexibility to support CGI practices.

  • Adaptive Learning Environments: Adaptive learning environments powered by algorithms can provide students with a personalized learning experience that caters to their unique needs and preferences. By analyzing a student’s performance and feedback, online platforms can generate customized content tailored to their strengths and weaknesses. This approach to learning aligns with CGI’s emphasis on personalized education, which recognizes that every student has a unique learning style and pace.
  • Virtual Manipulatives: Utilizing virtual tools, such as base-ten blocks, offers students an interactive experience to experiment with variables and visualize outcomes. This approach enables them to select the appropriate device that aligns with their current understanding and apply critical thinking and creativity to solve a given problem.
  • Real-world Problem Solving: Online platforms can offer practical problem-solving exercises that mirror real-life challenges. This approach aligns with cognitively guided instruction’s emphasis on applying mathematical concepts to everyday situations. By bridging the gap between theory and practical significance, students can gain a deeper, contextual understanding of mathematics and its relation to the world around them.

By incorporating CGI practices with online platforms’ capabilities, we can anchor each student’s learning experience in student-centered, data-driven instruction.

The Idaho Study: A Snapshot of Research-Based Technology in Action

Imagine Math ISAT Performance Research Brief
Read the Full Study

Imagine Math is one supplemental, personalized online program that incorporates the features highlighted above. It presents students with problems, equips them with virtual tools, and adapts its levels of support in response to students’ answers. “Imagine Math’s personalized learning platform aligns with each student’s needs while providing the right amount of challenge to help the student achieve grade-level proficiency,” said Sari Factor, Chief Strategy Officer at Imagine Learning (New Study Reveals Significant Gains in Student Math Performance with Imagine Math, 2023).

This year, a study was conducted to assess the impact of Imagine Math on students’ academic performance. The study analyzed over 4,000 math assessment scores from the Idaho State Assessment Test (ISAT) of students in grades 4 through 8. The assessment scores were taken from schools across four different districts in Idaho during the 2021-22 academic year. Key takeaways from the research include:

  • The relationship between Imagine Math lessons passed, and ISAT score growth is positive for all grades and statistically significant for grades 4 through 7.
  • Positive and significant relationships between Imagine Math lessons passed and ISAT math score growth for various student subgroups, including special education students, English learners, students eligible for free or reduced-price lunch, and Hispanic/Latino or American Indian/Alaskan Native students.

These findings underscore the potential of platforms like Imagine Math that align with student-centered methodologies to enhance student outcomes.

The Future of Math Instruction

In today’s rapidly evolving society, education has significantly shifted due to technological advancements and a more comprehensive understanding of how individual students learn. By leveraging technology that incorporates research-based instruction, educators can create a more engaging and effective learning experience for students, leading to better academic outcomes and a more promising future.

About the Author – Erin Springer

Erin Springer is a former elementary school teacher who transitioned to supporting other teachers as a Professional Development Specialist at Imagine Learning. She is enthusiastic about helping teachers use educational technology to improve student outcomes, save time, and understand students’ needs.

Citations:

Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2014). Children’s Mathematics: Cognitively Guided Instruction (2nd ed.). Heinemann.

Imagine Learning. (2023, June 20). New Study Reveals Significant Gains in Student Math Performance with Imagine Math [Press release]. https://www.imaginelearning.com/press/study-reveals-significant-gains-student-math-performance-imagine-math/

September 7, 2023 10:21 am

Soft Skills with Big Impact: the 4Cs of STEM

Make STEM classrooms a playground for curiosity, a canvas for creativity, a stage for communication, and a hub for collaboration. When students embrace these skills, they’re not just preparing for the future — they’re shaping it.

“Hey Siri, how many rings does Saturn have?”

“Alexa, tell me what the square root of 1089?”

“ChatGPT: give me HTML code to embed a basic calculator on a webpage.”

There was a day when students had to ask their teachers, librarians, or even consult an encyclopedia for this type of information. But those days are long (like really long) gone, and the teacher is no longer the only keeper of information in the room.

Since the teacher’s role is evolving due to new technologies, and certainly students are not motivated to memorize what Alexa already knows, what should STEM classrooms be focused on? What skills are employers in STEM careers looking for if ChatGPT can produce code for free?

A 2018 survey by the Association of American Colleges & Universities showed, “that just 34 percent of top executives and 25 percent of hiring managers say students have the skills to be promoted. Many of those skills are soft skills — communication, team work, problem-solving — that are critical in a quickly shifting job market. Entry-level skills change every few years; it’s the habits of learning to learn and navigating the ambiguity of a career that will prove most valuable to undergraduates in the long run.”

The National Education Association has boiled these soft skills down to the 4 Cs: Creativity, Critical Thinking, Communication, and Collaboration. Let’s explore why these 4Cs are critical to providing a modern STEM education that gives students real career opportunities.

1. Critical Thinking: where curiosity begins

Imagine a classroom buzzing with questions. Except, not fact-based “how many rings does Saturn have” questions. Questions like: is it possible for New York City to become carbon neutral? What would that plan look like? Or: why does the kind of water (fresh or salt) affect how long it takes an ice cube to melt? That’s the power of critical thinking at work. It’s all about encouraging young minds to ask, “Why?” and “How?” Critical thinkers don’t just accept things at face value; they dig deeper. When students learn to analyze information, separate facts from opinions, and spot patterns, they become problem-solving heroes.

Picture a group of students exploring a science experiment. Instead of just following a set of instructions, they’re asking themselves, “What will happen if we change this variable?” That’s critical thinking igniting their imagination — it’s like a spark that lights up their learning journey.

2. Creativity: where imagination takes flight

Creativity isn’t just for artists — it’s a skill that every STEM student needs. It’s about looking at a problem from a different angle and dreaming up new solutions. Think of it as the magic wand that turns ordinary ideas into extraordinary ones.

Take a moment to think about a famous inventor, like Thomas Edison. He didn’t just stumble upon the light bulb; it took him 1000 attempts to find a design that worked. Creativity is what made him keep going, even when things got tough. Encouraging our students to think outside the box, to come up with wild ideas, and to believe that they can change the world — that’s the heart of creativity in STEM education.

3. Communication: bridges between minds

Imagine a world where nobody understood each other. It would be chaotic, right? Communication is like a bridge that connects our thoughts to the world. In STEM, it’s not enough to have brilliant ideas; you also need to share them effectively.

Think about a young engineer who designs an amazing new gadget. If they can’t explain how it works to others, their idea might never see the light of day. Teaching students how to express complex ideas in simple terms empowers them to inspire, collaborate, and bring their innovations to life.

4. Collaboration: teamwork for triumph

Remember the saying, “Two heads are better than one”? That’s the spirit of collaboration. In a world where problems are more complex than ever, working together is key. Collaboration is like a puzzle; each piece has its role, and when they come together, they create something amazing.

Think about a group of students working on a science project. Some are great at designing, others excel at research, and a few are natural leaders. When they pool their talents, their project becomes a masterpiece. It’s the same spirit that built the tallest skyscrapers and sent humans to the moon.

Putting the 4Cs into action

Imagine a classroom where students use their critical thinking skills to solve a real-world problem. Maybe they’re designing a water-saving system for their school garden. They brainstorm creative ideas, like using rainwater and self-watering plants. Then, they work as a team to build the system and explain their design to their classmates. These students are embracing the 4Cs in action: critical thinking, creativity, communication, and collaboration.

Empowering educators for success

As educators, you’re the guides on this exciting journey. You hold the keys to nurturing the 4Cs in your students. Encourage them to question, to dream, to share, and to work together. Make STEM education a playground for curiosity, a canvas for creativity, a stage for communication, and a hub for collaboration.

When students embrace these skills, they’re not just preparing for the future — they’re shaping it.

Imagine Learning STEM

Prepare the next generation of STEM leaders with digital and hands-on learning aligned to the 4 Cs.

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About the Author – Carolyn Snell

Carolyn Snell started her career in education teaching first grade in San Bernardino, California. A passion for the way technology and stellar curricula can transform classrooms led her to various jobs in edtech, including at the Orange County Department of Education. Her knack for quippy copy landed her a dream job marketing StudySync—an industry leading ELA digital curriculum. Now, as the Senior Content Marketing Manager for Imagine Learning, Carolyn revels in the opportunity to promote innovative products and ideas that are transforming the educational space for teachers and students.

Twig Science Reporter Moves to Monthly Releases 

Imagine EdgeEX

Same great videos, now with a deeper classroom archive

Twig Science Reporter is now releasing new episodes monthly to ensure each video maintains the high production and editorial quality educators expect. This change also allows us to enhance the platform experience, making it easier to explore and use the full archive. The result: more impactful videos and greater classroom flexibility with both new and past content. 

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Twig Science Reporter

Imagine IM K–8 Rated “All Green” by EdReports 

Imagine IM

Top marks for quality, usability, and accessibility

Imagine IM, the certified IM 360 math curriculum optimized by Imagine Learning, has earned the highest possible rating — “Meets Expectations” — in all EdReports K–8 categories. This recognition affirms Imagine IM’s quality, ease of use, and inclusive design, giving educators a trusted solution for impactful, student-centered math instruction. 

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Imagine+ Screener Now Rated “Convincing Evidence” by NCII 

Imagine Plus Screener
Whoo Hoo Pip

K–2 assessments meet top technical standards for MTSS 

The Imagine+ Screener is now listed on the NCII Academic Screening Tools Chart with “convincing evidence” — NCII’s highest rating — for validity, reliability, and classification accuracy. This recognition affirms its value as a research-backed screening tool to help educators identify students who need additional support. 

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Whoo Hoo Pip

New Single-Screen Display in Imagine Sonday System Essentials 

Imagine Sonday System

Switch seamlessly between slides and student data

Educators using Imagine Sonday System Essentials can now choose a single-screen display option for daily instruction. This layout keeps lesson slides, attendance, and progress tracking visible in one place, making it easier to stay organized and focused while teaching.

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Imagine Sonday System reading sounds screen

New Teacher Actions Report in Imagine EdgeEX

Imagine Edgenuity
Imagine EdgeEX

View and export course edits by teachers and admins 

A new report in Imagine EdgeEX™ helps administrators track educator and administrator actions within courses, including customizations. The Teacher Actions Report provides a downloadable view of who made changes and when, offering added visibility to support oversight and consistency.

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screen showing course customizations

October 23, 2025 8:00 am

Imagine Learning Launches Heart Work, a New Podcast and Multimedia Series Elevating the Voices of America’s Educators 

First collection, “Rewriting a Literacy Crisis,” follows educators through the challenges and triumphs of reshaping how America learns to read.

TEMPE, AZ – October 23, 2025 – Imagine Learning, a leader in K–12 digital-first learning solutions, today announced the launch of Heart Work, a new podcast and multimedia initiative that presents an honest profile of America’s educators, capturing the raw stories unfolding in today’s classrooms. Heart Work presents candid, deeply human insights from teachers, administrators, and leaders navigating change in education.  

Heart Work is built around collections, each one exploring a transformation taking place in our classrooms. Debuting today, the first Heart Work collection, “Rewriting a Literacy Crisis,” explores one of the most urgent challenges facing U.S. schools: helping every student become a confident reader. Through the experiences of Pendergast Elementary School District in Phoenix, Arizona, and educators from the School District of Philadelphia, the series shows states and schools embracing the Science of Reading and exploring new frameworks to improve literacy outcomes. Each episode combines documentary storytelling with practical insights, presenting an unfiltered view of the reality of change and the courage it takes to embrace it.

Heart Work’s multi-platform experience includes: 

  • Immersive podcast episodes interweaving conversations with educators, real classroom moments, and first-person reflections 
  • Short, documentary-style videos that bring viewers inside real classrooms, capturing the emotion, creativity, and quiet determination of educators as they navigate change and inspire learning 
  • A library of articles and resources providing deeper context 
  • Live events connecting educators nationwide 
  • Social media conversation-starters and community-builders 

“With Heart Work, Imagine Learning is expanding its role as a champion for educators and lifelong learners, creating a space where authentic storytelling meets actionable ideas,” said Leslie Curtis, Executive Vice President & Chief Administrative Officer at Imagine Learning. “The platform highlights not just the challenges of today’s classrooms, but also the creativity, compassion, and resilience needed to successfully address those challenges.” 

Future collections will explore topics including math anxiety and the path to numeracy confidence, the ethical use of AI in classrooms, and the ever-evolving art of teaching in the digital age. Educators, administrators, and advocates can also join the Heart Work Club for exclusive access to new episodes, articles, and events.

Heart Work is now available on all major podcast platforms. To listen to the first collection, join the community, or to learn more, visit imaginelearning.com/heart-work.

About Imagine Learning

Imagine Learning creates K–12 learning solutions that support the boundless potential of students in more than half the districts nationwide. Empowered with data and insights from educators, we innovate to shape the future of education with a robust, digital-first portfolio of school services and core, courseware, and supplemental solutions.

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The Case for Knowledge Building in Reading Instruction

Lauren Keeling | 10/21/2025 | 6 minutes

For every young reader, there’s a quiet moment when learning to read stops being about sounding out words. But what follows? Former teacher and principal Lauren Keeling explores the shift and reflects on how we move from the “reading wars” toward a model of literacy that honors both the science of reading and the humanity of why we learn to read — and truly gives students the skills they need for the real world.

A shelf filled with photo frames, books and awards from Lauren Keeling's home.

There’s a moment in every elementary teacher’s school year when the question shifts from “Can they sound it out?” to “Do they understand what they are reading?” It’s a quiet shift, but it marks the beginning of deeper work for themselves and their students. The work that asks not just how students learn to read, but why they read, what they know, and how that knowledge shapes their understanding of not only what’s on the page, but what’s in the world.  

We know that reading is more than letters and sounds working together on a page. Reading is where skill meets substance, where meaning is made, and where connections begin. But for many of us, we learned the hard way that while decoding is essential, it’s not enough. 

We’ve Missed the Mark 

The latest NAEP scores tell a sobering story: we are not where we need to be. In 2024, reading scores for both fourth and eighth-grade students declined again, continuing a downward trend that began well before the pandemic. 

Only 31% of fourth graders score at or above the NAEP Proficient level. Even more troubling, 40% of fourth graders and a third of eighth graders scored below the Basic level. That means that they struggle with even the most fundamental reading tasks. 

But these numbers aren’t just statistics. They represent children — children who are being asked to read texts they cannot understand, answer questions they cannot access, and engage with content they’ve never been given the tools to explore. Many might be able to make words from the letters they see and sounds they hear, but as the scores suggest, most can’t cross the bridge to making meaning from those parts and pieces. 

We’ve spent years debating how to teach reading, but somewhere along the way, we lost sight of why it’s so important.  

The Case for Knowledge Building 

Most of you will be familiar with what is now commonly dubbed the “reading wars.” It’s a debate that has long divided educators into camps: phonics versus whole language, skills versus meaning, decoding versus comprehension. Somehow, the rich, layered process of learning to read has been reduced to a simplistic tug-of-war. Yes, students must learn to decode. Phonics instruction is foundational, especially in the early years. But decoding alone does not create readers. It creates word-callers — students who can pronounce the words but cannot grasp their meaning.  

I began my career as a whole language teacher, raised by the very practices I was now passing on. My classroom was filled with stories, rich conversations, and joyful reading experiences. But somewhere along the way, the ground began to shift. Suddenly, phonics was at the forefront of reading instruction, and I found myself learning the foundations of letters and sounds alongside my kindergarteners. It was a humbling experience, transformative in fact, and it changed everything about how I taught reading. 

An image of a photo frame, a sign that says 'Teaching is a work of Heart' and some wooden letters that spell out 'Keeling'
An image of a hand written note from a child to Lauren Keeling

But even as my students grew more confident in sounding out words, a new challenge emerged. They could read the words, but they couldn’t always reach the meaning. They could decode, but they couldn’t connect. That moment, that tension between skill and understanding, was the beginning of my journey into knowledge building. It was the realization that reading is not just about getting through the words. It’s about getting into them. 

When we focus solely on decoding, we strengthen one part of what we call Scarborough’s Reading Rope. But without the other strands, especially background knowledge, students can read the words but can’t grasp the meaning. As Natalie Wexler writes in The Knowledge Gap, “You can’t comprehend a text if you don’t have enough relevant knowledge about the topic to make sense of it.” 

The Power of Knowledge Building 

I’d like you to picture a group of kindergarten students sitting on their classroom carpet listening to a story about the beach. The words are vivid: waves crashing, sand between toes, seagulls squawking overhead. For many children, the story feels distant no matter how intently they listen. Why? Because the beach is not a lived experience. They’ve never seen it, felt it, or heard it, and the vocabulary feels foreign. Comprehension falters — not because they lack ability, but because they lack context. They can’t practice reading, speaking, and listening skills because they’re overwhelmed by trying to catch up with the content they just don’t understand.  

Conversely, when content is thoughtfully selected and rooted in what children know, the words are no longer abstract. For early readers, this is critical. And it can’t be left to chance. Not all students have equal access to dinner-table conversations, museum visits, or vocabulary-rich environments, which makes it even more important to build knowledge intentionally. When we do, we reduce students’ cognitive overload, give them the schema they need to make sense of complex texts, and scaffold their learning with real-world connections.   

Now, I want you to picture a kindergarten classroom exploring the topic of toys and play — something much more familiar to five- and six-year-olds. Students are interviewing one another, asking questions like, “What’s your favorite toy?” and “What game do you love to play?” One child draws a picture of their favorite stuffed animal, another writes a few words about tag, and a third shares a story about using building blocks at home. When the teacher gathers the class to share, every child has something to say. They speak with joy, confidence, and connection because the topic is familiar. Most importantly, they’re able to focus on the skills of reading and writing because the meaning is already within reach. 

It’s Both/And … and More 

Building background knowledge isn’t just about giving early readers information. It gives them access. Last year, I visited the School District of Philadelphia — you’ll hear why in our second podcast episode — and met with Deputy Superintendent, Dr. Dawson. He said to me, “The question we need to ask ourselves is, ‘Do they have the skills to be able to succeed in life to set them up for a limitless future?’” For too many students, the answer is no — and through no fault of their teachers.   

Moving beyond the “reading wars,” decoding versus knowledge, and all the other practices we argue about means letting go of sides and moving toward something better: a literacy model that honors the science of how children learn to read and the humanity of why they need to. A model that teaches students to decode words … and decode the world.  

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About the Author

Lauren Keeling is a seasoned education professional with a unique blend of experiences. A former broadcast journalist, elementary teacher, and principal, she now combines her passion for education with her love of storytelling at Imagine Learning. Above all, Lauren is a dedicated literacy advocate pursuing a doctorate in Leadership with a focus on Public and Non-Profit Organizations to further her impact on education nationwide. 

Lauren Keeling

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October 17, 2025 8:00 am

Philadelphia’s Math Momentum Highlighted by The Inquirer

Published by: The Philadelphia Inquirer

The Philadelphia Inquirer reports that third-grade math proficiency in the School District of Philadelphia increased by 13 points over three years — a signal of meaningful progress in early-grade instruction and system-level recovery. The district credits new curriculum, instructional coaching, and a focus on foundational skills as key drivers. Imagine Learning is proud to be one of the partners supporting this work.

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October 9, 2025 5:14 pm

Imagine Learning launches a digital K–5 literacy program that aims to prepare students for the future 

Published by: ETIH

Imagine Learning, a digital curriculum solutions provider, has launched Dragonfly, a K–5 English Language Arts program that combines skills, knowledge, and dynamic media.

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October 9, 2025 5:14 pm

Imagine Learning Unveils Innovative K–5 Literacy Program 

Published by: Investors Hangout

Imagine Learning, known for its commitment to enhancing educational opportunities, has introduced a groundbreaking K–5 English Language Arts program called Dragonfly.

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