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.

September 15, 2026 8:00 am

Imagine Learning and AIM Institute Collaborate to Advance Research-Informed Literacy Instruction 

Collaboration brings together Imagine Learning’s curriculum expertise and AIM’s research-to-practice perspective, beginning with Dragonfly™, Imagine Learning’s new K–5 core literacy curriculum.

TEMPE, Ariz. — September 15, 2026 — As states strengthen literacy requirements and districts work to translate the science of reading into effective classroom instruction, educators are navigating evolving research, new legislative requirements, and increasing expectations for student outcomes. To help meet these challenges, Imagine Learning today announced a thought leadership and advisory collaboration with the AIM Institute for Learning & Research (AIM), a nationally recognized leader in structured literacy, professional learning, and the science of reading. 

As a strategic advisor to Imagine Learning, AIM will provide literacy and research-to-practice expertise that informs the company’s work with educators and schools. This consultation and feedback will support Imagine Learning’s work to connect current research with practical applications while reducing the complexity educators face in implementing evidence-based literacy practices. 

“Districts don’t need more literacy initiatives. They need greater coherence,” said Kinsey Rawe, Executive Vice President and Chief Product Officer at Imagine Learning. “AIM has earned a national reputation for helping educators translate literacy research into classroom practice. Through this partnership, we’re strengthening how Imagine Learning connects curriculum, professional learning, and practical resources so educators can implement evidence-based instruction with confidence.” 

Dragonfly, Imagine Learning’s new K–5 core literacy curriculum grounded in the science of reading, will be the first program informed by the collaboration. The curriculum combines explicit foundational skills instruction with knowledge-building experiences designed to develop skilled readers. AIM’s expertise will inform Dragonfly’s continued development, along with related educator resources and professional learning. Imagine Learning’s Academic Design and Professional Learning teams will also complete AIM Pathways training to deepen internal literacy expertise and strengthen educator support. 

“Effective literacy instruction requires more than access to research or high-quality instructional materials; it requires systems intentionally designed to translate evidence into sustained classroom practice,” said Kristen Wynn, Head of AIM Institute for Learning & Research. “That means aligning leadership, curriculum, assessment, and data-informed decision-making around a comprehensive, multi-component approach to literacy — while equipping educators with ongoing professional learning, job-embedded coaching, and implementation support. Our advisory collaboration with Imagine Learning reflects a shared commitment to building the coherence and capacity schools need to strengthen instruction, respond to students’ needs, and improve literacy outcomes over time.” 

In addition to providing advisory input on Dragonfly curriculum, AIM will collaborate with Imagine Learning on white papers, webinars, conference presentations, and other resources focused on knowledge-building, integrated reading and writing, and literacy implementation. These combined efforts will provide district leaders and educators with practical guidance as literacy research and instructional expectations continue to evolve. 

The collaboration reflects a shared belief that effective literacy instruction depends on coherence among research, curriculum, professional learning, and implementation. Imagine Learning and AIM seek to help schools build literacy systems that better support educators and encourage leaders to use resources and student data to improve student outcomes. 

About Imagine Learning

Imagine Learning supports educators with curriculum and learning solutions designed to improve student outcomes. Serving students in more than half the districts nationwide, the company delivers a portfolio of core curriculum, courseware, supplemental solutions, assessment, and school services, combining high-quality curriculum, actionable insights, and instructional support to help districts make measurable progress. Nationwide, the company partners with school systems to meet the needs of each learner.

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September 14, 2026 8:00 am

Imagine IM High School Earns All-Green EdReports Ratings Across Traditional AGA and Integrated Math Pathways

Both math pathways meet expectations across all three gateways, with 100% scores for rigor and mathematical practices, as well as in teacher and student supports.

TEMPE, Ariz. — Sept. 14, 2026 — Imagine Learning today announced that both high school pathways of Imagine IM have earned all-green ratings from EdReports, meeting expectations across all three gateways evaluated by the independent, educator-led curriculum reviewer.

Imagine IM AGA, which includes Algebra 1, Geometry, and Algebra 2, and Imagine IM Integrated 1–3 each met expectations for Focus and Coherence, Rigor and Mathematical Practices, and Teacher and Student Supports. Both pathways earned 100% gateway scores in Rigor and Mathematical Practices, as well as in Teacher and Student Supports.

For districts evaluating high school mathematics materials, the results provide a strong, independent signal that Imagine IM meets expectations for quality across both traditional AGA and integrated pathways. Whether a district uses a traditional sequence or an integrated one, Imagine IM offers standards-aligned instruction, mathematical rigor, and instructional support.

“Earning all-green ratings across both high school pathways affirms the strength of the learning experience Imagine IM is designed to create,” said Kinsey Rawe, Executive Vice President and Chief Product Officer at Imagine Learning. “Students are not simply learning procedures or focused only on getting the right answer. They are making sense of problems, explaining their thinking, and building the deep mathematical understanding they will need for what comes next.”

EdReports found that both pathways balance conceptual understanding, procedural skill and fluency, and application while meaningfully connecting mathematical content with the Standards for Mathematical Practice. The reviews note that the materials “help students develop conceptual understanding, procedural skill and fluency, and application.” They also recognize the Imagine IM’s instructional guidance, learning progressions, year-long planning resources, assessment system, and support for determining instructional next steps.

Imagine IM is built on the latest Illustrative Mathematics IM® v.360 curriculum and optimized by Imagine Learning, a Certified Partner of Illustrative Mathematics. The program’s problem-based approach places students in an active role as mathematical thinkers while providing teachers with print and digital resources that support planning, instruction, assessment, and meaningful mathematical discourse.

These high school findings build on Imagine IM’s existing K–8 EdReports results. Across its current K–12 reviews, Imagine IM has earned all-green ratings in every core gateway reviewed by EdReports.

To learn more about Imagine IM and view the complete EdReports findings, visit EdReports.org.

About EdReports

EdReports is an independent nonprofit that publishes free, educator-led reviews of K–12 instructional materials. Its evidence-rich reports evaluate how materials are designed, including their alignment to college- and career-ready standards and other indicators of quality. Learn more at edreports.org.

About Imagine Learning

Imagine Learning supports educators with curriculum and learning solutions designed to improve student outcomes. Serving students in more than half the districts nationwide, the company delivers a portfolio of core curriculum, courseware, supplemental solutions, assessment, and school services, combining high-quality curriculum, actionable insights, and instructional support to help districts make measurable progress.

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September 9, 2026 8:00 am

Imagine Learning Foundation Names Nine Recipients of 2026 Signature Grants 

Foundation awards $630,000 to nonprofits supporting student well-being, mentorship, and youth service.

Tempe, Ariz. — Sept. 9, 2026 — The Imagine Learning Foundation (ILF) today announced $630,000 in awards under its 2026 Signature Grant program to nine nonprofit organizations working to support the well-being of young people at home and in their communities. 

This year’s recipients reflect both the breadth of the Foundation’s ongoing work and a new emphasis on Learning Through Service — supporting programs that give young people meaningful opportunities to serve, lead, collaborate, and make a difference in their communities. The Foundation is also continuing investments addressing chronic absenteeism, basic needs, mentoring, tutoring, and student homelessness. 

The grants continue the Imagine Learning Foundation’s five-year trajectory of investments in organizations addressing factors that can shape a young person’s ability to thrive. Since 2021, the Foundation has awarded more than $1.86 million through 40 grants, reaching more than 413,000 students in 1,700 communities across the United States. Its previous investments have addressed student mental health and well-being, chronic absenteeism, homelessness, basic needs, and other challenges facing young people and their families. “When the Board of Directors of Imagine Learning and I launched the Imagine Learning Foundation five years ago, I envisioned an initiative to support learners outside of the classroom,” said Jonathan Grayer, chairman and CEO of Imagine Learning. “Five years later, I am proud to see this vision being fulfilled year after year. We are honored to support this year’s grant recipients as they develop the next generation of leaders.” 

Learning Through Service is a new funding priority for 2026 and builds on the Foundation’s broader commitment to creating supportive environments for learners beyond the classroom. The Foundation sought programs that create authentic, age-appropriate opportunities for young people to lead, collaborate, reflect, and grow while engaging the families, caregivers, mentors, and community members around them. 

“Every year, we have the opportunity to learn from organizations that are deeply connected to young people and their communities,” said Chris Graham, chairman and president of the Imagine Learning Foundation. “This year, we were especially excited by programs that invite young people to be part of the solution — to work alongside their families, peers, and mentors, contribute to something meaningful, and discover what they’re capable of along the way.” 

The 2026 Signature Grant recipients are: 

  • Youth Volunteer Corps — $100,000: Supporting youth-centered service opportunities that enable young people to lead and contribute in their communities.
  • SOS San Antonio — $100,000: Supporting youth service programming that connects young people with meaningful opportunities to learn through service.  
  • SchoolHouse Connection + Attendance Works — $100,000: Continuing their work addressing chronic absenteeism and student homelessness, with a new research and AI focus.  
  • Anderson Humane — $75,000: Developing youth-led service opportunities through animal welfare and community engagement.  
  • Sleep in Heavenly Peace — $75,000: Expanding its work providing beds and essential sleep resources to children in need while adding opportunities for youth service.  
  • City Year — $50,000: Supporting mentorship and tutoring for students.  
  • Operation Warm — $50,000: Supporting young people through mentoring and access to essential items.  
  • Catie’s Closet — $50,000: Addressing basic needs that can contribute to chronic absenteeism.  
  • Boys & Girls Club of Alameda — $30,000: Supporting youth-centered community service experiences.  

With its 2026 Signature Grants, the Foundation is building on that work while creating more opportunities for young people to experience themselves not only as learners, but as contributors to the places they call home. 

To learn more about the Imagine Learning Foundation and its Signature Grant Program, visit the Imagine Learning Foundation website. 

About the Imagine Learning Foundation 

Imagine Learning Foundation is a nonprofit organization dedicated to fostering the well-being of learners and those who support them at home and in their communities. Established in 2021, the Foundation provides funding to mission-aligned national nonprofit organizations focused on enhancing the well-being of youth, families, and educators, with an emphasis on accelerating student achievement. Imagine Learning Foundation is the philanthropic initiative of Imagine Learning, a leading creator of K–12 learning solutions, working alongside teachers to support 18 million students in over half of the districts nationwide. 

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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See Student Thinking in Real Time with LiveLearn for Imagine IM

Imagine IM

August 2026

View class-wide responses as learning happens so you can quickly identify needs and adjust instruction 

The new Student Response Grid in LiveLearn gives teachers a live, class-wide view of student responses during instruction. Quickly see who may need additional support, adjust instruction based on what you see, and respond to your students’ needs while learning is happening.

Make Mathematical Thinking Visible with CueThink in Imagine IM

Imagine IM

August 2026

Help your students explain their reasoning while gaining deeper insight into how they approach
math problems 

CueThink supports problem-solving by guiding your students as they explain their mathematical reasoning with digital tools. Teachers gain insight into how students approach a problem, not just whether an answer is correct, providing more information to guide instruction. 

Meet Imagine ClassMate, Your AI Assistant for Imagine IM

Imagine IM

August 2026

Create math practice, plan lessons, find resources, and draft family communications with curriculum-informed AI  

Imagine ClassMate helps teachers save planning time with AI tools designed specifically for Imagine IM. Create math practice, build lesson plans, find curriculum resources, and draft family communications in multiple languages, all grounded in your Imagine IM curriculum. Learn more in the Imagine ClassMate Help Center or by watching the video.

New Assessment Accommodation in Imagine EdgeEX Courses

Imagine EdgeEX

August 2026

Support IEPs by reducing the number of incorrect answer choices available on multiple-choice questions 

Teachers have a new way to support student IEPs in Imagine EdgeEX courses. This new accommodation lets teachers reduce the number of incorrect options on multiple-choice questions by one or two. Deactivated choices remain visible to your students but appear grayed out and cannot be selected.

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Accommodations/Modifications in Edgenuity courses

Curriculum-Informed ClassMate AI Tools Come to Imagine EdgeEX

Imagine EdgeEX

August 2026

Save time on planning, communication, and instruction with AI tools informed by high-quality curriculum 

ClassMate brings curriculum-informed AI tools to Imagine EdgeEX to help teachers streamline common tasks. Built on high-quality instructional materials, learning science, and pedagogy, ClassMate supports planning, communication, and instruction while helping teachers make more efficient use of their time.

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ClassMate demo

Case Management Support for Special Education Teams

Imagine IM

August 2026

Dedicated support helps districts manage IEP compliance, coordination, documentation, and required processes 

Imagine Learning School Services case managers work alongside district teams to provide added capacity for IEP processes. From managing timelines and documentation to coordinating meetings, annual reviews, reevaluations, and transition planning, they help keep special education programs organized and compliant while giving educators more time to support students with exceptional needs. 

Access Traverse Content Anywhere with the Mobile App

Traverse

August 2026

Give your students access to social studies content offline through the mobile version of Traverse 

Your students can now use the mobile version of Traverse to access course content offline. This update extends access beyond a consistent internet connection, giving students more flexibility to use their social studies content when and where they need it.