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.

Tell Me More

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.

ClassLink SSO for Small Group Targeted Instruction 

Imagine IM

February 2026

Students enrolled in Small Group Targeted Instruction can now access sessions directly through ClassLink. With one-click login, your students spend less time navigating credentials and more time engaged in instruction. Clever is also supported, giving districts flexibility while simplifying access and supporting consistent participation in high-impact tutoring. 

Screenshot of a Small Group Targeted Instruction session

More Flexible Scheduling in Imagine+ Assessment 

Imagine IM

February 2026

Bulk reassign assessments and reopen testing windows with fewer steps 

We’ve expanded the Flexible Scheduler in Imagine+ Assessment to give administrators more control. You can now bulk reassign an assessment to a group of students at once, making it easier to provide another opportunity without manual updates. You can also reopen a closed assessment window, so testing can resume without creating a new schedule. These updates help you save time and keep assessment plans on track. 

Learn More
Student reassignment page for Imagine Plus Assignment

New Submission Alert in Imagine+ EarlyBird Screener 

Imagine IM

February 2026

Pop-up notifies users when subtests are incomplete before submission 

We’ve added a new pop-up alert in Imagine+ EarlyBird Screener to reduce confusion around incomplete results. If a student or educator attempts to submit the screener with subtests still in progress or incomplete, a pop-up window lists those subtests and explains that unfinished sections will not appear in the report. This update helps ensure your students receive complete, accurate results and sets clearer expectations before submission. 

February 24, 2026 9:00 am

Imagine Learning Foundation Announces 2026 Signature Grant Cycle to Expand Well-Being of Learners Beyond the Classroom

New funding priority will support nonprofit partners empowering K–12 youth as leaders and contributors in their communities.

Tempe, Arizona — February 24, 2026 — The Imagine Learning Foundation (ILF) today announced the launch of its 2026 Signature Grant Program, continuing its commitment to expanding meaningful opportunities to support the well-being of students and their support groups nationwide — at home and throughout the communities where they live and grow. 

The 2026 grant cycle will prioritize nonprofit organizations that engage young people in authentic, age-appropriate service experiences rooted in their homes, neighborhoods, and community spaces. The focus reflects ILF’s continued evolution toward supporting programs that build connection, confidence, and purpose to support academic growth and achievement. 

For the 2026 cycle, the Imagine Learning Foundation will prioritize nonprofit partners who intentionally design service opportunities where youth can lead, collaborate, reflect, and succeed. 

ILF seeks programs that: 

  • Activate a student’s full support ecosystem: families, caregivers, mentors, and community members
  • Integrate reflection and skill-building into service experiences
  • Center youth voice and leadership
  • Foster connection and a strong sense of purpose
  • Extend enriching learning environments beyond the classroom 

Unlike traditional volunteer initiatives, ILF’s 2026 focus is on service as a meaningful learning pathway — not just participation, but ownership and growth. 

“Young people want to make a difference,” said Chris Graham, Chairman and President of the Imagine Learning Foundation. “When we create space for them to lead and serve in their own communities, we’re supporting more than just academic learning — we’re helping them discover their strengths and their sense of purpose.” 

By supporting community-rooted, youth-centered service, ILF seeks to help students grow in a manner that will expand into everyday life, empowering students to flourish beyond the classroom, which improves learning outcomes. 

How to Apply 

Eligible nonprofit organizations are invited to apply for the 2026 Imagine Learning Foundation Signature Grant Program, with applications due by April 9, 2026, at 11:59pm PST. Award decisions are expected to be announced in June 2026. 

For eligibility requirements, application guidelines, and deadlines, visit www.imaginelearningfoundation.org. 

About 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 non-profit organizations that focus 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 digital-first solutions, working alongside teachers to support 18 million students in over half of the districts nationwide.

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February 23, 2026 8:00 am

Imagine Learning Partners with Modern Classrooms Project to Drive Stronger Math Outcomes Through Improved Implementation 

New partnership supports districts in deepening instruction and accelerating student growth in math.

Tempe, Arizona — February 23, 2026 — Imagine Learning today announced a partnership with the Modern Classrooms Project (MCP) to help districts accelerate student achievement in math through stronger curriculum implementation. The partnership enhances support for Imagine IM, Imagine Learning’s K–12 problem-based math curriculum, by equipping teachers with clear systems for differentiation, pacing, and small-group instruction. 

Districts nationwide are demonstrating that sustained curriculum implementation, paired with ongoing professional learning, leads to measurable growth in math achievement. Schools that maintain consistent lesson structures and invest in teacher support are seeing improved proficiency rates and stronger student problem-solving skills. 

“When teachers have the right support, students make real gains,” said Krysia Lazarewicz, Vice President of Professional Learning & Customer Success at Imagine Learning. “This partnership strengthens the daily classroom systems that lead to stronger outcomes in math.” 

Building Classrooms That Deliver Results 

In schools where Imagine IM is implemented well, students tackle meaningful problems, work together, and explain their thinking. Teachers guide discussion and connect ideas — keeping learning centered on student reasoning. 

Sustaining that level of instruction requires systems that help teachers manage diverse learning needs without losing momentum. 

The Modern Classrooms Project provides those systems through: 

  • Blended instruction that creates time for targeted small-group support 
  • Flexible pacing so students move forward when they demonstrate understanding
  • Embedded mastery checks that generate clear, actionable next steps 
  • Ready-to-use materials aligned to a high-quality curriculum 
  • Year-long mentorship and coaching to ensure strong implementation 

These supports work alongside Imagine IM and can integrate directly into Imagine Learning’s platform. 

After using Modern Classrooms Project’s tools and resources, one educator shared, “The Modern Classroom program is a transformative approach that empowers teachers to create more flexible and student-centered learning environments. This training equips teachers with valuable tools and strategies to increase student engagement and success, and the ongoing mentorship ensures that teachers feel supported throughout the process. It’s a great investment in both teacher development and student achievement.” 

Sustaining Growth 

This partnership is designed for districts in year two and beyond that want to deepen differentiation, expand small-group instruction, and strengthen classroom consistency. 

By combining Imagine IM with MCP’s support model, districts gain a clearer path from curriculum adoption to sustained student growth. 

“Effective math instruction requires both strong materials and strong systems,” said Kareem Farah, Co-founder & CEO at Modern Classrooms Project. “We’re excited to support teachers using Imagine IM and help them meet the needs of every learner.” 

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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New Quick Score Feature in ILC Speeds Up Grading 

Imagine IM

January 2026

Teachers can now enter scores faster — no need to open each submission 

Quick Score is now live in Imagine Learning Classroom, giving teachers a faster way to enter scores for student work done outside the platform. Use the new panel to score from the assignment view, with min/max buttons or manual entry. Quick Score saves time when grading printed work or in-the-moment instruction, removing the need to click into each submission. 

Watch the Demo
Imagine Math Demo video

New MOY Subtests and Office Hours for Imagine+ EarlyBird Screener 

Imagine IM

January 2026

Support for interpreting data and planning next steps is now available weekly 

The Middle of the Year Imagine+ EarlyBird Screener includes new subtests to support grade-level literacy insights. To help educators use their data effectively, free weekly office hours are now available. Join Reading Specialist Sharon Amos for guided support on reviewing results, spotting trends, and connecting data to instruction. 

See the Details
Imagine Plus Screener with EarlyBird flyer

Sortable Tables Now in Imagine Language & Literacy Reports 

Imagine IM

January 2026

Imagine Language & Literacy usage reports now include sortable tables at both the school and group levels. Educators and administrators can quickly sort by total or average weekly usage to spot trends, recognize participation, and target support. Data reflects the selected time frame, giving teams a clearer view of engagement and implementation. 

Updated Lesson Details in Progress Reports 

Imagine IM

January 2026

Improved table layout and clearer labels help educators interpret data faster 

We’ve refreshed the Lesson Details table under Progress by Lesson to make lesson status easier to understand at a glance. The column now labeled “Last Lesson Activity” clarifies recent status changes. A new Outcome column shows passed lessons with a green check and “tested out” with an arrow icon — helping educators quickly assess student progress with confidence. 

New Video Tutorials in Imagine Language & Literacy 

Imagine IM

January 2026

Short, targeted videos support onboarding and answer common questions in-product

We’ve added 16 new video tutorials to support in-product onboarding in Imagine Language & Literacy. Each 2–5-minute video covers a frequently asked question and appears where it’s needed most — on the homepage and in page-level Quick Tips. Topics include assessments, placement, instructional tools, and more, making it easier for educators to learn as they go.