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.

New Quick Score Feature in ILC Speeds Up Grading 

Imagine IM

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 

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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 

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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 

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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 

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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.

New Feedback Support in SoR Lesson Plans 

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Imagine Language & Literacy now includes guidance for responding to student errors 

We’ve added corrective feedback guidance to all 10 Science of Reading lesson plans in Imagine Language & Literacy. This update supports teachers in responding to student errors with clarity and encouragement. Find the new guidance in the printable lesson plans under Teacher Resources — designed to make instructional feedback more effective and confidence-building. 

New Pre-Reading Printables for Leveled Books

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Offline activities in Imagine Language & Literacy boost engagement before reading 

Imagine Language & Literacy now includes offline pre-reading activities to support student engagement and teacher feedback. Designed to pair with the digital Think Aloud with Blurb task, these printables help students get ready to read. Find them in Teacher Resources → Leveled Books → Leveled Books Printables. 

Clearer Assessment Views in Imagine Language & Literacy 

Imagine IM
Imagine IM

New widget shows BOY, MOY, and EOY status for all students in one place 

To support clearer progress monitoring, Imagine Language & Literacy and Imagine Español now display beginning, middle, and end of year assessment status in a single widget. All students appear in each view, even if a score is missing, with clear indicators of assessment status. Teachers can now quickly see what data is available and how growth is being measured. 

New Icon for Imagine Math Live Teaching 

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Updated screen icon reflects design change, service remains the same 

We’ve updated the Live Teaching icon in Imagine Math. The new teal icon replaces the previous photo, but the service itself remains unchanged. Starting in grade 3, certified teachers provide live, 1:1 support in English or Spanish to help students when they need it most. 

Learn More

How Great Leadership Starts with Great Partnership

Lauren Keeling | 01/29/2026 | 6 minutes

Navigating instructional change isn’t easy. It can be an anxious, messy, and even contentious process. In this blog post, Lauren asks how leadership can strengthen that work by building trust and inviting teachers into the process — and explores how meaningful progress depends on shared ownership rather than top-down direction.

Teacher reading to kids in a classroom

What does it take to be a great leader through change? Sadly, there’s no single answer (wouldn’t it be easier if there were?), but one thing is clear: effective leadership isn’t defined by a job description. 

We commonly think of leadership in terms of plans, protocols, and priorities, but sometimes, it’s just asking the right questions at the right time. Other times, it’s knowing when to step back so a teacher can step forward. Often, it’s simply pausing to listen — really listen. Somewhere between the district memo and the classroom door, between the pacing guide and a teacher’s intuition, lives this less-obvious kind of leadership. It’s neither loud nor flashy. It asks, “What do you think?” and waits patiently for an answer. 

I’ve spent the last few years studying the more human-centered approach to leadership and the last two decades learning about it from some of the very best in education. As a Curriculum Advisor, I have the privilege of being shoulder-to-shoulder with teachers and leaders from every corner of the country. I strategize with educators who are leading the charge on change and seeking alignment between their instructional practices and what they know is best for students. I hear from administrators leveling the hierarchy when their team meets. They aren’t the boss: they’re stakeholders. And I can tell, almost instantly, when teachers have been at the table from the start. Their posture is different. Their questions are deeper. Their ownership is evident. 

During my years as an educator, I’ve been part of many curriculum adoptions and change initiatives — as a teacher, as a principal, and as a partner to schools — and I’ve seen them soar, and I’ve seen them sink. I can only hope that I helped initiatives in my district soar, but I know for a fact I was the reason some sank. And the difference was almost always the same: collaboration. Not the kind that’s written into an email, but the kind that’s built on trust, time, and shared purpose.  

School Admin

Kelsie Pennington, Assistant Director of Interdisciplinary Literacy in the Pendergast Elementary School District, and Akin Akinniyi, School Counselor at Villa De Paz Elementary School.

School Admin

We often discuss collaboration in education. It shows up in mission statements, in professional learning communities, in the language of reform. But too often, what we call “collaboration” is just coordination. Or worse, compliance. The decisions have already been made. The meeting is just a formality. And the people most impacted by the change — teachers — are left to implement something they didn’t help shape.  

This disconnect is what inspired my dissertation research. I wanted to understand what collaborative leadership really looks like in the day-to-day work of schools, especially during moments of significant instructional change. I am in the thick of interviews and data collection, focused on elementary educators and administrators navigating curriculum reform. But the reality is, I’ve been asking these questions for a long time, not as a researcher, but as a partner in change management. I sit at a lot of tables, from coaching sessions and leadership meetings to curriculum planning days. And in those spaces, I’ve been listening, wondering, and asking questions: What does collaboration feel like? What helps it thrive? What gets in the way? 

What I’ve found isn’t surprising but deeply affirming. When collaboration is real, it’s relational. It’s built on trust, not titles. It’s not about everyone agreeing, but it’s about everyone being heard. Teachers described feeling most engaged when their voices were invited early, when their expertise was honored, and when leaders created space for shared decision-making. Administrators described the tension of balancing mandates with meaning, and the intentional work it takes to shift from “managing change” to “leading with.” Teachers described it as “safe.” 

Principle González

Erin Serock, a school-based teacher leader in the School District of Philadelphia, and Abraham Gonzalez, school principal at Villa De Paz Elementary School.

School Admin

Here’s the simple truth: collaboration isn’t always efficient or neat, but it is necessary. And when teachers are part of that process, they become co-authors in the work. Recently, I spoke with Jana Murphy and Nicole Silva, two instructional coaches who led a major instructional shift in  Marshfield Public Schools. They spoke to this directly. As they put it, the work “was bumpy… it’s always going to be bumpy,” but they emphasized how valuable their collaboration meetings were, giving them space to “hear [teachers’] thoughts and perspectives and worries and concerns.” That ongoing relationship building, they said, “has been what’s sustained us” through the process. What I found especially powerful about their approach was how they didn’t shy away from vulnerability themselves, reminding their teams, “This is uncomfortable for us too. We have not taught this way either.” 

As schools continue to navigate change — new standards, new materials, new expectations — we have a choice. If we want sustainable change, we need to stop treating collaboration like a checkbox. We have to build structures that invite the teacher’s voice early, before the decision is made. We also have to redefine leadership as something shared, not something held. And we have to remember that buy-in isn’t something you get, it’s something you build. So the next time we gather around the table, whether it’s a PLC, a leadership team, or even after a long day together with our team, may we remember that collaboration extends beyond a strategy. It’s a stance, a commitment, a way of being together that says: you matter here.     

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About the Host

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.

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