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.

Text-to-Speech Now Available in Imagine IM

Imagine EdgeEX

December, 2024

Increased accessibility for all students 

We are thrilled to share Imagine IM’s latest enhancement: text-to-speech. 

With text-to-speech, students can hear their assignments read out loud, making it easier to connect with the content. As the words are spoken, they’re highlighted on the screen, improving focus and supporting literacy development. 

Teachers have full control of the text-to-speech feature in class settings. You can adjust it for the entire class or turn it on for specific students, making it adaptable to your classroom’s unique needs. 

Intelli-Sync is Expanding to Middle School Math, ELA, and Physical Science

Imagine EdgeEX

December, 2024

Support grade 6 students with synchronous online instruction

Starting in spring of 2025, Intelli-Sync will expand its middle school offerings to support 6th grade math and ELA and middle school physical science. This expansion provides schools with an effective solution for filling teacher vacancies in these high-demand subjects.  

With these additions, districts can meet their instructional needs with expert certified teachers of record in high school subjects and middle school math, ELA, and physical science. 

Learn more about the Intelli-Sync service and discover why blending synchronous and asynchronous instruction is so effective.  

6th grade boy using Intelli-Sync services

Imagine MyPath Grades 6–12 Lesson Refresh

Imagine EdgeEX

December 2024

Enhanced visuals and audio to increase student engagement

The Imagine MyPath grades 6–12 lessons are getting updated! While the video scripts, Mastery Checks, worksheets, and other resources you are familiar with will stay largely the same, updates to the visuals and audio will make the lessons more dynamic and engaging for your students. With approximately 40 lessons currently complete, you can expect to see the refreshed versions of all the lessons release on a rolling basis between now and September 2025. Keep an eye on the updated lesson video list in Imagine MyPath in the Help Center for the most up-to-date list of newly refreshed lessons. 

December 6, 2024 4:21 pm

School of the Week: Students thrive at Thomas Mifflin School

Published by: The Philadelphia Tribune

The success of the Thomas Mifflin School does not just rely on the students’ academic excellence and personal growth. The teachers, parents and staff also play a pivotal role by providing students with endless opportunities they might not receive anywhere else.

Read Full Article

May include subscriber-only content

Traverse Explorer

U.S. History 

The Attack on Pearl Harbor 

Explore the events of December 7, 1941, at Pearl Harbor. 

Engage

Learn about Pearl Harbor’s location significance in the Explainer video. 

Analyze

A Day of Infamy

Genre: Speech | Creator: Franklin D. Roosevelt | Date: 1941 

Background 

One day after the Japanese attack on Pearl Harbor, President Franklin D. Roosevelt delivered this speech to a joint session of Congress. In describing the actions of the Japanese military, Roosevelt hoped to convince Congress to declare war against Japan and usher American troops into World War II. 

Discover President Roosevelt’s reaction to the attack on Pearl Harbor.

Transcript: 

Yesterday, December 7, 1941—a date which will live in infamy—the United States of America was suddenly and deliberately attacked by naval and air forces of the Empire of Japan. 

The United States was at peace with that Nation and, at the solicitation of Japan, was still in conversation with its Government and its Emperor looking toward the maintenance of peace in the Pacific. Indeed, one hour after Japanese air squadrons had commenced bombing in the American Island of Oahu, the Japanese Ambassador to the United States and his colleague delivered to our Secretary of State a formal reply to a recent American message. And while this reply stated that it seemed useless to continue the existing diplomatic negotiations, it contained no threat or hint of war or of armed attack. 

It will be recorded that the distance of Hawaii from Japan makes it obvious that the attack was deliberately planned many days or even weeks ago. During the intervening time the Japanese Government has deliberately sought to deceive the United States by false statements and expressions of hope for continued peace. 

The attack yesterday on the Hawaiian Islands has caused severe damage to American naval and military forces. I regret to tell you that very many American lives have been lost. In addition American ships have been reported torpedoed on the high seas between San Francisco and Honolulu. 

Yesterday the Japanese Government also launched an attack against Malaya. 

Last night Japanese forces attacked Hong Kong. 

Last night Japanese forces attacked Guam. 

Last night Japanese forces attacked the Philippine Islands. 

Last night the Japanese attacked Wake Island. And this morning the Japanese attacked Midway Island. 

Excerpted from “President Franklin D. Roosevelt’s ‘Day of Infamy’ Speech.” 

Collaborate

Lift-A-Line 

Have students identify one phrase from A Day of Infamy they particularly noticed. Have them use this line to write a Lift-a-Line poem. Students should 

  • start with the line they lifted from the source; and  
  • write several lines that communicate an idea or emotion connected to the source or chapter. 

Partner students to share their poems and discuss similarities, differences, surprises, and takeaways. 

Call on several students to share how writing or discussing their poems shaped their understanding of the source or chapter.  

Teacher Resources

Think Like a Historian: Sourcing Information

Use this additional sourcing information to further contextualize the source in order to deepen students’ analysis and evaluation. 

Summary

This is the first part of the famous speech from President Roosevelt to a joint session of Congress the day after the Pearl Harbor attack. In the speech, he informs the public about the bombing. 

Purpose

The purpose of the speech was to persuade both Congress and the American people that war was the only way to respond to the Japanese attack. 

Intended Audience

The audience was Congress, the American people listening on the radio, and the broader international audience of Japanese leaders and U.S. allies. 

Source Considerations

Roosevelt had long wanted the United States to become involved in World War II, and the bombing of Pearl Harbor was the tipping point. The speech was aired live on the radio. Roosevelt concludes the speech by asking Congress to declare war. They did so 30 minutes later. 

Scaffolding and Differentiation: Reading Comprehension Support

Genre    

The power of this speech, combined with the shock of the attack, persuaded Congress to quickly declare war, and it won the assent of the American populace. Ask students to reflect on the rhetoric Roosevelt uses. 

Vocabulary  

Vocabulary that may challenge students includes infamy and solicitation. Be sure students are aware that Guam, the Philippines, Wake Island, Midway Island, and Hawaii were U.S. territories at the time of World War II. 

Analyze and Discuss

To extend discussions, consider asking the following questions.

  • What are two quotes from the source that reflect the author’s perspective on the bombing of Pearl Harbor?
    • (Answers will vary but may include “Yesterday, December 7, 1941—a date which will live in infamy—the United States of America was suddenly and deliberately attacked” or “I regret to tell you that very many American lives have been lost.”) 
  • How would you summarize each of these quotes in your own words?
    • (Answers will vary but may include “The decision to cover some candidates more than others is often driven by economics, as outlets want to publish stories they think will drive traffic;” “many publications differentiate themselves by shifting from news to analysis;” or “Thanks to data-journalism tools that make verification fast and accurate, fact-checking has become a major part of the election media cycle.”)

December 2, 2024 10:00 am

Imagine Learning Acquires Pango Education to Advance AI-Powered Personalized K–12 Solutions

Strategic Acquisition Accelerates Imagine Learning’s Efforts to Create Impactful, Curriculum-Informed AI™ for Schools

Tempe, Arizona — December 2, 2024 — Imagine Learning, the nation’s largest provider of digital-first curriculum solutions, today announced the acquisition of Pango Education, a UK-based generative AI platform tailored for educational purposes. This strategic move enhances Imagine Learning’s capacity to deliver innovative, AI-driven solutions that empower educators and create impactful learning experiences.

Imagine Learning’s acquisition of Pango Education accelerates the development of its proprietary Curriculum-Informed AI™ tools, designed to address the growing need for personalized, standards-aligned educational solutions. With Pango’s innovative technology, Imagine Learning will enhance its ability to support educators in creating custom lesson plans and assessments, streamlining workflows, and responding quickly to evolving curriculum standards nationwide. This integration ensures that Imagine Learning’s solutions not only save teachers time but also deliver more engaging and effective learning experiences for students, meeting the diverse needs of today’s classrooms.

Elevating Education with Curriculum-Informed AI™

Imagine Learning’s Curriculum-Informed AI™ represents a new paradigm in education technology, providing a safe, reliable, and curriculum-aligned foundation for AI-powered tools. Unlike solutions trained on broad internet data or static textbooks, Imagine Learning’s AI operates within its research-based curriculum to ensure every interaction meets the highest educational standards.

“We are excited to integrate Pango Education’s innovative AI technology into Imagine Learning’s robust curriculum portfolio, setting the stage for transformative advancements in personalized learning,” said Jonathan Grayer, Chairman and CEO of Imagine Learning. “This acquisition amplifies our ability to customize lesson plans, adapt to evolving state standards, and create seamless, impactful learning experiences for the 18 million K–12 students we serve.”

Pango was founded in London, England, in 2018 by former math educator Adam Still and software engineer Richard Still. Their platform was developed to help teachers save time by streamlining access to diverse educational resources. By bringing Pango’s technology into its portfolio, Imagine Learning will expand its ability to offer educators practical, customized tools that address classroom needs more efficiently and effectively.

“Integrating Pango’s AI capabilities allows us to provide teachers with more control and flexibility in creating lesson plans and assessments,” said Jason Fournier, VP of Product Management, AI Initiatives at Imagine Learning. “This alignment with our rigorous content standards ensures that educators can meet the unique needs of their students while adapting quickly to curriculum and standards changes. The result is a set of tools that keeps pace with the demands of today’s classrooms.”

Imagine Learning reinforces its commitment to empowering educators with tools that address real-world challenges in the classroom by integrating Pango’s technology. Combining curriculum-aligned innovation with practical solutions advances Imagine Learning’s mission to support teachers and enhance student learning outcomes. This acquisition marks another step forward as Imagine Learning provide resources to meet the evolving demands of K–12 education.

About Imagine Learning

Every classroom, every student is bursting with potential. That’s why we pursue relentless innovation at the intersection of technology, people, and curricula. Imagine Learning creates K–12 digital-first solutions, working alongside teachers to support 18 million students in over half of the districts nationwide. Our core portfolio includes Imagine IM, Imagine Learning EL Education, Twig® Science, and Traverse. Our robust supplemental and intervention suite equips learners with personalized instruction for English and Spanish literacy, math, coding, and more. Imagine Edgenuity® and Imagine EdgeEX offer innovative courseware solutions, complemented by Imagine School Services’ Certified Teachers. Imagine Learning. Empower potential. Learn more: imaginelearning.com.

Organize Courses into Trimesters, Quarters, or Modules in Imagine EdgeEX

Imagine EdgeEX

November, 2024

More flexibility with course organization

Educators can now create custom course splits. They can organize a course into trimesters, quarters, or modules to align with their grading/marking periods. 

Course customization in Imagine EdgeEX

Filter the Launchpad in Imagine EdgeEX

Imagine EdgeEX

November, 2024

Quickly find exactly the information you need

Get to what you need in the Launchpad faster! Educators can now use filters in each widget to view the specific enrollments they wish to act on — saving them time. 

Create Sections in Bulk in Imagine EdgeEX

New Views Available in Imagine MyPath Cumulative Standards Proficiency Report  

Imagine EdgeEX

November 2024

Now Available: District-and School-Level Views 

Have you had a chance to use the new Cumulative Standards Proficiency Report yet? Using student performance data from lesson mastery checks, this report provides a comprehensive view of students’ mastery of grade-level state standards to help you to easily identify skill gaps, tailor instruction, and support student learning.  

The report is available at the student-, class-, and now school- and district-levels. Read more about this helpful report and how to use it. 

school vs district views

New Rostering Experience Across Supplemental Suite

Imagine Learning Supplemental Suite

November 2024

Easily print scannable student login cards 

Additional functionality has been added to the new rostering experience for Imagine Language & Literacy, Imagine Español, Imagine Galileo K–12, Imagine MyPath, Imagine Science Corner, and Imagine Purpose. Educators can now print student login cards for classes or individual students.  

These cards also contain a QR code that can be scanned with the device’s camera to log in without a username and password. We recommend sending family letters home with login cards so parents and caregivers understand how to help students use these programs outside of school. Learn more. 

ID card example