Building Conceptual Understanding and Habits of Mind in Mathematics (2024)

May 21, 2024 9:04 am

Teachers spend a lot of their own time finding the right resources to connect with every student. We know it’s a time-consuming task, especially with everything else on their plates. High-quality instructional materials (HQIM) lighten the load, helping ensure consistent, engaging lessons while giving teachers back some much-needed time.

High-Quality Instructional Materials in Imagine IM

What Are HQIM?

As educators and districts recognize the critical role curriculum plays alongside effective teaching, the focus on HQIM has intensified nationally. A growing body of research points at one thing: instructional materials directly impact student outcomes (Kane et al., 2016). But the reality is, not all teachers have access to HQIM or the professional development and support to implement these resources effectively.

But what are HQIM? Generally, HQIM are recognized as materials that are aligned to state standards and include evidence-based strategies, inclusive practices, and embedded teacher support. And when it comes to nurturing positive math identities — the demand for engaging resources has never been higher.

The Impact of HQIM in Math

The truth is, math not only prepares students for future careers; it also enhances critical thinking and problem-solving skills essential for everyday life. Recent research shows significant shortcomings in math education, underscoring the urgent need for materials that address learning gaps and prepare students for the complexities of modern careers.

There’s no question that teachers’ expertise is crucial to boosting student outcomes, but mounting evidence shows that materials do matter, with EdReports revealing that only 41% of math materials fully meet standards. Fortunately, we can reverse this trend by giving teachers access to resources that exemplify the principles of HQIM in math.

Verified HQIM

Imagine IM scores “All Green” on EdReports

Illinois Success Story

CCSD59 wanted a problem-based curriculum that was accessible for all students. The result? Significant gains in math proficiency with Imagine IM.

Digital-Forward Tools and Features

An instructional experience that leverages the power of digital tools and problem-based curricula.

How Does Imagine IM Meet Key HQIM Criteria?

Definitions of HQIM vary, but at their core they share vital components. At Imagine Learning, all of our core programs are designed to deliver key benchmarks for HQIM.

1. Standards-Aligned Content

There’s no doubt about it — standards-aligned materials give all students the opportunity to acquire the necessary skills to progress academically and move into future careers.

Math educators can enjoy peace of mind with Imagine IM, an enhanced IM v.360 program that’s fully aligned with Common Core and state math standards. Given that Illustrative Mathematics CEO and cofounder Bill McCallum was a lead writer of the Common Core State Standards, the curriculum’s adherence to these benchmarks is especially robust and well-founded.

2. Best-Practice Pedagogy

Research-based instruction helps teachers meet the diverse learning needs of their students. Whether through the use of manipulatives or real-world problem-solving, research-based strategies make math easier and improve performance.

That’s why Imagine IM has a problem-based instructional framework that helps structure lessons so students are the ones engaging in mathematics. Activities and routines give teachers opportunities to see what students already know, what they can notice, and what they can figure out before they have concepts and procedures explained to them.

To support student understanding, Imagine IM integrates three key aspects of mathematical rigor: conceptual understanding, procedural fluency, and the application of these skills to solve mathematical problems. The result? Students emerge more confident, ready to tackle complex challenges.

3. Equity and Inclusion

In a time when math proficiency is declining, it’s vital that we give every student an equal shot at success. Imagine IM is designed with three key principles in mind to support all learners:

  • Providing access for everyone
  • Presuming competence
  • Providing a strength-based approach

The program emphasizes endurance and perseverance through carefully crafted structures that address the complexity of contexts, numbers, and computations, accommodating different levels of understanding in complex mathematical contexts. Comprehensive supports for multilingual learners ensures all materials are inclusive and unbiased, representing a wide range of cultural identities.

4. Teacher and Student Experience

Imagine IM provides an unparalleled IM v.360 resource for both teachers and students, offering enhanced materials designed to support educators in planning and conducting lessons across diverse instructional settings. With a premium classroom solution tailored specifically to their needs, teachers can refine their skills as facilitators with high-quality, point-of-use supports that streamline their workflow and offer valuable implementation guidance. Exclusive print versions of Teacher Guides and Student Workbooks are seamlessly integrated with digital components, ensuring the integrity of Illustrative Mathematics content in any classroom model.

The curriculum’s instructional routines establish frameworks that enable all students to actively participate in mathematical discussions, fostering fluency in digital tools, problem-solving abilities, and effective communication of reasoning. Through rigorous problem-based design and engaging resources, Imagine IM cultivates a supportive community where students of all backgrounds can build confidence and acquire skills applicable throughout their academic journey, careers, and beyond.

5. Measuring Student Learning

Imagine IM offers opportunities for both formative and summative assessment that empower teachers to measure student understanding and progress toward learning goals.

Teachers are equipped to monitor student progress through digital task statements, section checkpoints, and cool-downs. These provide real-time feedback and data to inform instructional decisions.

Digital assessments allow students to access, record, and submit their questions and answers for a variety of technology-enhanced item types including multiple choice, multiple select, drag-and-drop, cloze, graphing, labeling, constructed response, short essay, and drawing types.

6. Professional Learning

Simply selecting HQIM isn’t enough. Teachers need robust professional learning to support their use in the classroom — that’s why professional learning is a crucial pillar of HQIM.

Imagine IM does more than just introduce educators to the curriculum — it equips them with the tools for implementation success. Virtual and in-person professional learning options meet diverse needs, while the digital platform offers ongoing self-directed professional development, plus insightful narrative and lesson example videos.

  • Year one: Focus on building teachers’ understanding of problem-based math instruction, helping them master both print and digital resources and establishing effective classroom routines.
  • Year two: Training emphasizes capacity building and specialization, enabling teachers to fully leverage specialized features and refine their instructional strategies.
  • Year three and onwards: The focus shifts to sustaining and enriching these practices, ensuring continued engagement and effectiveness.

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Building Conceptual Understanding and Habits of Mind in Mathematics (2024)

FAQs

How do you build conceptual understanding in math? ›

7 Strategies to Teach Conceptual Understanding in Math
  1. Spiral Practice Through a Well-Thought-Out Scope and Sequence. ...
  2. Use High-Order Tasks to Build Critical Thinking Skills. ...
  3. Visual Representations for Better Retrieval. ...
  4. Manipulatives and Hands-On Learning. ...
  5. Connect Concepts Instead of Teaching Math Shortcuts.
Apr 17, 2023

What does conceptual understanding mean in math? ›

Conceptual Understanding in Math: Definition

Students with conceptual understanding of mathematics can apply and adapt prior knowledge to new tasks, in effect making math applicable beyond solving just a single math problem. Again, it is useful to compare conceptual understanding to procedural fluency.

What is the mathematical habit of mind? ›

The Mathematical Habits of Mind (MHM) are an integral part of the College- and Career-Readiness Standards for Mathematics. The Mathematical Habits of mind are the skills and dispositions students need developed in their PK-12 education. The follow documents examine each of the Mathematical Habits of Mind in depth.

What is an example of conceptual learning in math? ›

Often contrasted with procedural math instruction, conceptual math focuses on explaining why processes work rather than on how to perform a process. A great example to illustrate a conceptual versus procedural approach is with subtraction that requires regrouping, or borrowing.

What is building conceptual understanding? ›

With conceptual understanding, students fully grasp the connections between math facts, rules, and principles and can create specific solutions without losing their actual meaning. It's a powerful web of math ideas forming an organic whole that's strongly connected with student math experience.

How do you develop conceptual thinking? ›

How to start thinking conceptually
  1. Observe leadership.
  2. Use challenges as case studies.
  3. Seek outside knowledge.
  4. Stay up-to-date on the industry.
  5. Apply new practices.
  6. Discuss concepts with colleagues.
  7. Find a mentor.
  8. Learn about the organization.
Jul 21, 2022

How to improve conceptual understanding? ›

Read critically.

Reading books, articles, blog posts, reports, and studies can help you practice thinking in new ways and open your mind to new perspectives. It can also push you to conceptualize new types of problems and generate creative ideas.

How to understand concepts in maths? ›

Understanding Mathematics
  1. Explain mathematical concepts and facts in terms of simpler concepts and facts.
  2. Easily make logical connections between different facts and concepts.
  3. Recognize the connection when you encounter something new (inside or outside of mathematics) that's close to the mathematics you understand.

How to teach basic maths concepts? ›

10 Strategies for effectively teaching math to elementary schoolers
  1. Use hands-on learning methods. ...
  2. Incorporate visuals. ...
  3. Integrate math games into math lessons. ...
  4. Connect math concepts to everyday life. ...
  5. Allow students to explain their reasoning. ...
  6. Give frequent feedback and direction. ...
  7. Reward progress. ...
  8. Personalize lessons.
Sep 9, 2021

How can I sharpen my mind in maths? ›

6 Mental Math Strategies | Tips and Tricks for Students
  1. Rounding up to the nearest ten. ...
  2. Work from left to right. ...
  3. Use multiplication hacks. ...
  4. Bump the decimal over to easily find a percentage. ...
  5. Make guesstimates. ...
  6. Break down the problem.
Nov 9, 2020

How can I train my brain to think mathematically? ›

Simple Tips & Tricks for How to Get Better at Math
  1. Brush Up on Basic Math Problems. ...
  2. MentalUP Math Games. ...
  3. Use Mental Math. ...
  4. Practice Math in Everyday Scenarios. ...
  5. Solve Puzzles and Riddles. ...
  6. Break Down Complex Problems Into Smaller Ones. ...
  7. Join a Study Group. ...
  8. Utilize Practice Tests.
Jul 21, 2023

What is the habit of mind concept? ›

The Habits of Mind are a set of thinking dispositions at the core of social, emotional, and cognitive behaviors. They are displayed by intelligent people in response to problems, dilemmas, and enigmas.

How do you explain conceptual understanding in math? ›

Conceptual understanding refers to an integrated and functional grasp of mathematical ideas. Students with conceptual understanding know more than isolated facts and methods. They understand why a mathematical idea is important and the kinds of contexts in which is it useful.

What do you mean by conceptual understanding? ›

Conceptual understandings, or generalizations, are statements that show a relationship between concepts. They help us design engaging, relevant units for your students by providing a bigger picture of the content.

How do students demonstrate conceptual understanding? ›

Provide students with examples of a concept and invite them to find common attributes and write their own definitions using a stem, such as, “Migration is when _____.” Share a concept and ask students to generate their own examples or non-examples. These can be represented in words or pictures.

How to increase conceptual understanding? ›

3 Ways to Promote Conceptual Thinking. 1. Using categorizing, naming, and sorting activities: In order to understand individual concepts, students need to grapple with examples, non-examples, and attributes of a concept. We can ask students, “What is it like?” and invite them to describe the key features.

How is conceptual understanding developed? ›

Simply put, engaging and encouraging students to reach the concept's meaning and apply it to other solutions is one of the ways to develop conceptual understanding. Active participation is critical for building conceptual understanding.

What is conceptual approach to teaching mathematics? ›

As the name suggests, a conceptual approach requires a greater focus on teaching the concepts or ideas of mathematics and making sure students understand the connections between them.

What is conceptual understanding methods? ›

Conceptual understanding should act as the foundation of math instruction rather than rote memorization of procedural skills like algorithms and equations. It helps students move beyond understanding the “what” of mathematical operations to the “why” and “how”.

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