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 to 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 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 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.

What is an example of conceptual learning in math? ›

With the conceptual learning approach, students would have schema, or prior knowledge and experience to draw on, that would help them understand how numbers are composed and can be broken apart. In our example, 54 can be broken down to (50+4) and 29 can also be seen as (20+9).

How can teachers support students in building conceptual understanding of mathematics concepts and skills? ›

To guide students toward more robust conceptual understanding, teachers need to give students opportunities to explore, engage in productive struggle, explain their thinking and connect their existing knowledge to the new content.

How to improve conceptual understanding? ›

Use these examples to apply conceptual thinking to your work:
  1. Reflect on project outcomes. ...
  2. Assess the reach of proposed solutions. ...
  3. Create organizational models and frameworks. ...
  4. Identify how your work supports the whole organization. ...
  5. Apply different ideas to projects. ...
  6. Practice identifying the context and purpose.
Jul 21, 2022

Why is it important to have a conceptual understanding of math? ›

To be successful in math, it is not enough to merely memorize steps. It is critical to understand why those steps work. A conceptual understanding of division allows the learner to navigate the process more quickly and check reasonableness along the way.

What is conceptual understanding methods? ›

Higher-order tasks are essential to building the critical thinking skills that lead to conceptual understanding. This type of thinking includes connecting ideas and expressing abstract thoughts. A great way to teach this is through fun “brain-teasers” that your students can complete after finishing any assignment.

What is conceptualization of mathematical ideas? ›

The term “conceptual understanding” refers to a comprehensive and practical grasp of mathematical concepts. Children who understand concepts are aware of more than isolated facts and methods. They comprehend why a mathematical concept is significant and how it can be applied in various situations.

How can I sharpen my mind in maths? ›

You'll give them the confidence to put their calculator away and start solving problems under their own steam!
  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 does it mean to build conceptual understanding in math? ›

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.

What is conceptual understanding math problem? ›

Conceptual understanding in math is the creation of a robust framework representing the numerous and interwoven relationships between mathematical ideas, patterns, and procedures. This framework can be used to coherently integrate new knowledge and solve unfamiliar problems.

What is 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 to develop mathematical understanding? ›

Talking with peers and adults about the patterns they or others have made, and matching and copying patterns provide opportunities for children to investigate patterns. They develop understandings about the ”repeating part of patterns” when these ideas are made explicit through games, music, chants, and actions.

How can I improve my math concepts? ›

8 Ways to Improve Math Skills at Home
  1. Understading the Concepts. ...
  2. Try Game-based Learning. ...
  3. Bringing Math Into Daily Life. ...
  4. Sketch & Practice Word Problems. ...
  5. Set Realistic Goals. ...
  6. Engage With A Math Tutor. ...
  7. Focus On One Concept At A Time. ...
  8. Embracing Technology to Improve Math Skills.
Jan 23, 2023

What is the procedure of conceptual understanding? ›

A Conceptual Understanding Procedure, or CUP, is a teaching procedure designed to aid development of understanding of concepts that students find difficult. They have been developed in physics but could be designed for other areas of study such as chemistry, mathematics and biology.

What are the components of conceptual understanding? ›

They state that there are three components of conceptual understanding: comprehension, operations and relations.

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