--- title: Schemas Are Key to Deep Conceptual Understanding description: In order to develop the kind of deep conceptual understanding students need to solve complex problems, they have to build schemas. ST Math helps students build those schemas through its visual instructional approach, by presenting puzzles that use a variety of models and non-routine problems. image: https://2024.mindresearch.org/hubfs/Schemas.png --- [![](https://2024.mindresearch.org/hs-fs/hubfs/MIND-logo-2018.jpg?width=1701&height=623&name=MIND-logo-2018.jpg)](http://www.mindresearch.org/) [![mind logo](https://2024.mindresearch.org/hubfs/graphics/logos/MIND-logos-color2.svg)](https://www.mindeducation.org/) [![mind white logo](https://2024.mindresearch.org/hubfs/graphics/logos/MIND-logos-white2.svg)](https://www.mindeducation.org/) - [Our Approach](https://2024.mindresearch.org/our-approach) - [Why MIND?](https://2024.mindresearch.org/why-math-education) - [Our Research](https://2024.mindresearch.org/our-research) - [Our Patents](https://2024.mindresearch.org/patents) - [Our Impact](https://2024.mindresearch.org/impact) - [Our Partners](https://2024.mindresearch.org/partners) - [Partner Stories](https://2024.mindresearch.org/partner-stories) - Our Programs - [ST Math](http://www.stmath.com/) - [InsightMath](http://www.insightmath.com/) - [MathMINDs](https://www.mindresearch.org/mathminds) - [Life at MIND](https://2024.mindresearch.org/careers) - Resources - [Blog](https://2024.mindresearch.org/blog) - [Math Discourse](https://2024.mindresearch.org/puzzletalks) - [Podcast](https://2024.mindresearch.org/edtech-podcast) - [News](https://2024.mindresearch.org/news) - [Activities](https://2024.mindresearch.org/stem-resources) - [Donate](https://store.mindresearch.org/pages/donate) **Student privacy****:** learn more about our commitment to keeping students safe [Read More](https://www.mindresearch.org/privacy-policy) ![MIND-on-Math_Blog-Header-5](https://2024.mindresearch.org/hs-fs/hubfs/graphics/headers/_blog-headers/MIND-on-Math_Blog-Header-5.png?width=2000&height=667&name=MIND-on-Math_Blog-Header-5.png "MIND-on-Math_Blog-Header-5") Category Community Teaching & Learning Technology & Games Research & Outcomes Neuroscience Celebrations & Successes [![Subscribe](https://no-cache.hubspot.com/cta/default/237516/a35fb57d-2960-4554-a0f3-e7bb5946fc70.png)](https://cta-redirect.hubspot.com/cta/redirect/237516/a35fb57d-2960-4554-a0f3-e7bb5946fc70) [Research & Outcomes](https://2024.mindresearch.org/blog/topic/research-outcomes) # Schemas Are Key to Deep Conceptual Understanding By [Eric Sbar](https://2024.mindresearch.org/blog/author/eric-sbar) - - - - - [mailto:?subject=Schemas%20Are%20Key%20to%20Deep%20Conceptual%20Understanding&body=Schemas%20Are%20Key%20to%20Deep%20Conceptual%20Understanding%20https://2024.mindresearch.org/blog/schemas-deep-conceptual-understanding](mailto:?subject=Schemas%20Are%20Key%20to%20Deep%20Conceptual%20Understanding&body=Schemas%20Are%20Key%20to%20Deep%20Conceptual%20Understanding%20https://2024.mindresearch.org/blog/schemas-deep-conceptual-understanding) - **Concept, (n.) \\ ˈkän-ˌsept \\:** an abstract or generic idea generalized from particular instances **Conceptual (adj.) \\ kən-ˈsep-chə-wəl \\:** of, relating to, or consisting of concepts **Understanding (n.) \\ ˌən-dər-ˈstan-diŋ \\** a : the power of comprehending especially : the capacity to apprehend general relations of particulars b : the power to make experience intelligible by applying concepts and categories Like many educational buzzwords, [conceptual understanding](https://www.stmath.com/conceptual-understanding) is one that has been defined in enough different ways that it starts to lose meaning. The focus of many conversations around conceptual understanding is also shallow, focusing on the idea that students need it, and less about how it is actually acquired. Which is unfortunate, because the “how” is the most important part. So we’re going to talk about the “how,” because having a deep conceptual understanding of math concepts is critical for problem solving success. #### What is Conceptual Understanding? But just so we don’t gloss over the “what,” let’s clarify our working definition of conceptual understanding. As we saw in our dictionary definitions above, concepts are ideas generalized from particular instances, and understanding is making sense of experiences by seeing the relationships between concepts and applying them. So we could say: > 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. The key to developing the robust framework we mentioned above can be summed up in one word: schemas. We’ve talked about [schemas](https://2024.mindresearch.org/blog/schema-in-education) before—blueprints that describe an object, a string of events, an idea, or really...anything. From a neuroscience perspective, conceptual learning requires building schemas. Schemas are neural networks, and the way those networks get created and connected ends up defining your concept, or understanding of the topic. And when we talk about having “deep conceptual understanding in math,” we’re talking building schemas of mathematical concepts that give students the ability to solve problems they haven’t seen before. Not only do today's standards speak to the need for students to build conceptual understanding, the newer assessment problems require it. Here’s just one quick example of how older assessment questions tested students’ knowledge of volume, compared to how more recent ones assess that same topic. **OLD** ![Old Assessment Question--Volu](https://2024.mindresearch.org/hs-fs/hubfs/rigor-example1%20(1).png?width=258&name=rigor-example1%20(1).png) **NEW** ![rigor-example2](https://2024.mindresearch.org/hs-fs/hubfs/rigor-example2.png?width=261&name=rigor-example2.png) As you can see, the problem on the left (the old one) essentially provides the key to the solution. Just plug the numbers into the algorithm. In contrast, the problem on the right not only requires a deeper understanding of volume, but also allows students to solve that problem in multiple ways. Whereas the older assessments would provide a series of questions in which the same problem solving approach could be used over and over again, newer assessments also vary the problems to test for conceptual understanding. This newer volume question is completely different than the rectangular prism one above: ![Sample Question 3-1](https://2024.mindresearch.org/hs-fs/hubfs/Sample%20Question%203-1.png?width=600&name=Sample%20Question%203-1.png)This is a great, because we know that memorizing rules and math facts is not as effective as learning through [creative reasoning](https://2024.mindresearch.org/blog/creative-problem-solving-research). In order to solve new and non-routine problems, students must have robust schemas built for the underlying math concepts. #### How Do We Build Conceptual Understanding? We talked earlier about how schemas are the key to deeper conceptual understanding. So the real question then becomes: how do we help students build schemas? Rather than teaching math as a series of isolated concepts that students compartmentalize into rigid sets of rules and procedures, we want them to consider concepts as they relate to one another: ![Schema Vid](https://2024.mindresearch.org/hs-fs/hubfs/Schema%20Vid.gif?width=600&name=Schema%20Vid.gif) #### Conceptual Learning With ST Math One example of building conceptual understanding is the approach visual instructional program [ST Math](https://www.stmath.com/) takes, by teaching foundational concepts visually, then connecting ideas to symbols and language. The puzzles in ST Math utilize a variety of visual models to present math concepts in non-routine ways. This approach allows students to build schemas quickly, as they interact with and manipulate models, and receive immediate, informative feedback. They see their choices play out, and can adjust their approach to a problem by incorporating that feedback, through the [perception-action cycle](https://2024.mindresearch.org/blog/perception-action-cycle). The program requires students to think outside the box and creatively apply what they have learned to solve challenging problems. Many puzzles allow multiple solutions. As a result, students experience autonomy as they learn to transfer their knowledge at each increasingly rigorous step of the learning path. ![Pouring Volume Gif](https://2024.mindresearch.org/hs-fs/hubfs/Pouring%20Volume%20Gif.gif?width=400&name=Pouring%20Volume%20Gif.gif) With these volume problems in ST Math, students can develop a schema for volume that goes beyond length x width x height, to develop a deep conceptual understanding that allows them to solve problems they haven’t seen before. ![Helicopter Gif](https://2024.mindresearch.org/hs-fs/hubfs/Helicopter%20Gif.gif?width=400&name=Helicopter%20Gif.gif) You can learn more about ST Math and how it supports deep conceptual learning, as well as experience some of the games yourself at [stmath.com](http://stmath.com). Want the latest from ST Math? [Sign-up](https://www.stmath.com/#signup) for our ST Math newsletter and be the first to hear about our offers and announcements. [![Explore Conceptual Understanding Blog CTA](https://no-cache.hubspot.com/cta/default/237516/4b7b1e1b-8029-4bb2-bd39-35a57164b645.png)](https://cta-redirect.hubspot.com/cta/redirect/237516/4b7b1e1b-8029-4bb2-bd39-35a57164b645) ![Eric Sbar](https://2024.mindresearch.org/hubfs/Blog/Authors/eric-sbar-headshot.png) ### About the Author Eric Sbar is Regional Vice President of West Partnerships for MIND Research Institute. He is a musician and educator, and enjoys connecting with math through nature while hiking, camping and sailing. ### Comment #### [Building Conceptual Understanding](https://2024.mindresearch.org/blog/building-conceptual-understanding-math) [MIND Goes to Milwaukee to Launch MathMINDs Games](https://2024.mindresearch.org/blog/milwaukee-mathminds-games-launch) ### Search Result By: ![feature image](https://2024.mindresearch.org/hubfs/Blog/Images/Inside-our-Minds-logo-teal-800x800.png) [Featured Podcast](https://2024.mindresearch.org/blog/topic/featured-podcast) ### [Rethinking Attendance in Edtech](https://2024.mindresearch.org/blog/rethinking-attendance-in-edtech) [Listen Now](https://2024.mindresearch.org/blog/rethinking-attendance-in-edtech) ##### LATEST PODCAST EPISODES ###### BY MIND RESEARCH INSTITUTE - [Rethinking Attendance in Edtech](https://2024.mindresearch.org/blog/rethinking-attendance-in-edtech) - [People, Process, and Penguins: Designing Math Experiences](https://2024.mindresearch.org/blog/people-process-penguins) - [Bridging STEM Gaps with STEMconnector CEO Jo Webber](https://2024.mindresearch.org/blog/bridging-stem-gaps-with-stemconnector-ceo-jo-webber) - [The EdTech Genome Project: Talking Implementation with Elizabeth Birie](https://2024.mindresearch.org/blog/edtech-genome-project) - [From Meeting the Moment to Foundational Change](https://2024.mindresearch.org/blog/from-meeting-the-moment-to-foundational-change) ##### [See all podcasts](https://www.mindresearch.org/edtech-podcast) ## Interested in Contributing? 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