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On June 22, 2021, we will launch updated strategies for the Math PK-2 model, as well as additional updates to the Navigator that highlight equity, SEL, and culturally responsive teaching. To learn more, visit our Site Updates (available in the "About" menu at the top of any page).
Hover to see how factors connect to Long-term Memory. Then click connected factors to explore strategies related to multiple factors.
Long-term Memory can store information indefinitely. We can move skills and knowledge into Long-term Memory by repeatedly practicing. When students have math skills, background knowledge, and arithmetic facts in their Long-term Memory, they have the tools they need to tackle new math problems.
When short-term memories are rehearsed, they become consolidated and move to Long-term Memory. There are two main types of Long-term Memory:
Explicit (Declarative) Long-term Memory refers to memories that can be consciously remembered.
Implicit (Nondeclarative) Long-term Memory stores the memories that do not require conscious thought.
Schemas exist in Long-term Memory as an organizational system for our current knowledge and provide a framework for adding future understanding. New information that comes into our Long-term Memory may be more readily encoded in memory when it is consistent with a current schema making learning easier when we have the appropriate Background Knowledge as context.
Students activate more cognitive processes by exploring and representing their understandings in visual form.
Analyzing incorrect worked examples is especially beneficial for helping students develop a conceptual understanding of mathematical processes.
Project-based learning (PBL) actively engages learners in authentic tasks designed to create products that answer a given question or solve a problem.
When students explain their thinking process aloud with guidance in response to questions or prompts, they recognize the strategies they use and solidify their understanding.
Math games allow students to practice many math skills in a fun, applied context.
Response devices boost engagement by encouraging all students to answer every question.
When students create their own number and word problems, they connect math concepts to their background knowledge and lived experiences.
Analyzing and discussing solved problems helps students develop a deeper understanding of abstract mathematical processes.
As students solve problems in a group, they learn new strategies and practice communicating their mathematical thinking.
Flexible grouping is a classroom practice that temporarily places students together in given groups to work together, with the purpose of achieving a given learning goal or activity.
As students walk through stations working in small groups, the social and physical nature of the learning supports deeper understanding.
As students work with and process information by discussing, organizing, and sharing it together, they deepen their understanding.
When students have meaningful conversations about math and use math vocabulary, they develop the thinking, questioning, and explanation skills needed to master mathematical concepts.
Having students teach their knowledge, skills, and understanding to their classmates strengthens learning.
Students deepen their understanding and gain confidence in their learning when they explain to and receive feedback from others.
Students deepen their math understanding as they use and hear others use specific math language in informal ways.
Rhyming, alliteration, and other sound devices reinforce math skills development by activating the mental processes that promote memory.
A mnemonic device is a creative way to support memory for new information using connections to current knowledge, for example by creating visuals, acronyms, or rhymes.
Easy access to seeing the relationships between numbers promotes Number Sense as students see these connections repeatedly.
A word wall helps build the Math Communication and vocabulary skills that are necessary for problem solving.
Providing math tasks with high cognitive demand conveys high expectations for all students by challenging them to engage in higher-order thinking.
CRA is a sequential instructional approach during which students move from working with concrete materials to creating representational drawings to using abstract symbols.
Knowing the language of math is critical because students must use this language to understand math concepts and determine calculations needed.
Thinking of and about patterns encourages learners to look for and understand the rules and relationships that are critical components of mathematical reasoning.
Discussing strategies for solving mathematics problems after initially letting students attempt to problem solve on their own helps them understand how to organize their mathematical thinking and intentionally tackle problems.
Teaching students to recognize common problem structures helps them transfer solution methods from familiar to unfamiliar problems.
In guided inquiry, teachers help students use their own language for constructing knowledge by active listening and questioning.
Math centers support learner interests and promote the development of more complex math skills and social interactions.
Instruction in multiple formats allows students to activate different cognitive skills to understand and remember the steps they are to take in their math work.
When teachers connect math to the students' world, students see how math is relevant and applicable to their daily lives.
A strengths-based approach is one where educators intentionally identify, communicate, and harness students' assets, across many aspects of the whole child, in order to empower them to flourish.
Writing that encourages students to articulate their understanding of math concepts or explain math ideas helps deepen students' mathematical understanding.
Providing space and time for students to reflect is critical for moving what they have learned into Long-term Memory.
When students engage in a dialogue with themselves, they are able to orient, organize, and focus their thinking.
When students monitor their comprehension, behavior, or use of strategies, they build their Metacognition.
Adding motions to complement learning activates more cognitive processes for recall and understanding.
Communication boards are displays of graphics (e.g., pictures, symbols, illustrations) and/or words where learners can gesture or point to the displays to extend their expressive language potential.
Brain breaks that include movement allow learners to refresh their thinking and focus on learning new information.
Providing physical and virtual representations of numbers and math concepts helps activate mental processes.
Connecting information to music and dance can support Short-term and Long-term Memory by engaging auditory processes, Emotions, and physical activity.
Research shows physical activity improves focus and creativity.
Transforming written text into audio activates different parts of the brain to support learning.
Tossing a ball, beanbag, dice, or other small object activates physical focus in support of mental focus.
Visual supports, like text magnification, colored overlays, and guided reading strip, help students focus and properly track as they read.
Multiple display spaces help develop oral language skills as well as Social Awareness & Relationship Skills by allowing groups to share information easily as they work.
Multiple writing surfaces promote collaboration by allowing groups to share information easily as they work.
Decreasing extra audio input provides a focused learning environment.
Children's literature can be a welcoming way to help students learn math vocabulary and concepts.
Continual use of foundational skills with different problems reinforces a conceptual understanding of math skills.
10 minutes in each math session devoted to building fluent retrieval of basic math facts sets the foundation for learning new concepts.
Daily review strengthens previous learning and can lead to fluent recall.
Spending time with new content helps move concepts and ideas into Long-term Memory.
Practicing until achieving several error-free attempts is critical for retention.
Having students verbally repeat information such as instructions ensures they have heard and supports remembering.
By talking through their thinking at each step of a process, teachers can model what learning looks like.
Teachers sharing math-to-self, math-to-math, and math-to-world connections models this schema building.
Wait time, or think time, of three or more seconds after posing a question increases how many students volunteer and the length and accuracy of their responses.
Visualizing how ideas fit together helps students construct meaning and strengthens recall.
Visual representations help students understand what a number represents as well as recognize relationships between numbers.
Sentence frames or stems can serve as language support to enrich students' participation in academic discussions.
Providing visuals to introduce, support, or review instruction activates more cognitive processes to support learning.
Learning about students' cultures and connecting them to instructional practices helps foster a sense of belonging and mitigate Stereotype Threat.
Translanguaging is a flexible classroom practice enabling students to listen, speak, read, and write across their multiple languages or dialects, even if the teacher does not have formal knowledge of these additional languages.
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This is our homepage. You can access many of the features of the Navigator here, and learn more about how learner variability intersects with topics in education and learning. To start, select a content area – we call them Learner Models – to visit a factor map.
Factor maps show research-based concepts, "factors," that likely impact learning. They are organized into four categories: Learner Background, Social and Emotional Learning, Cognition, and Content Area. The map is interactive. Move your cursor over a factor to see connected factors. Select any factor to visit its summary page. We'll look at factor summary pages next.
This is a factor summary page. It provides a brief definition and review of the factor, a factor connections diagram, additional resources, and strategies that support this factor. On the strategy card, the multi-colored boxes show all the factors that it supports. Select a strategy to visit its summary page.
Strategy summary pages have an overview, information about using the strategy in different learning environments, resources of interest, the factors this strategy supports, and related strategies you can explore. To view all the strategies in a content area, use the strategies tab at the top of the page. We'll look at all the Strategies for this learner model next.
The strategy page shows ALL of the strategies for that learner model. You can select factors of interest for you or your learners, and it will narrow the strategies to only those that match all of the factors selected. This makes it easy to find key strategies to better design for learner variability. Again, select the strategy name to visit its summary page. Use the plus signs on each strategy card to add a strategy to a workspace. We'll explore those next.
The “Tools & Workspaces” tab on the navigation bar or the “My Workspaces” button on the account menu takes you to a page that shows your workspaces. There are two tabs on the My Workspaces page: a Workspaces tab and a Reports tab. The Workspaces tab lists workspaces you can personalize and update. You can create new sections, move cards between sections, add annotations, share with collaborators, and write reflections. The second tab, "Reports", are a kind of workspace created through the Instructional Design Tool or the Product Assessment Tool and have fewer personalization options.
There are three, step-by-step tools you can access on the Navigator to help make workspace or a workspace report. The Learner Centered Design Tool has four steps and helps you create a workspace. First, enter basic information and select a content area of interest. Second, select a few factors that you want to focus on. Third, review connected factors you may not have considered. Note – you don't have to select any extra factors on this step if you don’t want to. The fourth and final step, review and select strategies that you want to use, and save them to a workspace.
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Learner variability is the recognition that each learner is a unique constellation of strengths and challenges that are interconnected across the whole child. Understanding these connections and how they vary according to context is essential for meeting the needs of each learner.
It disrupts the notion of a one-size-fits all education. Understanding learner variability helps educators embrace both students’ struggles and strengths as we connect practice to uplifting the whole learner.
Throughout the site, we talk about "factors" and "strategies." Factors are concepts research suggests have an impact on how people learn. Strategies are the approaches to teaching and learning that can be used to support people in how they learn best.
Use the Learner Centered Design Tool to build a workspace. Go to Learner Centered Design Tool.
Or, create a new blank workspace for your product or project.
Use one of the guided tools to build a workspace.
Or, create a new blank workspace for your product or project.
Make a copy of this workspace.
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On this page, using your heatmap, you will be asked to select factors to further explore, and then select new strategies you might incorporate into upcoming instruction. Once done, click “Show Summary" to view your Design Summary Report.
On this page, using your heatmap, you will be asked to select factors to further explore, and then select new strategies you might incorporate into upcoming instruction. Once done, click “Show Report” to view your Design Summary Report.
By selecting "Show Report" you will be taken to the Assessment Summary Page. Once created, you will not be able to edit your report. If you select cancel below, you can continue to edit your factor and strategy selections.
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Learner variability is the recognition that each learner is a unique constellation of strengths and challenges that are interconnected across the whole child. Understanding these connections and how they vary according to context is essential for meeting the needs of each learner. It embraces both students’ struggles and strengths. It considers the whole child.
Throughout the site, we talk about "factors" and "strategies." Factors are concepts research suggests have an impact on how people learn. Strategies are the approaches to teaching and learning that can be used to support people in how they learn best.
The Learner Variability Navigator is a free, online tool that translates the science of learner variability into factor maps and strategies that highlight connections across the whole learner. This puts the science of learning at teachers' fingertips, empowering them to understand their own practice and support each learner.
