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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 Safety. Then click connected factors to explore strategies related to multiple factors.
Safety is being and feeling physically and psychologically secure at home, at school, and within our neighborhood and larger community. Students who feel safe are better able to focus on learning and therefore learn math more quickly. Students who feel less safe tend to miss school and participate less often in class activities, missing out on learning opportunities.
There are four key types of safety that affect a student's learning:
Bullying
Even under teacher supervision, bullying, primarily verbal aggression and exclusion behaviors, is common in classrooms. Bullying is unfortunately also common in the broader community outside of school. Students who are bullied in person or online experience higher rates of depression and anxiety and have lower levels of academic achievement. Perpetrators of bullying also experience higher levels of depression and suicidal thoughts.
Home Safety
Safety at home is critical to students' development because students who live in unsafe homes can suffer from chronic stress. Students can feel unsafe at home for many reasons, such as:
The traumatic effects of living in an unsafe home can in turn make it difficult for students to reach their full potential at school.
Neighborhood Safety
Students who live in safe neighborhoods have better academic outcomes, including learning math, than students who witness violence in their communities. Exposure to violence and crime in the community is linked to many negative outcomes because students who live in unsafe neighborhoods experience chronic stress that has implications for their mental health, an aspect of Emotion.
School Safety
The reduction of bullying and school violence are two main goals of school Safety. Because of the many repercussions of bullying, all states have implemented legislation to combat bullying in school and cyberbullying that moves into the school space.
The prevalence of school shootings in recent years is also an important concern. Students who survive these traumatic events are at risk for experiencing serious psychological issues such as post-traumatic stress disorder. Yet, despite the increase in the number of victims of school shootings, overall crime rates in U.S. schools have declined in recent years due to increased security measures. More research on the impact of school security measures, such as active shooter drills, is however critical across different age groups. Early findings for older students suggest that, while active shooter drills enhance student preparedness, they also bring more attention to the threat from potential shooters, which can increase anxiety.
Building with blocks is ideal for promoting early geometric and Spatial Skills.
Students activate more cognitive processes by exploring and representing their understandings in visual form.
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.
Free choice supports learner interests and promotes the development of more complex social interactions.
Math games use numbers and Spatial Skills, allowing students to practice many math skills in a fun, applied context.
Imagining allows students to step back from a problem or task and think about it from multiple angles.
As students solve problems in a group, they learn new strategies and practice communicating their mathematical thinking.
As students walk through stations working in small groups, the social and physical nature of the learning supports deeper understanding.
Teaching students through guided play encourages them to take an active role in their learning and supports the development of a broad array of cognitive skills.
When students have meaningful conversations about math and use math vocabulary, they develop the thinking, questioning, and explanation skills needed to master mathematical concepts.
Students deepen their understanding and gain confidence in their learning when they explain to and receive feedback from others.
Students develop their skills by listening to and speaking with others 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.
Cards with strategies for managing emotions help students remember how to act when faced with strong feelings.
Timers help students learn to self-pace and transition.
A word wall helps build the mathematical vocabulary and Language Skills that are necessary for problem solving.
In explicit number naming, the structure of the number name labels the number in Place Value order and clearly states the quantity.
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 with math games, manipulatives, and activities support learner interests and promote the development of more complex math skills and social interactions.
Through short but regular mindfulness activities, students develop their awareness and ability to focus.
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.
A parent evening meeting about how to support numeracy at home with one follow-up meeting with each family has shown strong results for students' math development.
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.
Setting overall goals, as well as smaller goals as steps to reaching them, encourages consistent, achievable progress and helps students feel confident in their skills and abilities.
When students reframe negative thoughts and tell themselves kind self-statements, they practice positive self-talk.
Providing space and time for students to reflect is critical for moving what they have learned into Long-term Memory.
Adding motions to complement learning activates more cognitive processes for recall and understanding.
Brain breaks that include movement allow learners to refresh their thinking and focus on learning new information.
Providing physical 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.
Incorporating multiple senses with strategies like chewing gum, using a vibrating pen, and sitting on a ball chair supports focus and Attention.
Using earplugs or headphones can increase focus and comfort.
Transforming written text into audio activates different parts of the brain to support learning.
Tossing a ball, beanbag, 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.
Having space where students can go supports Self-regulation and individual deliberate practice.
Multiple tables and chairs on wheels allow for setting up the classroom to support the desired learning outcomes of each activity.
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.
Providing ways for students to adjust sound level supports individual auditory needs.
Providing ways for students to meet their individual temperature needs supports focus and Self-regulation.
Spaces that are structured, organized, and clean provide increased room for collaboration and active learning.
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.
Teachers support language development by using and providing vocabulary and syntax that is appropriately leveled (e.g.
Content that is provided in clear, short chunks can support students' Working Memory.
Building positive and trusting relationships with learners allows them to feel safe; a sense of belonging; and that their academic, cognitive, and social and emotional needs are supported.
Teaching students how to label, identify, and manage Emotion helps them learn Self-regulation skills.
Actively and authentically encouraging all students to seek support, ask questions, and advocate for what they believe in creates a safe space for risk-taking and skill development and supports a Sense of Belonging.
By talking through their thinking at each step of a process, teachers can model what learning looks like.
Maintaining consistent classroom routines and schedules ensures that students are able to trust and predict what will happen next.
Providing students a voice in their learning is critical for making learning meaningful.
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.
Dot cards build number sense and promote early math skills, particularly Spatial Skills and Non-symbolic Number knowledge.
Visualizing how ideas fit together helps students construct meaning and strengthen recall.
Visual representations help students understand what a number represents as well as recognize relationships between numbers.
Providing visuals to introduce, support, or review instruction activates more cognitive processes to support learning.
Discussing race with students can range from celebrating the importance of diversity to understanding the impact of racism from the perspective of those who have been historically marginalized.
Family engagement happens when educators and schools collaborate with families to collectively support their child's learning in meaningful ways, both at school and at home.
Selecting culturally responsive materials, including multicultural and diverse resources, is critical for supporting all students.
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.
