Given the robust nature of learning sciences research, this website is best viewed on tablets and computers. A small screen experience is coming in the future.
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 Primary Language. Then click connected factors to explore strategies related to multiple factors.
Primary Language is the language a person has been exposed to from birth, which often does not match the language of instruction. Being bilingual or multilingual can have cognitive advantages which have been shown to contribute to advantages in mathematical reasoning. However, many students may encounter challenges because they are not only learning new mathematical concepts but also still learning the language of instruction. As the students gradually learn more complex mathematics concepts, the demand to use complex language expressions is also higher.
Although most languages use similar mathematical numbers and symbols, the counting systems used in different cultures and languages can vary, and the way these systems are structured may influence how students manipulate and interpret numbers. In addition, mastering mathematics involves defining, discussing, explaining, and justifying, wherein Language Skills play a key role. Unfortunately, in the early grades, bilingual and multilingual students are less likely to be identified as in need of special education services. It is important for educators to distinguish between difficulties that stem from learning disabilities and differences that stem from their language skills, or a combination of both, in order to provide the most appropriate support.
There are many terms for students in the United States whose native language is not English (e.g., Dual Language Learners, English Language Learners). For our work, we use the terms bilingual and multilingual.
The number of students who are learning more than one language is growing rapidly every year. Bilingual/multilingual students can experience different language acquisition patterns:
Although bilingual/multilingual students may not always have the mathematical Vocabulary in all of their languages, this does not mean they lack proficiency in mathematics. Students may prefer to use one language over another when solving problems or communicating in different situations to support their knowledge, experience, and understanding. The selection of the language typically relies on their Language Skills as well as the language used by the person communicating with them.
Understanding student background and their Home Learning Environment, and supporting hybrid language practices or translanguaging are important to promote math success. It is helpful for educators to understand their bilingual/multilingual students' prior experiences with Primary Language, the language of instruction, and mathematics instruction in each language. Other factors, such as Stereotype Threat, can lead to different trajectories that are sustained over time, particularly since bilingual or multilingual students may be labeled less competent than their monolingual peers. Overall, students' Primary Language and rich cultural backgrounds are considered learning assets that can extend opportunities for students to deeply engage in math and support their academic learning. Providing bilingual and multilingual students with inclusive educational support using a variety of modes in math learning spaces helps them achieve math success.
Teachers support language development by using and providing vocabulary and syntax that is appropriately leveled (e.g.
Building with blocks is ideal for promoting early geometric and Spatial Skills.
As students solve problems in a group, they learn new strategies and practice communicating their mathematical thinking.
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.
Students activate more cognitive processes by exploring and representing their understandings in visual form.
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.
Knowing the language of math is critical because students must use this language to understand math concepts and determine calculations needed.
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.
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.
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.
Teachers can help students understand that learning involves effort, mistakes, and reflection by teaching them about their malleable brain and modeling their own learning process.
As students walk through stations working in small groups, the social and physical nature of the learning supports deeper understanding.
Adding motions to complement learning activates more cognitive processes for recall and understanding.
In guided inquiry, teachers help students use their own language for constructing knowledge by active listening and questioning.
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.
Imagining allows students to step back from a problem or task and think about it from multiple angles.
Learning about students' cultures and connecting them to instructional practices helps foster a sense of belonging and mitigate Stereotype Threat.
Math centers with math games, manipulatives, and activities support learner interests and promote the development of more complex math skills and social interactions.
Math games use numbers and Spatial Skills, allowing students to practice many math skills in a fun, applied context.
When students have meaningful conversations about math and use math vocabulary, they develop the thinking, questioning, and explanation skills needed to master mathematical concepts.
By talking through their thinking at each step of a process, teachers can model what learning looks like.
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.
Using multiple methods of assessment can help educators gain a comprehensive understanding of learner progress across a wide range of skills and content.
Visualizing how ideas fit together helps students construct meaning and strengthen recall.
Providing physical representations of numbers and math concepts helps activate mental processes.
Easy access to seeing the relationships between numbers promotes number sense as students see these connections repeatedly.
Visual representations help students understand what a number represents as well as recognize relationships between numbers.
When teachers connect math to the students' world, students see how math is relevant and applicable to their daily lives.
Selecting culturally responsive materials, including multicultural and diverse resources, is critical for supporting all students.
Transforming written text into audio activates different parts of the brain to support learning.
Students develop their skills by listening to and speaking with others in informal ways.
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.
Having students verbally repeat information such as instructions ensures they have heard and supports remembering.
Providing visuals to introduce, support, or review instruction activates more cognitive processes to support learning.
Visual supports, like text magnification, colored overlays, and guided reading strip, help students focus and properly track as they read.
A word wall helps build the mathematical vocabulary and Language Skills that are necessary for problem solving.
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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.
