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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. Adolescents and adults typically rely more on memory-based strategies for solving 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.
Providing math tasks with high cognitive demand conveys high expectations for all students by challenging them to engage in higher-order thinking.
As students solve problems in a group, they learn new strategies and practice communicating their mathematical thinking.
Students activate more cognitive processes by exploring and representing their understandings in visual form.
Continual use of foundational skills with different problems reinforces a conceptual understanding of math skills.
Daily review strengthens previous learning and can lead to fluent recall.
Thinking of and about patterns encourages learners to look for and understand the rules and relationships that are critical components of mathematical reasoning.
Teaching students to recognize the structures of algebraic representations helps them transfer solution methods from familiar to unfamiliar problems.
Discussing strategies for solving mathematics problems after initially letting students attempt to problem solve on their own helps them understand how to organize their Algebraic Thinking and intentionally tackle problems.
Analyzing incorrect worked examples is especially beneficial for helping students develop a conceptual understanding of mathematical processes.
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.
The flipped classroom has two parts: cooperative group activities in class and digitally-based individual instruction out of class.
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.
Spending time with new content helps move concepts and ideas into Long-term Memory.
Learning about students' cultures and connecting them to instructional practices helps all students feel like valued members of the community.
Practicing until achieving several error-free attempts is critical for retention.
As students work with and process information by discussing, organizing, and sharing it together, they deepen their understanding.
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 allow students to practice many math skills in a fun, applied context.
Rhyming, alliteration, and other sound devices reinforce math skills development by activating the mental processes that promote memory.
When students have meaningful discussions about math and use math vocabulary, they develop the thinking, questioning, and explanation skills needed to master mathematical concepts.
Mnemonic devices help students remember mathematical concepts and steps of math and classroom processes.
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.
Brain breaks that include movement allow learners to refresh their thinking and focus on learning new information.
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.
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.
Visualizing how ideas fit together helps students construct meaning and strengthens recall.
Providing physical and virtual representations of numbers and math concepts helps activate mental processes.
Visual representations help students understand what a number represents as well as recognize relationships between numbers.
Multiple writing surfaces promote collaboration by allowing groups to share information easily as they work.
Connecting information to music and dance moves enhances Short-term and Long-term Memory by drawing on auditory processes and the cognitive benefits of physical activity.
Having students teach their knowledge, skills, and understanding to their classmates strengthens learning.
Decreasing extra audio input provides a focused learning environment.
When teachers connect math to the students' world, students see how math is relevant and applicable to their daily lives.
Students deepen their understanding and gain confidence in their learning when they explain to and receive feedback from others.
Providing space and time for students to reflect is critical for moving what they have learned into Long-term Memory.
Response devices boost engagement by encouraging all students to answer every question.
Children's literature can be a welcoming way to help students learn math vocabulary and concepts.
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.
Sentence frames or stems can serve as language support to enrich students' participation in academic discussions.
When students create their own number and word problems, they connect math concepts to their background knowledge and lived experiences.
Transforming written text into audio activates different parts of the brain to support learning.
Students deepen their math understanding as they use and hear others use specific math language in informal ways.
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.
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.
A word wall helps build the Math Communication and vocabulary skills that are necessary for problem solving.
Analyzing and discussing solved problems helps students develop a deeper understanding of abstract mathematical processes.
Writing that encourages students to articulate their understanding of math concepts or explain math ideas helps deepen students' mathematical understanding.
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