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Working Memory, a component of executive functioning, allows a person to temporarily hold and manipulate information to apply in other processes. With our Working Memory, we recall and apply the knowledge stored in our Short- and Long-term Memories to help understand what we are learning. Working Memory is likely required for retaining information during math problem solving, in particular with more novel or complex problem types. When Working Memory is overtaxed, a math student can appear to have a poor attention span and be easily distracted because they struggle recalling and using information.
Working Memory can also be called updating as it involves working with and updating information in memory. One influential model of Working Memory lays out four components, each considered to have a limited capacity. These separate components are responsible for maintaining verbal Working Memory, visual and spatial Working Memory, and for integrating information from these components that serves as a link between Long-term Memory and Working Memory. In addition, there is an executive control system which directs activities within these systems, including shifting and focusing attention between them.
Cognitive load is another important element of Working Memory and refers to the amount of mental effort being expended by Working Memory during different tasks. Cognitive Load Theory proposes that instruction can be designed in a way to reduce cognitive load. It also differentiates between different types of cognitive load:
Teachers support language development by using and providing vocabulary and syntax that is appropriately leveled (e.g., using simple sentences when introducing complex concepts).
Content that is provided in clear, short chunks can support students' Working Memory.
As students solve problems in a group, they learn new strategies and practice communicating their mathematical thinking.
CRA is a sequential instructional approach during which students move from working with concrete materials to creating representational drawings to using abstract symbols.
Students activate more cognitive processes by exploring and representing their understandings in visual form.
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.
Teaching students to recognize common problem structures 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 mathematical thinking and intentionally tackle problems.
Teaching students how to label, identify, and manage Emotion helps them learn Self-regulation skills.
Analyzing incorrect worked examples is especially beneficial for helping students develop a conceptual understanding of mathematical processes.
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.
Learning about students' cultures and connecting them to instructional practices helps all students feel like valued members of the community.
As students work with and process information by discussing, organizing, and sharing it together, they deepen their understanding.
Math centers support learner interests and promote the development of more complex math skills and social interactions.
Rhyming, alliteration, and other sound devices reinforce math skills development by activating the mental processes that promote memory.
When students have meaningful conversations about math and use math vocabulary, they develop the thinking, questioning, and explanation skills needed to master mathematical concepts.
Through short but regular mindfulness activities, students develop their awareness and ability to focus.
Short breaks that include mindfulness quiet the brain to allow for improved thinking and emotional regulation.
Mnemonic devices help students remember mathematical concepts and steps of math and classroom processes.
Multiple tables and chairs on wheels allow for setting up the classroom to support the desired learning outcomes of each activity.
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.
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.
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.
Research shows physical activity improves focus and creativity.
Maintaining consistent classroom routines and schedules ensures that students are able to trust and predict what will happen next.
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.
When students engage in a dialogue with themselves, they are able to orient, organize, and focus their thinking.
Sentence frames or stems can serve as language support to enrich students' participation in academic discussions.
Transforming written text into audio activates different parts of the brain to support learning.
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.
Students deepen their math understanding as they use and hear others use specific math language in informal ways.
Tossing a ball, beanbag, dice, or other small object activates physical focus in support of mental focus.
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.
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