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Mathematical Flexibility is the ability to maintain and shift among multiple representations of numbers and between problem-solving strategies in an adaptive manner. Students can use Mathematical Flexibility to better understand mathematical concepts and more adaptively use strategies to find solutions to math problems.
There are two key types of Mathematical Flexibility:
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.
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.
Continual use of foundational skills with different problems reinforces a conceptual understanding of math skills.
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.
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.
As students work with and process information by discussing, organizing, and sharing it together, they deepen their understanding.
Math games allow 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.
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.
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.
Math games and manipulatives for vision differences support math development for learners with visual needs.
Children's literature can be a welcoming way to help students learn math vocabulary and concepts.
Providing students a voice in their learning is critical for making learning meaningful.
When students create their own number and word problems, they connect math concepts to their background knowledge and lived experiences.
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.
Untimed tests provide students the opportunity to flexibly and productively work with numbers, further developing their problem-solving abilities.
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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