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Geometric Reasoning involves using abstract thinking to define, analyze, and make arguments about shapes and spatial relationships. Students must also be able to formalize these arguments in written proofs. Students' geometric knowledge provides concrete representations and models for abstract math concepts, which can serve as an entry point to higher-order math thinking skills.
Children begin with intuitive geometric knowledge (e.g., about shape and symmetry) which builds through exposure to events in the world. In school, this informal knowledge is built upon and expanded into more formal understanding of geometric concepts including:
Symmetry: Reflection across a line (e.g., folding) within a shape;
Congruence: The relationship between shapes through rotation, reflection, or translations; and
Similarity: The relationship between shapes whose sides are proportional and angles are equal.
Geometric Reasoning is scaffolded by Spatial Skills, which allow students to understand two and three-dimensional shapes and space, and by communicating and making arguments about these concepts through different channels, including sensorimotor and embodied activity.
Providing math tasks with high cognitive demand conveys high expectations for all students by challenging them to engage in higher-order thinking.
Students activate more cognitive processes by exploring and representing their understandings in visual form.
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 Algebraic Thinking and intentionally tackle problems.
Analyzing incorrect worked examples is especially beneficial for helping students develop a conceptual understanding of mathematical processes.
Math games allow students to practice many math skills in a fun, applied context.
Visualizing how ideas fit together helps students construct meaning and strengthens recall.
When teachers connect math to the students' world, students see how math is relevant and applicable to their daily lives.
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.
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, they recognize the strategies they or others use and solidify their understanding.
Analyzing and discussing solved problems helps students develop a deeper understanding of abstract mathematical processes.
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