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Algebraic Thinking is the ability to generalize, represent, justify, and reason with abstract mathematical structures and relationships. Algebraic Thinking is important for developing a deep understanding of arithmetic and helps students make connections between many components of their early math studies.
Algebraic Thinking allows students to move away from thinking and working with particular numbers and measures to understanding and reasoning with generalized relationships among them. Algebraic Thinking practices occur in these mathematical domains:
Providing math tasks with high cognitive demand conveys high expectations for all students by challenging them to engage in higher-order thinking.
CRA is a sequential instructional approach during which students move from working with concrete materials to creating representational drawings to using abstract symbols.
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 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.
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.
Math centers 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.
By talking through their thinking at each step of a process, teachers can model what learning looks like.
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.
Having students teach their knowledge, skills, and understanding to their classmates strengthens learning.
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 with guidance in response to questions or prompts, they recognize the strategies they use and solidify their understanding.
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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