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10.2: Mathematics

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    279264

    • This page is a draft and under active development. Please forward any questions, comments, and/or feedback to the ASCCC OERI (oeri@asccc.org).

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    Math Instruction

    Effective math instruction encompasses various strategies and components that work together to build a strong mathematical foundation for students. One of the core components of math instruction is computation, which involves teaching students to perform mathematical operations such as addition, subtraction, multiplication, and division accurately. Computation skills are fundamental for students to succeed in more complex mathematical concepts, and these skills are typically developed through repeated practice and reinforcement. Teachers often use structured activities and drills to help students become proficient in computational skills, while also ensuring that they understand the underlying concepts behind these operations, rather than simply memorizing procedures. Mastery of computation is essential for students to solve problems efficiently and with confidence.

    In addition to computation, problem-solving is a critical component of math instruction. Problem-solving involves applying mathematical concepts and skills to find solutions to real-world problems. It encourages students to think critically, reason logically, and explore multiple strategies for finding a solution. Problem-solving in math can range from word problems that require the application of operations to more complex, open-ended questions that require creative thinking. Teachers help students develop problem-solving skills by encouraging them to break problems into smaller, manageable parts, identify relevant information, and choose the best strategy to approach the solution. Effective problem-solving instruction also includes teaching students to check their work, evaluate their solutions, and consider alternative methods of solving the problem.

    Shelf of math manipulatives Shelf of math manipulatives in an elementary school classroom.

    To support both computation and problem-solving, math manipulatives are powerful tools that can enhance students' understanding of abstract concepts by providing hands-on, concrete representations of mathematical ideas. Manipulatives include objects such as base-ten blocks, fraction strips, counting bears, and pattern blocks that allow students to visually and physically manipulate mathematical concepts. For example, base-ten blocks help students understand place value, while fraction strips provide a tactile way for students to grasp fractional relationships. Using manipulatives helps students visualize math problems, making abstract concepts more concrete and accessible. These tools also provide opportunities for interactive learning and collaboration, as students can work together to solve problems and explore mathematical relationships through hands-on activities.

    Drawing is another effective strategy that supports math instruction, particularly when it comes to visualizing mathematical concepts. Drawing diagrams, charts, and graphs allows students to represent mathematical problems in a visual format, helping them organize information and understand relationships between different elements. For example, when solving geometry problems, students may draw shapes and label their parts to better understand the properties of the figures. In algebra, graphing equations helps students see the relationship between variables. Drawing can also be used in problem-solving to map out a plan or break down a complex problem into more manageable steps. Teachers encourage students to incorporate drawing as a method of thinking through mathematical concepts, as it helps to deepen understanding and reinforce learning.

    Finally, effective math instruction involves a balance of conceptual understanding, procedural fluency, and application. While computation and problem-solving are central to math learning, students must also understand the underlying concepts behind mathematical operations. Teachers encourage this understanding by making math relevant to students' everyday lives, using real-world examples to show how math is applied in various contexts. By integrating math manipulatives, problem-solving strategies, and visual aids like drawing, math instruction becomes a dynamic process that fosters a deeper understanding of mathematical concepts. A well-rounded math curriculum that incorporates these elements helps students develop both the skills and the confidence to tackle increasingly complex mathematical challenges.

    This page titled 10.2: Mathematics is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Kerry Diaz & Tenessa Sanchez.