Concept Based Mathematics by Staff.Patience Sharp https://padlet.com/psharp4/svg0axm7byzlsipq Made with a creative frenzy en-us 2020-07-15 21:30:33 UTC 2026-01-17 16:26:49 UTC hello@padlet.com "Where on the Structure of Knowledge and the Structure of Process should curriculum and instruction focus? Why?" psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606367551 2023-05-26 16:29:45 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606367551 How do the Structure of Knowledge and Structure of Process represent different facets of learning mathematics? Explain the symbiotic relationship between the two structures for learning mathematics. psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606369310 2023-05-26 16:31:44 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606369310 What is the distinction between processes, algorithms, and skills in mathematics? psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606369723 2023-05-26 16:32:15 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606369723 psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606376914 2023-05-26 16:41:59 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606376914 Mathematical processes are complex, sophisticated performances which are composed of strategies, algorithms, and skills. Specifically, they are: Problem Solving, Reasoning and Proof, Communicating, Making Connections, Creating Representations, and Investigating psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606387684 2023-05-26 16:56:48 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606387684 psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606390784 2023-05-26 17:01:27 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606390784 psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606391744 2023-05-26 17:03:01 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606391744 psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606392737 2023-05-26 17:04:38 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606392737 psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606393705 The Structure of Knowledge and the Structure of Process represent different aspects of learning mathematics. The Structure of Knowledge provides the conceptual framework, while the Structure of Process focuses on problem-solving skills. They depend on each other, with the Structure of Knowledge guiding the learning process and the Structure of Process reinforcing conceptual understanding. ]]> 2023-05-26 17:06:06 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606393705 Processes: Processes in mathematics refer to the overarching strategies, methodologies, and approaches used to solve mathematical problems or engage with mathematical concepts. Processes involve higher-order thinking skills, such as problem-solving, critical thinking, reasoning, and logical deduction. Mathematical processes are more general in nature and can be applied across various mathematical domains. They guide students in navigating mathematical challenges, identifying patterns, making conjectures, and developing proofs. Examples of mathematical processes include problem analysis, pattern recognition, generalization, conjecturing, proof-writing, and mathematical modeling. psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606395594 2023-05-26 17:08:43 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606395594 Algorithms: Algorithms are specific, step-by-step procedures or sets of rules used to solve specific types of mathematical problems. They are more focused and concrete than processes, providing precise instructions to accomplish a particular task. Algorithms are often used in areas like arithmetic, geometry, calculus, and discrete mathematics. They outline the sequence of operations or calculations needed to obtain a solution. For example, the long division algorithm, the quadratic formula, or the algorithm for finding the greatest common divisor (GCD) are all specific procedures designed to solve particular types of mathematical problems. psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606395817 2023-05-26 17:09:03 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606395817 Skills: Skills in mathematics refer to the individual abilities and proficiencies that students develop through practice and experience. These skills are specific to carrying out mathematical operations, using mathematical tools, and manipulating mathematical objects. Skills in mathematics can include computational skills (e.g., performing calculations with accuracy and efficiency), spatial skills (e.g., visualizing geometric shapes and transformations), estimation skills (e.g., approximating quantities), measurement skills (e.g., using units and converting between them), and data analysis skills (e.g., interpreting graphs and statistical measures). Skills are acquired through repetitive practice and can be further honed and refined over time. psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606396218 2023-05-26 17:09:33 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606396218 The curriculum and instruction of mathematics should focus on both the Structure of Knowledge and the Structure of Process. The Structure of Knowledge emphasizes the organization and progression of mathematical concepts, allowing students to develop a strong conceptual understanding. Meanwhile, the Structure of Process focuses on problem-solving skills and procedural fluency. By integrating both structures, curriculum and instruction enable students to build a solid foundation of mathematical knowledge while equipping them with the problem-solving abilities necessary to apply that knowledge effectively. Striking a balance between the two structures ensures a comprehensive and effective learning experience in mathematics. psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606404796 2023-05-26 17:21:18 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606404796 psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606405937 2023-05-26 17:22:34 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606405937 psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606414620 2023-05-26 17:35:14 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606414620 psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606415640 2023-05-26 17:36:53 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606415640 psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606418915 2023-05-26 17:41:55 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606418915 psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606420034 2023-05-26 17:43:33 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606420034 psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606422522 2023-05-26 17:47:08 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606422522 psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606427639 2023-05-26 17:55:19 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606427639 psharp4 https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606429302 2023-05-26 17:58:14 UTC https://padlet.com/psharp4/svg0axm7byzlsipq/wish/2606429302