Concept Based Mathematics by Leila Hurst

Structure of Knowledge

lhurst07 — 2025-02-09 04:24:15 UTC

Structure of Knowledge has multiple levels

Principle Generalization
Concepts
Topics
Facts

Facts

lhurst07 — 2025-02-09 04:26:42 UTC

Facts in math include memorized formulae in math symbols and vocabulary definitions. Information at this level cannot be transferred and applied in other scenarios. There is little to no depth of knowledge if the concepts.

Generalization, Principles, Topic and Concept Levels

lhurst07 — 2025-02-09 04:51:28 UTC

Topics are broader concepts that break down to specific micro concepts at the next level.

Generalization and Principles Level are statements of conceptual understanding that allow students to make connections between two or more concepts.

Structure of Process

lhurst07 — 2025-02-09 05:11:48 UTC

Principle Generalization
Concepts
Processes
Strategies
Skills

lhurst07 — 2025-02-09 05:20:59 UTC

Skills are small operations or actions that are embedded in strategies and allow the strategies to work.

Mathematical Process are complex, sophisticated performances, which are composed of strategies, algorithms, and skills. They are broad techniques that students draw upon to when learning math to and support understand of the concepts in a unit of work.

Problem solving
Reasoning and Proofs
Communicating
Making Connections
Creating Representations
Investigating

What is the difference between formulae and generalizations in mathematics?

lhurst07 — 2025-02-09 05:28:13 UTC

Formulae are mathematical facts that enable the student to use a skill. A generalization in mathematics is a conceptual understanding that allow students to make connections between two or more concepts. When a student has basic formulas memorized they can apply that formula to the type of problem they know it's meant for. On the other hand, when a student has a deeper understanding of the concepts they can evaluate the mathematical scenario and recognize similarities to other concepts that enable them to evaluate the problem.

What is the distinction between processes, algorithms, and skills in mathematics?

lhurst07 — 2025-02-09 05:28:36 UTC

Processes: Process are made up of strategies, algorithms, and skills. They are complex and sophisticated performances.

Algorithms: Rote learning processes. ex. Memorized formulas

Skills: Skills are small operations that, when appropriately applied, allow strategies to work such as creating a table of values or plot a graph.

Provide examples for each process.

lhurst07 — 2025-02-09 05:29:02 UTC

Problem Solving: interpret the question, look for a pattern, work backward.

Reasoning: Formulating and testing theories, use data to make a conjecture.

Communicating: Discuss as part of a group, write reflectively what you have learned. Using correct terminology to question, critique, clarify, and explain ideas.

Making Connections: Make connections between facts, symbols, and procedures. Make connections to the real world. Recognize similarities between old and new problems.

Creating Representations: Use words, drawings, tables, charts, graphs, diagrams, symbols, and technology.

Investigating: Investigate unfamiliar situations. Explore different methods by asking questions.

How is mathematics a language of conceptual relationships made of macro, meso, and micro concepts?

lhurst07 — 2025-02-09 05:29:34 UTC

Macro concepts are the broader constructs that include algebra, geometry, and calculus. Meso concepts are supporting concepts like trigonometry. Micro concepts are the supportive depth of understanding like ratio, angles, and similarities. In calculus you can see this demonstrated where calculus is the Macro concept, differentiation and integration are the meso concepts and slope, instantaneous rate of change, velocity, limits, derivative and summation are the micro concepts.

The concepts are grouped in large categories and the individual principles in those categories and then broken down again into principles and theories.

Explain the symbiotic relationship between the two structures for learning mathematics.

lhurst07 — 2025-02-09 05:30:01 UTC

The structure of knowledge consists of the definitions, facts and rules. The structure of processes supports the critical thinking, reasoning, proofs, generalization, and solving real world problems. Both structures depend on one another.

A real world example of macro, meso and micro modeling.

lhurst07 — 2025-02-09 07:20:48 UTC