EDE 3523 Mid-Term Study Guide Flashcards

Flashcards covering NCTM Principles and Standards, Common Core State Standards structure, Process Standards, Strands of Mathematical Proficiency, types of understanding, and Constructivism.

What are the six NCTM Principles for Teaching Mathematics?

Teaching & Learning, Access & Equity, Curriculum, Tools & Technology, Assessment, and Professionalism.

According to the NCTM Principles, what is the Access & Equity principle?

All students should have high expectations and the chance to learn math, no matter their background or ability.

What are the five NCTM Content Standards?

Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability.

What defines a Standards-Based Classroom?

A classroom where students can teach and explain to one another, learn to solve problems, explain thinking, discuss solutions, and focus on understanding concepts and skills rather than just using a formula to get the right answer.

What are the two types of standards within Common Core State Standards?

Content Standards (addressing mathematical content for each grade level) and Mathematical Practices (practices students engage in to learn the content).

What is the organizational structure of the Common Core State Standards from broadest to most specific?

Domains (large group of related standards), Clusters (smaller group focusing on concept connections), and Standards (specific expectation of what students should understand and do).

What are five of the Common Core State Standards Domains listed in the study guide?

Functions, Number and Operations-Fractions, Measurement and Data, Geometry, and The Number System.

What is disequilibrium in the context of learning mathematics?

Feeling confused or struggling with a math concept, which is a necessity for learning as long as students do not become permanently discouraged.

What is the teacher's role in fostering mathematical thinking and problem solving?

To support student learning rather than doing all the talking by asking purposeful questions, encouraging multiple strategies, and asking students to explain how and why they got an answer.

What are the five NCTM Process Standards?

Problem Solving, Reasoning & Proof, Communication, Connections, and Representation.

What are the five types of mathematical representations?

Real-life Contexts, Written Symbols, Manipulative Models/Physical Tools, Oral/Written Language, and Graphs, Tables & Diagrams.

What are the four types of mathematical connections?

Within one mathematics content strand, between two mathematics content strands, between mathematics and other subject areas, and between mathematics and the real world.

Which NCTM Process Standard was demonstrated by the Math Cubes activity?

Problem Solving.

Which NCTM Process Standards were demonstrated by the Visual Thinking activity?

Reasoning & Proof, and Communication.

Which NCTM Process Standards were demonstrated by the Cube Buildings activity?

Representation, and Connections.

What are the five Strands of Mathematical Proficiency?

Adaptive Reasoning, Strategic Competence, Conceptual Understanding, Procedural Fluency, and Productive Disposition.

How is Adaptive Reasoning defined in the 5 Strands of Mathematical Proficiency?

Capacity for logical thought, reflection, explanation, and justification.

How is Strategic Competence defined in the 5 Strands of Mathematical Proficiency?

Ability to formulate, represent, and solve mathematics problems.

How is Productive Disposition defined in the 5 Strands of Mathematical Proficiency?

Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy.

How is 'understanding' defined in mathematics education?

A measure of the quality and quantity of the connections that an idea has with existing ideas, existing on a continuum from instrumental to relational understanding.

What is the difference between Instrumental Understanding and Relational Understanding?

Instrumental understanding means doing something without understanding, while relational understanding means knowing what to do and why you're doing it.

What is the difference between conceptual and procedural understanding, and in what order should they be taught?

Conceptual understanding means understanding the meaning of concepts (WHY), while procedural understanding means knowing how to carry out procedures (HOW). Conceptual understanding should be taught first, followed by procedural understanding.

What is Constructivism and what are its implications for teaching mathematics?

Constructivism is the idea that students build their own knowledge by connecting new information to prior knowledge and experiences. Teachers should provide opportunities for students to actively explore, think, and solve problems rather than just memorizing information.