EDE 3523- Midterm Study Guide

What specific content is taught when teaching through problem solving?

Content (algebra, geometry, etc.)

What is Conceptual Understanding?

Is a flexible web of connections and relationships within and between ideas, interpretations and images of mathematical concepts

What are the benefits of Relational Understanding?

It is easier to connect previous knowledge and concepts to the new skills that are being taught. Relational understanding makes it easier to learn new concepts, retain previous concepts, and are able to deviate from formulas & rules given for different problems & makes them easier because of the connections that were made.

What is Procedural Understanding?

Knowing the rules and procedures used in carrying out math processes and of the symbolism that is used to represent mathematics

In the CCSSMC, what does Standards mean?

Math content students must master by the end of the year

In the CCSSMC, what does Clusters mean?

sub headers

What does understanding mean? How does it exist?

-A measure of the quality and quantity of the connections that an idea has with existing ideas -It exists on a continuum

What are the implications of constructivist theory for teaching mathematics?

-Build new knowledge from prior knowledge -Provide opportunities to talk about math -Provide opportunities for reflective thought -Encourage multiple approaches -Engage students in productive struggle -Treat errors as opportunities for learning -Scaffold new content -Honor diversity -Create classroom environment for doing math

What are the three types of information that teachers should provide to students? And when should each be provided?

-Mathematical Conventions = symbols, terminology, definitions, labels; should be provided only after students need them -Alternative methods = more efficient recording procedures;should be provided only as suggestions -Clarification of students' methods = to focus attention on the main ideas of the lesson.

What is Constructivism?

-Students have to be active in the development of their own understanding of math itself. -Students make connection between old ideas and new ones -Students are not blank slates; they do not absorb ideas. -This requires reflective thought

What are the types of connections?

-Within ONE content strand -Within TWO content strands -Between mathematics and the real world

What are the types of representations?

-pictures -written symbols -manipulative models -real-world situations -oral language -graphs,charts, diagrams

What are the Six NCTM Principles for Teaching Mathematics?

1. Equity = expectations and support for all students 2. Curriculum = collection of activities that are coherent, focus on important math, and are articulated across all grades 3. Teaching = understanding what students know and need to learn and challenging them to do well 4. Learning = students have to learn math with understanding; they build knowledge based on experience and prior knowledge 5. Assessment = should support learning of important math, should give both teachers and students useful information 6. Technology = essential in teaching and learning math, influences the math being taught, enhances student learning

What are the three features of a problem for learning math?

1. It must begin where the students are 2. The problematic or engaging aspect of the task must be due to the mathematics that the students are to learn 3. It must require justifications and explanations for answers and methods

What are the Five NCTM Content Standards?

1. Number and Operations 2. Algebra 3. Geometry 4. Measurement 5. Data analysis and probability

What are the Five NCTM Process Standards?

1. Problem solving 2. Reasoning and proof 3. Communication 4. Connections 5. Representation

What is a problem?

Any task or activity that poses a question for which the students have no prescribed or memorized rules or methods to use to solve it. Students do not see a 'correct' solution method.

******ESSAY QUESTION ON TEST****** What is the structure of the Common Core State Standards for Mathematical Content (Domains, Clusters, and Standards)?

CCSSM articulates state standards in a detailed form that can immediately be adopted and implemented as state-level curriculum frameworks. It focuses on the "Big Ideas" of mathematical content. CCSSM identifies Domains, rather than Content Standards, and Mathematical Processes, rather than Process Standards. Within each domain, are standards for mathematical content which define what students should understand and be able to do. Groups of multiple standards that have similarities are clusters of specific curriculum objectives. Standards define what students should understand and be able to do. Clusters are groups of related standards. These can also be closely related to other clusters. Domains are larger groups of related standards. Grade specific standards, and the domains are built up vertically, rather than horizontally. There are eleven domains. Under each domain is one or more clusters with a phrase to sum up the cluster. The standards for that cluster are listed under the phrase.

What is a Content Standard?

Coincide with NCTM Content Standards (number & operations, algebra, geometry, measurement & data, analysis/probability)

What order should Conceptual and Procedural Understanding be taught in?

Conceptual should be taught first.

In the CCSSMC, what does Domains mean?

General header with clustered standards that go with it

What is Instrumental Understanding?

Ideas are highly connected, doing something without understanding

What is Relational Understanding?

Ideas are isolated completely, knowing what to do and why

What is a Practice Standard?

Realized by the NCTM Process Standards (problem solving, communications, connections, representation, Reasoning & proof)

What content is taught when teaching about problem solving?

Strategies

What is the value of teaching through problem solving?

Students are able to learn through questions that are generated through solving problems. -Students are learning math by doing math.

What is Disequilibrium in the context of learning mathematics?

The feeling of confusion associated with struggling with a math concept

What is a "Standards-Based Classroom?

When a teacher uses a story problem to allow students to investigate a solution. Emphasizes understanding of concepts and processes. Assumes mastery of basic computational skills