Vocabulary

Question 1

Drill

Answer 1

Refers to repetitive, non-problem-based exercises designed to improve skills or procedures already acquired.

Question 1

Practice

Answer 1

Refers to different problem-based tasks or experiences, spread over numerous class periods, each addressing the same basic ideas.

Question 1

Conceptual knowledge

Answer 1

Knowledge rich in relationships and understanding- thoughtful, reflective learning

Question 2

Manipulatives

Answer 2

physical objects that students and teachers can use to illustrate and discover mathematical concepts, whether made specifically for mathematics or for other purposes- can be a testing ground for emerging ideas

Question 3

Algorithm

Answer 3

A process or set of rules to be followed in calculations or other problem-solving operations, esp. by a computer.

Question 4

General strategies for solving problems

Answer 4

draw a picture, act it out, use a model, look for a pattern, guess and check, make a table or chart, try a simpler form of the problem, make an organized list, write an equation

Question 4

Domains

Answer 4

In mathematics, the domain of definition or simply the domain of a function is the set of “input” or argument values for which the function is defined. That is, the function provides an “output” or value for each member of the domain.

Question 5

Relational Understanding

Answer 5

knowing what to do and why

Question 5

Games

Answer 5

A multiplayer game whose rules, strategies, and outcomes are defined by clear mathematical parameters.

Question 6

Procedural knowledge

Answer 6

Knowledge of formal language or symbolic representations, rules, algorithms, and procedures

Question 7

Cognitive demand

Answer 7

higher-level thinking—low cognitive demand tasks involve stating facts, known procedures, routine problems- high cognitive demand problems involve making connections, analyzing information, and drawing conclusions

Question 9

Reflective thought

Answer 9

the effort to connect existing ideas to new information- modify existing schemas to incorporate new ideas.

Question 10

Partial product

Answer 10

The product of one term of a multiplicand and one term of its multiplier.

Question 12

Instrumental understanding

Answer 12

doing something without understanding

Question 14

Constructivism

Answer 14

rooted in Jean Piaget’s work- the notion that learners are not blank slates but rather creators of their own learning- as learning occurs, the networks are rearranged, added to, or modified- brain is applying prior knowledge to make sense of the new information.

Question 15

Types of representations

Answer 15

pictures, written symbols, oral language, real-world situations, and manipulative models- help children construct ideas

Question 15

Pedagogical content knowledge

Answer 15

The interaction of the subject matter and effective teaching strategies which help students learn the subject matter- requires a thorough understanding of the content to teach it in multiple ways, drawing on the cultural backgrounds and prior knowledge and experiences of students.

Question 17

Context

Answer 17

the problem that begins the lesson should get students excited about learning math

Question 18

Process of problem solving

Answer 18

Understanding the problem, devising a plan, carrying out the plan, looking back

Question 19

Accommodation

Answer 19

Initially proposed by Jean Piaget, the term accommodation refers to part of the adaptation process. The process of accommodation involves altering one’s existing schemas, or ideas, as a result of new information or new experiences. New schemas may also be developed during this process.

Question 20

Assimilation

Answer 20

occurs when the new concept does not “fit” with existing network so the brain revamps or replaces the existing schema.

Question 21

Classroom discourse

Answer 21

The discussions and the interactions that occur throughout a lesson

Question 22

Teaching “about” problem solving

Answer 22

teaching students how to problem solve- can include teaching the process or strategies for solving a problem- “draw a picture” to help solve a problem

Question 24

“Unpacked content”

Answer 24

The “unpacking” of the standards is an effort to answer a simple question “What does this standard mean that a student must know and be able to do?” and to ensure the description is helpful, specific and comprehensive for educators.

Question 25

Sociocultural theory

Answer 25

Vygostky- mental processes exist between and among people in social learning settings, and from these social settings the learner moves ideas into his or her own psychological realm- the way in which information is internalized depends on whether it was within a learner’s zone of proximal development- semiotic mediation- the mechanism by which individual beliefs, attitudes, and goals are simultaneously affected and affect sociocultural practices and institutions. This theory focuses on how aspects of culture, such as values, beliefs, customs and skills, are transmitted from one generation to the next. According to Vygotsky, social interaction, especially involvement with knowledgeable community or family members, helps children to acquire the thought processes and behaviors specific to their culture or society. The changes or growth that children experience as a result of these interactions differs greatly between cultures; this variance allows children to become competent in tasks important or necessary in their particular society.