Instruction

Question 1

Integrated teaching

Answer 1

multiple concepts are used in problem-solving at once (current best practices)

Question 2

Non-proportional manipulatives

Answer 2

objects that are not proportional to each other with respect to shape and size. Often all of the items are the same size.

ex: counting tokens

Question 3

Informal Deduction (Geometric Learning Progressions)

Answer 3

Level 2. Students recognize attributes and properties that objects share and are able to follow logical arguments about the relationship among these properties.

Example: Problem solving that involves reasoning

Question 4

teacher wait time

Answer 4

the silence that often comes after a question has been asked but before students have finished considering their answer and/or find the courage to speak up

Question 5

line graph

Answer 5

a visual representation of data which shows change over time or in response to a manipulated variable

Question 6

verbal representation

Answer 6

word problems and verbal descriptions of how to solve a problem or what the solution means

Example: “We know that Sam gets $10 each week for allowance, so let’s make that a constant. And we know that Sam wants to save $150 to buy a new bicycle, so that’s a constant, too. But, what we don’t know is how long does Sam need to save - let’s make that X. So the equation is 10x = 150.”

Question 7

Rigor (geometric learning progressions)

Answer 7

Level 4. Students are able to work in different axiomatic systems.

Example: Writing mathematical proofs using formal language. A college level geometry course is taught at this level.

Question 8

Decimal grid

Answer 8

a model used to visualize multiplication between a whole number and a decimal; involves a 10 x 10 grid in which each square represents 0.01 and the entire grid is equivalent to 1

Question 9

concrete operational stage

Answer 9

the third stage of Piaget’s Theory of Cognitive development, occurring from 7 years old to adolescence, in which children begin to think logically and use inductive reasoning

Question 10

Visualization (Geometric Learning Progressions)

Answer 10

Level 0. Shapes are recognized by their appearances. Students can’t identify specific attributes or properties of the shapes. They might identify some characteristics but are not able to use them to categorize or sort shapes.

Example: Working with different sizes of the same shape

Question 11

Tape diagram

Answer 11

diagrams useful for visualizing operations with fractions; each rectangle is equivalent to 1 and subdivided into increments representing the numerators and denominators of fractions

Question 12

Symbolic representation

Answer 12

A model using symbols or variables to display a mathematical concept.

Example: Formula

Question 13

Bar graph

Answer 13

a visual representation of data which compares values in different categories

Example: the number of people who prefer each genre of movie

Question 14

symbolic/representational stage

Answer 14

Drawing pictures or symbols to represent numbers in an equation

Example: Squares

Question 15

Constructivism

Answer 15

Learning new behaviors by adjusting our current view of the world

Example: Research projects

Question 16

word wall

Answer 16

An on-going bulletin board with terms used frequently in the classroom; words are often added as they are introduced

Question 17

number line

Answer 17

a straight line where each number is equal distance from the next one

Question 18

Concrete representations

Answer 18

Using physical pieces to represent mathematical problems

Example: Manipulatives

Question 19

homogeneous group

Answer 19

group comprised of individuals working on the same level

Question 20

Abstract thinking

Answer 20

Using numbers or letter variables in an equation

Example: 13x=y

Question 21

Deduction (Geometric Learning Progressions)

Answer 21

Level 3. Students are able to construct and understand formal proofs.

Question 22

heterogeneous group

Answer 22

group comprised of individuals working on various levels

Question 23

numeric representation

Answer 23

A model using numbers to display a mathematical concept.

Question 24

pie chart

Answer 24

a graph in which a circle is divided into sectors that each represent a proportion of the whole. Pie charts are helpful when displaying the relative distribution of categories.

Question 25

set model

Answer 25

a model in which a set of objects represents the whole, and a subset of those objects (typically shown with a separate color) represents a fraction of the whole

Question 26

double number line diagram

Answer 26

Consists of two parallel number lines, each representing a different unit

Used to visualize and compare ratios

Question 27

Think-Pair-Share

Answer 27

Active learning activity in which the teacher provides a prompt, the students consider it individually (THINK), then pair up and brainstorm responses or solutions (PAIR), and then the students then share their results with the class (SHARE).

Question 28

Proportional manipulatives

Answer 28

objects that are proportional to each other with respect to shape and size

Ex: tangrams

Question 29

Compartmentalized Teaching

Answer 29

concepts taught one at a time in isolation of other concepts (no longer recommended)

Question 30

flexible grouping

Answer 30

grouping students based on their learning needs or interests

Question 31

Analysis (geometric learning progressions)

Answer 31

Level 1. Students begin to identify characteristics and attributes of shapes. They use appropriate vocabulary to describe attributes and are less concerned with characteristics (such as the orientation and size of shapes).

Question 32

manipulatives

Answer 32

Objects used by students to illustrate and explore mathematical concepts, such as to represent numbers in an equation

Example: Blocks, Coins

Question 33

area model (fractions)

Answer 33

a diagram used to visualize mathematical operations, especially multiplication and division

Question 34

behaviorism

Answer 34

learning theory rooted in the notion that all behaviors are learned through interaction with the environment

Question 35

Graphic / Pictorial Representation

Answer 35

graph or picture that serves as a visual model of a mathematical equation

Example: Number line

Question 36

Cognitivism

Answer 36

learning new behaviors by connecting current knowledge with new knowledge

Example: Teaching fractions by talking about pizza slices