Vocabulary

Question 1

Line Graph:

Answer 1

Shows change over time

Question 2

Bar Graph:

Answer 2

Shows change in numbers

Question 3

Stem and Leaf Plot:

Answer 3

Shows just raw data without any other variables. (Just numbers).

Question 4

Circle Graph:

Answer 4

Shows and compares parts to wholes. Indicates RATIO and means it must have a fraction or a percent as an answer

Question 5

Mean:

Answer 5

What is the AVERAGE

Question 6

Relational Learning:

Answer 6

Students know:
What to do
Why to do it
How to do it.

Question 7

Instrumental Learning:

Answer 7

Student knows “WHAT” to do without all the connecting dots

Teacher has failed students in showing how math connects.

Question 8

Multiple Representations:

Answer 8

Understanding is the measure of the quality and quantity of connections that a new idea has with existing ideas

Question 9

Multiple Representations:

Answer 9

Understanding is the measure of the quality and quantity of connections that a new idea has with existing ideas.
Moving from instrumental to relational learning.

Question 10

Golden Rules:

Answer 10

A). Every student must meet the learning objective.
B). Look for clues within the question and answers.
C). Answer like a Constructivist.

Question 11

Dilations:

Answer 11

Making shapes bigger or smaller

Question 12

Accommodations:

Answer 12

Changes in the environment or considerations or circumstances that you put in place with specific students in mind.

Question 13

Five Principles of Extraordinary Math Teaching:

Answer 13

Start with a question
Students need time to struggle
Teachers are NOT the answer key
Say "YES" to your student's ideas
Willingness to play!

Question 14

4 step process to problem solving:

Answer 14

Understand the problem
Devise a plan
Carry out the plan
Look back

Question 15

Constructivism:

Answer 15

Constructivism the notion that learners are not blank slates but rather creators (constructors) of their own learning.

Question 16

Mathematics:

Answer 16

The Science of Pattern and Order

Question 17

Language of Doing Mathematics:

Answer 17

Compare
Conjecture 
Construct
Describe 
Develop 
Explain 
Explore 
Formulate 
Investigate 
Justify 
Predict 
Represent 
Solve 
Use 
Verify

Question 18

“Doers” of mathematics

Answer 18

Students began to take the math ideas to the next level by:

(1) Connecting to previous material
(2) Responding with information beyond the required response
(3) Conjecturing or predicting

Question 19

What is important in learning?

Answer 19

Persistance, effort, and concentration.

Question 20

How does students share their ideas help?

Answer 20

Sharing different ideas help students to become strategic

Question 21

How do errors or strategies help students?

Answer 21

Mistakes are opportunities for learning.

Question 22

ZPD

Answer 22

Zone of Proximal Developement

Question 23

(Socioculture Theory) Lev Vygotsky’s Zone of Proximal Developement:

Answer 23

A “range” of knowledge that may be out of reach for a person to learn on his or her own, but is accessible if the learner has support from peers or more knowledgeable others.

Question 24

Problem-based or Inquiry learning:

Answer 24

It is through inquiry that students are activating their own knowledge and trying to assimilate or accommodate (or internalize) new knowledge.

Question 25

Scaffolding:

Answer 25

The idea that a task otherwise outside of a student’s ZPD can become accessible if it is carefully structured.

Question 26

What Does It Mean to Understand Mathematics?

Answer 26

Can be defined as a measure of the quality and quantity of connections that an idea has with existing ideas. Understanding is not an all-or-nothing proposition

Question 27

Examples of tools:

Answer 27

``` Pictures Written symbols Oral language Real-world situations Manipulative models ```

Question 28

Mathematics Proficiency:

Answer 28

The five strands involved in being mathematically proficient: (1) Conceptual understanding (2) Procedural fluency (3) Strategic competence (4) Adaptive reasoning (5) Productive disposition.

Question 29

Conceptual Understanding:

Answer 29

The comprehension of mathematicla concepts, operations and relations.

Question 30

Procedural Fluency:

Answer 30

Skills in carrying out procedures flexibily, accurately, effeciently and appropriately.

Question 31

Strategic Competence:

Answer 31

Ability to formulate, represent and solve mathematical problems.

Question 32

Adaptive Reasoning:

Answer 32

Capacity for logical thought, reflection, explanation and justification.

Question 33

Productive Disposition:

Answer 33

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

Question 34

The Mathematics Standard:

Answer 34

* Use NCTM and state or local standards to establish what mathematics students should know and be able to do and base assessments on those essential concepts and processes * Develop assessments that encourage the application of mathematics to real and sometimes novel situations * Focus on significant and correct mathematics.

Question 35

The Learning Standard:

Answer 35

* Incorporate assessment as an integral part of instruction and not an interruption or a singular event at the end of a unit of study * Inform students about what content is important and what is valued by emphasizing those ideas in your instruction and matching your assessments to the models and methods used * Listen thoughtfully to your students so that further instruction will not be based on guesswork but instead on evidence of students’ misunderstandings or needs.

Question 36

The Equity Standard:

Answer 36

* Respect the unique qualities, experiences, and expertise of all students * Maintain high expectations for students while recognizing their individual needs * Incorporate multiple approaches to assessing students, including the provision of accommodations and modifications for students with special needs

Question 37

The Openness Standard:

Answer 37

* Establish with students the expectations for their performance and how they can demonstrate what they know * Avoid just looking at answers and give attention to the examination of the thinking processes students used * Provide students with examples of responses that meet expectations and those that don’t meet expectations.

Question 38

The Inferences Standard:

Answer 38

* Reflect seriously and honestly on what students are revealing about what they know * Use multiple assessments (e.g., observations, interviews, tasks, tests) to draw conclusions about students’ performance * Avoid bias by establishing a rubric that describes the evidence needed and the value of each component used for scoring

Question 39

The Coherence Standard:

Answer 39

* Match your assessment techniques with both the objectives of your instruction and the methods of your instruction * Ensure that assessments are a reflection of the content you want students to learn * Develop a system of assessment that allows you to use the results to inform your instruction in a feedback loop

Question 40

Problem Solving:

Answer 40

* Works to make sense of and fully understand problems before beginning * Incorporates a variety of strategies * Assesses the reasonableness of answers

Question 41

Reasoning:

Answer 41

* Justifies solution methods and results * Recognizes and uses counterexamples * Makes conjectures and/or constructs logical progressions of statements based on reasoning

Question 42

Communication:

Answer 42

* Explains ideas in writing using words, pictures, and numbers * Uses precise language, units, and labeling to clearly communicate ideas

Question 43

Connections:

Answer 43

* Makes connections between mathematics and real contexts | * Makes connections between mathematical ideas

Question 44

Representations:

Answer 44

* Uses representations such as drawings, graphs, symbols, and models to help think about and solve problems * Moves between models * Explains how different representations are connected

Question 45

The Six Principles:

Answer 45

* Equity * Curriculum * Teaching * Learning * Assessment * Technology