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Elementary Math Methods > Vocabulary > Flashcards

Vocabulary Flashcards

1
Q

Line Graph:

A

Shows change over time

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2
Q

Bar Graph:

A

Shows change in numbers

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3
Q

Stem and Leaf Plot:

A

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

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4
Q

Circle Graph:

A

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

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5
Q

Mean:

A

What is the AVERAGE

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6
Q

Relational Learning:

A

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

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7
Q

Instrumental Learning:

A

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

Teacher has failed students in showing how math connects.

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8
Q

Multiple Representations:

A

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

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9
Q

Multiple Representations:

A

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.

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10
Q

Golden Rules:

A

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

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11
Q

Dilations:

A

Making shapes bigger or smaller

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12
Q

Accommodations:

A

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

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13
Q

Five Principles of Extraordinary Math Teaching:

A 
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!
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14
Q

4 step process to problem solving:

A

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

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15
Q

Constructivism:

A

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

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16
Q

Mathematics:

A

The Science of Pattern and Order

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17
Q

Language of Doing Mathematics:

A 
Compare
Conjecture 
Construct
Describe 
Develop 
Explain 
Explore 
Formulate 
Investigate 
Justify 
Predict 
Represent 
Solve 
Use 
Verify
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18
Q

“Doers” of mathematics

A

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

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19
Q

What is important in learning?

A

Persistance, effort, and concentration.

20
Q

How does students share their ideas help?

A

Sharing different ideas help students to become strategic

21
Q

How do errors or strategies help students?

A

Mistakes are opportunities for learning.

22
Q

ZPD

A

Zone of Proximal Developement

23
Q

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

A

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.

24
Q

Problem-based or Inquiry learning:

A

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

25
Q

Scaffolding:

A

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

26
Q

What Does It Mean to Understand Mathematics?

A

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

27
Q

Examples of tools:

A 
Pictures
Written symbols
Oral language
Real-world situations
Manipulative models
28
Q

Mathematics Proficiency:

A

The five strands involved in being mathematically proficient:

(1) Conceptual understanding
(2) Procedural fluency
(3) Strategic competence
(4) Adaptive reasoning
(5) Productive disposition.

29
Q

Conceptual Understanding:

A

The comprehension of mathematicla concepts, operations and relations.

30
Q

Procedural Fluency:

A

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

31
Q

Strategic Competence:

A

Ability to formulate, represent and solve mathematical problems.

32
Q

Adaptive Reasoning:

A

Capacity for logical thought, reflection, explanation and justification.

33
Q

Productive Disposition:

A

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

34
Q

The Mathematics Standard:

A
  • 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.
35
Q

The Learning Standard:

A
  • 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.
36
Q

The Equity Standard:

A
  • 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
37
Q

The Openness Standard:

A
  • 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.
38
Q

The Inferences Standard:

A
  • 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
39
Q

The Coherence Standard:

A
  • 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
40
Q

Problem Solving:

A
  • Works to make sense of and fully understand problems before beginning
  • Incorporates a variety of strategies
  • Assesses the reasonableness of answers
41
Q

Reasoning:

A
  • Justifies solution methods and results
  • Recognizes and uses counterexamples
  • Makes conjectures and/or constructs logical progressions of statements based on reasoning
42
Q

Communication:

A
  • Explains ideas in writing using words, pictures, and numbers
  • Uses precise language, units, and labeling to clearly communicate ideas
43
Q

Connections:

A
  • Makes connections between mathematics and real contexts

* Makes connections between mathematical ideas

44
Q

Representations:

A
  • 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
45
Q

The Six Principles:

A
  • Equity
  • Curriculum
  • Teaching
  • Learning
  • Assessment
  • Technology

Elementary Math Methods (7 decks)

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