Vocabulary Flashcards
Line Graph:
Shows change over time
Bar Graph:
Shows change in numbers
Stem and Leaf Plot:
Shows just raw data without any other variables. (Just numbers).
Circle Graph:
Shows and compares parts to wholes. Indicates RATIO and means it must have a fraction or a percent as an answer
Mean:
What is the AVERAGE
Relational Learning:
Students know:
What to do
Why to do it
How to do it.
Instrumental Learning:
Student knows “WHAT” to do without all the connecting dots
Teacher has failed students in showing how math connects.
Multiple Representations:
Understanding is the measure of the quality and quantity of connections that a new idea has with existing ideas
Multiple Representations:
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.
Golden Rules:
A). Every student must meet the learning objective.
B). Look for clues within the question and answers.
C). Answer like a Constructivist.
Dilations:
Making shapes bigger or smaller
Accommodations:
Changes in the environment or considerations or circumstances that you put in place with specific students in mind.
Five Principles of Extraordinary Math Teaching:
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!
4 step process to problem solving:
Understand the problem
Devise a plan
Carry out the plan
Look back
Constructivism:
Constructivism the notion that learners are not blank slates but rather creators (constructors) of their own learning.
Mathematics:
The Science of Pattern and Order
Language of Doing Mathematics:
Compare Conjecture Construct Describe Develop Explain Explore Formulate Investigate Justify Predict Represent Solve Use Verify
“Doers” of mathematics
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
What is important in learning?
Persistance, effort, and concentration.
How does students share their ideas help?
Sharing different ideas help students to become strategic
How do errors or strategies help students?
Mistakes are opportunities for learning.
ZPD
Zone of Proximal Developement
(Socioculture Theory) Lev Vygotsky’s Zone of Proximal Developement:
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.
Problem-based or Inquiry learning:
It is through inquiry that students are activating their own knowledge and trying to assimilate or accommodate (or internalize) new knowledge.
Scaffolding:
The idea that a task otherwise outside of a student’s ZPD can become accessible if it is carefully structured.
What Does It Mean to Understand Mathematics?
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
Examples of tools:
Pictures Written symbols Oral language Real-world situations Manipulative models
Mathematics Proficiency:
The five strands involved in being mathematically proficient:
(1) Conceptual understanding
(2) Procedural fluency
(3) Strategic competence
(4) Adaptive reasoning
(5) Productive disposition.
Conceptual Understanding:
The comprehension of mathematicla concepts, operations and relations.
Procedural Fluency:
Skills in carrying out procedures flexibily, accurately, effeciently and appropriately.
Strategic Competence:
Ability to formulate, represent and solve mathematical problems.
Adaptive Reasoning:
Capacity for logical thought, reflection, explanation and justification.
Productive Disposition:
Habitual inclination to see mathematics as sensible,useful and worthwhile coupled with a belief in dilligence and one’s own efficacy.
The Mathematics Standard:
- 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.
The Learning Standard:
- 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.
The Equity Standard:
- 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
The Openness Standard:
- 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.
The Inferences Standard:
- 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
The Coherence Standard:
- 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
Problem Solving:
- Works to make sense of and fully understand problems before beginning
- Incorporates a variety of strategies
- Assesses the reasonableness of answers
Reasoning:
- Justifies solution methods and results
- Recognizes and uses counterexamples
- Makes conjectures and/or constructs logical progressions of statements based on reasoning
Communication:
- Explains ideas in writing using words, pictures, and numbers
- Uses precise language, units, and labeling to clearly communicate ideas
Connections:
- Makes connections between mathematics and real contexts
* Makes connections between mathematical ideas
Representations:
- 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
The Six Principles:
- Equity
- Curriculum
- Teaching
- Learning
- Assessment
- Technology
