M3 Ch. 2 Wathall Synthesis by Jacqueline Fazekas https://padlet.com/jfazeka1/418vwm2ej1bahl0z en-us 2023-01-28 01:46:56 UTC 2023-01-28 04:03:26 UTC hello@padlet.com https://padlet.net/icons/png/1f4d0.png Concept-Based Mathematics jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459602341 2023-01-28 03:01:47 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459602341 Structure of Knowledge jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459602655 2023-01-28 03:02:57 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459602655 Structure of Process jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459602768 2023-01-28 03:03:26 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459602768 Principle Generalization jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459603777
  • Generalizations and principles are statements of conceptual understanding that allow students to make connections between two or more concepts
  • Principles are theorems
  • Theorems: statements that have been proven and connect explanations of conceptual understandings

    • ]]>     2023-01-28 03:06:55 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459603777     Concepts jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459604189
  • Timeless
  • Universal
  • Transferable
  • Abstract to varying degrees
  • One or two words or a short phrase
  • Have different examples that share common attributes

    • ]]>     2023-01-28 03:08:24 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459604189     Macro jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459604385 Give breadth of understanding and have greatest transferability across most disciplines.

    Examples: geometry, algebra, calculus ]]>     2023-01-28 03:09:10 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459604385     Meso jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459604589 Broken down macro concepts.

    Examples: trigonometry, functions, differentiation]]>     2023-01-28 03:09:54 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459604589     Micro jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459604685 Give supportive depth of understanding.

    Examples: ratio, angles, similarity ]]>     2023-01-28 03:10:13 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459604685     jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459604771 2023-01-28 03:10:34 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459604771 Topic jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459605427 "Broader" concepts: micro concepts.]]> 2023-01-28 03:12:58 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459605427 Facts jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459605749 Vocabulary, definitions, mathematical formulae in symbol form.
    • Rote memorization
    • Does not imply conceptual understanding
    ]]>     2023-01-28 03:14:12 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459605749     Processes jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459607195 Broad techniques that support the understanding of concepts.
    • Composed of strategies, algorithms, and skills
    • Six categories
    ]]>     2023-01-28 03:19:17 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459607195     Strategies jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459607762 A number of skills that learners use in a methodical and systematic way to support learning.]]> 2023-01-28 03:21:19 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459607762 Skills jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459607895 Small operations/actions that are embedded in strategies.
    • Allow strategies to work when applied appropriately
    • Examples: being able to create a table of values, plot a graph, or use trial and error to solve a problem 
    ]]>     2023-01-28 03:21:46 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459607895     Algorithms jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459608189 A set of computational rules to produce a specified outcome.
    • Consist of skills
    • Memorizing an algorithm does not imply conceptual understanding
    • Example: PEMDAS (parentheses, exponent, multiplication, division, addition, subtraction) 

    ]]>     2023-01-28 03:23:03 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459608189     Categories jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459609767 Each category can be broken down into strategies and skills.

    1. Problem Solving
    2. Reasoning and Proof
    3. Communicating
    4. Making Connections
    5. Creating Representations
    6. Investigating]]>     2023-01-28 03:29:11 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459609767     Problem Solving jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459610420 Thinking logically and making decisions in a systematic way.

    1. Understand the problem
    2. Devise a plan
    3. Carry out the plan
    4. Review and extend

    Examples:
    • Look for a pattern
    • Guess and check
    • Work backwards
    • Solve a simpler/similar problem

    ]]>     2023-01-28 03:31:41 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459610420     Reasoning and Proof jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459610590 The ability to make generalizations and provide explanations and justification for arguments.

    Examples:
    • Use data to make a conjecture
    • Ask “why”
    • Recognize mistakes

    ]]>     2023-01-28 03:32:20 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459610590     Communicating jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459610744 Talking and writing about mathematics.

    Examples:
    • Listen & discuss as a group
    • Use correct mathematical language
    • Explain ideas

    ]]>     2023-01-28 03:32:54 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459610744     Making Connections jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459611231 Expand understanding to related concepts because math is a cumulative body of knowledge.

    Make connections...
    • between facts
    • between symbols and procedures
    • to the real world
    • to old problems

    ]]>     2023-01-28 03:34:02 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459611231     Creating Representations jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459611439
  • Helps organize, record, and communicate ideas
  • Models and interprets a variety of situations

    • Examples:
    • Use words, drawings, tables, charts, graphs, diagrams
    • Include multiple representations

    ]]>     2023-01-28 03:34:57 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459611439     Investigating jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459611732 Furthering mathematical understanding by asking questions and using resources.

    Examples:
    • Explore different methodologies
    • Research relevant ideas
    • https://nrich.maths.org/2293

    ]]>     2023-01-28 03:36:13 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459611732     3 Levels jfazeka1 https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459613227 2023-01-28 03:43:11 UTC https://padlet.com/jfazeka1/418vwm2ej1bahl0z/wish/2459613227