https://padlet.com/ajhinoj3/yvo4sdtqizzrb194 en-us 2021-10-28 00:11:29 UTC 2021-11-08 20:29:23 UTC hello@padlet.com ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849852218 The structure of knowledge is comprised of two levels: the factual level and the generalizations and principles level.]]> 2021-10-28 01:12:51 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849852218 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849864543 The factual level is comprised of facts, memorization, and information that is not transferable to other concepts/topics. 
Ex: Pythagorean Theorem, names of triangles.]]> 2021-10-28 01:17:51 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849864543 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849874889 This level allows for connections between topics/concepts because of the statements of conceptual understanding (theorems).]]> 2021-10-28 01:21:49 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849874889 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849891481 While different, both fall under the structure of knowledge.]]> 2021-10-28 01:28:03 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849891481 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849907216 A formula that is represented by facts.]]> 2021-10-28 01:34:06 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849907216 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849914124 Theorems are proven statements, connecting explanations of concepts.]]> 2021-10-28 01:36:53 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849914124 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849915663 The structure of process includes the six mathematical processes, algorithms, skills, and strategies. ]]> 2021-10-28 01:37:30 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1849915663 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1850251628 These are broad techniques that can be applied to different disciplines, such as science or math. Each can also be broken down into skills, algorithms, and strategies that are or can be specific to mathematics.
1. Problem Solving
2. Reasoning and Proof
3. Communicating
4. Making Connections
5. Creating Representations
6. Investigating]]> 2021-10-28 03:57:51 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1850251628 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1850271675 These all make up the mathematical processes. Skills are small actions used in strategies that assist in obtaining a solution to a problem. Multiple skills make up a strategy. Algorithms are specific to math. ]]> 2021-10-28 04:07:45 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1850271675 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1850274911 2021-10-28 04:09:31 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1850274911 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1850277153 2021-10-28 04:10:48 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1850277153 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1850281861 2021-10-28 04:13:13 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1850281861 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1862844008 Think of the following when considering generalizations: two or more statements, use words like "may" and "can", provides goals and student understanding, endure beyond specific topics.
Think of the following when considering principles: factual truths, theorems, hold the generalizations together, do not contain words like "may" or "can". ]]> 2021-11-02 21:15:49 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1862844008 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1862846753 Two types of generalizations are overarching ones and topical ones, meaning that there are generalizations that are topic-specific and some that are not. 
Ex: logarithms as a process generalization including problems-solving and making connections.]]> 2021-11-02 21:17:43 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1862846753 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1865595207 Why and how? 
The area of the squares drawn from the two sides of a right-angled triangle represent the area of the square drawn from the hypotenuse. ]]> 2021-11-03 18:45:26 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1865595207 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1865595602 What is the significance? Why is this important? 
Knowing the area of the square drawn from the hypotenuse or of one side of a right-angled triangle can help solve/calculate for an unknown side. ]]> 2021-11-03 18:45:38 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1865595602 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1865604377 Generalizations that have risen to the level of theorem or law, based on facts and truths, no longer qualified. ]]> 2021-11-03 18:49:50 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1865604377 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1865617852 Students will understand that... 
In a right angle, the lengths of the two sides affect the length of the third.]]> 2021-11-03 18:56:07 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1865617852 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1865675547 Guiding students to discover generalizations and principles through inquiry as opposed to telling students the generalizations and principles and then having them study and focus on specific examples. It involves having students write in math.]]> 2021-11-03 19:25:55 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1865675547 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1865690713 Graphic organizer
Unit webbing tool
Time of reflection
Hint jar]]> 2021-11-03 19:33:45 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1865690713 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1876196969 A tool for planning concept-based units, with knowledge strands and process strands.]]> 2021-11-08 19:48:00 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1876196969 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1876207763 Begin with: 
1. Identify results
2. Determine acceptable evidence
3. Plan learning experiences/instruction
Remember that conceptual understandings must be at the forefront of planning.]]> 2021-11-08 19:52:33 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1876207763 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1876221128 There are three types of guiding questions that should allow students to make connections and draw out conceptual understanding: 
- factual
- conceptual 
- provocative/debatable ]]> 2021-11-08 19:58:18 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1876221128 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1876226894 Skills fall under general processes, and include problem-solving, making connections, proofs, and reasoning. ]]> 2021-11-08 20:00:58 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1876226894 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1876255569 Conceptual lenses create connections between factual informations and conceptual knowledge. They can be referred to as "key concepts" and encourage a focus on transferrable ideas. 
Generalizations are in each strand, and are enduring, essential understandings. ]]> 2021-11-08 20:14:01 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1876255569 ajhinoj3 https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1876265126 Application of all of the above, and can be supplemented. ]]> 2021-11-08 20:18:25 UTC https://padlet.com/ajhinoj3/yvo4sdtqizzrb194/wish/1876265126