https://padlet.com/jmcoop14/yqf1b38imljq5ek9 Wathall Chapter 2 en-us 2023-01-30 00:40:28 UTC 2026-03-07 17:28:51 UTC hello@padlet.com https://padlet.net/icons/png/1f929.png jmcoop14 https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460677466 Students can have different levels of understanding. While a students may know the facts of a concept, it is important that they develop a deeper level of understanding. ]]> 2023-01-30 00:47:35 UTC https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460677466 jmcoop14 https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460679711 A factual understanding of a subject means a student can recite rules or formulas. These does not demonstrate a deep understanding of the topic. The student's knowledge is trapped in that understanding. 
Example: Pythagorean Theorem ]]> 2023-01-30 00:51:02 UTC https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460679711 jmcoop14 https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460682019 A conceptual understanding of a subjects means a student is able to explain why they can use a formula or why a fact is true. The student is able to apply their understanding of the information outside the context of the problem. 
Example: Pythagorean Theorem
A student who understands Pythagorean Theorem can related the formula to the appropriate sides of a triangle. Their knowledge goes beyond memorization. ]]> 2023-01-30 00:54:46 UTC https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460682019 jmcoop14 https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460683097 Students learn in different ways. There are models to show students why the Pythagorean theorem works. Here is a song that explains the formula. This song can help your musically-inclined students. ]]> 2023-01-30 00:56:28 UTC https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460683097 jmcoop14 https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460683983 Summary of Wathall Chapter 2]]> 2023-01-30 00:58:02 UTC https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460683983 jmcoop14 https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460686601 Formulae and Generalizations represent different levels of understanding. ]]> 2023-01-30 01:02:11 UTC https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460686601 jmcoop14 https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460687255 Formulae: a mathematical relationship or rule expressed in symbols
Generalizations: a statement that is true for a whole topic or mathematical idea]]> 2023-01-30 01:03:25 UTC https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460687255 jmcoop14 https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460688779 A student with only a procedural or factual understanding are able to recite a formula. They may not be able to explain the formula, the purpose of the formula, or how it is derived.
Example: Quadratic Formula
A student may be able to recite the quadratic formula; however, they must know when to use it. ]]> 2023-01-30 01:06:09 UTC https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460688779 jmcoop14 https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460693809 Generalization require a student to synthesize what they have learned about a topic. This requires a conceptual understanding of the topic. 
Example: Quadratic Formula
A student may use a generalization to explain when the quadratic formula is useful. They may say, "The quadratic formula is used to find the x-intercepts of a trinomial, especially when the a of the trinomial is more than 2 or it is unfactorable." This demonstrates that the child understands the purpose and has come to a valid conclusion. ]]> 2023-01-30 01:13:39 UTC https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460693809 jmcoop14 https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460697046 Mathematics has its own language. The language is made of macro, mesh and micro concepts. Students must understand the all levels of the language. ]]> 2023-01-30 01:18:07 UTC https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460697046 jmcoop14 https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460699836 Macro concepts are the broad construct or idea. It is usually the name of the class a student is taking. 
For example: Geometry
Geometry is the study of the relationship between shapes, points, lines, surfaces, and arrangement. ]]> 2023-01-30 01:21:41 UTC https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460699836 jmcoop14 https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460701671 Meso Concepts are large areas of knowledge within a macro concept. 
Example: Geometry
Vectors and Trigonometry are meso connects in geometry. ]]> 2023-01-30 01:24:11 UTC https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460701671 jmcoop14 https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460703770 Micro concepts are the basis of understanding for meso and macro topics. Micro concepts supports the depths of understanding. 
Example: Geometry
A student is able to find the magnitude of a vector which supports their understanding of vectors (meso) and geometry (macro). ]]> 2023-01-30 01:26:48 UTC https://padlet.com/jmcoop14/yqf1b38imljq5ek9/wish/2460703770