Fall 2020 Session 7 - Geometry & Geometric Thinking by Monique Moss https://padlet.com/mmoss20s/8hqttmhbep08l4aj The chapter raises the question, "Why study geometry". After reading the characteristics of the van Hiele levels, how would you answer this question? PLEASE TYPE IN YOUR NAME IF YOU DON'T HAVE AN ACCOUNT. en-us 2020-09-26 18:52:34 UTC 2020-10-27 03:23:29 UTC hello@padlet.com Why study geometry? jschlam20s https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/839029618 The study of Euclidean geometry is an excellent tool for scaffolding other forms of mathematical thinking. The stages of thinking described in the van Hiele levels correlate to the development of sensorimotor and abstract thinking in children as they age. At their youngest, students grasp the spatial and visual qualities of shapes. Because shapes also express number and operation on number, they act as a intuitive visual model of these concepts. As abstract reasoning buds in the mind, students are able to observe and articulate qualities of shapes: Triangles have three sides, squares have four. These analytical observations become more nuanced and lead to logical deductions about shapes and their classifications: all sides of a triangle intersect, so it is not a parallelogram; opposite sides of a square do not intersect, so it is a parallelogram.]]> 2020-10-18 17:24:00 UTC https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/839029618 The Van Hiele model is a series of five levels that help students understand and conceptualize spatial ideas. The different levels help to describe the ways in which we think. Level 0 is the basic level, and students use visualization to recognize and represent items; in the case of geometry, geometric shapes. Level 1 allows students to analyze; shapes within a class and how they are similiar/different. Level 2 allows students to make informal deductions; if a shape has 4 sides then it is a square. Level 3 allows students to deduce, or analyze arguments pertaining to shapes; they can make a conclusion that all squares are parallelograms, but not all parallelograms are squares. The final level, 4 is rigor. This is achieved at a collegiate level, and allows students to compare and contrast different properties and classifications within geometry. Studying geometry is important, as it shows the progression of Van Hiele’s levels, and allows students to build on prior knowledge. Not only that, it expands that knowledge into deeper thinking. Looking at shapes, learning about the properties of shapes, learning how to manipulate those shapes, and then being able to compare and contrast those shapes allows a student's growth. Geometry is more than just a shape. It is about abstract thinking, logical reasoning, and manipulating different shapes dvalente20f https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/849510103 2020-10-21 16:46:50 UTC https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/849510103 https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/851249140 Questioning the study of geometry is valid, and can stem from an overall discomfort with mathematics. As educators we need to be prepared to justify its real-world applications. Geometry shows up in our everyday lives as tangible and three-dimensional space and shapes. The better we understand and teach geometric concepts, the more our students can see how big a role they play in their lives. 

The van Hiele theory is based on how students progress in their development of geometric thinking. They established the five levels of geometric thought in order to measure and make sense of students’ types of geometric ideas. (p. 502)  

The first step in the hierarchy (Level 0) is visualization. Students see and begin to group shapes. Then (Level 1) they move to the classification and analysis of shapes. Next (Level 2) comes the relationships between properties. Then (Level 3) they can develop proofs to later (Level 4) dive into axiomatic systems at the college level.  

There is a developmental sequence that goes hand-in-hand with how students interpret geometric shapes and their relationships and properties. This progression can begin in kindergarten in order to lay the proper groundwork for geometry class in high school. It makes no sense to wait to teach geometrical concepts in high school when we can start early. The van Hiele levels help teachers gauge student understanding of geometry, and how we can prepare our lessons to help them get to the next level. 

In the same manner that we should not teach multiplication and division without first teaching addition and subtraction, geometry should be taught in the order of levels. The kindergarteners that learn that a square is a rectangle can make better sense of geometric relationships in the higher grades.]]> 2020-10-22 05:10:25 UTC https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/851249140 Why study geometry? pjennings20s https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/851508851 By studying geometry by
 becoming grounded  in van Hiele's level of geometric thought, the student can use the levels  of visualization, analysis, informal deduction, deduction and rigor  to learn other subjects such  as linear algebra, physics and computer programming just to name a few.]]> 2020-10-22 07:18:00 UTC https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/851508851 spbernstein98 https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/853301780 2020-10-22 16:46:08 UTC https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/853301780 mrolka19f https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/857774759 2020-10-24 05:05:30 UTC https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/857774759 The study of geometry is important in all aspects because it allows you to explore and study shape and space in which we are exposed to every day, geometry also involves developing and applying spatial sense. After reading the Van Hiele levels of geometric thoughts, I realized how important and useful geometry truly is, to a point where children are expose to geometry when they are in kindergarten by starting at level 0, since they start with learning about shape and how they look like. As children go up in grades they will start to dig into the different aspects of geometry like classes of shapes, properties of shapes, relationships between properties, learning deductive systems of properties, and analysis of deductive systems. These levels are aligned with the developmental stages of a child which is why children start to learn about geometry at a young age starting with the simpler concept of geometry until they eventually create abstract statements about geometry. JessicaPerezz https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/858489900 2020-10-24 22:52:51 UTC https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/858489900 Why Study Geometry? rbraudiaz20s https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/858636571 Geometry is critical in order to understand space, shapes and their relationships. Learning geometry helps students develop spatial sense which gives them a logical and geometric framework to describe and analyze the world. The progression of developing geometric thinking through 0. Visualization, 1. Analysis, 2. Informal Deduction, 3. Deduction and 4. Rigor provides a developmentally appropriate and stimulating thinking based learning that can be useful in students' intellectual repertoire beyond geometry. If a student gets varied experiences practicing these levels, they will become skilled thinkers. ]]> 2020-10-25 03:15:21 UTC https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/858636571 Why Study Geometry pgottfried19f https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/860116289  
Why geometry?  To those 2nd graders who might not see architecture in their near future, geometry might seem abstract and unimportant.  However, through van hiele’s levels, we understand how we can not only teach geometry in a systematic and efficient way, but also one that challenges the students and fosters interest and excitement.  By going from visualization to sequential to developmental to age dependent and then finally experience dependent, students can start their geometry journey with exploration and eventually move to real world analysis.  Geometry becomes not just shapes on a paper, but a way to compare various things, how many triangles fit inside another shape.  It also pushes students to see objects with properties that can change, but that can also be finite and use this logic to make various statements.  Through van hiele’s levels, we can see geometry as something that builds on itself to become a useful addition to how students are able to address and assess the world around them. 
]]> 2020-10-26 01:01:51 UTC https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/860116289 Why Study Geometry- Corey Hirschhorn corey_hirschhorn32 https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/863940065 When looking at the ways in which geometry and geometric principles are accessed and used by people throughout their days, it can be hard to really quantify or comprehend how often we are utilizing certain pieces of information to make certain decisions throughout our day. Despite what field or interests a person may have, geometry is a key field within mathematics that prepares students to be able to understand the world and think critically about how two seemingly conflicting ideas can coexist at once (all squares are rectangles but all rectangles are not squares). In looking at van Hiele's levels of geometric study, it can be seen there are different foundational skills that must be established to allow for students to be able to conceptualize and internalize what the shapes are and how their properties help to defined them. By working through these levels in a sequential manner, students will be better prepared for being able to access the deductive and logical skills necessary for them in later mathematic and daily life experiences. These levels are designed to foster comprehension in students in a way that will allow them to progress through the various geometric concepts that is logical and builds upon itself. ]]> 2020-10-27 00:10:07 UTC https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/863940065 mmcgovern20s https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/864180493 2020-10-27 02:22:18 UTC https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/864180493 Emina Deljanin https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/864212494 2020-10-27 02:42:40 UTC https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/864212494 Studying geometry allows students to explore and analyze shapes and spaces. It also allows for students to make those real life connections for greater understanding. It will also, allow students to be more abstract as well as grasp a deeper level of thinking which benefit them in the long run. Van Hiele levels coincides with a child’s developmental stage. Level 0 is where students use visualization to recognize shapes. Level 1 is where the student analyzes and compares shapes. During the 3rd level, students analyze informal arguments and begin to develop geometric truths. The last level is the highest level where students compare and contrast different axiomatic systems of geometry. These levels will give each student the skillset to advance throughout their education. tlondono20f https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/864247800 2020-10-27 03:05:29 UTC https://padlet.com/mmoss20s/8hqttmhbep08l4aj/wish/864247800