van Hiele Model of Development of Geometric Thought :van Hiele Model of Development of Geometric Thought Friday, July 25, 2008


Agenda :Agenda Exit Cards Process Standard: Representation van Hiele Model Noon—head to Western Colorado Math & Science Center


I’m feeling like a because… :I’m feeling like a because… “I have many wonderful ideas, but they might all fall out before I get to implement them (like a tennis ball container)” “My mind keeps going around & around & around. However, there is some depth to my “aroundness.” “I’m feeling a little flat on top this time of day, but like its sides, I’m seeing infinite possibilities with what we are learning.”


I’m feeling like a because… :I’m feeling like a because… “It looks like a really fast flowing funnel where a lot of content is moving through.” “About ½ of me is obtuse and the ½ is acute. Some of the concepts in the a.m. session are not clear to me just yet, but I am able to clearly see where I can connect what I am learning to helping my students in other areas.”


I’m feeling like a because… :I’m feeling like a because… “I am learning so many interesting ideas. I am forever a lifelong learner like a circle that keeps on going…”


I’m feeling like a because… :I’m feeling like a because… “I’m sitting here in one place. I feel tired today. Let’s move around more like yesterday. (Thank you for what you taught us today.)”


I’m feeling rather like a at the moment because… :I’m feeling rather like a at the moment because… “it looks like a LUGNUT!! The TI-84 stuff is overwhelming!”


I’m feeling like a because… :I’m feeling like a because… “if you rotate this 180 degrees or reflect it about this line, it will look like this. Which is a circus prop, and I feel like my teaching math might turn into a circus. But this class is helping a great deal.


I’m feeling like a because… :I’m feeling like a because… “I am becoming more rounded in my knowledge. I hope to be a circle by the end and be well-rounded.”


Process Standard: Representation :Process Standard: Representation Create and use representations to organize, record, and communicate mathematical ideas Select, apply, and translate among mathematical representations to solve problems Use representations to model and interpret physical, social, and mathematical phenomena.


What are representations? :What are representations? An algorithm that represents a problem solving situation A four-quadrant graph that represents data collected in the classroom A model that shows the relationship between a fraction and percentage A diagram that illustrates area or perimeter


Slide 12:“Representation is both about helping students find their own ways to represent math ideas and about helping them understand conventional representations of math ideas.” “Students should be encouraged to represent their ideas in a way that makes sense to them.” Introduction to Representation Grades 6-8, Ennis & Witek, 2008


How do we assess representation? :How do we assess representation? Observe students and engage them in conversations about their work Interview and conference with students Use a performance-based task Collect samples of their work (portfolio)


The van Hiele Model :The van Hiele Model Level 0 Visualization Level 1 Analysis Level 2 Informal Deduction Level 3 Formal Deduction Level 4 Rigor Levels used for instruction & assessment


Properties of the Model :Properties of the Model Sequential Not determined by age—maturation Some students can advance without understanding Mismatch (materials/instruction & level)


Phases of Learning :Phases of Learning Gradual process or steps Progress of student is highly dependent on instruction Emphasis on language is critical All phases happen within each level Describes how one moves kids from level to level Moves from more teacher directed to student


Experiences :Experiences Requires a lot of time Good example Level 1 #6 Continually ask students “How do you know?”


Assignment :Assignment Read Chapter 4: Visualization, Spatial Reasoning, and Geometric Modeling Work through the following activities: Cross Sections of 3-D Shapes pg.67 I Took a Trip on a Train (applet) pg.69 The Race pg.78 Read “Looking Back & Looking Ahead” p.81 Plan for final product due on Friday.