I love online chats, but my brain NEEDS 8 hours of rest or I just don’t function. The problem? Night time chats get my wheels turning and I cannot shut down.
Some ideas I jotted down following Wednesday’s #geomchat to-do or at least think about:
1. Use a variety of construction stations, then jigsaw students together with the same construction, allowing them to share experience, how-to of their method then discuss the pros/cons of each.
There was a bit of debate which is better tech or hands-on tools. Design will often use the technology available, but I believe many of my students could benefit from the hand tools. For example, my husband works with tiles a lot. It amazes me the designs they often have to produce without the use of fancy tools and technology. They must rely on the understanding of basic constructions and spatial reasoning to often cut pieces from square tiles which eventually are used to create masterpieces in building projects.
2. I prefer patty paper myself when I am looking for a specific outcome, leading students but letting them discover the big ideas. However, I am a huge fan of geogebra or other technology when it comes to exploration as well.
For example, last year in Mathematics Teacher there was an article about duals of polygons. We began with paper pencil on grid paper, drawing polygons, creating the dual, looking for patterns, then asking our own questions. Students then had to devise a plan for investigating duals to answer their questions. It was a difficult task for some students because they had never been asked to think on their own, while others flourished. Question examples How do areas / perimeters of the dual compare to original figure? When will the triangles outside of the dual be congruent? Are the side slopes of the dual related to side slopes of original polygon? How many duals does it take to get a dual similar to the original? Technology allowed students to explore a larger variety of polygons in a shorter amount of time.
3. My last thought from the evening was triggered by a response to the question, What is the point / significance of constructions?
Jessica (@algebrainiac1) tweeted at 8:13 PM on Wed, Jul 10, 2013:
A1: Bc it can be done indep of calcs & nos.We need to teach that math is not about nos,but about objects adhering to certain rules #geomchat
This made me think of our #lit4math chat last summer…how we should think of mathematics as a language. In geometry, our nouns are the objects – points, segments, lines, polygons, planes, circles, etc. and our verbs are what we do with those objects – name location, measure, how we transform/ move them. It has me wondering about a different approach to teaching geometry. For example, asking students what are the basic building blocks of shapes, when we combine them, here is what we get…but letting them answer the big question, how/what can we do with them? Then using their responses to intro our tools such as slope, distance, transformations to describe their attributes. Maybe building that toolbox early on???
A question I shared with Jessica for our next #geomchat … transformations are recommended early on in geometry with CCSS, I am wondering how others are adjusting their curriculum to make this a focus? Introducing them as a tool we use to manipulate our figures, is that the right idea?
Suggestions are encouraged and welcomed!
Pam Wilson, NBCT
5 Practices for Orchestrating Productive Mathematical Discussions, Smith & Stein
Teach Like a Pirate, Dave Burgess
From Ashes to Honor, Loree Lough