Constructions!

I LOVE CONSTRUCTIONS! I plan on teaching them as an ongoing concept.

Last summer, I was introduced to them at a workshop. I was never taught constructions when I was in high school or college. This was brand new. I went home and completed a detailed step by step and guideline for myself. I will share this. If it doesn't make since or you have another way or constructive criticism, please let me know. I did teach some this past year and the experience went really well. The students loved them and it helped build a stronger connection and understanding amoung the fundamental concepts of Geometry.

 

I begin constructions with a diagram and a few 'rules' or guidelines for myself and my students.

I couldn't tell you how I folded and glued these ten pages togther, but this is the coolest document that I think I've ever done. It is front and back and about 9 feet long.

One side is my initial attempt and additional practice. The other side is my detailed steps and constructions. I hope that these make sense, and if not, you can find a lot of great videos on youtube!

 

 

 

 

 

 

 

 

This last one is a confusing combination of my discovery and the presenter's approach. I always knew that SSA was not a postulate/theorem of triangle congruency. How? "Because you don't say ASS in class!" is what my high school teacher told me. It wasn't until my third year of teaching that I figured it out. I actually learned this through Khan Academy and of course put it to paper. The way the presenter approached it, you would never have a problem with the 'a-word' in class, but I couldn't tell you what or how she said it.

 

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A Theory to the Success of Algebra 1

Mathematics is a language all its own, right? So why aren't we teaching it as such? You know summertime; it's the time we teachers spend in workshops soaking in the theoretical views of the 'experienced'. I actually really enjoy workshops, specifically when I'm at that table that just explodes with ideas!

Back to the THEORY: If math is a unique language, then I should be teaching students to listen, write, read, and speak its language.

I realize that I spend so much time focusing on one component-writing the math. I need to teach fluency in math that focuses on all four of these areas.

I have observed several foreign language teachers come and go. The great teachers have their students fluent in these four areas. Students read, write, listen, and speak the language.

As I think back to high school, I was an excellent memorizer. I didn't really know how to read the notation or why solutions were written a specific way, but I could tell you what I needed to put where based on context clues. Then when I got to college, I had one of those professors. He spoke, read, wrote, and listened for the language of mathematics. He expected the same from us. I struggled like you wouldn't believe; however, after I graduated and entered the world of education for mathematics, I noticed the difference in my math language and others. Now, I am not an expert or near perfect, but I notice that my students have a higher level of math skills because I hold myself to high standards when using the language of mathematics.

GOAL: Even though I can read, write, listen, and speak the language of mathematics, I need to expect that from my students.

CONCLUSION: This is all just a theory based on self reflection and observation. We'll see how it unfolds over this next year.

 

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