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Day 105: Investigation of Trapezoids & Kites

First stop was a quiz on last week's worksheet, and then off to the computer lab so the students could explore properties of trapezoids and kites.

My hope was that if students now have a firm understanding of *how* we test ideas about shapes (use slope for parallel/perpendicular, distance formula for length, use midpoint for bisecting, etc), then then can use computer software to readily create shapes that would be problematic to explore with a pencil on graph paper.

I chose to use Geometer's Sketchpad because that's what I've been using since college geometry, but after spending the last few days exploring Geogebra, I'll probably switch over to that in the future.

I wrote up VERY explicit instructions, detailing what students should do, step by step, to achieve a proper shape. "Use the segment tool to draw a line segment, select a new point and create a parallel line by clicking here," etc. Of course, my best efforts were thwarted by students who absolutely refuse to read directions and immediately claim they did, but couldn't understand them. Students would call me over to ask why their quadrilateral didn't look right, and I could quickly see that they skipped step #4. "No I didn't!" they would emphatically deny. "Well actually yes, you never placed the two new points as instructed." I would reply. Then they'd get sheepish and laugh and admit the must have missed that part.

That, in a nutshell, sums up most of my difficulties teaching 10th graders (the probably isn't generally as bad with the 11th and 12th graders in my physics and astronomy classes). A complete and total refusal to even bother paying attention to given instructions, no attempt and determining what went wrong on their own, and complete denial of any wrong doing when confronted. I understand this is simply a matter of maturity, but this strikes me as behavior one would encounter with 6th graders who might be 11 or 12 years old. I have some experience working with the same age level I do now in other school districts and I never saw maturity levels like I do now, which leads me to believe the issue is somehow correlated to community and socio-economic status. It provides a launching point for a very interesting discussion of fixed vs. growth mindsets, but that's a discussion for another venue.
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