...Planning For a New Year of Geometry...
I have mentioned earlier that in my Geometry classes we work on forming "basic chunks of knowledge" (yes, I am deeply affected by Barbara Oakley's teaching) and build fluency with them before they actually plunge into writing proofs. Last year I increased the intensity of the Proofs Unit, including more sophisticated problems, on top of that, Common Core pressure contributed to time shortage, so I needed a reliable way to ensure that all (?!) of my students could follow through with proofs independently, therefor I decided to use some hands-on practice, that allows kids to quickly "sketch" their thoughts before those slipped away: without worrying about the proper order, notation or writing fast enough... This would allow the final "combing" through the chunks of learning, "catching" last kinks my students may have had in their cause-and-effect connections within the vocabulary-symbols-diagrams bits of Geometry. For that, I had them work with MINI-ProofBits in small groups (of 2 and 3) without me facilitating at the board... To eliminate as much Cut&Paste as possible, I laminated a few sets of bits, color-coding the sets for an easy collection/storage. If you ever go for it, use a 5mil Matte laminate pouches to avoid reflection and make them less slippery.
I was generally pleased with the outcome: the bits were big enough for students to handle, yet, small enough for a set to fit on a desk; it was easy for me to scan their work for further intervention....
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| Tactile experience with proofs may help some students understand how they work. |
A few surprises: students actually eagerly asked each other for an opinion on what should be next, having those accountable talks we always want to hear.It was especially nice to see when groups came up with alternative proves... As the kids were discussing who was correct, and why, and what was the difference in the other group's approach, it almost felt like they were moving around the "lego-blocks of their thoughts" in the form of the Bits. It is almost as if they could touch their houghts, see them and not just talk about them... it made a difference for the weaker students: a tangible model of the process helped them make sense of the proof process. Of cause those were the simplest proofs, but the idea of how they work was loud and clear.
Some issues to work out: So....this year I might have some 2-year remedial Geometry courses, and I feel I need to provide this tactile experience. However, since this time my classes will be big (30-34 ss) it will be a challenge getting my laminated sets back in full or cutting them in class... so I decided to try something different:
I will give every student a disposable set of ProofBits, that needs to be cut only once and will last until they are ready to sketch their proofs with pen&pencil. This is how it works, so far:
1) Organize ProofBits vocabulary in groups: those pertaining to segments are on one sheet; the ones about angles are on the other, and the basic axioms/theorems involved are on the 3rd sheet;2) Use 3 different colors of paper to distinguish between those 3 groups; Staple them on the left.
3) Every proof-bit is repeated on the page at least 5 times (in line). I numbered each line for reference and organized the terms in the order that would help kids with weak memorization skills (did I just say a forbidden word?!) get a grip on what links to what.
4) Cut between those lines, but leave the strips connected at the stapled side (it will look like vermicelli ); cut it to the size of a notebook (this could be done for HW )
5) Tape that pack of vermicelli in the back (or the front) of a notebook. It is now ready for work: no need to mess with scissors-just crease one Bit at a time and tear it off. Voila! Cut it Once, Paste it while it Lasts!
I will update you later in the year on how this goes, but feel free to join testing this beta version out with me.
