First Week of School ...planting seeds for an effective year of learning.

   I bet that regardless of how seasoned one is as a teacher, there is always a question in one's mind about the best way to spend that first week of school...
   It is the time to establish procedures, lay out expectations and open lines of communication. I also find it to be the best time to start building the Thinking Culture. Throughout the year my students and I consistently work on  making connections between the topics we learned or were familiar with before a course started. I often model the creation and use of mind maps, and it had always been on my mind how to help students come up with their own ones, rich with knowledge at their current curriculum level. I had some success with it over the years, but I always felt that there could have been a better way to explain how I want my students to work on it.
  I realized that it makes more sense to have this conversation far removed from Geometry topics, but with something engaging, something that kids could be curious about, yet not overwhelmed by it. I chose the topic of Saving Energy.  Last year I finally structured it into a formal How To Mind Map Lesson Plan  for the first week of school. This kind of helped me commit to the idea of weaving Mind Mapping throughout the curriculum. This meant that my expectations for the amount of work we would be able to get out of "thinking this way" during the school year was doubled, and doubled it was! I followed up with a little home project on making a mind map on class expectations, and was pleasantly surprised with the outcomes: so many students demonstrated artistic skills and creativity well above and beyond my own... and one more surprising effect: seeing the results actually changed my first impressions of the students or, rather helped me see their facets that I had not seen yet... I included some samples for your appreciation.

    This summer, the "silly" in me, and the spirit of experimentation, helped me make the video (see below), in the hopes that it will be easier for my students to refresh our class conversation, when it starts to fade away. Feel free to check it out here or on my youtube channel. It is one of my first ones...but it already gave me a taste of skills for the 21st century...but it could be a different post...

   So...for this September I animated my lesson and Included the Project description in SmartNotebook, to make the presentation more streamlined, with visuals, to get my point across faster, plus, if my colleges ever wanted it, it would be available for them.

(almost) no Cut & Paste

...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.... 

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.

Tinkering for Teaching Geometry Proofs

   We begin preparation for Geometry Proofs long before the unit officially starts: in our Algebra class. Justifying steps while solving equations with an appropriate property,  helps build the idea of "every step has a legitimate reason to be done, and is done with purpose".

   In the first weeks of Geometry class we zero in on definitions and the use of their structure ("if..., then..."). This helps identifying "the cause and effect" for following actions, and, essentially, for statements and reasons we will be using in proofs.
   Every lesson, for weeks before the Proofs Unit, I pepper my students with short jeopardy-style questions: " "Segment bisector" implies.....", ""Midpoint" implies...". Every day we use ProofBits, like the ones on the photo below to help students see regularity and structure used in the process. The same questions 

are also given in the form of symbols or/and diagrams. This allows students to appreciate the structure of definitions, their importance and meaningfulness of symbols and diagrams in geometry.
  These little daily recall exercises ease student's transition to formal proofs. I personally find the process of writing them beautiful and mentally satisfying, and I hope my kids see the beauty and satisfaction in it, once the stress of trying to remember steps is gone.

This photo "gives it all out": I've been using my "proof-bits" for quite a while, and my magnets started to loose color and shape. It was definitely the time for an update! Thank goodness for a long summer vacation: I learned how to use my gadgets, and made a new set.

It is now bigger and more unified, which means it will be easier for students to see/recognize and work with the bits. It is also a full collection of vocab, postulates and theorem one would need in class.  To make it more functional, I laminated them (matte finish) and glued them o to a magnet sheet. This is very easily done, since the template is made to fit the 8.5"x5.5" sticky address labels. The size of each Bit is about 8"x2", so they are very easy to see from any point in the classroom. 

You may see the preview of the ProofBits HERE.

Cool Class Management Tool

I think my time "pinning" just payed out: these bouncy balls might be a cute way to quiet down my students one day.This is a nice free resource!

Even High School Students Like Cute Things :) 

You will need to turn on the microphone on your desktop: the challenge is to keep the noise level down to keep the balls from bouncing :).