Hi! I'm Christina - one of the mathematics consultants/instructional coaches @HamiltonCoESC in Cincinnati... and I'm the current President @ohioctm#OCTMchat
A1: inch cubes have been so meaningful with my students! The ability to physically move things around slows down their thinking and makes them ponder more #octmchat
Cubes - inch cubes and centimeter cubes - are versatile for many things. I also like inch tiles. And algebra tiles really opened my eyes - wish I'd had those when I was in Algebra! Was I supposed to choose just one?!? #octmchat
A1: I have to pick just ONE?! UGH!
So... back in the day when I was a Geometry teacher, I loved Patty Paper! :)
Now that I'm a coach, I love fraction bars, open number lines, ten frames, rekenreks... and the list goes on! :) #OCTMchat
A1 Algebra Tiles! After using them with my daughter for the first time (for both of us) she said she had to stop playing and get back to math. 😂 #octmchat
A2. Some HS students think that toys are for little kids. Once they see how it can help or at least show them the math in a different way, they're sold. #octmchat
A2: Students can become off task and frustrated if the teacher is not careful - they need a lot of coaching, questioning, and guiding in the beginning #octmchat
A2 I think the greatest challenge for me was to start. Kids need that time to play first and it is so challenging to allow that time for exploration #octmchat
A2. Some HS students think that toys are for little kids. Once they see how it can help or at least show them the math in a different way, they're sold. #octmchat
A2: I have to remind myself to SLOW DOWN and let the students explore the manipulative... and to explicitly make connections between the pictorial and abstract representations #OCTMchat
A2 I struggle with kids wanting to move past the concretebefore they are ready because they are toys... I try to focus on the term tools, but it isn’t always effective. #octmchat
Q2: mostly incorporating negative numbers. Sometimes it feels more complicated then"rule" but I am always reminding myself to take it back to the conceptual understanding and that seems to help. #octmchat
If they already know the procedure, Ss can become frustrated by having to "show" what is happening. i've challenged them to match the procedure with the visual and act out what is happening. Linking representations builds conceptual understanding. #octmchat
A2: At some point, bigger ideas need to be extrapolated from their use, but the key is finding the balance of when that time is, cannot be too early #octmchat
A2: Instead of spaghetti @batty314 , I use string licorice a lot in geometry. (radian, triangle inequalities, etc) The struggle was the "straightness" factor and the creativeness of teenagers to make jewelry and other with the juicy goodness. #octmchat
Using manipulatives with SMP 3 allows students to make their thinking visual in ways other than writing a series of symbols & equations. Allows opportunities to discuss and revise ideas. #octmchat
A3: So... when the 8 Mathematical Practices first came out I realized how guilty I was as a former Geometry teacher of just HANDING Ss the tools they were going to need instead of allowing them to choose... "appropriate tools" became a way for see "student voice" :) #OCTMchat
