#TMC17 Post 3: My Morning Sessions
I love the way TMC is designed with its varying lengths of presentations. There are 3 morning sessions that are 2 hours each, for a total of 6 hours so you can really dive deep into a subject. Then, there are afternoon sessions that are an hour. There are "My Favorites" that can be 5 or 10 minutes. And, finally, we end with a Flex session for anything you might have come up with last minute depending on conversations along the way and this is an hour long. It is so well designed.
I was torn between two AM sessions, but I ultimately chose Teaching Risks Tasks with Peg Cagle, Cal Armstrong, and William Thill. These people have been working with PCMI for a long time. It was so great to watch how they orchestrated their teacher moves around us. It was like an eloquent dance.
Here is the link to their page. Link
Day 1 = 1 problem in 2 hours!
Today had us look at this Visual Pattern from visualpatterns.org. I have used these a lot and always asked the same question - How many ___ in Step 43?
They put a twist on it. "As the step changes, ______ also changes."
We thought about it individually. Then, discussed it with our group and added to our list. Finally, we brainstormed as a class on a big whiteboard and wrote all our ideas down.
I came up with: #rows, #columns, #total blocks, #in each row, #in each column.
Our group added: area, perimter, #line segments, layers, how many moves it would take to make the shape into a square.
Our class added: #bigger line segments, #vertices of polygon corners, # squares - unit vs all squares, #rectangles, #surrounded - touching adjacent sides (we called this sort of like minesweeper), #hexagons, #polygons, #tetris pieces.
We were instructed to find someone one or 2 we wanted to work on one of these attributes with. I chose to work on the number of rectangles with Marsha and Rachel. We drew the first 8 steps and started organizing by the dimensions of the rectangles and began counting. We were a great team. Marsha wrote, I counted, and Rachel looked for any patterns and noted it. We noticed a lot of things but did not have enough time to get as far as we wanted. Note: we spend 2 hours on this class and could have used 2 more hours!
Day 1 Notes:
Morning Work Pictures:
AM pics 1: playing with stickies as the squares: AM Pic 2: our rectangle counting:
Great team: Marsha, Rachel, and myself:
Day 2 - Analyze videos of teachers teaching:
We watched videos of teachers teaching. We saw an American teacher introduce linear group work, followed by a Japanese teacher having the students work on solving a word problem involving systems of equations. We had great, in-depth conversations. We looked at the questions themselves. We looked at the teachers' questions and teachers' moves. We were critical. Annie Fetter suggested we audio tape ourselves teaching by turning our phone on for group work and taping for about 10 minutes. Then analyze it for what did I say, how did I react, what did I do, what are my questioning strategies, write down every question you asked, what type of question you asked, and track T, S1, T, S2, T, S3, etc. See who does the talking.
Some things we did notice was the American teacher seemed to jump in and save the students. Tip: Don't hijack the question! Suggestion, when working in a group and a student has a question for the teacher ask the group if anyone knows. Teacher then to ask other students for help first.
The Japanese teacher seemed to be more prepared and anticipated the students' strategies. He had manipulatives ready to be used and titles of strategies to be hung up. It was more of a lesson on strategies for solving systems instead of just getting the final answer.
We learned that Japanese teachers learn about "kikkon-shido" which means "walking among the desks - not to save, just to note their work. They are also taught to use the blackboard - why would you write anything on the board if you just plan to erase it?
Day 2 Notes:
Day 3: Rich Task Implementation: Looking at worksheets:
When looking at an assignment - whether it is a worksheet or activity - list the opportunities to learn that are created and supported for both the student and teacher by both a traditional use of the task an alternative task being suggested. So, if you have a regular worksheet - it has benefits. If you want to change it up a bit, how are you changing the learning opportunities. Are all the changes what you intended? Are they better than the traditional?
Worksheets 1: We looked at one worksheet with solving systems of equations in the traditional way - solve some by substitution, some by elimination, and some by graphing. Each problem was picked intentionally. On the graphing, a slope of 5/7 was chosen so students could "move" slope instead of making a table. On the other graphing problem, the dreaded x = 7 was thrown in to see how students would do with it. The second "alternative" worksheet had 16 problems in squares that asked the student to sort them. Some of them were non-linear. We suggested students might simply sort into linear/non-linear. Nothing on this worksheet actually asked students to solve the systems. Our group suggested one could introduce this at the start of the unit and have students cut and glue their sort to a paper and explain why they chose to sort that way and then collect. Teach the unit and then do it again and see if their process changed.
The next worksheet was your typical area, perimeter, and circumference review sheet. Instead of asking students to do the problems, ask them to analyze the problems! Ask questions like:
Which are the 3 hardest problems?
Which are the most valuable to you in preparing for our quiz?
Which 3 are the easiest?
Which 3 are most challenging to most of the class?
For hmwk: pick the most interesting problem, do it, and write about why you chose it. How cool!!!!
Asking students to analyze problems will slow down the "grinder students".
"Answer-getting isn't math." ~ Peg Cagle
If you are still concerned they are just trying to get the answers, then give them the answers. Shift the focus, time, and energy. This will encourage them to do it and then find their errors.
If you know you will be assigning a worksheet for homework and do have time to start it in class, how about if you switch it up and start with the hardest problem first, then the easier problems will be done at home.
Hand out a worksheet where all the work is done and all have errors. However, the directions are not to fix the errors, instead..."What is this person confused about that led them to this mistake? Bonus: Give another problem that might help them to see and understand their misconception." How great. I have done the fix the mistake. I love this added explanation.
Side note: Allow students to bring an index card to a test where the students put their common mistakes on the card. "Mistakes I am Likely to Make Card."
Day 3 notes:
Three days that were so full of rich goodness! Thank you!