1. we approached problems from different perspectives — hands-on manipulatives (or concrete manipulatives), virtual manipulatives, and paper/pencil were may favorite mixtures

[example: Traffic Jam Activity: http://mathforum.org/alejandre/frisbie/jam.html and also here: http://mathforum.org/clime/page1.html ]

2. I would just do a little bit at a time each day — I wrote that up later and it’s here:

Think You Don’t Have Time to Use the PoWs

http://mathforum.org/pow/teacher/PoWsDontHaveTime.pdf

The pdf refers to the Math Forum’s Problems of the Week (PoW) but I think the general ideas could be applied to any problem solving activities.

Activities consist of as many different things i can do, this way i see different students strengths and can focus on their strengths. Using m&m’s to find volume, having them make posters, working in pairs. The “a mile wide, and inch deep” concept is so brand new for me and i am excited to have students discussing with each other and having hem come up with rules and theories based on their investigations. It almost feels like science class ]]>

When I walked in everyday Mary was finishing warm up exercises and going over homework. This took longer than I thought it would, and I was often left with 30 minutes or less to teach. Once it was my time to work with the class,I had students work on an investigation. When we reflected as a class, I reflected questions back to the students. “Can anyone answer Katie’s question? What do people think about what Tony said?” Sometimes there were uncomfortable silences as I waited for students to think about how to explain something. Mary had a hard time with this. She would jump in and say, “You know I think I can explain that really well, if you can’t.” I met with Mary after class and said, “I am trying to get discourse going. I want students to explain things to students. They can do it. We just need to give them time.” Unfortunately, because of the short amount of time I had, the class never made the leap to the regular discourse that I wanted them too. I left frustrated and slightly defeated.

But I also left ready to do better with the next teacher. I also met will Sally ahead of time. I explained that for the type of investigations I wanted to do I needed the warm up to be only 5 minutes. Also, my schedule didn’t overlap with hers, so I wasn’t late everyday. I also asked that we trade off for longer periods of time and that we didn’t interrupt each other’s lessons. I asked Sally if she would write up notes for me everyday on how things are going. Also, I would do the same for her later. She decided to also make a videotape of me everyday in addition to the notes she would give me. I began the first investigation and my heart pounded. We reflected as a class and I asked a student to present. The student made many mistakes, but I resisted the urge to explain it myself. I asked students if they had questions or comments for the student at the board. Students were unsure what to do at first, but slowly, students began to correct the struggling student. I kept going with the idea that students could answer students questions. By the end of the first week, a student raised their hand and said, “I have a problem I am struggling with. I’d like to come up to the board and see if the class can help me.” Sally lit up. “This is really neat,” she said. “I’m going to keep doing this.”

I walked away smiling and knowing that next year, I’ll try again with Mary.

]]>It is very hard not to help too much because students don’t like to be uncomfortable.

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