Studying Classroom Teaching as a Medium for Professional Development Proceedings of a U.S.-Japan Workshop (2002) / Chapter Skim
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Appendix I: A Written Case: Pattern Trains at Sixth Grade
Appendix I: A Written Case: Pattern Trains at Sixth Grade
Pages 231-247
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From page 231... ...
The project is codirected by Edward Silver, Margaret Smith, and Mary Kay Stein and is housed at the Learning Research and Development Center at the University of Pittsburgh. For additional information about COMET contact Margaret Smith by phone at (4129 648-7361 or by e-mai!
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From page 232... ...
In order to ensure student success, ~ have started to make some modifications in the curriculum, at times putting in an extra step or taking out something that seems too hard; rewriting problem instructions so that they are clearer and at an easier reading level; and creating easier problems for homework. In addition, during classroom instruction ~ try to break a task into small subtasks so that students can tackle one part of the task at a time.
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From page 233... ...
~ just hoped ~ could forget that it was there. Discussing the Square Pattern Trains In order to get things started, ~ asked students to make observations about the pattern.
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From page 234... ...
These experiences have had an immediate positive effect on Desmond he would actively participate in class following these episodes. So Desmond came up to the overhead, and I gave him the black square and asked him to measure the third train.
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From page 235... ...
These experiences have had an immediate positive effect on Desmond he would actively participate in class following these episodes. So Desmond came up to the overhead, and I gave him the black square and asked him to measure the third train.
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From page 236... ...
~ explained that she had noticed that the squares on the ends always have three sides they each lose one on the insideand that the ones in the middle always have two sides. ~ used train three (shown in the diagram below)
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From page 237... ...
~ quickly got out my pattern blocks and built the train shown below on the overhead. ~ told students that ~ wanted them to work with their partners and build the first three trains in the pattern, find the perimeters for these three trains, and then to find the perimeters for the lOth, 20th, and lOOth trains.
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From page 238... ...
The lesson containe(1 too much whole group teacher questioning anti students explaining anti not enough time for students to stretch and discover independently/collaboratively. ~ wondered, in particular, what most students really un(lerstoo(1 about Angela's method.
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From page 239... ...
He has been working with Catherine anti others anti has had one year's experience teaching "this new way." Catherine is now beginning her fourth year of the math project. THE PATTERN TRAINS Part 2 David Young David Young has just started his second year at Quigley Middle School.
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From page 240... ...
The new unit that we starte(1 yesterday uses trains of pattern blocks arrange(1 in some geometric sequence. The unit is suppose(1 to help students visualize anti (1escribe geometric patterns, make conjectures about the patterns, (letermine the perimeters of APPE N AX
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From page 241... ...
APPE N DIX Geffing Startecl: The Square Tile Pattern ~ started by building the pattern of squares shown below on the overhead and asking students to work with their partners to find the perimeters of the first four trains in the sequence. Emily immediately asked for pattern blocks so she could actually build the trains.
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From page 242... ...
Although this was a perfectly good approach for the tenth figure, it was going to be less helpful when we started considering larger trains. I asked if anyone did it another way.
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From page 243... ...
Kendra asked how he knew that there were eight squares on the inside of the train. Joseph said that he had looked at the first four trains and noticed that the number of squares on the inside was two less than the train number the second train had zero squares on the inside, the third train had one on the inside, and the fourth had two on the inside.
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From page 244... ...
In a few cases where the students were really stuck ~ suggested that they try to see if they could find a connection between the train number and the perimeter as a few students hall (lone in the last pattern. Once it appeared that most pairs had ma(le progress on this task, ~ asked James to come up and buil(1 the fourth train and (lescribe the pattern.
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From page 245... ...
She quickly said "7." ~ asked her how she did it so fast, and she responded, "After the first one you just add one every time. The fourth train is 6 so the fifth train would be one more." ~ then asked if anyone could tell me what the perimeter of the lOth train would be.
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From page 246... ...
," ~ asked as ~ moved from group to group. Discussing the Hexagon Pattern After 15 minutes all students had completed patterns 2 and 3.
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From page 247... ...
See, the second train has four, the third train has six, so the tenth train would have 20." ~ thanked Carmen for sharing her solution and asked if anyone had another way. Joseph was again waving his hand.
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