previous table of contents appendix B table of contents next
1.14 Cynthia: "They're all the same colours but I'm putting them in different spots."
1.15 When asked why she used all the same colours, Cynthia responds, "Cause I was trying to see - - to get them in the right place." EWT Simple Deduction
1.16 Cynthia still gets three white pegs.
1.17 Cynthia makes her third guess.
1.18 After the teacher gives her two white pegs, she looks at the board and says, "I probably put a brown one there."
1.19 Teacher: "Pardon me."
1.20 Cynthia: "I probably put the brown one in there and it’s the right spot." EWT
1.21 Teacher: "You probably put the brown one in there and it’s the right spot?"
1.22 Cynthia: "No, I meant that um, I put the brown one in but there was another that went in the same spot but it was a different colour."
1.23 Teacher: "Are you going to use brown next time?"
1.24 Cynthia: "No . . . cause I might get it all wrong." EWT Simple Deduction
1.25 Cynthia makes her fourth attempt at figuring out the code. (3:28)
1.26 The teacher asks Cynthia if she remembers what a black peg indicates and Cynthia states that she forgets. The teacher goes over the significance of the peg colours again.
1.27 Cynthia is asked why she used two yellow, "Because I didn't want to use blue."
EWT Simple Deduction
1.28 Cynthia says she doesn't know why she doesn't want to use blue. (She had a blue peg placed correctly in turn 3.)
1.29 Cynthia makes her fifth attempt. She gets two white pegs. (3:30)
1.30 Cynthia looks at the board and says, "Those are two threes, so that makes six in all of them." (She points to the pegs she got in turn 1 and turn 2.)
1.31 Cynthia studies the board and makes her final attempt at breaking the code. (3:32)
1.32 She uses two green pegs.
1.33 When she receives two white pegs, she smiles and rests her head in her hands. She then asks, "Can I pick somebody to come over here?" (She wants somebody else to come play the game.)
Game 2: Jared
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The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-82
To Beginning of Section | To End of Section
2.0 Jared comes to play a game, stating that he is "good at this game." (3:33)
2.1 Jared correctly goes over the rules of the game.
2.2 Jared makes his first guess.
2.3 The teacher gives him 2 white pegs for his guess and he quickly starts working on his second guess.
2.4 Jared uses only two of the same colours (red and brown) and the teacher questions him as to why. (3:36)
2.5 Jared: "Because right here (turn 1) I know that there's the same colour but not in the right spot." EWT Simple Deduction
2.6 He receives two white pegs again.
2.7 Jared starts on turn three and begins by placing red and brown pegs in the board. (3:37)
2.8 The teacher asks him why he started with brown and red first.
2.9 Jared: "Cause these are the same ones that are supposed to be there but are in the wrong spot."[or the other two could have been right] EWT Simple Deduction
2.10 Jared receives 1 black peg and 1 white peg and immediately begins to work on turn 4. He starts by placing a red in the same position as turn 3.
2.11 Jared places a brown in the fourth hole, and says he is doing so because it wasn't right, "there or there or there." (He indicates the three other positions he has tried brown in.) EWT Simple Deduction
2.12 Jared uses only red and brown pegs on his fourth turn.
2.13 The teacher asks him why he has chosen to do so.
2.14 Jared: "Because it isn't one of the other colours." EWT Simple Deduction
2.15 Teacher: "What are you hoping to find out?"
2.16 Jared: "It'll be right."
2.17 The teacher says, "I don't have to put in any pegs this time."
2.18 Jared questions, "why?"
2.19 The teacher asks Jared to look back over what he has done. He begins to work on his fifth turn. He chooses orange first.
2.20 the teacher asks him why he chose orange.
2.21 Jared: "Because these two aren't it and the others ones must be." (He indicates the brown and red in turn 2, and then points to the green and orange.) (3:39) EWT Simple Deduction
2.22 Jared receives four white pegs.
2.23 Jared begins turn number six. He begins by placing green in the third position. The teacher questions why.
2.24 Jared: "Because I never tried right there." EWT Simple Deduction
2.25 Jared gets two white and two black. The teacher asks him if he would like to try again.
2.26 Jared creates his seventh guess. (3:43)
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-83
To Beginning of Section | To End of Section
2.27 As Jared is placing his pegs, he puts a yellow peg into the second position and states, "no that's wrong," and moves it again. When asked, he says he knew it was wrong because he tried it there before and it was wrong. EWT Simple Deduction
Game 3: Jared
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3.0 Jared plays another game. Alicia comes over to watch so she can learn how to play. (3:47)
3.1 Jared takes his first turn.
3.2 Jared gets three white pegs for his first turn.
3.3 Jared quickly takes his second turn. He keeps three of the same colours (blue, green and brown.)
3.4 The teacher gives him one black peg and one white peg.
3.5 Jared quickly takes his third turn. (3:49)
3.6 the teacher gives him 1 black peg again and 3 white pegs.
3.7 Alicia: "Do you have to get all whites to get it?"
3.8 The teacher goes over how to win with Alicia.
3.9 Jared takes his fourth turn. He uses green, orange, brown and yellow. The teacher asks him why he decided to use green this time.
3.10 Jared looks at the board and then states: "Oh, I made a mistake. I meant to put in a blue." (3:51) EWT Simple Deduction
3.11 Jared receives 1 black and 3 white.
3.12 The teacher asks if he knows what colour is in the right spot.
3.13 Jared: "Yep, yellow. Cause it's the same as there." (He points to his third turn.)
EWT Simple Deduction
3.14 Jared takes his fifth turn. (3:52)
3.15 He checks the positions that each colour has been in before placing his pegs.
3.16 Jared cracks the code.
Game
4: Alicia
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-84
To Beginning of Section | To End of Section
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4.0 Alicia takes her first turn and gets three black pegs. (3:55)
4.1 Alicia takes her second turn.
4.2 Alicia keeps three pegs in the same place and uses a new peg in the third position (orange). She is asked why she did this.
4.3 Alicia: "Um because I never used - - orange yet and I had one wrong colour."
EWT Simple Deduction
4.4 The teacher gives Alicia three black pegs.
4.5 Alicia completes her third try and cracks the code! (3:57)
Game 5: Alicia (Note this game was not completed because class was dismissed.)
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5.1 Alicia begins a new game. (3:58)
5.2 Alicia takes her first turn. She gets two white pegs.
5.3 Alicia takes her second turn and uses the same colours as in turn one and switches only two of the peg's positions.
5.4 Alicia offers no explanation as to why she didn't choose any new colours.
5.5 Alicia takes her third turn. (4:00)
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-85
To Beginning of Section | To End of Section
5.6 Alicia continues to use the same four colours even though she only got two white pegs for them on the first to turns.
5.7 The teacher questions Alicia again about why she has chosen the colours she has used.
5.8 Alicia: "Because I never tried it that way." (Note that orange and red are still in the same position.) EWT Simple Deduction
5.9 Alicia gets two white pegs.
5.10 Alicia takes her fourth turn and continues to use the same four colours. She switches the position of the red and orange peg but keeps the yellow and blue where they were before even though she still has not received a black peg. (4:01)
5.11 When she completes her turn she looks up and smiles at the teacher.
5.12 When the teacher gives her two white pegs once again, she sighs and put her head on her hands that are resting on the table.
5.13 The teacher questions Alicia again as to why she continues to use the same four colours.
5.14 Alicia: "Because the whites means the right colour but in the wrong spot."
EWT Simple Deduction
5.15 Teacher: “ . . .but you only have two that are the right colour."
5.16 Alicia looks at the teacher and laughs a little. Then she puts back the pegs she had originally picked out that were the same as the previous four turns.
(Note: Class has been dismissed at this point and the game is ended early.)
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-86
To Beginning of Section | To End of Section
Activity: Mastermind
Note: The chart representing the game board is set up so that the number of each row indicates the order in which guesses were made. The right hand column indicates how many white pegs (w) and how many black pegs (bk) the guess earned. A white peg indicates that there is a peg that is the right colour but not in the correct spot. The black peg indicates that the peg is the right colour and in the correct spot.
Interesting points??
There was not a lot of "meat" in these four games. Maurice was inexperienced at this game and did not seem to think through his guesses based on the information he was given. You may want to skim over a few points made by Kyla however. Look at 1.3 - 1.10 and 2.5 -2.10.
Game 1: Kyla
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1.0 Kyla and the teacher discuss the game. Kyla says that she has played the game before but forgets all the rules. (3:26)
1.1 Kyla begins her first game. (3:27)
1.2 She receives 1 black peg and 2 white pegs.
1.3 Kyla takes her second turn.
1.4 The teacher asks Kyla why she used the colours she has used and she shrugs her shoulders.
1.5 The teacher gives Kyla 1 black peg and 2 white pegs for her guess.
1.6 Kyla: "This is getting really confusing! . . .Cause before I used to peek at my sisters. I used to flip up the lid. (When I played with her.) "
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-87
To Beginning of Section | To End of Section
1.7 Kyla makes her third guess. (3:30)
1.8 The teacher questions Kyla about her choices and she once again shrugs her shoulders.
1.9 The teacher gives Kyla two white pegs and asks her if she knows anything about the colour of the pegs now.
1.10 Kyla: "The yellow is supposed to be right here! (She points to the third position.) Cause I tried it right here (the third position in first turn) and right here (third position in second turn) and right here (third position on third turn) but I only got white. I put the green there (first position) again and it's not right! " EWT Multi-Step Deduction
1.11 Kyla takes her fourth turn and figures out the code. (3:32)
1.12 Before showing Kyla that she has figured out the code the teacher questions Kyla about her choices. She says she does not know why she choose the pegs she did.
Game
2: Kyla
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2.0 Kyla starts a new game. (3:33)
2.1 Kyla receives 1 white peg and 1 black peg for her first guess.
2.2 the teacher asks Kyla if she can tell how many of the four pegs are the right colour and she states, "I don't know." She then goes on to explain that she knows that two are the right colour but she does know which ones they are.
2.3 Kyla takes her second turn. (3:35)
2.4 Kyla receives two white pegs.
2.5 Kyla takes her third turn. (3:36)
2.6 Kyla receives two white pegs and sighs.
2.7 The teacher questions Kyla about where she had one in the correct place and which one she thinks it might be.
2.8 Kyla points to the blue peg in the first row and then changes her mind. "I never got a black one right there. (She points to the blue in the second turn.)"
2.9 Kyla indicates that the green can not be correct either in the first try. "Cause on this one (turn three) I didn't get a black."
2.10 Kyla states that the orange one on turn one must be in the correct spot then realizes it can not be. "Cause I got a black one right here - - no! Oh my! It's yellow." EWT Multi-Step Deduction
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-88
To Beginning of Section | To End of Section
2.11 Kyla takes her fourth turn and receives 1 black peg and 2 white pegs. (3:39)
2.12 Kyla takes her fifth turn and receives 1 black and 1 white. (3:40)
2.13 Kyla indicates that she would like a seventh turn.
2.14 Kyla figures out the code. She says that she does not know why she picked the colours that she used.
Game
3: Maurice
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3.0 The teacher and Maurice discuss the game. Maurice indicates that he has never played Mastermind before. (3:44)
3.1 Maurice makes his first guess and earns 2 white pegs.
3.2 Maurice makes his second guess. He uses only two of the colours he used in the first turn. When asked why he used the red and blue again he said, "because I thought they were the right colours." EWT Simple Deduction
3.3 Maurice earns four white pegs for his guess.
3.4 Maurice takes his third turn and earns two black pegs and two white pegs. (3:47)
3.5 Maurice stops and studies the game board for a brief period before making his fourth guess.
3.6 Maurice: "I changed the blue and red around."
3.7 The teacher asks Maurice if he has learned anything new about the code. He is unable to state any new information.
3.8 Maurice takes his fifth turn. (3:49)
3.9 When asked what he had done, he stated, "I just changes these two (yellow and brown)."
3.10 He indicates that the other two colours are the same as in number three.
3.11 Maurice makes a sixth attempt at breaking the code. He earns 4 white.
3.12 Maurice makes a seventh attempt at figuring out the code. (3:51)
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-89
To Beginning of Section | To End of Section
3.13 Maurice: "I just changed the red, the purple (brown) and the yellow."
3.14 Maurice earned four white pegs once again.
Game
4: Maurice
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4.0 Maurice begins a new game and makes his first guess and earns three white pegs. (3:55)
4.1 Maurice quickly makes his second guess. He uses three of the same colours as he used in turn one. (3:56)
4.2 The teacher gives him two white pegs for his guess and asks Maurice if he knows anything new.
4.3 Maurice: "It's blue. Cause if there's three (white pegs) there (in guess one). I changed the blue and I only got two." EWT Simple Deduction
4.4 Maurice takes his third turn and earns three white pegs. (3:58)
4.5 Maurice makes his fourth attempt and earns 1 black and 1 white. (3:59)
4.6 Teacher: "Now what are you thinking about?"
4.7 Maurice: "It's not two orange."
4.8 Teacher: "How do you know it's not two orange?"
4.9 Maurice: "Um, there might be."
4.10 Maurice takes his final two turns making very little changes in his guesses. He is unable to figure out the code.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-90
To Beginning of Section | To End of Section
Activity: Connect Four on the computer. Note that there are many different shaped playing boards. In addition, the number of markers that need to be placed in a row vary as well. This is indicated at the top of each game chart.
Wherever there are three x's on the game chart, indicates that there was no place there on that particular game board.
Notes: There was a lot of conversation during games 11 and 12. The others were not too "meaty".
Game 1: Jerome and David
Game 2: Jerome and David. Not finished. Students changed the game setup shortly after starting. (3:22)
Game 3: David
Needed to win: 3 in a row
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xxx |
3.0 David chooses a new game. (3:24)
3.1 David says it is going to be easy to win at this game.
3.2 After the third marker is placed, the teacher asks if anyone can win. David states "no" and indicates that he wants to play a "bigger one."
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-91
To Beginning of Section | To End of Section
Game 4: David
Needed to win: 3 in a row
Winner: Computer
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4.0 David starts a new game. (3:25)
4.1 When he places 3, the teacher asks David why he placed it there.
4.2 David indicates by pointing to the screen that he hopes to get three in a row diagonally starting from 1. Simple Deduction
4.3 Before placing 9, David "holds" the marker over the position where 9 is placed to see what it looks like.
4.4 When the computer wins, David states, "That's how I was going to win."
Game 5 : Jerome
Needed to win: 3 in a row
Winner: Jerome
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5.0 Jerome begins a new game. (3:27)
5.1 Jerome quickly wins.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-92
To Beginning of Section | To End of Section
Needed to win: 3 in a row
Winner: David
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6.0 David begins a new game. (3:29)
6.1 David quickly wins.
Game 7: Jerome and David
Needed to win: 4 in a row
Winner:
Computer
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7.0 Jerome and David begin a new game. (3:31)
7.1 After placing 3, Jerome points out that he would like to make a diagonal (7, 3 and _).
Simple Deduction
7.2 When asked why 5 was placed where it was, David responds, "Cause he woulda' won." Simple Deduction
7.3 Jerome blocked the computer with move 9.
7.4 The computer wins. Neither Jerome nor David noticed that it was possible for the computer to win once 21 was placed.
Game 8: David
Needed to win: 4 in a row
Winner:
Computer
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-93
To Beginning of Section | To End of Section
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8.0 David begins a new game. (3:35)
8.1 On move 7, David realizes that the computer can win. "He can win any way at all!"
Simple Deduction
Game 9: Alicia
Needed to win: 4 in a row
Winner:
Computer
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9.0 Alicia begins a new game. (3:37)
9.1 The computer wins.
Game 10: Seth
Needed to win: 4 in a row
Winner:
Computer
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10.0 Seth begins a new game. (3:42)
10.1 On turn 15, Alicia tells Seth to put the marker on top of 14.
10.2 When Seth places 15 Alicia shouts, "No, not there!"
10.3 Seth: "Yes, I know what I am doing."
10.4 The computer places 16 and wins.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-94
To Beginning of Section | To End of Section
10.4 Seth: "I was trying to do this!" (He points to the diagonal running from 15 through 7.) Simple Deduction
Game 11: Alicia
Needed to win: 4 in a row
Winner:
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11.0 Alicia begins a new game. (3:45)
11.1a Seth to Alicia on move 5, "I know what he's doing. Block him right there! (position 7)"
11.2b Alicia places a 'block' at the opposite end of what Seth suggested and states, "I know what I'm gonna do next."
11.2c Seth points out, "He'll do that (points to position 7)."
11.2d Alicia places 7 where Seth indicated. After move 7, Seth says, "You won't beat us mister sly one! . . .We're gonna block him... Nice try computer, very sly."
11.2e Seth: "You won't beat us mister!"
11.3 After Alicia places 11, Seth says, "He'll make four right there." (He points to 10, 13, 12 and 19.)
11.3 a Alicia: "I know. (She places 13 where Seth indicated that a row could be made by the computer).
11.4 Seth pleads with Alicia to put 15 on top of 14. "What if he puts two there? (Two on top of 14.)
11.4a Before move 15, Seth says, "Definitely don't put one right there (position 21)."
11.4b Alicia: "Why?"
11.4c Seth: "Cause he'll go across there (creating a horizontal row starting at 12 moving right)."
11.5a Seth: "I know what he's doing."
11.5b Alicia: "I'm not doing it right away."
11.5c Seth: "Put it right there!"
11.5d Alicia: "No, I don't need to."
11.5e Seth: "Yes! He'll win! I'm telling you!"
11.5f Alicia: "No, he won't win. Trust me."
11.5g Alicia puts 15 in place.
11.5h Seth: "What if he puts two there?"
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-95
To Beginning of Section | To End of Section
11.6 Before placing 19, Alicia holds the marker in front of various places and examines to see if they are good positions. (3:49) Simple Deduction
11.7 Seth warns Alicia not to place 21 in position which it is finally placed. "He'll go up like that." Seth points to a diagonal starting at 6. Simple Deduction
11.7a Alicia explains that the computer can not create a diagonal there because number 15 is blocking it.
11.8 Seth on move 25, "Put one right there. If he puts one right there (in that position) he wins!"
11.8a Alicia intentionally blocks the computer on move 25.
11.9 Neither Seth nor Alicia noticed the winning position for the computer at spot 26.
Game 12 : Cynthia
Needed to win: 4 in a row
Winner:
Computer
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12.0 Cynthia begins a new game. (3:52)
12.0a The teacher states that no one has been able to beat the computer.
12.1 Cynthia: "I think I will. I'm really good at this game."
12.2 After 2 is placed by the computer, Cynthia is asked if she has a plan.
12.3 Cynthia: "I'll put one right here (17) and one right here (3) and if he blocks that right there (4) then I'll put one right here (the third position on the bottom row.)"
Multi-Step Deduction
12.3a Cynthia states before she places number three: "What did I say again?"
12.4 Cynthia states after the computer places 4, "If he puts one more right there - - I'm gonna block that next time he puts one right there (on the bottom next to 4) cause if he puts one more there then he only has two more to do." Multi-Step Deduction
12.5 Before she places 5, she states: "Three more up there (directly above 3)." (3:53)
12.6 After the computer places number six, Cynthia states "I definitely need to put one right there (position 7)."
12.7 Cynthia: "cause then he won't have - - if I put some up there (position 9) then he'll go over there (position 11)." Simple Deduction
12.7a After Cynthia places 15, she is asked why she did so.
12.7b Cynthia: "Um - - cause if he put it right there (position 14), then . . . I thought he'd have four." Simple Deduction
12.8 After Cynthia places 17, she says "don't don't don't", hoping that the computer won't place a marker in spot 18 so she can win on the next turn.
12.9 The computer wins on move 18.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-96
To Beginning of Section | To End of Section
12.10 Cynthia: "I wanted to put it there! - - I didn't see that there."
Game 13: Cynthia
Needed to win: 4 in a row
Winner:
Computer
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13.0 Cynthia starts a new game. (3:56)
13.1 Cynthia: "This time I'm gonna get that computer."
13.2 The teacher asks Cynthia if she has a plan this time. She sidetracks and says, "Ah, I lost it (The marker). I hate it when I lose it."
13.3 After Cynthia places 9, she indicates that she thinks the computer will place its marker in position 12.
13.4 Before she places number 11, Cynthia states, "I should not put it right there (position 18). When asked why she points to the diagonal created by 10, 8 2 and position 19). (3:58) Simple Deduction
13.5 After move 19, Cynthia points to the position over 15, indicating that she would like the computer to place a marker there which would help her create four in a row going across the top from 19 over. Multi-Step Deduction
13.6 The computer wins with move 20.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-97
To Beginning of Section | To End of Section
Activity: Tic Tac Drop (Similar to Connect Four. It was played on the computer.)
Notes: Due to technical difficulties, there is no videotape available until game 6!
Game 1: Maurice
Needed to win: 3 in a row
Winner:
Maurice
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1.0 Maurice begins the first game.
1.1 Maurice: "If I can get two next to each other - - then I'll win." Simple Deduction
1.2 Before the computer places number two, Maurice is busy saying, "Don't put any there. (Next to number 1)."
1.3 The computer places number 2.
1.4 Maurice: "Yes! I won! I won!"
1.5 Maurice: "That's the same way I always win Kirsten!"
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-98
To Beginning of Section | To End of Section
Game 2: Ira
Needed to win: 3 in a row
Winner:
Computer
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2.0 Ira begins game two.
2.1 The computer places number 2 and Maurice states, "Ira can not win."
2.2 The teacher questions why he has said that.
2.3 Maurice responds: "Not my way!" Simple Deduction
2.4 After move 10, Maurice states: "Oh God! He won. He won. He won."
2.5 Ira: "No!"
2.6 Maurice: "He got two there. (He points to 8 and 10, noting that the computer can place a marker in either one of the empty spots next to them.)" Simple Deduction
2.7 Maurice speaks clearly and purposely into the microphone: "I won and Ira lost."
Game 3: Maurice
Needed to win: 3 in a row
Winner:
Maurice
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3.0 Maurice begins a new game.
3.1 After the computer places number 2, Maurice begins, "Yes by, I won."
3.2 Ira: "No - - You need one more." Simple Deduction
3.3 Maurice places number 3. "See, I won." (He points to the two ways that he can win.)
Simple Deduction
3.4 Maurice wins.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-99
To Beginning of Section | To End of Section
Game 4: Ira
Needed to win: 3 in a row
Winner:
No winner
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4.0 Ira decides to try a different board configuration.
4.1 The game is quickly played resulting in a tie game - no winner.
Game 5: Maurice
Needed to win: 4 in a row
Winner:
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5.0 Maurice begins a new game. He changes the options to get four in a row to win.
5.1 After number two is placed Maurice states: "I don't need diagonals because - -" (he indicates that he will try vertically starting from 1.) Simple Deduction
5.2 Ira to Maurice on move 11: "Put it right here! Put it right here! (Position 11)"
5.3 Maurice explains why, "Cause he could of went up there." (He indicates 2, 8 and 10)
Simple Deduction
5.4 Maurice says to the computer: "You're not gonna win."
5.5 As the game is played, Ira also speaks to the computer, "Don't think about it mister!"
5.6 The computer wins.
NOTE!!!!!!!!: The videotape recorded all games from here.
Game 6: Ira
Needed to win: 3 in a row
Winner: Ira
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-100
To Beginning of Section | To End of Section
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6.0 Ira begins a new game. (3:29)
6.1 After Ira places number one, Maurice says, "You shouldn't of done it there."
6.2 the teacher asks Maurice to explain why he thinks that it wasn't a good move.
6.3 Maurice: "In the middle you can almost always win right off the bat." Simple Deduction
6.4 Before Ira places 5, Maurice coaches him as to where to put it. (3:29)
6.5 Ira: "I know. See this tricky plan."
6.6 Ira: "If I never put the ball there (position 5) , I would of had it there (position 6) and then I could've won."
6.7 Maurice after move 9: "You won. - - Ira won."
6.8 Ira: "No."
6.9 Maurice: "Here and you can win." Simple Deduction
6.10 Ira: "Don't worry."
6.11 Maurice: "You can win two ways. Cool!"
6.12 Ira wins. "This is easy man!"
Game 7: Maurice
Needed to win: 3 in a row
Winner: Maurice
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7.0 Maurice begins a new game but chooses to get three in a row. (3:31)
7.1 Maurice: "It'll be easier (to win with three in a row.)"
7.2 Maurice offers no explanation when asked why it will be easier.
7.3 Maurice after move 1, "If he don't put it next to me, I won." Multi-Step Deduction
7.4 After the computer places 2 Ira becomes excited, "Oh yes, this is easy man! The computer doesn't watch!"
7.5 Maurice wins the game.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-101
To Beginning of Section | To End of Section
Game 8: Laura
Needed to win: 3 in a row
Winner: Computer
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8.0 Laura plays a new game. (3:32)
8.1 Laura indicates after move 1: " I know a way I can get him." She points to a vertical row of three starting at 1 and the diagonal that can be formed beginning at 1.
Simple Deduction
8.2 The computer wins.
Game 9: Laura
Needed to win: 3 in a row
Winner: Computer
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9.0 Laura starts a new game. (3:34)
9.1 After move 9, Laura quickly points out to the teacher that she stopped the computer from making three in a row. (3:35)
9.2 After move 10, Laura grins. The teacher asks her what she is going to do.
9.3 Laura tells the teacher that the computer has won.
9.4 The teacher states that the computer does not have three in a row.
9.5 Laura points to the spaces above 5 and 6 to indicate where the computer can win. Simple Deduction
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-102
To Beginning of Section | To End of Section
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