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19.2 Teacher: "There are two sets there."
19.3 Leonard: "Ah" (He selects 1 purple squiggle, 2 red squiggles, 3 green squiggles.) "They're the same thing and they're different…" EWX Simple Deduction
19.4 Seren: "They have to be all the same or all different."
19.5 Leonard: "Yeah."
19.6 Teacher: "Show me that again."
19.7 Leonard: "They're all different numbers and all the same shape and different colours."
EWT Simple Deduction
19.8 Leonard: "So that's a point for me. Finally, I finally got a point!"
19.9 The teacher indicates that there is another set similar to the one Leonard just found.
19.10 Leonard quickly identifies this set. (1 red diamond, 2 green diamonds and 3 purple diamonds)
19.11 Leonard correctly explains why these cards make a set.
19.12 Teacher: "I'm gonna show you one more set."
19.13 Leonard: "They're all different numbers, same shape and different colours."
EWT Simple Deduction
Set
Note: This group had extreme difficulty in identifying sets.
20.0 Students were asked if they played Set before. All students stated that they had played. (3:45)
20.1 The teacher laid down six cards and had the students figure out how many different shapes there were.
20.2 Joline counted each card and concluded that there were six different shapes on the cards.
20.3 Veronica and Jocelyn disagreed with Joline's answer.
20.4 Veronica explained why she didn't agree. "Some are just different colours but they're the same shape."
EWT Simple Deduction
20.5 Joline looks at the cards more closely and correctly identifies that there are only three different shapes.
21.0 The teacher asks the students to decide how many different collared cards are present. (3:46)
21.1 The students quickly identify the three different colours.
22.0 The teacher asks the group to figure out how many different numbers there are on the cards.
22.1 Jocelyn and Joline point to the cards as if counting silently in their heads.
22.2 Jocelyn: "Six."
22.3 Teacher: "Can you tell me what the six different numbers are Jocelyn?"
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22.4 Jocelyn: "1,2,3,4,5,6."
22.5 Teacher: "can you show me the one with the four?"
22.6 Jocelyn looks at the fourth card then states, "none."
22.7 Veronica: " It only goes up to three."
22.8 Teacher: "So how many different numbers do we have?"
22.9 Joline thinks about it for a while and looks at each card again and says "three."
23.0 The teacher goes over the rules of the game. (3:47)
23.1 Joline informs the teacher that "they" already know how to play the game.
23.2 The teacher continues to review the rules of the game.
23.3 The teacher lays three cards (2 red diamonds, 2 green squiggles and 2 purple ovals ) on the table and asks the group to tell her if they are a set.
23.4 The group concludes that it is a set.
24.0 The teacher changes the 2 red diamonds for 2 purple squiggles and asks the group if the three cards are a set. (3:48)
24.1 Veronica: "They're a set. They got different colours but they got one the same colour and the rest of them are the same colour." EWT Simple Deduction
24.2 The teacher then asks if the cards make a set.
24.3 Veronica: "They're the same number. The same colour, only two of them."
EWT Simple Deduction
24.4 Teacher: So they're not all the same colour are they? Are they all different?"
24.5 Joline: " But they are the same set."
24.6 Teacher: " Are they a set though?"
24.7 Joline: "Oh."
24.8 Teacher: "Are they a set?"
24.9 Joline: "Yeah. No."
24.10 Veronica: "No."
24.11 Teacher: " why do you say no Veronica?"
24.12 Veronica: "Because they're not the same colour." EWT Simple Deduction
24.13 Jocelyn: "Yes they are a set because they are ... three, there's two of each and ...
EWS Simple Deduction
24.14 The teacher reviews the three attributes that they need to attend to and questions whether the three cards are all the same or all different for each one.
24.15 The group points out that there are two shapes that are the same so they are not all different and they are not all the same.
25.0 The teacher lays down 3 purple squiggles, 2 purple squiggles and 1 purple squiggles. (3:50)
25.1 Veronica: "They're almost a pair. They're all different and the same."
25.2 Joline: "All the same colour. They're all the same shape. But not the same number."
EWX Simple Deduction
25.3 Teacher: "They're all different numbers. But they're all a…"
25.4 Joline: "Like."
25.5 "Teacher: "No, they're all different numbers."
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25.6 Joline: "Like, 1,2,3."
25.7 Teacher: "Yeah, so that's a set."
25.8 Joline: "So just pretend she's 1, I'm 2 and she's 3." (She passes 1 card to each girl.)
25.9 Veronica: "I'm number 1, Joline's number two and Jocelyn's number three!"
EWN analogy
25.10 The teacher goes over the three attributes and reviews why these cards are a set.
26.0 The teacher lays down nine cards and asks the group to see if they can find a set. (3:52)
26.1 Both Joline and Veronica point to sets of three cards.
26.2 Joline goes first and points to 3 red diamonds, 3 green ovals and 3 green diamonds. "I think, this one, this one and this one."
26.3 Veronica points to 2 red diamonds, 1 green diamond and 3 red diamonds.
26.4 Veronica: " They're not the same colour. Not all of them are the same colour but these are the same shape." EWX Simple Deduction
27.0 The teacher lets Joline go ahead and choose her three cards. She chooses a purple diamond, a green squiggle and a red squiggle.
27.1 Teacher: "Do you think this is a set Joline?"
27.2 Joline: "No."
27.3 Teacher: "Why not?"
27.4 Joline: "Cause these are the same (the squiggles) and this is different (the diamond). And they're one, one, one." EWT Simple Deduction
27.5 Teacher: "Okay, so they're all the same number and they're all a different colour, but are they all the same shape?"
27.6 Joline: "No."
27.7 Joline returns her cards.
28.0 Jocelyn attempts to find a set. (:53)
28.1 Jocelyn picks 2 red diamonds, 3 green diamonds and 3 red diamonds.
28.2 After looking at the cards, she changes the 2 red diamonds for 3 green ovals.
28.3 Jocelyn: "These two ( 3 green ovals and 3 green diamonds ) are the same colour and they're the same number." EWX Simple Deduction
28.4 Teacher: " But are all of your cards the same colour or all the same number?"
28.5 Jocelyn nods no.
28.7 Joline: "They're all the same number."
28.8 teacher: "Are they all the same shape or different shape?"
28.9 Jocelyn: "No."
28.10 Teacher: "So are they a set?"
28.11 Jocelyn decides that the three cards are not a set and returns places them back with the rest of them.
29.0 Joline attempts to find a set but only selects 1 red squiggle and 2 red diamonds.
30.0 Veronica chooses 3 green diamonds, 3 red diamonds and 2 red diamonds. (3:55)
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30.1 She switches the 3 green diamonds for 1 red squiggle.
30.2 Veronica: "They're all the same colour."
30.3 Veronica: "Not the same shape. Only these two are." EWX Simple Deduction
30.4 Teacher: " Are they all different shapes?"
30.5 Veronica nods her head yes then says, "they're only the same colour. That's all."
30.6 After going over the three conditions, Veronica states she thinks that she has finally found one. She picks 3 green diamonds, 3 red diamonds and 2 red diamonds.
30.7 When asked if these cards make a set, Veronica shakes her head no. She is asked to explain why.
30.8 Veronica: "Cause that's (3 green diamonds) a different colour. They're the same shape but only these two are the same number." EWT Simple Deduction
31.0 The cards are put back and Jocelyn tries to find a set. She takes up cards then puts them back. (3 purple ovals, 3 green ovals and 2 purple ovals) (3:57)
31.1 Jocelyn decides upon 1 red squiggle, 1 purple diamond and 1 green squiggle.
31.2 Jocelyn explains that they are not a set because "they're not the same shape and they're not the same colour. None of them are the same colour." EWX Simple Deduction
31.3 Teacher: "Are they all different shapes?"
31.4 Jocelyn: "Yep."
31.5 Teacher: "Tell me the shapes you have."
31.6 Jocelyn: "Diamonds and squiggles."
31.7 Teacher: "Are they all different?"
31.8 Jocelyn nods yes.
31.9 Veronica points out that two are the same shape.
31.10 Joline tries again. She picks 2 red diamonds, 3 red diamonds and 1 green diamond then switches I green diamond for 1 red squiggle. Then she chooses 3 purple oval, 2 purple ovals and 3 green ovals.
32.0 Veronica: "Hey, I think we give up." (3:58)
32.1 The teacher asks what made it really difficult for them to find sets.
32.2 Veronica explains that all the cards are different.
33.0 The teacher walks them through finding a set. She isolates the cards with diamonds on them. They all agree that the set can't be all the same colour. The girls try many combinations before they discover 1 purple diamond, 2 red diamonds and 3 green diamonds.
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Set : The rules were to find three cards that were all the same or all different in shape, number and colour.
Interesting points???
Note in 7.0 - 7.7, Kirsten chooses three cards and explains why she feels it is a set. She notes that two are the same shape but appears to think this satisfies the condition for shape. When questioned by the teacher on the next attribute, number, she seems to "act" as if she knows it can't be right ... probably because of the teacher's questioning. If she was not questioned, would she have given it a second thought?
Laura chooses the same cards (8.7) as Kyla did in 6.0
1.0 The teacher went over the instructions of the game with the group beginning by having students note how many different colours, shapes and numbers were on the cards. (12:20)
1.1 After reviewing the three attributes, the teacher lays down three cards at a time and questions whether the cards make a set.
1.2 The teacher lays down 3 green diamonds, 2 red diamonds and 1 red diamond and asks if it is a set. (12:22)
1.3 Kirsten nods yes the three cards make a set and states, "cause there's two red and one green." EWX Simple Deduction
1.4 Teacher, "so are they all the same colour?"
1.5 Kirsten, "No."
1.6 Teacher, "Are they all a different colour?"
1.7 Kirsten, "Yes. Except for two." Laura, "No."
1.8 Teacher," No they're not."
1.9 The teacher quickly goes over the three cards again with the entire group and discusses why they do not make a set. The students answer questions asked about each attribute. When the group is discussing the colours of the set, she indicates, "there's two red and one green so that can't make a set."
2.0 The teacher lays down three purple squiggles, 2 red diamonds and 1 green oval and asks the group if they make a set. (12:23)
2.1 Laura states yes very quickly and when asked why says, "Cause they're all different colours, they're all different shape and they're all different number."
EWT Simple Deduction
3.0 The teacher lays down one more example before playing the game. She places 2 purple squiggles, 1 purple diamond and 3 green diamonds on the table. (12:24)
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3.1 Immediately, Kirsten points to the two purple cards. "Two of them, two of them are -- that one is a different colour (indicates the green card) and two of them are the same."
3.2 Laura, "They're not all the same colour. They're not all the same shape."
3.3 Kyla, "They're all same number -- no, they're all different numbers."
EWX Simple Deduction
3.4 Kirsten, "They're all different shape and all different colours except for the two of them." (Pointing to the two purple cards.) EWX Simple Deduction
3.5 The group all agree that the three cards on the table can not be a set.
4.0 The teacher informs the group that she will begin to play the game. She will lay down nine cards at a time and let whoever sees the first set start. (12:25)
4.1 Kyla puts up her hand before all the cards are on the table. When asked to identify her set, she points to 3 red squiggles, 3 purple squiggles and then she points to one other card without clearly indicating which one it is.
4.2 When asked what card would be her third one, she points to the two purple squiggles.
4.3 Kirsten states that these cards do not make a set, "Because that's (2 purple squiggles) only two." EWT Simple Deduction
4.4 Kirsten picks 1 green squiggle, 2 green ovals and 2 green diamonds. (12:26)
4.5 Teacher, "Now, let's look at these three things (pointing to the card with colour, shape and number written on it). Are they all the same or all different colour?"
4.6 Kirsten, "All the same colour."
4.7 Teacher, "What else?"
4.8 Kirsten, "All the different shapes and all different numbers."
4.9 Laura, "No they're not."
4.10 Teacher, "Why do you say no?"
4.11 Laura points to the two cards with 2 shapes on them. "No, they're not."
EWT Simple Deduction
5.0 Laura tries to find a set. She chooses 3 red ovals, 3 red squiggles and 2 red diamonds. (12:27)
5.1 Teacher, "Now tell me why you think those are a set."
5.2 Laura tries to explain why these cards make a set. "They're all the same colour - - They're not all the same shape." Simple Deduction
5.3 Teacher, " Are they all a different shape?"
5.4 Laura nods yes. EWT
5.5 Teacher, "So if they're all different then that's okay. They're all a different shape."
5.6 Laura grins as she looks at the last attribute, number. When questioned why she says, "they're not all the same number."
5.7 Teacher, "Are they all a different number?"
5.8 Laura, "Yes. No."
5.9 Teacher, "Which two are the same?"
5.10 Laura points to the two cards with 3 shapes on each.
6.0 The cards are returned and Kyla is asked to find a set. Without hesitation she picks 1 green squiggle, 2 purple squiggles and 3 purple squiggles. (12:28)
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6.1 Teacher, "Now why do you think that is a set?" Simple Deduction
6.2 Kyla, "They're all different kinds of numbers. . . They're all the same shape. But both of those are the same colour." EWT
7.0 The cards are put back and both Kirsten and Laura are waving their arms in the air indicating that they have sets. (12:29)
7.1 Kirsten chooses 1 green oval, 2 green ovals and 2 green diamonds.
7.2 As the cards are picked out, Kyla is nodding her head "no."
7.3 Kirsten, "They're the same colour. Two of them are . . . the same shape. And they're all the same - - number" EWT Simple Deduction
7.4 Teacher, "Are they all the same number?"
7.5 Kirsten nods her head no.
7.6 Teacher, "So are they all a different number?"
7.7 Kirsten does not respond and simply watches the teacher. The two other group members answer no.
8.0 Laura eagerly tries again. After a few changes, she picks 1 green squiggle, 2 red diamonds and 3 red ovals. (12:30)
8.1 Laura, "they're all different colours."
8.2 Teacher, "Are they all different colours?"
8.3 Laura, "They're not all different colours."
8.4 The teacher asks Laura to see if she can make a switch so that a set can be made. The rest of the group is asked to try to find one as well.
8.5 The group makes many attempts by rearranging cards with no success.
8.6 Kyla chooses to trade 1 green squiggle for 3 red squiggles.
8.7 Kirsten, "They're all red, they're all different shapes but they're not all different numbers." The cards are switched back.
8.8 Laura, "They're not all different colours."
8.9 Kirsten, "They're all different numbers. They're all different colours."
EWX Simple Deduction
8.10 Laura, "No, they're not."
8.11 Laura chooses 3 green squiggles, 2 red diamonds and 3 red ovals.
8.12 Teacher, "You have to think about colour, shape and number."
8.13 Kyla, "This one goes here." (She changes 3 green squiggles for 3 red squiggles.)
8.14 Kyla, "They're different shapes, they're all the same colour (she realizes this is not a set) they're not different numbers." EWX Simple Deduction
8.15 Kirsten stretches and yawns and says, "this is so tricky."
8.16 Laura takes 1 green squiggle, 2 purple squiggles and 3 purple squiggles.
8.17 Kyla indicates that the set won't work, "because these two are the same (the purple cards) and this one is different." Simple Deduction
9.0 The teacher decides to take in all the cards and lay down just three cards at a time and have students explain why or why not they are sets. (12:33)
9.1 The teacher puts 2 green diamonds, 2 purple squiggles and 1 purple squiggle.
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9.2 Kyla quickly explains that these cards do not make a set because two are one colour and the third is another colour. She also indicates that the colour that is a different colour is also a different shape. EWT Simple Deduction
10.0 The teacher lays three cards (3 purple diamonds, 2 red squiggles and 3 green diamonds) down for Kirsten to examine. (12:34)
10.1 When asked if the cards make a set, Kirsten does not indicate yes or no but immediately points out that two of the cards contain the same shape.
10.2 The teacher asks again if the cards make a set.
10.3 Kirsten, "She nods no."
10.4 Teacher, "Why do you think it is not a set?" Simple Deduction
10.5 Kirsten, " I mean it is . . . cause . . . that one (3 purple diamonds) and that one (3 green diamonds) are the same shape." EWT
10.6 Teacher, "So is it a set?"
10.7 Kirsten looks at the teacher and pauses unsure. Then she nods her head to indicate that they do not make a set.
11.0 The teacher lays out 1 purple diamond, 3 green squiggles and 2 red ovals. (12:34)
11.1 Laura, "They're not all the same colour. They're not all the same shape. And they're not all the same numbers." EWX Simple Deduction
11.2 Teacher, "So does that make a set?"
11.3 Laura shakes her head "no."
11.4 Teacher, "Are you sure they don't make a set . . ."
11.5 Kyla, "It do make a set cause . . . there's one, two and three Simple Deduction
11.6 Kirsten, "And they're all different colours." Simple Deduction
11.7 Kyla, "And they're all different numbers. And they're all different shapes."
EWX Simple Deduction
12.0 The teacher lays down three cards (1 purple oval, 2 purple diamonds and 1 red oval) for Kyla. She correctly identifies and explains that the cards do not make a set. (12:35)
12.1 Kyla, "No, cause these two are the same colour and that's like the same colour. And that's the same as that one (pointing to the 2 one ovals). And these 2 are a one and that one is a two - it's not a set. There is no three." EWX Simple Deduction
13.0 Three cards are placed on the table for Kirsten - 2 green ovals, 3 red ovals and 1 green diamond.
13.1 Kirsten, "This is going to be so easy."
13.2 Kirsten states that these cards do make a set. She once again says that they're all different shapes even though two cards contain ovals and 1 contains a diamond.
13.3 When asked again by the teacher if the cards make a set, Kirsten says that they are not a set.
13.4 The teacher asks Kirsten to explain why she said no.
13.5 Laura says, "Yes they are a set."
13.6 Kirsten says, "I mean yes."
13.7 The teacher asks for an explanation once again.
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13.8 Kirsten, "Because there's 3 here, 1 here and 2 there." Simple Deduction
13.9 Teacher, "So there's three different numbers. What about colours?"
13.10 Kirsten, "That one's green and that one's a green one. And 2 of them are the same shape (ovals) and they're all different numbers." Simple Deduction
13.11 When asked what shapes are on the cards, Kirsten simply point to them but does not name them. "Two of them are the same and that one is a different one."
EWT Simple Deduction
13.12 Teacher, "So are they all the same?"
13.13 Kirsten nods her head yes.
13.14 When questioned about her response she nods her head no.
13.15 The teacher asks Kirsten to point to the card that is different. Kirsten points to the three red ovals.
13.16 Teacher, "Is that a different shape?"
13.17 Kirsten points to the 1 green diamond.
13.18 Teacher, "Okay, do they make a set?"
13.19 Kirsten, "No."
14.0 Cards were laid down for Laura. (12:38)
14.1 Laura stated that 1 red diamond, 2 green squiggles and 3 green ovals were "all a different shape, not all the same colour and they're all different numbers."
EWX Simple Deduction
14.2 When asked if they were a set, she said nodded yes first then nodded no when asked to explain why it was a set.
14.3 Laura, "they're not all the same."
14.4 Teacher, "They're not all the same what?"
14.5 Laura, "Colour, shapes - -"
14.6 The teacher restates that they can be all different and asks what makes these cards not a set.
14.7 Laura, "This one (1 red diamond) is not a green squiggle or an oval. This one isn't a diamond (2 green squiggles) or that one's not an oval." EWT Simple Deduction
14.8 Kyla, "It was a set."
14.9 Teacher puts cards back out, and asks if it was a set.
14.10 Kyla, "No."
14.11 Teacher, "Why is it not a set?"
14.12 Kirsten, "Because these two are the same colour and this one is different."
EWT Simple Deduction
14.13 The cards are all removed and the groups are changed.
15.0 The teacher goes over the rules of the game. Maurice and Ira state that they have played the game before. (12:40)
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15.1 Maurice suggests having same colour, same shape and same number as how to make a set.
15.2 Teacher, "You could have all different."
15.3 Saul, "It could be the same colour and not the same shape."
15.4 The teacher lays down three cards at a time and goes through the process of identifying whether or not the cards make a set before the game starts. After going through three groups of cards, the game begins. The group was able to quickly decide if the cards that were placed on the table were or were not a set. The teacher models using the checklist.
15.5 The teacher lays down 2 green ovals, 3 red ovals and 3 red squiggles.
15.6 Teacher, "Are these cards all a different colour?"
15.7 Maurice, "Yes."
15.8 Teacher, "Are they all a different colour?"
15.9 Ira, "One isn't."
15.10 Teacher, "One is green and 2 are red so they're not all a different colour so that can't be a set because I can't say 'all'. Not all a different colour and not all the same colour." She collects the cards.
15.11 Three new cards are laid out (2 green ovals, 3 green squiggles and 1 green diamond).
15.12 Teacher, "Okay, let's see. Now. Are they all the same colour or all a different colour?"
15.13 Maurice, "Yes. All the same."
15.14 Teacher, "They're all the same colour so we can go, 'Check! We've got that one.' Okay, now. What about shape? Are they all the same or all different numbers?"
15.15 Ira, "No."
15.16 Maurice and Saul, "All different shapes."
15.17 Teacher, "Okay, check! We've got that one. Now what about number? Are they all the same or all different numbers?"
15.18 All, "All different numbers."
15.19 Saul, "1,2,3."
15.20 Teacher, So these three cards make a set because they're all the same, all different, all different" (pointing to the checklist). One more example is given.
16.0 The teacher begins the game by laying down nine cards. When 5 cards have been placed on the table, both Maurice and Ira begin shouting set. (12:44)
16.1 Maurice chooses 1 green diamond, 2 green ovals and 3 green squiggles. "This one, this one and this one."
16.2 Teacher, "Okay, why do you think this is a set?"
16.3 Maurice, "Because they are all a different shape, all different number and all different, I mean all the same colour." EWT Simple Deduction
17.0 Maurice's cards are taken from the table and are not replaced by three more. There are just six cards left on the table. (12:45)
17.1 Saul shouts set and chooses 1 red oval, 1 green oval and 1 green squiggle.
17.2 Saul, "They're all different shapes. . . and they're all same number."
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Simple Deduction
17.3 Teacher, "Are they are different shapes?"
17.4 Saul, "Yep and they're all the same number."
17.5 Ira, "No, these two (1 green oval and 1 red oval) are not different shapes."
17.6 Saul, "Anyway - - they're all the same number." EWX Simple Deduction
17.7 Saul's cards are put back with the remaining three.
18.0 Ira quickly chooses 1 green oval, 2 red diamonds and 3 purple squiggles. (12:46)
18.1 Ira has no difficulty explaining that the cards are a set because they are different colours, different shapes and different numbers. EWX Simple Deduction
18.2 Teacher, "Do you guys all agree?"
18.3 Saul and Maurice, "Yeah."
19.0 The teacher removes Ira's set from the table, leaving only three cards. She asks if anyone can explain why or why not the remaining cards are a set.
19.1 Saul almost immediately tells the teacher that 2 purple diamonds, 1 green squiggle and 1 red oval can not be a set because two are the same number. Then he adds, "that's all." EWT Simple Deduction
19.2 These cards are taken from the table and nine more are placed on the table.
20.0 When three cards have been laid down, all the members of the group begin to shout set. (12:47)
20.1 Maurice chooses 1 purple oval, 3 red squiggles and 2 green diamonds.
20.2 Maurice indicates that these cards are "All different in colour, all different shape and all different number." EWX Simple Deduction
20.3 Teacher, "Does anyone disagree?"
20.4 Ira, "Yes."
20.5 Teacher, "Why do you disagree?"
20.6 Ira, "Oh! I mean no."
21.0 Maurice's cards were removed from the table, leaving six.
21.1 Saul chose 1 red diamond, 2 purple ovals and 3 green ovals. (12:48)
21.2 When asked if they are a set, Saul says no, " . . .because two are the same number, I mean same shape." EWT Simple Deduction
21.3 Teacher, "There may not be a set in these 6 cards. I will give you a point if you can tell me why they are not, … I am very impressed with you."
22.0 Saul's cards are put back with the others and three more are added to create a total of nine. (12:48)
22.1 Maurice chooses 3 red diamonds, 1 red diamond (which he quickly puts back), 1 red squiggle, and then he pauses.
22.2 The teacher asks Maurice if he is looking for a certain card. He responds by saying, "I made a mistake."
22.3 The teacher asks Maurice what card would he like to have, if he could get any card at all.
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22.4 Maurice says he'd like to have two ovals and notices 2 purple ovals on the table. He places this card with the two he has already chosen. EWT Simple Deduction
22.5 Maurice is asked if these cards will make a set.
22.6 Maurice, " No, cause these two are the same colour." Simple Deduction
22.7 Maurice's cards are placed back with the others.
23.0 Saul chooses 1 red diamond, 2 purple squiggles and 3 green ovals. (12:50)
23.1 Saul states that they are all different in number, colour and shape. The group agrees.
EWX Simple Deduction
24.0 Three cards are added so that there are nine cards on the table. Maurice quickly calls set and takes 1 red squiggle, 3 green diamonds and 2 purple ovals.
24.1 Maurice explains why these cards make a set.
24.2 Maurice, "They're all different colour. All different shape and all different number."
EWX Simple Deduction
24.3 Saul, "How many points do you have to have to win?"
24.4 Teacher, "When all the cards are gone."
25.0 Maurice's set is removed and three more cards are added to the table to keep a total of nine. (12:51)
25.1 Ira shouts set and takes 1 purple diamond, 2 red ovals and 2 green squiggles.
25.2 As soon as he places the three cards in front of him he says, "Oh no, no, no."
25.3 The teacher asks why he is saying this.
25.4 Ira, "that wasn't it."
25.5 Maurice, "I would have changes the red one." EWS Simple Deduction
25.6 He changes 2 green squiggles for 3 purple ovals then says, "No, no, no."
25.7 Ira pushes the 3 purple ovals back with the others. He pauses then pushes his other two cards back.
25.8 Ira places his elbows on the table and rests his head in the palms of his hands and gives up.
26.0 Saul chooses 3 red diamonds, 2 green squiggles, and 1 purple squiggle. (12:52)
26.1 Saul, "They're all the same shape. Oh, no" Saul shakes his head and looks towards the camera.
26.2 When questioned why he said no, he explains "They're (the cards with the squiggles) the same shape." EWT Simple Deduction
27.0 Saul's cards are put back and Maurice removes 2 green squiggles, and then pauses for a while. He places his hand on several cards but does not take any.
27.1 The teacher says that the students should have the cards in mind before they indicate they have found a set. The cards are put back.
27.2 Saul calls set and takes 3 green diamonds and 2 green squiggles.
27.3 Maurice calls, "Time up, time up."
27.4 Saul puts his cards back.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-32
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28.0 The teacher announces that this is the last game. All three students look for sets. Saul and Maurice both say "Got one!"
28.1 Saul takes some cards and puts them back. As he is looking for his cards, Ira starts talking. (12:53)
28.2 Ira, "I hate myself."
28.3 Teacher, "Why do you say that?"
28.4 Ira, "I'm dumb." Ira bangs his head on the table.
28.5 Teacher, "Why do you think that?"
28.6 Ira, "Cause I'm stupid." Ira looks up into the camera.
28.7 Teacher, "But why would you say that?"
28.8 Ira, "I can't find pairs!"
28.9 Teacher, "You have one already."
28.10 Ira starts looking at the cards again.
29.0 The teacher tells the students the she sees a set that contains three different colours. (Note: There is only one green card on the table.) (12:55)
29.1 Maurice shouts set and immediately chooses the card containing the 2 green squiggles. Then he picks 1 purple squiggle and stops. Finally he picks 3 red ovals.
29.2 The teacher asks if he found a set.
29.3 Maurice says no because two of the cards are the same shape.
EWT Simple Deduction
29.4 Teacher, "Alright now, was there any card that you chose because you knew there had to be three different colours?
29.5 Maurice points to the green card.
29.6 Teacher, "I said you had to use 3 different colours so it would have to be that one because it is the only green card."
30.0 Saul, "Set! Do they have to be all different?"
30.1 Teacher, " . . .no…"
30.2 Saul, "Can things be the same?"
30.3 Saul chose 1 purple diamond, 2 green squiggles and 3 red ovals. He quickly tells us why they make a set.
31.0 The teacher ends the game and asks the students if they have any tips they have to help other students play the game. (12:57)
31.1 Maurice asks if the game can continue.
31.2 Saul said, " . . . I looked around . . . for things that were the same colour. . . and I took one of them. Then I looked around for one that was a different colour and a different shape - - and number. Then I added on one more of those. And then I had a set."
Simple Deduction
31.3 Maurice said, "Look for all different shapes. . . and all different colours."
EHT Simple Deduction
32.0 The teacher lays out 6 cards (3 purple ovals, 2 red ovals, 2 red squiggles, 3 red diamonds, 3 purple ovals and 3 purple diamonds.) "Let's look for all different shapes."
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-32
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32.1 They all start waving their hands.
32.2 Maurice chooses 1 purple squiggle, 3 purple squiggles and 3 purple diamonds.
32.3 Teacher, "Are they all the same number?"
32.4 Maurice, "No. They're all the same colour"
tape
ends.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-34
To Beginning of Section | To End of Section
Notes:
The tables for each game indicate how the markers were played. The number indicates the order a marker was played. "R" and "B" stand for red and black.
Since this was the first day of taping, I experimented with different setups in hopes of getting some insight into how the students were "thinking" about the game. The best game occurred when I went against two students however at times they whispered so low that they couldn't be heard. During the next day, I plan to try this again but give them the audio microphone to whisper in (somehow).
Very little was said during most of the games. I've tried to highlight the times when things were said or actions were made to indicate what a student was doing.
Note for some games hypothetical moves are indicated by a letter-number combination, i.e., B5. B5 indicates second column, 5th row from the bottom.
Game 1
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18 b |
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5 b |
17 r |
14 b |
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7 b |
4 r |
15 r |
13 r |
16 b |
9 b |
10 r |
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6 r |
2 r |
3 b |
12 r |
11 b |
8 r |
1 b |
1.0 Jerome (red) and David (black) played the first game. (3:26)
1.1 The markers fell out of the game twice, so this game was abandoned after the second time.
1.2 Red had two consecutive turns (12 and 13) because when the markers fell out, the students were unsure of who was next.
1.3 After #16 David says, "Yeah, I got ya!"
1.4 Cynthia joins the game.
1.5 David, "You can be on my team. Now, you gotta help me…[unclear]."
1.6 Cynthia whispers with David and points to the area over 14b. David says, "No, no, no, no!"
1.7 The markers fell out again and the game was abandoned.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-35
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Game 2
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9 b |
15 b |
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8
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14
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16
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18
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4 r |
12 r |
13 b |
17 b |
after red |
7 b |
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2 r |
10 r |
11 b |
3 b |
5 b |
6 r |
1 b |
Note: After red indicates where the marker was placed after red had won (8, 14, 16, and 18). The student was unaware that the player had just made a connect 4.
2.0 A new game is started. This time Cynthia and David play against Jerome and the teacher. Cynthia and David use the black markers. (3:30)
2.1 The teacher instructs the students to work together.
2.2 Cynthia, "Like ways to, like ways to put it in?"
2.3 Teacher, "Yeah."
2.4 Cynthia, "Oh," (puts her hands over her mouth) "we had a plan. If we put one there then."
2.5 David, "No it was here." (Pointing to a diagonal)
2.6 Cynthia, (picking up a marker) "Okay, let's just go."
2.7 David, (still talking about prior game) "And if he put it right there then."
2.8 Teacher, "Wait now Cynthia, you can't put it there until David decides where it's going to go. Both of you have to do it."
2.9 Cynthia, "At the same time?"
2.10 Teacher, "No. Okay, David's going to start."
2.11 The game has only just begun with two markers put in the board and the teacher reminds all players to work as a team and discuss their moves.
2.12 Cynthia, "But he tells me what to do. That's no fair."
2.13 On move 6, Cynthia places a black marker out of turn where 6r is eventually placed. She has taken a turn immediately after David her teammate has placed 5b.
2.14 Cynthia gets excited and shouts that her team has won. "We won!"
2.15 When Cynthia is informed that it is not her turn she apologizes, "Oh, I'm sorry."
2.16 Cynthia again plays out of turn and puts a marker in B1 but this is removed.
2.17 Cynthia and David whisper. Jerome whispers with the teacher and points to B1 and then points to A2-D2.
2.18 David places #11 and tells Cynthia, "Now you put it…"
2.19 Jerome places #12.
2.20 Cynthia gets ready to place #13. David points to where he wants it to go.
2.21 Teacher, "Now, why do you say there?"
2.22 David, "So it will go across." EWT Simple Deduction
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-36
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2.23 A few markers are placed. When it's Jerome's turn Cynthia goes, "Put it here, put it right here" (pointing to C3).
2.24 David moves Cynthia's finger away from the board because he thinks she is showing Jerome too much.
2.25 Jerome places the marker where Cynthia pointed. Cynthia hurriedly tries to place the next one but drops it so David places a marker in D2.
2.26 Cynthia, "Hey, he just had a turn." (She had been aiming to put her marker in C4.)
2.27 Teacher, "Work as a team."
2.28 David, "Go!"
2.29 Both Cynthia and David become very excited after 16b is played. They do not appear to notice that the teacher and Jerome can now win.
2.30 Teacher, "Now it's our turn." Jerome places the winning marker2.7 Jerome places 17r to win the game.
2.31 David places a marker in the second row from the bottom, fifth column, and both he and Cynthia excitedly shout, "We won!" They do not seem to realize that the other team has already connected four in a row.
Game 3
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4 b |
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3 r |
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2 b |
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1
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5
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7
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9
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8 b |
6 b |
3.0 Another game is started. This time Cynthia and David are red. (3:33)
3.1 The teacher asks that students discuss their "plans" with their teammate before placing any markers.
3.2 Cynthia starts to put in a red marker. She and David have not discussed what they will try to do.
3.3 David: "No, no. That's not where our plan is. I got a good plan."
3.4 Cynthia: " No, we have a plan and he's looking!"
3.5 David and Cynthia quickly connect four along the bottom.
Game 4
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12
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10
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4 r |
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9 b |
11 b |
6
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3 b |
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8 r |
7 b |
5 b |
2
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1 b |
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-37
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4.0 A new game is started. Cynthia and the teacher play against David and Jerome. (3:36)
4.1 As the game is about to begin Cynthia says, "I know what to do." Cynthia whispers to the teacher.
4.2 Teacher, "Okay, we'll try that."
4.3 David and Jerome whisper to each other.
4.4 On the 5th turn Cynthia says, "We can go over here if you want." (She points to 5b).
4.5 On the 11th turn, David tells Cynthia that if she puts her marker in the second row from the bottom, sixth column, she could get four in a row. EHN Simple Deduction
4.6 Cynthia places 11b. "Four."
4.7 David places 12r to win the game. He shouts, "Ha, ha. We win. You're not allowed to get four. We tricked ya!"
Game 5
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29
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25
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27
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31
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26 b |
24 b |
23 r |
28 b |
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11 b |
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30 b |
21 r |
18 b |
15 b |
14 r |
19 r |
10 r |
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22 b |
20 b |
17 r |
12 r |
13 b |
9 b |
8 r |
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1 b |
2 r |
5 b |
4 r |
3 b |
6 r |
7 b |
5.0 A new game is started. Cynthia and the teacher (red) play against David and Jerome (black). (3:39)
5.1 After #5 is placed the boys laugh.
5.2 Teacher, "Where are you going to go?"
5.3 Cynthia, "Oh."
5.4 Teacher, "Why shouldn't you have dome that?" (no response)
5.5 While Cynthia is figuring out where to put 19 she says, "Oh no, we're trapped!"
5.6 Teacher: " Why do you say that?"
5.7 Cynthia: "Cause if I put that one down there (pointing to where 20b was later laid), he's gonna get that one (pointing to where 21r was later laid). If I put that one down there (pointing to where 22b was later placed), he's gonna get that one there (pointing to where 30b was placed)." EWT Multi-Step Deduction
5.8 On the 23rd turn, Cynthia placed her marker so she could block the other team.
5.9 Cynthia: "Cause they would have got three, four."
EWX Simple Deduction
5.10 During turn 27 Cynthia tells David and Jerome: "You could put it right there (she indicates the fourth row from the bottom, first column.)
5.11 David: "And then you'd get it right there!" (He indicates the row of four that could be created in the fifth row from the bottom, starting in the first column.)
5.12 Cynthia: "No I won't."
5.13 David: "I'm not falling for that trick."
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page B-38
To Beginning of Section | To End of Section
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