(An adaptation from an old problem from India). A goose meets a flock of geese. The goose says ‘Hello, a hundred of geese’. The leader of the geese answers, ‘No, we are not a hundred. If there were also a half of our number and you, goose, then together there will be a hundred’.
How many geese were in the flock?
Case Dan, Initial Calculations
Case Dan, Visual
Case Dan Video
Case Dan, Transcript:
Dan: Alright The question was a goose meets a flock of geese the goose says hello a hundred of geese the leader of the geese answers no we are not a hundred if there were also half of our number and you. Goose then together there will be a hundred how many geese were in the flock?
Alright so first of all I took a hundred. The number we were looking for to get minus the one goose that came up and said hello we have ninety-nine geese. Then I took muh divided that by two to get a new a new half right here but and I came with forty-nine and a half geese in the flock, which is not possible because you can’t have half a geese So after thinking about it and reading the question a few more times I came up with this problem still trying to get the hundred geese er what we’re coming to and minus your one goose that came up you have ninety-nine now when I divide that by three which gives me thirty-three so thirty-three would be the the half of the the half of their number So if there’s sixty-six there’s ah well ninety-nine minus thirty three gives you sixty-six So if there’s sixty-six and you take half of that and add it to the flock then you got—er you got ninety nine, then you add the one goose that came up and said hello which makes a hundred which answers the question an therefore this one has to be right and this one has to be wrong.
Case Lana, Initial Calculations
Case Lana, Visual
Case Lana, Video
Case Lana, Transcript
Lana: Ok this is called fun with Geese The question says A goose meets a flock of geese The geese says Hello a hundred geese Leader the—the leader of the geese answers No we’re not a hundred It whirl–It we’re . also sorry
Researcher: It’s Ok Keep going
If we were also a half of our number any you goose together ruled a hundred How many geese are to a flock so right here, that’s the simplest number right here, it’s forty-nine, because it says right here if you have half of half of a flock plus you will equal a hundred.Therefore, you say there is forty-nine in the flock plus the one geese, so if you get half of thatand it’s pictured on here so we want to say that x is half so a hundred times one half equals fifty,
so we have the forty-nine, which is this flock of geese and the one goose when you add that together it is fifty, so let’s just say we added—well yeah it’s going to be ninety-nine geesewe add these two so together it is going to be a hundred you know half of a hundred is fifty so yeah
Case Diana Initial Calculations
Case Diana Visual
Case Diana Video
Case Diana Question
Diana: A Flock of Geese; an adaptation from an old problem from India. A goose meets a flock of Geese The goose says hello to a hundred of Geese The leader of the Geese says that no we are not a hundred And there are also half our number And yur—and you goose then there will be a hundred. How many geese are in the flock. Step one I draw—I drew a picture up here for a better understanding, which was one flock of geese and one flock of goose. Step two, I identify the number of geese and goose; then add it up one flock of geese and one flock of goose, which is two, and I plug in the variable for it; so 2x the number geese flock. Step three I looked back at the problem and I took the one hundred and looked at, and I looked back at step and I took 2x divided by one. 2x equals one hundred divided by two 2x use—uh fifty so there was fifty number of Geese in the flock, and that’s what I got; that’s the answer.
Researcher: That’s good—that’s good.
This model has evolved from the ideas of Tomasello (2003), McCafferty (2002) and many others. Specifically, The model below of a Shared Attentional Frame is an adaptation of Tomasello’s (2003) rendering of the “Structure of a linguistic symbol” (p. 29) and a “Joint attentional frame” (p. 26).
McCafferty, S. (2002). Gesture and creating zones of proximal development for second language learning. The Modern Language Journal, 86, 192-202.
Tomasello, M. (2003). Constructing a language: A usage-based theory of language acquisition. Cambridge, MA: