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Interviews (individual)

Longitudinal data

Qualitative research

This interview with researcher Alston and Milin, with the presence of teacher Mrs. Barnes, occurred on February 7, 1992, the following day of the classroom work with Michael on the five-tall Tower problem. In this interview Milin was asked to recall the problem and how he solved it with Michael. His first response indicated use of a random strategy to build a tower pattern and the use of the color opposite strategy to generate the second in a pair: “Michael and I kept on building them and putting another one exactly like that but different colors…we looked at the colors and all the yellows turned to red, and all the reds turned to yellows” (20-2). He claimed there was a total of thirty-two. In response to how they knew they were all different tower combinations, he explained that they monitored for duplicates by checking each tower against the collection of towers. Milin generated towers by cases to solve and justify the problem. In this interview he told the researcher about towers with exactly one of a color cube and towers with exactly two of a color cube adjacent, generated in a staircase pattern.
The next part involved the issue of duplication between the towers with two red cubes, their color opposite towers, and the towers with three red cubes. It began with Milin’s initiation of the category of “three’s,” at which point the researcher asked him what a tower of “three” would look like. He built an example that was already in his set (YYYRR in Group E in Sran’s dissertation, 2010) and both the teacher and researcher asked if he would count it into his set. He exclaimed that he would not and then he tried building another tower, namely YYRRY. However, again it was a duplicate of Group E, so he concluded, “you can’t make any others with three” (line 206). Next the researcher and teacher aid him to generate more tower patterns. He ended up finding 12 towers with three of one color and two of the other with some separation. The end of the interview involved a discussion about the relationship between five-tall towers and other heights. Milin gave some estimations and guesses to what he thought the solutions were and built some to prove or contradict his guesses. He was left with the four-tall towers task for homework.

Social science

doi:10.7282/t3-e248-d631

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