Introduction of “social open-ended questions”

“Social open-ended questions” refer to questions that deal with social issues familiar to children and in which their diverse values and mathematical models are expressed when looking for answers. The image below, which was published in the Asahi Shimbun, features a “hit-the-target” game (a social open-ended question). The teaching material was created based on a real story from a cultural festival. The question is set at a scene of a hit-the-target game, asking “A first-grade student threw a ball three times. The student hit the 5-point area and 3-point area, and then on the border between the 3-point area and the 1-point area the third time. The fourth-graders, who thought up the game, debated how many points they should give. How many points would you give?”
When some children solve this problem, they say, “I would like to be nice to the first grader, so I would give three points. The math model is 5 + 3 × 2 = 11” or “As the first-graders have come all the way here, I would like to give three points plus one point. The math model is 5 + 3 + (3 + 1) = 12.” In this way, they express their values that they “care about the first-grader.” On the other hand, some answer, “I would give two points as the middle because I would like to give points to everyone on an equal basis. The math model is 5 + 3 + 2 = 10 (or (3 + 1) / 2 = 2 and 5 + 3 + 2 = 10)” (idea of equality) or “I agree with giving points to everyone on an equal basis, but I would give one point because the ball occupies more in the one-point area. The math model is 5 + 3 + 1 = 9” (idea of area). In this way, they come up with the “idea of equality for all.” In short, their mathematical models change according to the values of children. Children share such ideas, and they ask questions and give opinions to each other while engaging in critical thinking. Through these activities, they reflect on their own thoughts.
The Asahi Shimbun showed an interest in such a lesson with social open-ended questions and published the article with the headline “Values change answers.”