Logical Fun, Part II

Here is the long overdue follow-up post to Logical Fun, Part I.

The previous post left off with the following logic problem being posed to the students:

A man is looking at a portrait.  A passerby asks him whose picture is he looking at, and this is his response: “Brothers and sisters have I none, but this man’s father is my father’s son.” Who is in the portrait?

As soon as I read the problem, a number of students (about a third of the class) started saying that they know the answer because they heard the problem before.  I encouraged them to still think through it and make sure that what they thought was the answer made sense.

Interestingly, everyone who thought they knew the answer from before, remembered it incorrectly (or perhaps they had heard a different, similar problem).

The students were then told to discuss their thoughts in small groups.  As with several previous problems, some students immediately started thinking outside the box and asking insightful questions.

One student brought up, “The problem says brothers and sisters have I none.  What if he had them and they passed away?” We had to agree that in this case we are going to take “have” to mean “never had”.

Another student asked about half-siblings and step-siblings.  After some discussion, we decided that half-siblings count as siblings and step-siblings do not affect the answer.

When we finally started discussing the problem as a class, we had three proposed answers: the man himself, his father, and his son.  Only one person voted for each of the last 2, and the rest voted for the man himself (a few abstained, saying they weren’t sure).

I then asked them who “my father’s son” is.  They all agreed that it must be the man himself.  So the problem became:

“Brothers and sisters have I none, but this man’s father is me.”

At this point, most of the class said that they wanted to change their vote to “the man’s son”.  However, we still had a few that insisted that the answer must be “the man himself”.

I decided not to say anything else myself, but let the students discuss it among themselves for a bit longer and convince each other.

In the end, we had one non-convert whose reasoning was “I heard this problem before and I’m sure that the answer was the man himself, so I am sticking with that.”

It was hard to argue with that, but I did tell him to try to reason it out for himself and not to rely on his memory or what he was told by others.

I already mentioned in the previous post how impressed and happy I was with the students’ freedom of thought and lack of fear.  I can’t say that the discussions were perfect, without any yelling or hurt feelings.  But overall, the class was a very enjoyable experience, definitely for me, and I believe for the students as well.

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About aofradkin

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.
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One Response to Logical Fun, Part II

  1. Pam says:

    As a child, I always gave up on brainteasers such as these. I have a much better appreciation of them as an adult! I love reading your stories of how you coach your students through math and logic problems — how you help them NOT give up.

    Like

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