Discovering and Creating Mathematics Part 2: Does investigating problems make it easier to pose interesting problems?

After my first post on discovering and creating mathematics, I decided it was about time I sat down again with a random topic to see where I could take it in 30 minutes.

I decided to try and define a triangle root and see what happens. Below are some scribbles with the direction it took me (Apologies that’s it’s messy but it’s hopefully still readable).

I wonder if anyone else fancies exploring triangle roots in a different way and seeing what they can come up with in 30 minutes?

One of the most interesting aspects I’m finding of open investigation is that you naturally start asking more and more questions. Is it easier to pose problems in Mathematics during an investigation than if you simply try to pose a problem just by thinking about a topic?

Since being a Mathematician is so heavily dependent on asking interesting, fruitful questions to investigate, this to me is an important question. I regularly encourage students to pose mathematical questions and I’m sure I have a way to go in gaining a deeper pedagogical understanding of student problem posing in mathematics.

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4 Responses to Discovering and Creating Mathematics Part 2: Does investigating problems make it easier to pose interesting problems?

1. I would totally agree – I think that teaching with problems seriously engages student curiosity and often is the first impetus for *them* to pose the interesting problems. today in class we were investigating finding points on a given line that were equidistant from the coordinate axes. After we found a number of ways to do this (and realizing there was more than one point) – a student asked,”Is there always more than one?…in fact, is there always one?” I sat there and said,”what do you think?” And we left the question there in the air – many student will come tomorrow having tried to figure that out I’m sure. Nice post.

• Hi Carmel,

I like that you just left the question of equidistant points from the co-ordinate axes floating. Sometimes I feel like I always want to investigate student questions and get annoyed when we don’t have time but then you’re right that some will go away and try it for themselves. Thanks for the comment.

Dan

2. Great post – interesting idea for an investigation.

3. Thanks Andrew. I’ve just realised that you emailed me recently and I never got the chance to look read it. I’ll skim back over the emails and hopefully I can reply with an answer that is still relevant.