Conceptual Math and Minecraft

I really enjoy working with different people and getting a different perspective on teaching things. At the moment I am discussing with another teacher at my school about teaching conceptual math, rather than contentual. (I know that is not a word, but you get my meaning)

Usually I teach the students 'how' to do things, not the 'why do it like that' or the 'why it works that way' stuff. I know that students retain the knowledge better when they understand how it works, but I had 'forgotten' it and had stopped using that in my classes. I am lucky enough to be working with a teacher that has reminded me what conceptual thinking and teaching is and how we can use it.

So the first thing we are talking about is fractions, everybody LOVES fractions, because they make so much sense. That statement is of course a lie, so how do we teach fractions conceptually, and can Minecraft help students visualise some of these concepts easier is really the point of this post/brain dump.

The basic concepts we would like students to understand at this stage are: equivalent fractions, adding and subtracting fractions and multiplication and division of fractions. My colleague had already written the conceptual worksheets for equivalent, adding and subtracting concepts. In my opinion they clearly lead students to an understanding of the concepts we are trying to get across. So now we are trying to address the multiplication and division of fractions.

Multiplication was fairly easy, it is just a matter of the language we are using when we are talking about it and some diagrammatical representations (I think Minecraft might be useful here but I will continue this a bit farther on). So instead of reading one third times one fifth, we are swapping out the "times" for an "of". So the question becomes one third of one fifth. Mathematically speaking this is fine, and I think that will get the point across to the students what the multiplication of fractions is actually 'doing' or finding out.

Division had me stumped for a while, again until I talked to others and got different perspectives. This concept relies on the understanding, or at least using the language, that division means how many fit in. So how many one fifths are there in one third rather than one third divided by one fifth. Which is something I had not considered before, but I think will really help students grasp the concept.

The interesting thing about the division concept was that it was a diagram that the other teacher started to draw that made it click for me. So I think that one of the most important things for building conceptual understandings like this is having an image/picture/model to look at and mess around with. And it is at this point where I started thinking I could use Minecraft, particularly for the model of multiplication. However there was a niggle that would not leave me alone (and still has not). Is Minecraft actually going to be 'better' than drawing in pen and paper for the students? In terms of engagement my answer is "of course it will be better" but in terms of the student understanding I am not sure it is going to make it any better. So lets talk about time, that thing that I always complain about.

If students explore these concepts visually in Minecraft, will the time taken to gain that image/picture/model be comparable to the time it would take to do it with pen and paper? Notice I am not even considering whether it will be faster, the models I can think of are 2-dimensional, and the instructions I give to students for creating their first few representations in Minecraft will, while not fully, be mostly 2-dimensional, or at least just as easily represented in 2-dimensions. So should I use Minecraft just because I can? What benefits will using Minecraft give the students? It is not an increased understanding, it is not a decrease in time taken.

Could the benefit be in that more easily memorable and therefore easily accessible image/picture/model just because they did it in Minecraft? I mean that was reason enough for me to do my first ever lesson in Minecraft, giving students a model of how neurotransmitters work, not a complete model, but a model regardless. Same as the solids, liquids and gases model the students and I completed, I feel that the students got a great model of a concept. However both of those 'feel' different to this idea. Those opportunities gave the students a different perspective than they could get by using paper and pen or discussion.

So when should I use Minecraft? If I am not increasing student understanding more than other options, I am not decreasing the time taken and I am not giving them a different perspective. Is this particular concept worth exploring within the world of Minecraft or should I stick to a paper and pen model? I would value any input as to when you think it is 'worthwhile' using Minecraft, what tips it over the edge for you into a 'must use' for the activity?