Lately I have been struggling with the term ‘meaningful’ when it comes to my education classes. We know that when a lesson is meaningful to a student, they learn better and remember more, but how do we really create meaningful content?

I have heard a lot of phrases said to me by both my professors and peers that go something along the lines of, “you make content meaningful by referencing things they like.” One example given to me was a math question, “If Snoop Dog buys 60 watermelons and eats 1/2 of them, how many watermelons does he have left?” I can not help but think, how is this meaningful? Does referencing someone in the realm of pop culture really engage their curiosity and make them want to do fractions? I really doubt it.

Instead I want to propose that we make content meaningful by the processes of scaffolding, deeper structure and concrete representations. If we use what they already know, they essentially feel less stressed about always having to learn “something new”. For example, what do you think of when you have to multiply two fractions together? You most likely start racking your brain for the “rule” that you learned in grade 7. When you think long enough you remember that you multiply the top and multiply the bottom to get the numerator and the denominator of the answer. For example, you want to solve this:

2/3 X 3/4 =

So you would start by multiplying 2 X 3 to get 6 in the numerator, and 3 X 4 to get 12 in the denominator Your answer then is 6/12 which reduces to 1/2. In my opinion, there is no meaning here, and your **knowledge of multiplying fractions is limited to “the rule”**. What if I said I could create meaning by giving you a deeper understanding of what we actually did there.

I am going to use a concrete representation of the fractions to show a visualized image of what we do when we multiply fractions.

Here is a visual representation of the multiplication:

2/3 X 3/4 = 6/12

The first box is a representation of 2/3 and the second is a representation of 3/4. By overlapping the two boxes we have created the answer, the whole box represents the denominator (we split it into twelfths) and the part that is shaded by both colours is the numerator which is 6.

I assure you that if you had a hard time remembering the rule of multiplying fractions from back in grade 7, that you will never forget again. By looking at these pictures we have created connections in your mind, the connections are the electrical currents that contain what you know and what you can remember. If this is the first time you have seen fractions represented visually then I can say I taught you something. I created deeper understanding by using a representation and hopefully you know now why we “multiply the numerators together and then multiply the denominators together.” I believe that this is truly making the content meaningful and interesting and I did not reference Snoop Dog once.

So where does this leave me? I am starting to grasp the idea of making my lessons meaningful, so that students really understand what is going on. If we work with what they know to build new concepts then they really aren’t learning anything new, but expanding their knowledge. This is new to me, and as I said, this is something that has been rolling around in my brain for quite a while. Do you have any suggestions about making a lesson relevant and meaningful? Am I on the right track? What are the strategies you use?

I don’t currently teach math but you’re right on with visual representations as one of “multiple ways of knowing” or seeing a problem and solution — also Dan Meyer of TED Talks clips is fascinating. He shows how to have students create the problem themselves, then solve, with complete relevance. Best wishes!

Thanks for reading and posting, Fran. I will have to look those Ted Talks up!

I take it the green in the box is the answer?

I understand your point – I will have to show them how to get the answer coming soon. I don’t have any manipulatives so I will have to draw it carefully.

o.k. so it did take a second to figure out the boxes but I totally get your point. And the Snoop Dog reference with the melon made my eyes stretch.