Does "discovery" in math have undertones of "no absolutes?"

[Guest Xapis10]

I think it would be very interesting.

[LizzyBee]

I don't think that's the intent. I think the idea behind discovery math is that if kids can be guided to discover how math works, they will understand and retain the information and concepts more permanently than if they are simply told, "Here's how you do it." Discovery math can also help kids get excited about math and help them see how math can be used to solve problems and build things.

[boscopup]

There are definitely absolutes in math. I don't think you need to worry about that. :)

[serendipitous journey]

Well, there is a sense in which certain mathematical concepts cannot be instantiated in the physical universe -- something "perfectly" of a particular shape, for ex., if for no other reason than at the very small scales the fabric of the universe gets a bit probabilistic and sort of bumpy -- and so some mathematicians might focus on such things. I am sure that some fruity math thinkers have been, and are, relativists in their math. But math as such doesn't get very far if there is no fundamental theorem -- no "absolute" -- to start from.

 

Whether or not our culture's mathematical concepts are absolutely true, or whether math is a cultural artifact, is another question I've run across. However, I haven't seen a serious thinker argue that mathematical axioms are culturally constructed per se, just that our cultural ideas may constrain what we allow -- as in the Greeks who abhorred a vacuum and therefore banished 0 in many calculations and, I gather, infinity too. So there's some writing about cultural relativism in math, but what I've found is buried in other books (like on the history of 0).

 

Discovery math depends on there being a truth for the child to discover. IMHO. :)

Edited July 21, 2012 by serendipitous journey

[Monica_in_Switzerland]

I would almost think (without any investigation into the theories of the creators of curriculua) that discovery math would actually REINFORCE the concept of mathematical absolutes. If even a child is capable of discovering mathematical principles, then this is because those principles are actually Laws (absolutes) which are "discovered" vs human made.

[Guest Xapis10]

I would almost think (without any investigation into the theories of the creators of curriculua) that discovery math would actually REINFORCE the concept of mathematical absolutes. If even a child is capable of discovering mathematical principles, then this is because those principles are actually Laws (absolutes) which are "discovered" vs human made.

 

Thanks for the comments.

[Farrar]

Discovery is just about the pedagogy, not the material.

 

I will add though that there's not an absolute right way to get the answer in math. There are several ways to solve even simple arithmetic problems. So in that sense, there's no one absolute. I know that as a child, I was taught that there was only one "right" way to do addition with regrouping, but, for example, Miquon teaches it a different way. Still, if you mean will 2+2 always be 4, then yes, of course. And discovery has nothing to do with that.

 

And forgive me, but the aside seemed like a complete non-sequitor. What does the author of Mathematics Made Meaningful's religious views have to do with the C-rods or using discovery to teach math? We used that book and there's nothing in there about religion at all that I can remember.

[Crimson Wife]

A good "discovery" or constructionist curriculum will eventually have the student using the traditional algorithm. It's the bad curricula like TERC Investigations or Every Day Mathematics that minimize or skip the traditional algorithms entirely.

 

Miquon, Art of Problem Solving, MEP, etc. you don't need to worry about. :001_smile:

[FO4UR]

Discovery approach maths teach the child to search for the absolute, the law, the pattern.

 

I see your dc are young. Go buy Miquon and some Cuisenaire Rods and dive in. :001_smile: It's a satisfying way to learn - and really know - math.