Struggling with Math: My Experience in Grade 12 Advanced Functions

[novae]

Hey, I'm in grade 12, taking advanced functions at the moment. I just wrote my last test of the year and flunked it. I understood the concepts really well, hell, this was the easiest test I've ever written, and I still managed to screw my self overcause of two stupid mistakes (not including some calculation errors that I might have made in the thinking question I didn't recheck).

Stupid mistake 1) Solving a problem with the equation already given to me, but being so fn blind, I can't even see that there was a phase shift in the sinusoidal function I was given. I simply input my angle, didn't apply the phase shift cause I couldn't see it and yeah that entire question is now incorrect.

2) I was supposed to graph a function, idk what,I was thinking, but I forgot to factor out for the stupid k value. The function I had was something like: f(x)= 1/2Sin (3x-pi)+10.
The format of the function is f(x)=aSin[k(x-d)]+c
So, clearly I was supposed to factor out the 3. Didn't realize until much later what I did. Unfortunately, I used mapping notation. I honestly don't know what I was thinking here, I know how to do these questions, I've done them so many times, it's grade 11 stuff. I understand them, but like my brain was actually poop.
Let's add a third one onto this:

3) There was an identity that I could have solved for bonus marks cause as soon as I looked at it, I knew what to do, but she kept telling us the identity was going to be extremely difficult before the test, so I decided what I was thinking was probably wrong and didn't attempt it. :)

The third one just teaches me not to be dumb and attempt a question anyways. I don't really know what to do about my poor attention to detail and going blank and screwing up concepts I already know.
What sucks even more is that there are only like 2 or 3 questions per category we are marked on, so if I screw up one question from any, my mark is done.
((What I mean is that we have categories we're graded on like communication, thinking and inquiry, knowledge and understanding, and application.))

I actually want to go cry cause this isn't the first time this has happened.
Like for our last test, I did this thinking question on another test, got a 75 on it cause I messed up my signs at the very end. Everything else in my solution before that was correct.
There's just something I always mess up and because of not having many questions per category, my mark suffers.

 

[dkotschessaa]

Hey, I'm in grade 12, taking advanced functions at the moment. I just wrote my last test of the year and flunked it. I understood the concepts really...

I'm just stopping you there, not to be rude or anything, but because this is a very common refrain on math tests. This happened to me a lot and still does.

Having a conceptual understanding of something in mathematics often leads us to the conclusion that we should then be able to take a test which requires us to know the details. Unfortunately this is almost never the case. To really to well in math, I've found (the hard way) that you have to really practice the details.

Here's a great video from a Coursera course I took (I recommend taking the whole course. It's free) called "Learning How to Learn."

The title is "illusions of competence."

https://www.coursera.org/learn/learning-how-to-learn/lecture/BuFzf/illusions-of-competence

She says some buzzwordy things about working memory and such, and that's based on terminology she's laid out earlier in the course, but I think you can get the idea.

A really good example of this is going through the textbook and looking at examples.

"Oh, that makes sense." [turn page]
"Yup, makes sense." [turn page]

Of course they make sense! It's all laid out there in front of you. But could you solve the example as a problem on your own without looking at the example? whoops!

So for me, I had to do a lot of self-testing. This meant doing problems under test like circumstances - a timer, no book in front of me. It was amazing because I really thought I knew "the concept" but when I sat down to do this I realized I didn't really know anything! It

As for details like minus signs, I hear you there. Fortunately the math I do now is heavily "conceptual" (definition, theorem, proof) and so I do not do a lot of calculation, but there are still DETAILS. And the ironic thing is that the details are where you REALLY have true deep understanding.

When it comes to long calculation details your only option is to keep re-checking (hard to do on a test, I know), but also, make sure the answer you arrive at makes sense, and for that you have to lean on your understanding of the topic.

-Dave K

 

[Delta2]

Maybe overconfidence is your problem, I mean it looks to me like when you first saw the exam questions you probably said to yourself "This is too easy , this is grade 11 stuff I can do it fast and easy " and you didn't pay too much attention through working out the answers.

But oh well to make mistakes is human, all we can do is to learn from our mistakes and not repeat them.

 

[TeethWhitener]

Just to pile on, there's a passage from Jim Hefferon's Linear Algebra book that's stuck with me:

Finally, a caution for all students, independent or not: I cannot overemphasize that the statement, “I understand the material but it is only that I have trouble with the problems” shows a misconception. Being able to do things with the ideas is their entire point.

 

[Stephen Tashi]

Having a conceptual understanding of something in mathematics often leads us to the conclusion that we should then be able to take a test which requires us to know the details. Unfortunately this is almost never the case. To really to well in math, I've found (the hard way) that you have to really practice the details.

Another way to put that thought: "There is a difference between comprehension and drill".

For example, it is not difficult to comprehend how to throw a hand grenade, but if you look for videos of hand grenade accidents on the web, you can see that execution and comprehension are two different things.

Drill is needed when you must do things in limited time. A test usually limits your time and sometimes your own concept of how much time you need to spend limits your time. Drill makes you familiar with the types of "stupid mistakes" that are possible.

 

[dkotschessaa]

For example, it is not difficult to comprehend how to throw a hand grenade, but if you look for videos of hand grenade accidents on the web, you can see that execution and comprehension are two different things.

It's very apropos. Those integrals can really blow up on you if you aren't careful!