10 Math Tips to Save Time and Avoid Mistakes - Comments

[fresh_42]

Greg Bernhardt submitted a new PF Insights post

10 Math Tips to Save Time and Avoid Mistakes

Continue reading the Original PF Insights Post.

 

[QuantumQuest]

Really good advice and list of tips. From my own experience in the past I'll stress out the third one: Think or Write? adding the benefit of focus to this, as it helps being more focused than when thinking, not only in calculations but in general as someone tackles a problem in the context of the limited time of an exam.
Also, easiest questions first is something often overlooked under stress conditions but it is really indispensable. This cost me once a generous -30% because I spent a great lot of time on a hard problem as I knew how to solve the other ones. I finally solved it but I didn't have the time to write down all the rest.

Education, in my view, is a huge interconnected system of chains of stepwise improvements across disciplines and failure is an inherent part of the process. This - as is pointed out in the insight article, has to be taken as an opportunity to learn from the mistakes and go to the next level. There is nothing that can be undone after an exam failure but there is no need to undo anything either.

 

[DS2C]

Great stuff. As far as skipping hairy questions, I just experienced this on my midterm. The question made no sense to me at all and I spent too much time on it already. So I skipped it and came back at the end to give it another go. Still couldn't do it. Turns out the question had a typo and could not be solved nor simplified. Glad I eventually skipped it!

 

[WWGD]

One good reason to read everything first is that you get the ball rolling on those problems at a subconscious level. When/if you go back to them later, you have (subconsciously) done some of the work, broken down the question somehow./somewhat

 

[Greg Bernhardt]

Great resource for students!

 

[PetSounds]

As someone who has a tendency to lose points because of tiny, stupid errors right at the ends of problems, I'm bookmarking this. Thanks.

 

[ISamson]

From a student's point of view (I am one!) it is a very good tip resource!
Great insight.

 

[WWGD]

If I may, this one has been helpful to me recently: I have around 3 options (with in-betweens, but let's keep it simple for now) of what I intend to do with material at a given point:
1) Thorough reading and getting myself
2) Skimming, intro reading, breaking material down.
3)Reviewing

I try to decide base on the context, including considering my mental condition, which I can do. Under ideal conditions I try 1: enough time, rested and clear-minded.
Under worse conditions, tired and/or on public transportation,I try just reviewing. I often text myself notes on important things and I just check them while there. The idea is that if you have a clear goal of which of the three you will do, it is easier to get them done, and feel satisfied you did what you set out to do. You may even do this at a more "micro" level and do changes as you read the material. It is not realistic to fully get material that is new when you are not fresh , let alone tired, etc.

 

[Biker]

This honestly happens to me a lot. How I deal with this is by solving everything again before exams not because I need to understand everything from the beginning or memorize problems but to ensure that my hand and my mind are focused and don't make silly mistakes like forgetting a sign..etc. It just bumps my confidence. Also, If I have not revised before the exam or a quiz, When I solve a question, I always get the feeling that I did something wrong so I go back, check then continue which wastes time.

I myself like to not read questions. If I am nervous, I don't want to read them and say "This might be difficult" because of how an equation looks. It distracts me while solving other questions. I simply go one by one, If I am not able to solve it or I need more time I leave it for the end.

Really nice insight

 

[vela]

The third suggestion is really good. I'm amazed at the reluctance of my students to write stuff down. They repeatedly try to do calculations in their head, invariably make mistakes, and ending up spending way more time on a problem than they should have.

Here are a few suggestions I have:

Check your algebra as you go. After you write down a line, go back and redo the calculation. You can often catch simple arithmetic errors, sign errors, and the like. It's a lot easier to catch and fix those as you go than after you get to the end and discover your final result is wrong.

Figure out the best way to do the algebra. When I did homework, I wasn't satisfied with simply getting to the correct result; I wanted to find the most efficient or elegant way to get there. After a while, it made a big difference. I learned to do algebra faster and with fewer mistakes than my peers. And it was eco-friendly: while my classmates would turn in 30-page homework assignments, I'd be turning in 12 pages.

When doing physics problems, don't plug numbers in right away. For one thing, it reduces the amount of stuff you have to write. The less you have to write, the less likely you'll make a careless mistake. And when you do make a mistake (and you will make a mistake sometime), it's a lot easier to find it when you're working with variables instead of numbers.

Learn to use your calculator. The device is supposed to save you time, not be another source of errors because you don't know how to enter $5.42\times 10^{-4}$ correctly.

 

[cccccttttt]

As a math teacher of many years certainly support the 10 tips.

But would add an 11th:

"DRAW IT TO KNOW IT"

Much of the brain is devoted to visual processing.

Using words came along a very long time later.

So have found this an effective approach:

1. draw diagram to illustrate the theorem, concept, or process

2. discuss in detail till student says "that's easy, let's move on".

3. give student a blank sheet of paper

4. ask them to draw diagram from memory.

5. compare with original

6. good match: congratulate them as we "move on" to the next topic

7 poor match: go back to step 2.

We all deceive ourselves to some degree as to what we really know.

Seeing the diagram is a vital feedback.

The act of drawing uses visual, motor, and kinesthetic senses to cement
the info into the nervous system.

Once students experience success, they find it works just as well when studying alone.

ct

 

[Mark44]

"DRAW IT TO KNOW IT"

This is excellent advice. For some reason, students are often reluctant to draw an image of the situation, thinking that doing so will take too much time. This is often a false economy, as taking a short time to get the wrong answer is not an optimal solution.

Another possible reason is that, students are often enamored of working with algebraic symbols. Using the visual part of the brain adds some insight that isn't possible with the algebra alone.

 

[gmax137]

But would add an 11th:

"DRAW IT TO KNOW IT"

Ahh, I see Mark44 beat me to it; this definitely is "excellent advice."

 

[fresh_42]

"DRAW IT TO KNOW IT"

This is excellent advice. For some reason, students are often reluctant to draw an image of the situation, thinking that doing so will take too much time.

I really have forgotten this, resp. I thought of it afterwards. In my experience, one of the reasons they don't draw something is, that it actually does take too much time. However, the reason is, that they start to draw accurately, chose a scaling on the axis, recognize it doesn't match the situation, take - no search for - an eraser, erase nearly everything and start again at zero, don't find their compass and so on and so on. At least this is what I've experienced. It's hard to get them known, that a drawing is about the principles of a problem and not the statics of a building. I think this should be practiced far more often than it actually is. At least I mentioned the drawings as a reason to prepare for. But you're right, it should have been on a more prominent place.

 

[nepsaol]

Great list! I normally have problems keeping calm during exams and would consider myself a master of "shitty mistakes", especially when it comes to simple algebra that I normally have no problem with. All in all, this article gives you great tools to improve the structure of problem solving. Thank you, this is very much appreciated!

 

[WWGD]

2.

We all deceive ourselves to some degree as to what we really know.
ct[/QUOTE]
https://en.wikipedia.org/wiki/Dunning–Kruger_effect

 

[fresh_42]

https://en.wikipedia.org/wiki/Dunning–Kruger_effect

Dang, you figured out why I'm here.

 

[DS2C]

What are some tips on drawing out a problem? For example if you have very large numbers, or imaginary numbers, it can be hard to visualize.

 

[Mark44]

What are some tips on drawing out a problem? For example if you have very large numbers, or imaginary numbers, it can be hard to visualize.

I don't think problems involving numbers (real or complex) fall into the category of drawing a sketch, although an Argand diagram of a complex number might be helpful. Argand diagrams are used to locate complex numbers in a two-dimensional plane. The number i is located at a point one unit above the origin.
The kinds of problems I have in mind are various applied problems in calculus, such as find the area beneath a curve, finding the volume of some solid, finding the amount of work done in lifting something a certain distance, etc. I'm also thinking of problems in trig, where sketching a triangle is helpful, or problems in linear algebra, to be able to visualize a plane or line in space.

 

[DS2C]

Great thanks Mark. Ill keep these in mind for future reference!

 

[dkotschessaa]

I love the "Write instead of think." step. I tend to think of doing proofs as 'thinking on paper."

A bit of a modern challenge to the usual idea of doing easy questions first:

https://lifehacker.com/improve-your-test-scores-with-the-hard-start-jump-to-e-1790599531

Short version:
1. Try the hard problems first, but don't waste too much time on them
2. Do the easy problems
3. Go back to the hard ones to finish

By starting 1, you get your brain rolling (subconsciously) on the harder problems while you are doing other stuff. Sometime it takes our brains a bit to pull stuff out of the filing cabinet.

 

[wormbread]

As a math teacher of many years certainly support the 10 tips.

But would add an 11th:

"DRAW IT TO KNOW IT"

Much of the brain is devoted to visual processing.

Using words came along a very long time later.

So have found this an effective approach:

1. draw diagram to illustrate the theorem, concept, or process

2. discuss in detail till student says "that's easy, let's move on".

3. give student a blank sheet of paper

4. ask them to draw diagram from memory.

5. compare with original

6. good match: congratulate them as we "move on" to the next topic

7 poor match: go back to step 2.

We all deceive ourselves to some degree as to what we really know.

Seeing the diagram is a vital feedback.

The act of drawing uses visual, motor, and kinesthetic senses to cement
the info into the nervous system.

Once students experience success, they find it works just as well when studying alone.

ct

Right on! I had a Calculus and an Engineering professor both say that when in doubt, draw it out.

 

[Greg Bernhardt]

I would always rush and make the dumbest mistakes. Seeing things that weren't there, not seeing things that are there and even things like adding when there is clearly a minus sign!

 

[SciencewithDrJ]

Greg Bernhardt submitted a new PF Insights post

10 Math Tips to Save Time and Avoid Mistakes
View attachment 212648Continue reading the Original PF Insights Post.

It would certainly help to make a diagram of the problem, that surely helps a lot.

 

[scottdave]

Great tips. Number 4 Units are your Friends, goes right along with the article, which I just finished. https://www.physicsforums.com/insights/make-units-work/

 

[fresh_42]

Great tips. Number 4 Units are your Friends, goes right along with the article, which I just finished. https://www.physicsforums.com/insights/make-units-work/

I know, I've already bookmarked it into my personal list of FAQ insights for quotation.