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Coping with Carelessness: Strategies, Stresses, and Mindsets

Date: 01/14/2016 at 10:47:00
From: Mary Corrigan
Subject: Careless Errors

Our son, a high school junior, is currently taking Advanced Placement BC 
Calculus. He has always excelled in math (and all other subjects), and 
never had to study much, because he easily understands concepts. He has, 
however, always had a tendency of making careless mistakes. 

This year this tendency has become a particular problem, with his grades 
suffering for the first time. Part of his tests are multiple choice -- no 
calculator allowed. Here, he does not have to show any work. But this 
part needs to be turned in prior to starting on the next section, one 
where calculators are allowed. On the calculator section, he does need to 
show his work; and the brevity of the short answers often belies the many 
intermediary steps they required.

After these tests, he comes home all stressed out. My son is very 
ambitious and puts a lot of pressure on himself; and I think now in his 
junior year, this is getting to him. He says he has become increasingly 
anxious about math tests because of the importance of doing well to get 
in to a very good engineering school. My son's teacher says all his 
mistakes have been careless ones, not conceptual ones: he makes simple 
calculation errors, or misreads questions, or omits units, or runs out of 
time, depriving him the opportunity to check his work. 

In the past he has tried to redo questions twice, checking his answers 
thoroughly; however, he no longer has the time because the tests are more 
challenging and just ask more questions.

The teacher's advice is to change his attitude going into a test. I am not 
sure how to best help as a parent without putting more stress on him by 
emphasizing the issue. Could you please provide some additional advice?



Date: 01/14/2016 at 17:27:16
From: Doctor Floor
Subject: Re: Careless Errors

Hello Mary,

It is of course hard to judge your son and his mathematical abilities 
from your message alone. But in my work as a teacher, I see pupils 
(European, not American) in my classes struggling with similar problems. 

From those experiences, here are three observations that I hope help you 
and your son cope with his difficulties.

1. Smart kids often have surprisingly poor strategies

Smart kids often have learning strategies that seem lazy or careless, due 
to the fact that they haven't been really challenged in younger years. 
Because of this lack of challenge, there has never been any motivation to 
develop learning strategies or solving strategies. Easy tasks pave the way
for good grades, and the cycle reinforces itself.

But at some point in a school career, relying on talent alone turns out 
to be not enough. Even worse, teachers often think that by high school, 
high-performing kids must have good strategies. If you or your son 
recognizes any of this, it would be wise to talk with him and preferably 
his teacher or a tutor about learning strategies such as planning for 
test preparation, making good summaries and schemes, etc.

Similar problems arise not only with learning strategies, but also with 
solving strategies. It is not unusual that smart kids are careless with 
their math homework, which they dismiss as "repetitive" or "boring." They 
often do it without much concentration, or sometimes fail to do it 
entirely, rationalizing, "I already understand it." 

But practice is needed to develop better solving strategies; and at some 
point, those strategies are needed! You wrote: "he makes simple 
calculation errors, or misreads questions, or omits units, or runs out of 
time, depriving him the opportunity to check his work." It sounds like 
your son has been getting into trouble with solving strategies. Unless 
caused exclusively by stress, it is unlikely that this only applies 
to tests. 

So the key is in his homework. Do not only complete homework, but *review 
it.* Learn from your mistakes. Even when you do it correctly, wonder if 
you could have done it smarter, or quicker. If you encounter a trick or 
novel thought, make a note. Be concentrated and targeted in your review.

Dull, repetitive homework is important. Practice is needed, just as it is 
needed for sports or for driving a car, where mere conceptual 
understanding is not enough, either.

2. Too much stress holds you back

A test is meant for you to show what you are able to do. It requires 
concentration; and while a bit of stress helps you concentrate, an 
overload certainly doesn't. 

People cope with this very differently, so consider these as only the 
most general of observations:

- Be confident. If you know you are well-prepared, there is no need to be 
stressed. And this you should see in broadest perspective: you have 
learned enough, trained enough (by completing and reviewing homework), 
know how much time you have, and know how you can parcel out that time 
among the different parts of the test. 
- At the same time, be realistic about what to expect. This is 
particularly important if the test turns out to be more difficult than 
you thought, or time pressure is higher than you thought.
- Force yourself not to think of any consequences while taking the test. 
Just take your test, and stick with taking the test. Other thoughts will 
only break your concentration. Prepare ahead of time so that if you do 
lose concentration, you already have a way to re-focus and get back on 
track. Perhaps abdominal breathing, perhaps saying a sort of mantra in 
your head, or doing some other kind of routine. Follow the example of what 
athletes do. (Have you ever watched the routine that Rafael Nadal goes 
through before serving?) Again: be prepared!
- If you can show your abilities in a test, that is the best you can do.

3. Mindset Matters

Quite a few kids have a mindset that holds them back. It is called fixed 
mindset, and comes with the thought, "It doesn't really matter if I do the 
homework or not; either I will understand it or I won't." Often kids who 
are labeled as "smart" or "intelligent" develop such a mindset. These kids 
think their intelligence is fixed, learning is understanding, and that 
developing intelligence does not exist (e.g., by homework). 

By contrast, a "growth mindset" posits that developing intelligence is 
possible. Research shows that there is indeed a correlation between 
mindset and intellectual development. 

This is not an easy matter to address all at once. I recommend searching 
online for the phrase "fixed and growth mindset" to learn more about how 
to get started.

I hope this helps a bit. I'll leave the question open to see if other math 
doctors have something to add.

Best regards,

- Doctor Floor, The Math Forum
  http://mathforum.org/dr.math/ 



Date: 01/15/2016 at 10:45:19
From: Doctor Ian
Subject: Re: Careless Errors

Hi Mary,

To add to what Doctor Floor said, here are some more thoughts on the 
subject of 'careless errors,' and what to do about them:

    http://mathforum.org/library/drmath/view/52382.html 

I hope this helps.

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 



Date: 01/15/2016 at 11:52:05
From: Mary Corrigan
Subject: Thank you (Careless Errors)

Hi Doctor Floor,

We can't thank you enough for your response! It was spot-on! 

I feel all your points are excellent and will be very useful. I can't 
wait to share your response with our son (he came home with the flu 
yesterday), because I think he will now understand the underlying issues, 
make the adjustments needed, and as a result cope better. The difficulty 
will be for him to accept that he needs more practice even if he already 
"understands" concepts, and to figure out how to change his habits.

While we were familiar with "smart kid" issues and the danger of not 
being challenged, we had not anticipated that this would become THE 
instant when everything would back-fire. 

Sincerest thanks again for your very insightful and thorough answer!

Mary
quot;boring.
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