Wild About Math!Making Math fun and accessible

9Nov/0715

How to get past “stupid” Math mistakes

I was recently asked how I deal with silly mistakes many of us make in algebra or arithmetic, especially in the context of a tutoring session. Common errors include forgetting to carry numbers when adding, getting confused about operating with plus and minus signs in one problem, and multiplying two digits incorrectly.

I consulted Michael Sheppard, director and lead educator for Big Sky Learning Center in Santa Fe. Michael shared a number of suggestions based on his 19 years of experience teaching kids in one-on-one and group settings. I've combined Michael's excellent suggestions with some of my own:

1. Reframe

Referring to arithmetic or algebra errors as "silly" or "stupid" mistakes carries a tremendous amount of emotional charge. Students may feel that they themselves are silly or stupid due to errors they are committing. In truth, the errors are likely caused by emotional and physiological causes, and perhaps a lack of understanding of key concepts. Thus, any judgment the tutor or student holds about the behavior leading to the errors is problematic for two reasons.

1. Such judgments are almost always based on incorrect understanding of the source of the errors ; tutors may feel that a student is lazy, careless, or not paying enough attention.
2. Judging a student's behavior is detrimental to the student's self-esteem.

As we will see, the true causes of the problem can be addressed without laying blame on the student or on his behavior. A healthy reframing of the situation is this:

Acknowledge that there are emotional and physiological causes of the errors and perhaps gaps in mathematical understanding that the tutor and student can address in a constructive manner.

2. Manage the emotional aspects of the situation

Judging, blaming, and shaming are counter-productive. It's best to unconditionally support the student regardless of how many problems he solves correctly. Holding the intention that the student is smart, creative, and resourceful will go a long way toward minimizing emotional stressors. Praising the student for trying, even if he makes a mistake, is very helpful in getting past the judgment that the student is somehow a better person if he gets the right answer.

Relaxation techniques, movement (see item 6), exercise, guided visualizations, meditation, EFT, and other modalities can help to disperse stress when it builds up.

3. Slow down

Many of us do calculations too quickly and fail to slow down even when it is in our best interest. There are two major causes of this behavior.

1. We want to prove to ourselves or to others that we are intelligent and we have been conditioned to believe that smart people think (and talk) rapidly.
2. We are emotionally or physically stressed and by speeding up our mental processes we numb out the feelings we're having.

Slowing down, being willing to look at emotional factors, and changing our attitudes about how "faster is better" will go a long way toward reducing errors.

4. Breathe

Shallow breathing leads to tension and stress in the body; both reduce clarity of thought. When we are frightened or anxious, as in just before or during a test, our breathing slows down.

The solutions is simple. Breathe more slowly and deeply. Sheppard has his students do the following when taking a test or doing a set of problems:

1. Put a big blue dot next to each problem description. Evey time the student starts a new problem the blue dot reminds him to breathe.
2. Take three very slow and deep breaths when starting a new problem.

5. Hydrate

The human brain consists mostly of water - 80% in fact. By the time a student notices he is thirsty he is sufficiently dehydrated that his ability to think clearly and retain information is impaired. In the field of search and rescue it is well known that most accidents are a result of dehydration. A very common scenario is that a hiker becomes lost, runs out of water or doesn't drink regularly, becomes mentally impaired, then falls or is otherwise injured.

Another proponent of proper hydration is Brain Gym. Brain Gym is a healing modality that emphasizes whole brain learning and often dramatically improves student performance. Brain Gym students are reminded to drink water before engaging in mental activity.

An eight once glass of water before starting a homework session or test is helpful as is drinking water consistently throughout the day.

6. Take movement breaks

Movement helps the mental and creative processes. Taking regular breaks is important to keep the brain alert. Possible break activities include:

1. Stretching
2. Juggling (Sheppard encourages students to learn to juggle as a way to reset their brains. I suspect that the left-right brain integration of juggling is helpful as well.)
3. Balloon fights (Another Sheppard idea which I only recommend with a tutor or parent and not in the classroom.)
4. Walking around
5. Doing a few jumping jacks

7. Pay attention to nutrition

Many of us are very sensitive to what we eat. Foods we are allergic to, problems with digestion, sugar, processed foods, and insufficient protein in the diet can all potentially affect us. It's worth undertaking an investigation to see if eliminating suspect foods improves clarity and concentration.

8. Strengthen the foundation

A final consideration, often overlooked, is the effect of poor mathematical understanding on Math performance. A student who doesn't understand how negative numbers are related to positive numbers will more easily make mistakes in manipulating numbers with mixed signs. Rote memorization with no solid foundation will likely lead to a greater number of errors with a smaller than desired chance that the student will check and find the errors.

Ferreting out the source of calculation errors may not always be easy but the process can be very straightforward and rewarding. Keeping the focus on finding and correcting the emotional, physiological, and foundational causes of the situation benefits everyone and keeps the student's self-esteem intact.

1. Sol,

Thanks a lot for sharing these excellent thoughts. No doubt ll math teachers have encountered very good students who consistently make errors that we might call “silly mistakes”. I have been guilty of calling them that, and this will stop immediately. The many non-mathematical suggestions here may be the most impartant part for some students, and I will be looking at these in the future as well.

This is an every good resource for teachers and tutors of mathematics, and I hope a solid community of teachers gathers here to exchange ideas and share stories.

Stan

2. Stan,

I’m glad you find this resource useful. As more people bring me their “how to learn Math” questions I’ll do research and write more articles.

Sol

3. I bookmarked this post. I’m so guilty of the “silly mistakes” accusation with my son. These suggestions are certainly much more positive, & I look forward to giving them a try.

4. Make my name Sherry, not Sherr. 😉

5. Sherry,

I hope the suggestions help. Do report back after you’ve tried some if you feel inspired.

Sol

6. Whatever “silly” mistakes the students make, I believe, we should not let them lost confidence. They are learning and learning through mistake is one good way where they can identify their own mistake and do self-correction. Give them time and our patience. It will help them gain more, directly and indirectly.

7. I am interested in the balloon fights idea as a way to reset and use another part of the brain for physical activity. Tell us more on that! Sounds like a fun way for the kids to get past test anxiety.

8. I highly appreciate these ideas. I think they lead to better performances of students.

9. Thanks for writing this. I was also accusing my son for silly mistakes. Now I know what I have to do..

10. exellent,,,,,, still now i miss all these things….. am very interesting in mathematics.. from now by adopting am going to master in maths.

11. even i talk rapidly and solve fast ..but ii hatttteeee maths!!! and i am not emotionally disturbed …!!

12. Wow didn’t know you had this great article, should have dug deeper while going through your site. Btw, can I obtain your permission to post this in full in a Singapore education forum? Of course all credits will be given to you as the author.

13. @Whitecorp — republish away! Thanks.

14. Hi sol thanks a million. The URL repost is http://forums.sgclub/singapore/how_get_past_380418.html

15. Thank you for this article I have found it very interesting. I am currently in Graduate School and this afternoon I decided to look for a solution to my problem on internet.

It’s very frustrating because I have a good understanding of the concepts and moreover I would often be the one who participates in class and gives the right answers. However when I take a pen and do some calculus I do every possible mistakes and not only one time but every time. And in test situations as well in non-test situations.

My problem is definitely not a problem of understanding, because I can write things as stupid as 4*4=8. Many times I forget coefficients from one line to the other, I forget terms and this kind of things. Even when I tell myself : okay I’ll do it very slowly I find myself to have forgotten a term of a summation in previous lines !! One time my teacher told me : don’t feel oblige to make mistakes to compensate your good answers…

I feel bad about it because my grade doesn’t reflect my level for this happens in every course in which calculus is involved and since I study engineering that’s quite a problem. Last year I ranked in the top 10 of my promotion with very poor results in courses with lot of calculus, and very good in those with less. It’s hurting me very much because it seems like there is no solution.

I really enjoyed what you said about “changing our mind about smart people who would be the ones who go fastly”, and about slowing down. I’ll pay more attention on it but I feel like having already tried to slow down. After reading this article I realize that my problem might be psychological, but I can’t find a solution that would fit me. If you have some additional advices regarding my particular case I would be grateful.