I have a question for teachers of science and math on DU.

[KlatooBNikto]

Last year one of my children was struggling with Math in her 7th grade class. I deceide to watch her study habits and removed all TV, iPods, IMs and other distractions. This did not produce any better results.So I looked at what she could be doing wrong because she is a straight A student in all her other classes.

I happened to notice that she was studying math curled up in her bed and reading problems and solving them in her head and claiming that she knows how to solve them.

By coincidence, I remembered a book by Alfred North Whitehead, a great educator in Britain who was a collaborator with Bertrand Russell.The book was titled AIMS OF EDUCATION. In that book, he states that Math needs to be studied by children with a pencil and paper in hand solving the problems by writing, if necessary repeatedly in order to not just solve the problem at hand but also to see the connections between different sets of problems. He says that in our modern lifestyles while our visual stimulation is enhanced, the connection between the hand and the brain centers is lost by less use.

After I insisted to my daughter and my other children that they start using the pencil-paper approach to solving problems, I am beginning to see an improvement.May be it is simply that they remember things better this way.Whatever it is, I will take it.

Any thoughts?

[donco6]

1. That's a technique often used today.

It's often required on standards assessments as well. The students can't just mark the correct answer, they have to show their progression through the problem.

One drawback is that kids who are particularly creative can come up with alternative answers that don't follow the "usual" progression. I've found a number of these in my grading and award the kids points as if they'd gotten the "right" answer, but on standards tests, they don't give any leeway at all.

I think it's a good thing, overall. At least you can see where they may be going off-track. But keep in mind "off-track" isn't always "wrong".

[KlatooBNikto]

2. Thank you.I thought at this young age, they need to be able to learn

some standard problem solving techniques before they can even think creatively. I hope my kids are able to learn Math better this way.

[donco6]

5. You might want to check on

whether they're breaking the problem down correctly as well. Progression is one thing, but knowing how to divide the problem into logical parts is another thing altogether.

For example,

Question: Jack walked from Santa Clara to Palo Alto. It took 1 hour 25 minutes to walk from Santa Clara to Los Altos. Then it took 25 minutes to walk from Los Altos to Palo Alto. He arrived in Palo Alto at 2:45 P.M. At what time did he leave Santa Clara?

Looks like a simple question eh? But there are several steps to perform to get to the answer.

First, you have to calculate how much time it took to get from Santa Clara to Palo Alto (1 hr 25 min plus 25 minutes). A subsection of the problem requires the student to remember that hours come in units of 60 (I have a LOT of students who try to put in 1.25 on their calculator to do this problem). Finally, the student has to subtract 1 hr 50 min from 2:45 to get the final result.

Dividing up the parts correctly is a big part of the battle.

[KlatooBNikto]

6. Good idea.Will get the kids to do just that.Thanks again.

[Lydia Leftcoast]

3. I'm not a math teacher, but I struggled with the stuff all the way

through high school.

When I took it up again as an adult, I came to it after having learned how to study linguistic theory, i.e. by writing down each step in the sequence.

Lo and behold, I found that the same approach worked with math! It really helped to write out the sample problems and then work out the real assignments through analogy with the sample problems. That was something that nobody told me all through high school.

I think that each school subject has its own appropriate study techniques and that a lot of time bright students have trouble with a subject because they've never been taught how to study it.

I certainly found that with my foreign language students. If the strugglers came to me for help, the first thing I did was ask about their study routines. With the rare exceptions of the learning disabled students, I found that most of them were studying Japanese as if it were a facts-based course instead of a skill-based course.

Interestingly enough, some of my best students were in math and engineering. They knew how to study something methodically and apply it to real life.

[clydefrand]

4. By all means pencil and paper and lots of each and

repetition. I know, I know, kids don't like it because it takes sooooooooooo long they say. BUT it pays off. Practice makes perfect in music, dance, sports, etc. right? Why not math?

Children need to use pencil...not a pen...and paper to do math. Calculators shouldn't be allowed until they can show you how to derive answers using the above tools.

Good luck. Teaching good study habits isn't easy. Takes a long time. I always asked my students, when they complained because I made them do their work over until it was acceptable, why they never had time to do it right the first time, but always had time to do it over until they got it right. They simply don't want to take the time. Patience and perseverance must be taught by parents and teachers alike.

[LiberalBadger]

7. study with a group

there is a bit of "doing" vs "following" as well as "can prove it" versus "i can get from here to there". Start out with the strict and then let them be more and more lenient.

Other big thing is to let people do math in groups - then they don't think that they are the problem but the problem is just hard. They also get a chance to teach themselves and that pushes them more to to the "prove it" stage.

Good luck!

[KlatooBNikto]

8. The idea is good but the implementation is going to be hard on the

parents.Have you ever had to deal with ten or twelve giggling teens talking nonstop about everything except the problem at hand? After one session with them trying to teach them science, I thought my head was going to explode!

[Festivito]

9. Struggling *and* able to solve in the head. Opps.

Perhaps she shall be so smart that no one will ever understand what she is thinking, although it could save the whole world, it will do no good like a siren to warn the deaf, police lights to warn the blind, or the unnoticed tree fallen in woods. But, with kids, you'll never really know for certain. So, good luck and make each move with love in your heart -- and you can't go wrong -- by me.

[kiraboo]

11. No matter how successful she is (or is not)

working out problems in her head, she will be graded in college according to the written proof of her ability to make the calculations. My husband is a physics and math professor and on occasion I grade for him. Students get full or partial credit according to their understanding of the problem as demonstrated by a step-by-step written description of their thinking process. A numerical answer with no calculations gets a quarter point... Don't you remember being told to "show your work"?

[the_outsider]

10. That's how we were taught maths and science in India

I grew up in India where teachers insist that every student must write down each step in detail for every math and science problem. Every week they will give math and science homeworks and the students will turn in the answers with every step shown in detail. Even in exams, you have to show all the steps and the answer sheet to a 3 hour exam will be 20-25 pages thick. Most of the questions were not multiple-choice. You would get partial credit based on how you handled the problem and full credit only if all the steps were shown AND the answer was correct. Calculators are not allowed in high school exams - neither in school internal exams nor in national entrance exams for prestigious technology schools like IIT. Calculators were allowed only in university exams. Not sure if it's the only way to teach maths or science or even the best way, but it surely didn't hurt me.

[alcuno]

12. I teach 7th and 8th grade math and it's all about process.

My best students write down all of their steps and self-correct along the way. They are able to verbally explain what it is that they have done. My weakest students, when giving an incorrect solution, are often not able to to tell why that is their answer.

We award points for the process. It's possible to make a simple math error and get the wrong answer while still being able to work the problem and understand the concept.

I've even noticed with boys the "two-handed" calculator usage; no pencil in sight. I think that they think they are at the controls of a video game. I've banned the responses, "I did it in my head" and "I did it on the calculator" in my classroom.

[pstans]

13. Writing it down

I am a college student studying to be a teacher. From what I learned, by thinking through a problem in your head you go through the steps a limited number of times. But by writing the problem down, you think of the step first, write it down, think about how to answer it, write the answer down, go onto the next step, look back at the steps before, and so on. When you write down the steps, you are much more actively engaged into the problem.

[JVS]

14. My Topology professor said that if you don't have a pencil and paper...

when you are reading something mathematical then you aren't really readiing it at all.

[roguevalley]

15. There is no better way. You start at the concrete level in your

learning and move to abstract, that is from seen to unseen or thought. Your daughter is trying to skip from the seeing is knowing to thinking it through and she can't do it. If you can see it, you can build constructs in your mind to think it. For her not to do the first step is to invite disaster. Go with pen and paper. Once its learned, she can go farther up the learning curve.

[karlrschneider]

16. I was never a "formal" teacher, but I've done a LOT of teaching...

from math to English to meteorology and flying. One thing I discovered is that the -method/approach- to a problem is more useful and productive than the actual -answer-, even if it happens to be 'right.'

"Show me how you got there" is an effective, if more challenging, tool than praise for a result with no 'paper trail'.

:D