# Teaching Math

This is a guide to internal links, ie posts I’ve written.

Could you use tags instead? Sure, but the tags won’t organize the list for you.

Algebra | Geometry | Algebra 2 /Trigonometry |

Combinatorics | Logic | Math puzzles for high school |

Outlook on teaching | other blogs and sites about teaching math |

This page is currently under construction. If some of the links above are not live, or go to an empty page, check back. There will be regular updates until this is 100% linked.

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18 Comments
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Math must NOT be taught with calculators. These instruments of destruction are destroying students everywhere. When is this madness going to stop?

Graphic calculators are big help for algebra II; let’s students visualize math concepts. However,calculators for arithmetic calculations delay the learning process confuse students and create dependency.

I agree with both the original comment, and the reply. Students do need to understand how to do math first, before learning how to do the work on their calculator. Teaching calculators too early is basically giving the students a crutch to lean on, and they fall over when they can’t have it.

However, provided that students have a firm grasp on the concepts being taught (which comes with time and practice), I don’t see harm in using calculators to expedite the calculations. I understand math concepts, but that doesn’t mean that I need to write everything out longhand. A calculator is an indispensable tool for me, but I can consider that I have earned the luxury of its use. Graphing calculators can help complete more time-consuming projects much faster than drawing out graphs by hand.

Another thing to consider on this subject: given the increasing prevalence of iPads and other technology, it may be a good idea to allow our young to familiarize themselves with these tools at an early age, if for no other reason than to allow them to be competitive with others who are using them. Nothing says that this can’t be done with supervision though, and in moderation. These tools will never replace solid understanding of concepts, though.

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what is wrong with Calculators. We should embrace this technology that previous generations were without. Perhaps one should have the basic understanding of mathematics to solve say systems of equations by hand, but once they are competent why not use technology to do them so that more complex problems can be solved, problems that might actually demonstrate how that particular math could be used in the real world so to speak.

I agree. There needs to be a basic understanding of the concepts in addition to using the calculators.

How are they destroying students everywhere? How is more useful for a student in high school to do 456*256 by hand then with a calculator?

I often use calculators to “discover” mathematics. For example, take a graphing calculator and put several different translations of a parent function in your y= and graph. Ask, “how does changing the numbers in equation appear to affect the graph?” Then take the knowledge gained one step further by asking “Why do you think changing that number makes that change in the graph?” Ooooh…….now we’re spending less time “doing” math and more time creating understanding…..yeah, that’s destroying lots of my students.

I think when learning an application of a math problem a calculator should not be a useful tool. Yes, at that point it would cripple a student. When the student has been tested from ground up and has proven that the application is mastered, I would expose my students to the usage of a calculators. A calculator is a modern tool in technology and should encompass the course……. Yes mathematics becomes very difficult but the grass root should not be forgotten! Although modern technology should not be ingnored.

Regarding the 456 * 256. How is it more useful for a high school student to do this my hand?

Well, they wouldn’t even be doing this by hand. Let’s see… Since 256 is 6 more than 250, which is quarter of 1000, maybe I can just do 256/4, which is 114 (easy math), and then add three zeros for an answer of 114000. Just as quick as punching a calculator, but it involves using your brain to do a mini-problem solving, on top of the problem at hand. How could be expect students to understand higher concept mathmatics when they can’t even figure out that the answer to 456*256 can be approximated in just as short time w/o a pen and paper?

Want a more accurate answer? since 256 was 6 more than 250, 6*400 is 2400. So, take our previous estimate and,

114000 + 2400 = 1164000. All doable in one’s head. and now I’m off by 300.

Is using a calculator to graph helpful? Maybe yes and maybe no. I took calc in HS using TI-80’s. In college I took Calc II and we didn’t use any calculators. So we used horse-driven carriages and albeit I am not saying that calc’s should not be used because “we did it the old fashioned way”, but because a calculator is a tool to assist us speed along things that we already know the basis for and already understand.

Not being able to understand number theories and simple math concepts because the student is too used to punching numbers into a calculator definitely does not make them ready for higher-level conceptual thinking.

I’ve had many Physics students in my class that refuse to let go of their calculators. Some of them get wrong answers and do not understand why the position (or the absence) of parenthesis makes a difference. They understand the rules of parenthesis, but haven’t really practiced it in their head, so the parenthesis is just a stupid button that they should be pressing w/o thinking of the math that is actually taking place. First week of class, I get students who get wrong answres and can’t figure out why they got it wrong and trying to explain the parenthesis doesn’t help until I make them do it on paper the wrong way (as they typed it in their calc)…

Take a Chemistry class, and then try to have them perform calculations on scientific calculators regarding gaslaws and most of them will do okay. You ask for relationships between variables, and they look at you with a blank stare. Clearly, the one who understandts that relationships between variables here is the calculator, not the student.

This is why calculators, although not banned in my class, are not encouraged in my class, and if you take exams/quizzes w/o it, I give them a bonus point.

If one is building a building and has a helpful “machine” that will just pop out foundations on demand, it will definitely help us build buildings faster. however, how will we be able to talk about static and dynamics of the building if the person who built it says, “Hey man, I don’t know anything about foundations. i just press the button and then use whatever I get w/o questioning”…

Yes– but I bet you don’t do your taxes by hand or without a computer

Actually, I did. I guess that comes with having learned to do math by hand as a kid, and enjoying. I’d rather do something important like that by hand rather than using a calculator. And forget about a computer, why should I pay for software to do something I can do for free by myself in 20 minutes?

Hi, have you checked out this fun pac-man style game to learn your factors?

Factor Feeder

Hmm. clearly self-promotion, which meets my definition of spam. But a genuinely fun math game… I’ll write something plugging it. Nicely done!

Yes calculators are wonderful things. However, doing the memorization and constantly working out problems helps solidifies numeric concepts. When I use a calculator I know generally what my answer will look like.

I have had a student (HS) who couldn’t do a division problem if it was expressed as a fraction. The caculator used the ÷ symbol and it didn’t match the symbol she was given.

There is a place for calculators and students should be warned about how easy it is to get a wrong answer if they are not careful.

Math should be taught with…. animated videos! I made a new one on factoring trinomials where a>1. It’s on my blog if you have time to watch (and comment).

http://zerosumruler.wordpress.com/

School’s almost out for the summer, but my students have already checked out. And I don’t mean “checked out” as in they’re not doing anything; they’re literally checked out of the building! I guess that’s what happens when a school scheduled final exams to be given 3 weeks before the end of the year. ANYWAY, my point is that I am going to have some free time on my hands and would LOVE some suggestions on more topics to cover with videos….!

Hello Ms. Andersen,

I am contacting you about one of our mathematics books that has been receiving a lot of attention recently, and been in the top ten on Amazon for both children’s mathematics and general titles. Reviewed by NPR last weekend, it is a children’s mathematics book which uses monsters to help children count and understand prime numbers, and I believe it would be of great interest to your readers.

While the illustrations are appealing to a very young audience, the book is actually geared toward children in grades 4-8. Adult mathematicians are also drawn to it for its innovative approach to mathematics.

Please take a look at the links below, which will provide you with more information on the book.

And please let me know if you require any additional information on the book. I will be happy to help.

http://crcpress.ning.com/forum/topics/monsters-book-a-monster-on

http://www.crcpress.com/product/isbn/9781568815787

Thanks!

Judy Thomas

CRC Press

Good afternoon,

My name is Olivia Damavandi and I am a current student at Columbia University Graduate School of Journalism. I am focusing on stories in The Bronx, one of which is about the reported mistreatment of math teachers at Bronx Science.

I’d greatly appreciate your contribution to the story. Please email me as soon as possible. My email address is ord2103@columbia.edu.

Thanks so much,

Olivia Damavandi

I’m retired and working at a private learning center. Many of the students are sent and paid for by the DOE for both ELA and Math tutoring. The center runs standard diagnostic tests to uncover deficiencies. Many of the junior and senior high school students test poorly in Math without a calculator. They don’t get great scores on high school entrance exams and college tests because they just blindly use calculators.

I just tutored an 8th grade boy for 1 hour who thought you multiplied 284 by 12 by adding 284 to itself 12 times. He ran out of steam when he was asked to multiply together two 3 digit numbers. He kept asking for a calculator.

At the center, it’s back to basics. Students are not permitted to use calculators until they’ve shown proficiency in a series of tests through high school Algebra. The tests identify weaknesses in particular skills and sub-skills. They receive remedial materials based on the sub-skill not mastered and cannot move on to the next skill unless they pass a final test with a score of 100%. These tests include problem solving using a particular math skill.

If the student applies himself, both their school and standardized test grades rise dramatically within a year.