The Bad and the Ugly #1

rectangle mathematical misinformationI thought I should share some of the things that surprise or enrage me. Clearly, I'm thinking here of mathematical strategies or resources that reinforce errors, not political, ethical or world issues.

Take, for example, the mathematical misconception that a square is somehow not a rectangle. In many quarters this is a very strongly held idea. An idea, that (by any mathematical definition) is wrong. However, it's easy to see how this error is reinforced...

Here's a poster spotted in a school only a few days ago:

bad, bad poster

Obviously, from the information presented here, a square could never be part of the set of objects we call rectangles! Bad, bad poster.

I didn't scream, or tear it down (yes, that was my first thought), but I did discuss it with the teacher. It now takes pride of place as the first of our 'Bad and Ugly' items.

If you've spotted anything that is equally erroneous and annoying feel free to moan about it in the comment box below. I'd love to hear your thoughts.

18 Comments

Comment viewing options

Select your preferred way to display the comments and click "Save settings" to activate your changes.
yoyo123's picture

 at last!   I have been

 at last!   I have been screaming into the wilderness about squares/rectangles for ages!   my pet peeve is the misuse of =   3+2 = 5 +2 =7..   noooooo!
up
4 users have voted.
MaryGilmartin's picture

Hello all, I have just found

Hello all, I have just found this site and am so far very impressed by the resources I have seen and am looking forward to deciding which I will use first. I came onto this thread as someone who is new to teaching as I am well aware that in all probablility I will commit some howlers along the way. I came across the 'Bad and Ugly' page by accident but would love to find a section that clearly addressed misconceptions in an accessible and straight forward way.
up
2 users have voted.
johdu's picture

It's good to hear you are

It's good to hear you are enjoying the maths resources here. Thanks for the comments. The notion of addressing misonceptions in detail is useful, thanks for the suggestion - I'm sure it's something we will cover in the very near future. Cheers.
up
0 users have voted.
Pjyale44's picture

Does anyone use the word

Does anyone use the word oblong these days is it a correct mathematical term for a 2D shape with two straight long sides and two straight shorter sides.
up
0 users have voted.
johdu's picture

 Yes, 'oblong' is still a

 Yes, 'oblong' is still a useful term - it describes any none-square rectangle... but I agree, it does have a very archaic feel to it.
up
0 users have voted.
Pjyale44's picture

Thanks for that reassurance.

Thanks for that reassurance. I do sometimes use the word oblong with my year 1's because that's the word I was taught but always feel it is old fashioned and not PC!
up
1 user has voted.
Jherek's picture

First proper maths lesson for

First proper maths lesson for the last 3 years in year 3: This is a square. It is also a rectangle. This is a cube. It has 6 FACES.
up
0 users have voted.
johdu's picture

Thanks for the comment,

Thanks for the comment, That's a good one - a cube has FACES! Earlier this week spotted Mickey Mouse (who should know better) talking about a pyramid having triangular sides... ;-/  
up
0 users have voted.
Tina09's picture

And another identical one

And another identical one again today...
up
0 users have voted.
johdu's picture

Yeah, they're like metal

Yeah, they're like metal coathangers - you find one, you find dozens. Thanks for your continued vigilance, with everyone's help we will clean-up mathematics teaching ;-)  
up
0 users have voted.
Tina09's picture

Arrrgh... I saw this one on a

Arrrgh... I saw this one on a school walk around today. If I get the job I'll mention it!
up
0 users have voted.
johdu's picture

Yes, better wait until after

Yes, better wait until after the interview ... good luck!
up
0 users have voted.
Keamac's picture

I have always taught my

I have always taught my students that square is a rectangle and it frustrates me when I hear others say it is not. Mind you, I have discovered that many teachers (and parents) are not aware that both are in fact rectangles, or the reason why this is so.
up
0 users have voted.
bubbles13's picture

I heard a teacher once say

I heard a teacher once say that any round shape was a sphere...therefore the squashed mango was a sphere. Also that a pentagon must have 5 sides the same size.
up
0 users have voted.
Tina09's picture

Using 'sum' for any kind of

Using 'sum' for any kind of maths prob... grrrr.
up
5 users have voted.
johdu's picture

Yep, I couldn't agree more...

Yep, I couldn't agree more... an irritating yet fantastic way to reinforce a dozen misconceptions, and a complete shortcircuit of the logic of mathematical language. It never happens to 'Product' does it?!
up
0 users have voted.
beckakate's picture

"Upside down triangle" I

"Upside down triangle" I teach in the K-2 area and get annoyed when I hear teachers and subsequently students referred to a triangle that has been flipped from the standard representation of ie /\ -> \/as an upside down triangle. We don't call a flipped rectangle etc an upside down....!
up
1 user has voted.
johdu's picture

Yes, thanks. A great

Yes, thanks. A great addition: "upside down triangle", I love it! Its a shame that many published posters and resources always show 2d shapes sitting on a base line... leads to all sort of awkward misconceptions. A related consequence is the "tilted square" for a square that's not sitting on a baseline - its a square!  
up
1 user has voted.