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! guided tour
001 Differentiation
002 'Real' maths
003 Fractions
004 Manipulatives
005 Assessment
006 What technology?
007 Adult curriculum
008 Reflective Learners
009 Engagement
010 Class Time Use
011 Why I hate maths
012 Terminology
013 'Mathphobia'
014 The Nature of Maths
015 Show and Tell
016 Vertical Integration
017 Product to Process
018 Investigation Length
019 Preparation for Work
020 Success in Mathematics
021 Groupwork
022 Effective lessons
023 Impact of ICT
024 Mathematics Websites
028 Why under 16?
2010.07.15 Differentiation
2010.07.19 Differentiation (2)
2010.07.22 'Real' maths
2010.07.26 'Real' maths (2)
2010.07.29 Fractions
2010.08.02 Fractions (2)
2010.08.05 Manipulatives
2010.08.09 Manipulatives (2)
2010.08.12 Assessment
2010.08.16 Assessment (2)
2010.08.19 What tech?
2010.08.23 What tech? (2)
2010.08.26 Adult maths
2010.08.30 Adult maths (2)
2010.09.02 Reflective learner
2010.09.06 Reflective learner 2
2010.09.09 Engagement
2010.09.13 Engagement 2
2010.09.16 Class Time Use
2010.09.20 Class Time Use 2
2010.09.23 Why I hate maths
2010.09.27 Why I hate math 2
2010.09.30 Terminology
2010.10.04 Terminology 2
2010.10.07 'Mathphobia'
2010.10.11 'Mathphobia' (2)
2010.10.14 Nature of Maths
2010.10.18 Nature of Maths (2)
2010.10.21 Show and Tell
2010.10.25 Show and Tell (2)
2010.10.28 Vertical Integration
2010.11.01 Vertical Integratn 2
2010.11.04 Product to Process
2010.11.08 Product to Proc. 2
2010.11.11 Investigation length
2010.11.15 Investigation leng 2
2010.11.18 Prepn for work
2010.11.22 Prepn for work 2
2010.11.25 Success in Maths
2010.12.03 Groupwork
2010.12.06 Groupwork 2
2010.12.10 Effective lessons
2010.12.13 Effective Lesson 2
2010.12.17 Impact of ICT
2010.12.20 Impact of ICT 2
2010.12.24 Maths Websites
2011.01.03 Maths Website 2
2011.01.07 Ideal curriculum
2011.01.10 Ideal curriculum 2
2011.01.14 Short or longterm
2011.01.17 Short or longterm2
2011.01.21 Continuing PD
2011.01.24 Continuing PD 2
2011.01.28 Why under 16?
2011.01.31 Why under 16? (2)
2011.02.04 Which is more fun?
2011.02.11 Blended learning
2011.02.14 Blended learning 2
2011.02.18 Fast tracking
2011.02.21 Fast tracking (2)
2011.02.25 Misconceptions
2011.02.28 Misconceptions 2
2011.03.04 Good Reads
2011.03.07 Good Reads (2)
2011.03.11 How do I  fractions
2011.03.18 How do I  lang
2011.03.21 How do I  lang (2)
2011.03.25 How do I  curric
2011.03.28 How do I  curric 2
2011.04.01 How?  next topic
2011.04.04 How?  nxt topic 2
2011.04.08 How?  Geometry
2011.04.11 How?  Geom 2
2011.04.15 How?Investigation
2011.04.18 How?Investigatn 2
2011.04.22 How? Do vs. learn
2011.04.25 How?Do vs learn 2
2011.04.29 How?Dig deeper
2011.05.02 How?Dig deeper 2
2011.05.06 'Big Ideas'
2011.05.09 'Big Ideas' (2)
2011.05.13 High school skill
2011.05.16 High school skill 2
2011.05.20 Journals
2011.05.23 Journals (2)
2011.05.27 Studentdriven
2011.05.30 Studentdriven (2)
2011.06.03 How?  Maths play
2011.06.06 How?Maths play 2
2011.06.10 Deeper thinking
2011.06.13 Deeper thinking (2)
2011.06.17 How?  Disjointed
2011.06.17 How?  Disjointed 2
2011.06.24 How?  Problems
2011.06.27 How?  Problems 2
2011.07.01 Holiday maths
2011.10.28 Extent of plans
2011.10.31 Extent of plans (2)
2011.11.04 Authentic is..?
2011.11.07 Authentic is..? (2)
Z_1 Thursday raw
Z_2 Monday raw
Z_consolidated
2011.02.28 Misconceptions 2
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Topic (followup to Friday, 25th February 2011):
What misconceptions are most common in mathematics?
As it happened on
Monday, 28th February 2011, 20:30  22:00 GMT
8:32 pm
ColinTGraham
:
Hello everyone and welcome to today's #
mathchat
8:33 pm
ColinTGraham
:
The topic is: "What misconceptions are most common in mathematics?" For newcomers, don't forget the hashtag > #
mathchat
8:33 pm
harrysarms
:
#
mathchat
i am a grade 11 math student and am looking for examples of arithmetic or geometric sequences in real life?
8:34 pm
dweksler
:
@
harrysarms
Glad to have students join in and ask questions during today's mathchat :) #
mathchat
8:35 pm
ColinTGraham
:
@
harrysarms
Hi Harry, some examples of arithmetic sequences were put out earlier today on #
mathchat
8:35 pm
dweksler
:
@
harrysarms
Any guesses where to look to answer your question, Harry? #
mathchat
8:38 pm
ColinTGraham
:
David started us off with this misconception, any others to add? RT @
dweksler
: That a number bigger than infinity is (infinity +1) #
mathchat
8:38 pm
dweksler
:
#
mathchat
So, I'm sort of thinking of what things may grow in number over time  maybe a couple of rabbits, boy and girl?
8:40 pm
dweksler
:
@
ColinTGraham
Thinking that misconception is a possible answer from a 6 year old as they like to ask the question :) #
mathchat
8:40 pm
ColinTGraham
:
Things which I've always seen are related to fraction manipulations and exponents: 1/2 + 1/3 = 1/5 or 1/(2^x) = 2^(1/x) #
mathchat
8:41 pm
ColinTGraham
:
@
dweksler
Yes, I think I mentioned in last's week discussion of this that misconceptions are part of learning... #
mathchat
8:41 pm
dweksler
:
@
ColinTGraham
I most certainly AGREE with that! #
mathchat
8:43 pm
ColinTGraham
:
The value for us is to try and be aware of what the misconceptions are, & the best way of addressing them... algorithms confuse! #
mathchat
8:44 pm
bucharesttutor
:
RT @
ColinTGraham
: Things which I've always seen are related to fraction manipulations and exponents: 1/2 + 1/3 = 1/5 or 1/(2^x) = 2^(1/x) #
mathchat
8:45 pm
EarlSamuelson
:
division by zero equals zero & that reliance on memorization as opposed to understanding through reasoning constitutes "learning" #
mathchat
8:45 pm
ColinTGraham
:
@
dweksler
Your example of growth is a good example of confusion between arithmetic and geometric sequence... #
mathchat
8:45 pm
bucharesttutor
:
One misconception I was asked by my 4th grader, why is 1/2+1/2= 1 whole and why not 1/4 #
mathchat
8:46 pm
dweksler
:
@
bucharesttutor
What happens when you take two halves of an orange or apple and hold the cut sides facing each other? #
mathchat
8:47 pm
ColinTGraham
:
@
earlsamuelson
I think the 'need' for everything to have a defined value or place is difficult for many people to 'get over' #
mathchat
8:48 pm
bucharesttutor
:
Why is any number raised to the power of 0 equal to 1? Actually I need a specific answer pls #
mathchat
8:48 pm
ColinTGraham
:
@
bucharesttutor
That's best explored graphically... #
mathchat
8:49 pm
chris_1974
:
@
bucharesttutor
what about 0^0. That's when it gets interesting.Use indexlaws. 3^0 = 3^(22) = (3^2)/(3^2) = 9/9 = 1 #
mathchat
8:50 pm
ColinTGraham
:
@
bucharesttutor
You can also show: 1/2 * 1/2 = 1/4, by cutting one of the halves in half... to show 1/4 can be an answer, but to * #
mathchat
8:52 pm
bucharesttutor
:
@
chris_1974
frankly speaking 0 to power of 0 is undefined as per my knowledge #
mathchat
8:53 pm
chris_1974
:
@
bucharesttutor
yes  but its a *great* question to ask studetns #
mathchat
8:53 pm
ColinTGraham
:
@
chris_1974
So this suggests that you need to have explored index laws before you can explore the zero exponent... #
mathchat
8:53 pm
chris_1974
:
@
chris_1974
once they realise 0^n = 0, and n^0=1, it is a real curve ball. #
mathchat
8:54 pm
chris_1974
:
@
ColinTGraham
I do. Index laws for +ve integer powers, then to 0, and ve powers via division. #
mathchat
8:54 pm
EarlSamuelson
:
@
ColinTGraham
I attempt to connect algebraic representations to geometric whenever possible and make justifictions from there #
mathchat
8:54 pm
chris_1974
:
@
bucharesttutor
once they realise 0^n = 0, and n^0=1, it is a real curve ball. #
mathchat
8:55 pm
bucharesttutor
:
@
chris_1974
yes I did ask this question to a 9th grader and the answer was 0 #
mathchat
8:55 pm
ColinTGraham
:
Many misconceptions come from overgeneralizing 'facts' eg 2+2=4 becomes 1/2+1/2=1/4 (or 2/4!!) #
mathchat
8:56 pm
chris_1974
:
@
bucharesttutor
which begs the question, why not 1? #
mathchat
8:56 pm
ColinTGraham
:
@
earlsamuelson
I agree with that approach. There are a lot of misconceptions due to disconnects, and geometry is not done enough! #
mathchat
8:56 pm
dweksler
:
@
ColinTGraham
Is it fair to make the comparison with "M" and "W"  same shape but different orientation? #
mathchat
8:56 pm
bucharesttutor
:
Another problem I have seen is that students don't know whether there exists answers such as "undefined" or "meaningless" #
mathchat
8:56 pm
Janshs
:
@
chris_1974
what's the #
mathchat
topic/theme this eve?
8:57 pm
ColinTGraham
:
@
Janshs
Common misconceptions in mathematics, Jan #
mathchat
8:57 pm
chris_1974
:
@
Janshs
I think its common misconceptions in maths #
mathchat
8:58 pm
ruth4916
:
x^2 is not equal to (x)^2. Repeat,repeat,repeat...#
mathchat
8:58 pm
Janshs
:
@
chris_1974
aha! I have trouble some times convincing that root 2 times root 2 = 2 etc #
mathchat
8:59 pm
ColinTGraham
:
@
dweksler
Possibly, spatial awareness is another issue where problems result. Turn fractions upsidedown and multiply to divide?? #
mathchat
8:59 pm
EarlSamuelson
:
@
chris_1974
do they realize that n^5=>5 extra factors of n on top and that n^5=>5 extras on bottom;then n^0 => equal # top/bot #
mathchat
8:59 pm
bucharesttutor
:
@
ruth4916
the placing of the bracket could be very important here #
mathchat
9:00 pm
chris_1974
:
@
earlsamuelson
yes  fairly quickly. I get them to do it long hand a few times. They soon work it out! #
mathchat
9:00 pm
ColinTGraham
:
@
ruth4916
Order of operations is the keypoint here, in the absence of parentheses... #
mathchat
9:01 pm
EarlSamuelson
:
@
ColinTGraham
I agree completely....geometry is VERY powerful.......knowledge of it can put learners in a very solid position #
mathchat
9:02 pm
ColinTGraham
:
If overgeneralization is 1 source of misconceptions/error (as in language learning), does the order we introduce topics impact 2? #
mathchat
9:02 pm
EarlSamuelson
:
@
chris_1974
I think that's very effective.....graphing of such things can also be effective.....negative exponent is a reflection #
mathchat
9:02 pm
bucharesttutor
:
Another question by my S's, what is infinity/infinity, is it 1, is it undefined etc. #
mathchat
9:03 pm
chris_1974
:
@
earlsamuelson
agreed, also relating 2^(x) and (1/2)^x #
mathchat
9:05 pm
chris_1974
:
@
bucharesttutor
I'd want to to ask the question, what is infinity #
mathchat
#
gettingphilosophicallydeepnow
9:05 pm
EarlSamuelson
:
@
chris_1974
Yes!!! very powerful..... #
mathchat
9:06 pm
ColinTGraham
:
@
bucharesttutor
Any discussion around zero, infinity and other concepts is bound to be useful. Not enough discussion happens #
mathchat
9:06 pm
bucharesttutor
:
@
chris_1974
they may actually just reply Infinity is a very large number #
mathchat
9:08 pm
bucharesttutor
:
@
ColinTGraham
sorry can you be a little clearer about that? #
mathchat
9:09 pm
EarlSamuelson
:
@
bucharesttutor
are you referring to limits at infinity?.....might be a good place to introduce that #
mathchat
9:10 pm
ColinTGraham
:
Does the order we introduce topics impact on misconception? Should we leave exceptions zero, infinity, etc. until later? #
mathchat
9:11 pm
ColinTGraham
:
@
bucharesttutor
By discussion, I mean exploring the concept in more detail with Ss, especially when they raise the question #
mathchat
9:11 pm
ColinTGraham
:
@
bucharesttutor
Lessconfident teachers will use the "because it is" or "that's the rule" instead of discussing the "why" #
mathchat
9:12 pm
EarlSamuelson
:
@
ColinTGraham
I think if we open up a "can of worms", we need to be prepared to deal with the fallout out right then and there #
mathchat
9:12 pm
bucharesttutor
:
@
EarlSamuelson
exactly we face that scenario in limits but S's turn a blank face when faced with infinity and its kind #
mathchat
9:13 pm
ColinTGraham
:
@
earlsamuelson
Which comes back to identifying what "worms" are going to jump out of the "can"... if it's preplanned! #
mathchat
9:14 pm
EarlSamuelson
:
@
ColinTGraham
@
bucharesttutor
we need to be prepared to discuss why at any time if the topic comes up.......that's teaching #
mathchat
9:15 pm
EarlSamuelson
:
@
ColinTGraham
we need to be prepared for all cases........that's part of what makes teaching challenging and fun; anticipate #
mathchat
9:16 pm
ColinTGraham
:
What 'offthewall' activities do you use, or have you used, to point up misconceptions or explore a new area which is a minefield #
mathchat
9:16 pm
bucharesttutor
:
@
EarlSamuelson
@
ColinTGraham
agreed, we need to be proactive. In my case I'd start with limits, continuity, Calculus in that order #
mathchat
9:18 pm
mathsatschool
:
Joining in for a bit with my common misconceptions #
mathchat
. xaxis is x=0, y axis y=0.
9:19 pm
mathsatschool
:
double the sides = double the area / volume #
mathchat
misconceptions
9:19 pm
ColinTGraham
:
@
mathsatschool
So good luck with the z axis... #
mathchat
9:19 pm
bucharesttutor
:
@
ColinTGraham
I have never tried any out of the book theories to teach my Ss Math as I believe in keeping them simple n straight #
mathchat
9:20 pm
mathsatschool
:
All probs equally likely (and I was guilty of repeating this aged 12). "It's either raining or it's not!!" #
mathchat
misconceptions
9:20 pm
chris_1974
:
@
mathsatschool
i watched a collegue squirm recently, was trying to do bog standard enlargement with lowish set... #
mathchat
9:21 pm
ColinTGraham
:
@
bucharesttutor
Do you tend to rely on the same or similar approaches or do you mix things up Vijay? #
mathchat
9:21 pm
chris_1974
:
@
mathsatschool
comment from student was "its twice as long and wide but you can get 4 of them inside so its 4x bigger". #
mathchat
9:22 pm
ColinTGraham
:
@
mathsatschool
Statistics and Probability is probably a misconception in its own right! (says the statistician in me!) #
mathchat
9:23 pm
mathsatschool
:
A square is not a rectangle? #
mathchat
misconceptions And a square on its side is not a square, but a diamond!! (Bugbear of mine)
9:23 pm
bucharesttutor
:
@
ColinTGraham
I tend to more or less rely on the same approach but I vary the pace as per the students understanding #
mathchat
9:23 pm
ColinTGraham
:
@
chris_1974
Well if "it" was the area... ok. If "it" was the scale of enlargement... oops! #
mathchat
9:24 pm
chris_1974
:
@
mathsatschool
my fave question to sort out square's and rectangles is "Find 2 rectangles where P=A "(numerically) #
mathchat
9:24 pm
mathsatschool
:
Very common one  3.456>3.87 (for example) #
mathchat
misconceptions
9:24 pm
chris_1974
:
@
mathsatschool
have you come across the "sqaure of area 10" investigation. Sorts out "diamonds" too. #
mathchat
9:24 pm
ColinTGraham
:
@
mathsatschool
Once you get them to talk about rectangles instead of oblongs and ellipses instead of ovals... #
mathchat
9:25 pm
chris_1974
:
yup. RT @
mathsatschool
: Very common one  3.456>3.87 (for example) #
mathchat
misconceptions
9:26 pm
mathsatschool
:
@
chris_1974
Not familiar with that one. Possibly post it? #
mathchat
9:26 pm
ColinTGraham
:
@
bucharesttutor
Are there misconceptions or questions which you find it difficult to respond to? #
mathchat
9:26 pm
ash_eng
:
#
mathchat
another one that always makes me want to bang my head off the whiteboard is (x+y)^2 = x^2+y^2 @
mathsatschool
9:26 pm
TeaKayB
:
#
mathchat
misconceptions: "It looks like the same angle/length so it is."
9:26 pm
bucharesttutor
:
@
chris_1974
never seen this misconception although I guess I anticipate this in the near future lol #
mathchat
9:26 pm
mathsatschool
:
How about 'add a zero' for multiplying by 10! #
mathchat
misconceptions
9:27 pm
dotsmy
:
AMEN TO THAT! RT @
chris_1974
: @
chris_1974
once they realise 0^n = 0, and n^0=1, it is a real curve ball. #
mathchat
9:28 pm
mathsatschool
:
Or 1/3 = 0.3, 1/7 = 0.7 or even 1.7? #
mathchat
misconceptions
9:28 pm
chris_1974
:
@
mathsatschool
I'll write it up on my blog. May not be tonight, so feel free to subscibe (about to add subscribe box). #
mathchat
9:28 pm
ColinTGraham
:
Algorithmic subtraction... carry/borrow 1, instead of 10, 100, 1000 etc... #
mathchat
9:29 pm
bucharesttutor
:
@
ColinTGraham
yes some questions like what's the diff between a square n rhombus, I know the answer but not rightaway #
mathchat
9:29 pm
mathsatschool
:
@
ash_eng
Always! Have modular exam tomorrow and am STILL seeing it this end of y11! #
mathchat
misconceptions
9:29 pm
chris_1974
:
Can i apologise now for @
dotsmy
crashing #
mathchat
!
9:30 pm
ColinTGraham
:
@
bucharesttutor
Well, technically a square is also a rhombus... best to have a set of activities for classifying quadrilaterals #
mathchat
9:30 pm
bucharesttutor
:
Another question I was asked recently, why is 1 not a prime number? #
mathchat
9:30 pm
emth
:
Misconception: to convert a decimal into a percent, multiply by 100. #
mathchat
9:30 pm
mathsatschool
:
Not really a misconception but 'difference'? Well one's odd and one's even, one has a curve in the number, one has 3 digits..... #
mathchat
9:30 pm
ColinTGraham
:
She's a big girl, she can apologize for herself if she feels the need! RT @
chris_1974
: Can i apologise now for @
dotsmy
crashing #
mathchat
!
9:32 pm
ColinTGraham
:
@
bucharesttutor
Because of the way prime numbers are defined, they have exactly two factors 1 and themselves. 1 only has 1 factor. #
mathchat
9:32 pm
bucharesttutor
:
@
ColinTGraham
can you mail me some quadilaterals activities stuff? #
mathchat
9:32 pm
mathsatschool
:
how about a= 1, b=2, c=3, etc. Or n+1 MUST mean o (or 'm' as I got today!  y11 again...) #
mathchat
misconceptions
9:33 pm
EarlSamuelson
:
@
ColinTGraham
regarding algorithmic addition/subtraction......have a look at this
http://t.co/tpdAw9D
#
mathchat
9:33 pm
ColinTGraham
:
@
emth
Related is increased by 200% means two times bigger... percentages are another 'sticky' area... fractions again! #
mathchat
9:35 pm
dotsmy
:
@
ColinTGraham
"She" doesn't.(PS Get @
chris_1974
to tell you the one about 0.9 recurring being the same as 1. That's my favourite. #
mathchat
)
9:35 pm
mathsatschool
:
No difference between bars touching / bars separate (to be fair, most adults don't understand this too inc.scientists) #
mathchat
misconcept
9:35 pm
ColinTGraham
:
@
bucharesttutor
My Library tagged quadrilaterals
http://bit.ly/if0h6Q
these two sites are good starting points... #
mathchat
9:35 pm
bucharesttutor
:
Another troubled area for Ss, addition n subtraction of unlike fractions #
mathchat
9:36 pm
ColinTGraham
:
@
mathsatschool
Good luck on the 7,3,19,5 then... #
mathchat
9:36 pm
mathsatschool
:
Misconception #
mathchat
multiplying always makes the answer bigger, dividing smaller?
9:37 pm
chris_1974
:
#
mathchat
@
dotsmy
makes a good point with his 0.99... If a line is measured as 5 cm (neartest cm) why is 5.5 the upper bound, not 5.49999...
9:37 pm
mathsatschool
:
I could be thinking of these when all #
mathchat
tweeps have gone to bed! They keep appearing in my head!
9:38 pm
chris_1974
:
obv I know the answer, but students don;t always get it. #
mathchat
9:38 pm
chris_1974
:
@
mathsatschool
this is where a fun little "Always Sometimes Never" lesson leaps to mind. #
mathchat
9:38 pm
mathsatschool
:
And I say the main solution is to preempt them. Prepare for them coming in advance. Make a list. Share with others. As we are :) #
mathchat
9:39 pm
chris_1974
:
3 am job! RT @
mathsatschool
: I could be thinking of these when all #
mathchat
tweeps have gone to bed! They keep appearing in my head!
9:40 pm
ColinTGraham
:
@
mathsatschool
The key point may be to make a list... with appropriate teaching strategies/approaches. Hasn't someone done this? #
mathchat
9:40 pm
bucharesttutor
:
@
mathsatschool
yes we must try compiling all the misconceptions n then offer possible answers #
mathchat
9:41 pm
emth
:
#
mathchat
#
misconception
x * x = 2x
9:41 pm
mathsatschool
:
@
ColinTGraham
I don't know. Would be useful to find out. We could gdocs a list but not reinvent the wheel! #
mathchat
misconceptions
9:41 pm
bucharesttutor
:
This is an evergreen classic lol RT @
emth
: #
mathchat
#
misconception
x * x = 2x
9:44 pm
ColinTGraham
:
Does separation of topics or introduction of information 'piecemeal' compound things? What role do open investigations play? #
mathchat
9:44 pm
mathsatschool
:
Well count me in. #
mathchat
9:44 pm
EarlSamuelson
:
@
emth
very good point #
mathchat
9:44 pm
chris_1974
:
@
ColinTGraham
@
mathsatschool
could we create a similar to movemeon? # Tag collated by twapperkeeper, then edited to book. #
mathchat
9:44 pm
emth
:
#
mathchat
#
misconception
(10n)^2 = 100n^2 implies (10^n)^2 = 100^(2n) or 100^(n^2)
9:45 pm
ColinTGraham
:
@
chris_1974
That's what I was thinking, but using more than one archive solution... TwapperKeeper's been a bit iffy of late :s #
mathchat
9:45 pm
mathsatschool
:
Will stop with adding random misconception thoughts for now. #
mathchat
. Still work to do. (Unless I get itchy and really MUST add!) Lol
9:46 pm
emth
:
I would love to share these conversations with my colleagues in university! I will plan a presentation for tomorrow! #
mathchat
9:46 pm
EarlSamuelson
:
@
ColinTGraham
I think it CAN compound problems if care is not taken..... #
mathchat
9:47 pm
ColinTGraham
:
@
chris_1974
I was thinking #
mathmis
fewer characters... @
mathsatschool
#
mathchat
9:47 pm
chris_1974
:
@
ColinTGraham
works for me #
mathmis
#
mathchat
9:48 pm
ColinTGraham
:
Anyway, I'll set something up and tweet it out... the more nonmaths teachers who tweet, the merrier! #
mathmis
#
mathchat
9:49 pm
bucharesttutor
:
Anyway the bottom line is, it wd be wonderful for the all of us to get a copy of the Math misconception in one roof #
mathchat
9:49 pm
ColinTGraham
:
@
earlsamuelson
At what stages or with which topics is care especially needed, do you think, Earl? #
mathchat
9:49 pm
mathsatschool
:
@
chris_1974
@
ColinTGraham
Cool. and 'mis' implies mistakes OR misconceptions (as different entities....) #
mathchat
(with hashtag!)
9:50 pm
bucharesttutor
:
RT @
ColinTGraham
: Anyway, I'll set something up and tweet it out... the more nonmaths teachers who tweet, the merrier! #
mathmis
#
mathchat
9:52 pm
EarlSamuelson
:
@
ColinTGraham
oh boy!!!! That's a loaded question......there are so many areas that we can botch up when introducing #
mathchat
9:53 pm
emth
:
Handling #
misconceptions
: drill and practice! Hate me if you want, but it certainly plays a role. #
mathchat
9:53 pm
bucharesttutor
:
Teach the basics very well, grill them in their minds by surely making them work harder n practice more n more #
mathchat
9:53 pm
chris_1974
:
being aware of misconceptions they are likely to see  the most common ones for a starter. plan for it. #
mathchat
9:53 pm
EarlSamuelson
:
@
ColinTGraham
I think care needs to be taken at all times when attempting to instill thoughtful insights into math #
mathchat
9:54 pm
EarlSamuelson
:
@
bucharesttutor
I agree with that.......anticipate problem areas and be proactive #
mathchat
9:54 pm
ColinTGraham
:
How about "spot the mistake" where students have to identify the misconceptions (if they can!) #
mathchat
9:55 pm
emth
:
Teachers should make every effort to be aware of and understand the faulty logic behind #
misconceptions
. #
mathchat
(like now!)
9:56 pm
ColinTGraham
:
@
emth
What role does exploration play in the practice, or is it repetition of a 'set of procedures'? #
mathchat
9:56 pm
EarlSamuelson
:
@
ColinTGraham
that's a good approach......makes the students think more deeply #
mathchat
9:57 pm
GrampsyPete
:
RT @
emth
: Teachers should make every effort to be aware of and understand the faulty logic behind #
misconceptions
. #
mathchat
(like now!)
9:57 pm
emth
:
@
ColinTGraham
my students hated "spot the mistake" problems  a sure sign that they exercise the mind in just the right way! #
mathchat
9:57 pm
bucharesttutor
:
@
ColinTGraham
spot the mistake would be slightly asking for more as they need to know "concepts" b4 they know the misconception #
mathchat
9:58 pm
mathsatschool
:
@
ColinTGraham
ha! Just got the gcse reference. #
mathchat
#
notslowhonestguv
9:58 pm
ColinTGraham
:
@
emth
@
bucharesttutor
It can be a good diagnostic tool where students don't/can't see the misconception, though #
mathchat
9:58 pm
emth
:
@
ColinTGraham
I'm definitely a fan of inquiry/discovery, but motivating my students I find to be the hard part. #
mathchat
9:59 pm
ColinTGraham
:
@
mathsatschool
Codebreaker extraordinaire...! :P #
mathchat
#
notslowhonestguv
9:59 pm
ColinTGraham
:
@
emth
What age group are you dealing with Jared? #
mathchat
10:00 pm
emth
:
@
ColinTGraham
I just completed my internship and worked mostly with grade 10 students. #
mathchat
10:00 pm
ColinTGraham
:
OK thanks everyone for another lively and entertaining #
mathchat
10:01 pm
suburbanlion
:
@
ColinTGraham
I like the "spot the mistake" idea. I might have to try that! #
mathchat
10:01 pm
ColinTGraham
:
Thursday is World Book Day, so we'll be discussing recommended reading either for mathematics or teaching (or a break from both) #
mathchat
10:02 pm
EarlSamuelson
:
@
ColinTGraham
Thank yo Colin et.al..........that was very fulfilling #
mathchat
10:02 pm
bucharesttutor
:
@
ColinTGraham
agreed a diagnostic approach sounds pretty exciting #
mathchat
. Challenging Ss with misconception is worth a try.
10:03 pm
chris_1974
:
which reminds me  I'm taking my copy of "The man who counted" in to school to read to some classes on Thursday. #
mathchat
#
worldbookday
10:03 pm
emth
:
Thanks, glad I could catch the end! #
mathchat
10:03 pm
bucharesttutor
:
Thanks everyone for a wonderful n insightful #
mathchat
. Have a good one people :)
10:04 pm
ColinTGraham
:
From 10th March, we'll be trying the "How do I teach..." focused on more specific topics. Please add ideas:
http://bit.ly/aOhxOU
#
mathchat
10:05 pm
ColinTGraham
:
Don't forget to follow @
mathchat
to keep up to date with changes. Archive will be online shortly, I hope... #
mathchat
10:05 pm
ColinTGraham
:
@
bucharesttutor
Thanks, Vijay have a good night! #
mathchat
10:06 pm
chris_1974
:
I've just posted "Square of Area 10" in repsonse to tonights #
mathchat
& @
mathsatschool
.
http://bit.ly/fpNFg5
10:07 pm
ColinTGraham
:
@
emth
By that stage, you're fighting against 10 years of 'established' methods. Ss r more likely to question purpose of 'new' ways #
mathchat
10:07 pm
ColinTGraham
:
@
chris_1974
Ooh, Mr Instablog! #
mathchat
10:08 pm
mathsatschool
:
Thank You. RT @
chris_1974
I've just posted "Square of Area 10" in repsonse to tonights #
mathchat
& @
mathsatschool
.
http://bit.ly/fpNFg5
10:08 pm
bucharesttutor
:
@
ColinTGraham
Thanks again Colin for this wonderful #
mathchat
. Good Night to you as well.
10:09 pm
emth
:
@
ColinTGraham
Yes, luckily we have gone through quite a curricular reform in Sask. and inquiry is now central to the objectives. #
mathchat
10:17 pm
chris_1974
:
@
ColinTGraham
for me it's a good way of archiving ideas, and sharing them. #
mathchat
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What misconceptions are most common in mathematics?
As it happened on Monday, 28th February 2011, 20:30  22:00 GMT