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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
2010.11.08 Product to Proc. 2
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Topic (followup to Thursday, 4th November 2010):
Does the mathematics curriculum need to be designed much more towards process rather than product?
As it happened on
Monday, 8th November 2010, 19:30  21:00 GMT
7:33 pm
ColinTGraham
:
Hello and welcome to today's #
mathchat
7:34 pm
ColinTGraham
:
If it's your first time, don't try to follow everything, but interact with one or two people. Don't forget the hashtag > #
mathchat
7:34 pm
ColinTGraham
:
Today's topic is: Does the mathematics curriculum need to be designed much more towards process rather than product? #
mathchat
7:35 pm
ColinTGraham
:
Let's start as we did on Thursday by defining what we mean by 'product' and 'process' here #
mathchat
7:36 pm
carneysandoe
:
RT @
ColinTGraham
: 2day's topic: Does the mathematics curriculum need 2 B designed much more towards process rather than product? #
mathchat
7:41 pm
ColinTGraham
:
Any takers today? #
mathchat
7:44 pm
john_at_muuua
:
as an English interloper i'm on tenterhooks waiting to see how maths does it. am i missing something? #
mathchat
7:46 pm
rodaniel
:
By product do we mean the resulting work that students/teacher produce from an interaction with content, regardless of process? #
mathchat
7:46 pm
ColinTGraham
:
@
john_at_muuua
I'm not sure maths does it, any more than any other subject, John. The question is can more process be introduced #
mathchat
7:47 pm
millerblair
:
@
ColinTGraham
Would love to join you, but only 5 minutes of lunch left. #
mathchat
7:48 pm
rodaniel
:
By process are talking about the thinking/discourse/protocols/steps that students/teachers use to get to the desired result? #
mathchat
7:48 pm
john_at_muuua
:
@
ColinTGraham
see from my perspective the process is the key element. The journey not the destination. Is that the same for #
mathchat
?
7:49 pm
ColinTGraham
:
@
rodaniel
That would be one definition Roland. The next step is what happens to the result  an end or a step in the process #
mathchat
7:50 pm
rodaniel
:
Well said @
ColinTGraham
! but would most of our students identify the process as the important issue or the answer? #
mathchat
7:50 pm
ColinTGraham
:
@
john_at_muuua
Why do you see process as key? Is it not the application of the correct process... #
mathchat
7:52 pm
ColinTGraham
:
Where does content figure in this? Clearly product is an end of some kind and process is some kind of progression from A to B (Z) #
mathchat
7:52 pm
john_at_muuua
:
we see the curriculum as a spiral, continually enhancing the process, with the product not being a terminal result...#
mathchat
7:54 pm
john_at_muuua
:
4 example, writing a desc. That may B the product, but difft students & abilities will produce it using difft qualities & methods #
mathchat
7:54 pm
rodaniel
:
isn't part of the 'process' learning to apply processes efficiently/effectively? w/out focus on product then how do we evaluate? #
mathchat
7:55 pm
john_at_muuua
:
a 10 year old may not use competent analogy and cultural reference, but will still produce the product of a description.#
mathchat
7:55 pm
ColinTGraham
:
@
rodaniel
That is the underlying challenge, maybe, that there is too much emphasis on answer (product) rather than how you got it #
mathchat
7:55 pm
rodaniel
:
@
john_at_muuua
don't new standards allow us to move away from the spiral? and move into learning to develop deep understanding #
mathchat
7:56 pm
ColinTGraham
:
@
john_at_muuua
But does the assessment of the description take into account the process or is it evaluated as a product alone? #
mathchat
7:56 pm
rodaniel
:
w/ new standards 1 process is perseverence, what does this look like if we only teach one process or all do it the same way? #
mathchat
7:57 pm
john_at_muuua
:
A lot of English assessment has different degrees of quality. for example punctuation #
mathchat
7:57 pm
ColinTGraham
:
@
rodaniel
New standards maybe relate to your local situation. The UK National Curriculum for maths was last updated in 1999 #
mathchat
7:58 pm
john_at_muuua
:
full stops, commas, semicolons, ellipsis, apostrophes... all are elements of the process #
mathchat
7:59 pm
rodaniel
:
LOL, great point @
ColinTGraham
#
mathchat
So does the issue of what does perseverence in problem solving look like apply to UK?
7:59 pm
Janshs
:
@
ColinTGraham
#
mathchat
is the product the exam result and the process the enjoyment? after all these yrs am inclined to say love comes 1st
8:00 pm
ColinTGraham
:
Bloom's taxonomy, cognitive development, etc. also need to be taken into account. Application, understanding, creation... #
mathchat
8:00 pm
rodaniel
:
@
john_at_muuua
I like that thinking John, how do we assess problem solving? I really like this line... #
mathchat
8:01 pm
ColinTGraham
:
@
rodaniel
UK curriculum allows for students to do investigations and assess their ability to communicate findings mathematically #
mathchat
8:02 pm
Janshs
:
@
ColinTGraham
creation is so great #
mathchat
and perhaps the most difficult ... or is it? maybe we need to get excited over small creations
8:02 pm
john_at_muuua
:
@
rodaniel
different problems for different abilities. no terminal product. #
mathchat
8:02 pm
ColinTGraham
:
@
Janshs
I'd like to think so, Jan, but process is often seen as "show your working" which is in itself just more applied knowledge #
mathchat
8:02 pm
rodaniel
:
TIMSS shows American students not good problem solvers, so process of perseverence in PS now a focus, but what does it look like? #
mathchat
8:03 pm
rodaniel
:
@
Janshs
I agree, let them create, and let it be OK to create little things and to make small steps!! #
mathchat
8:03 pm
ColinTGraham
:
@
rodaniel
The statistician in me also says: critical thinking about data presentation, designing effective experiments... #
mathchat
8:03 pm
Janshs
:
@
ColinTGraham
yes that show your working stuff grrrr have had such good stdts over the yrs who've said eg "but is 3xsquared Miss" #
mathchat
8:04 pm
john_at_muuua
:
@
ColinTGraham
what does 'show your working' mean? Is it assessed? #
mathchat
8:04 pm
john_at_muuua
:
making mistakes. Active thinking. These are all parts of the 'process' #
mathchat
8:05 pm
rodaniel
:
@
john_at_muuua
It is in Kentucky on our state assessment, but that assessment is in danger. Students have choice to show steps or #
mathchat
8:05 pm
ColinTGraham
:
@
john_at_muuua
Assessed, yes, in the mark scheme for exams, some of the marks are awarded for writing out certain steps to answer #
mathchat
8:06 pm
drwetzel
:
Read The #
teachmath
Daily ? today's top stories are contributed by @
drwetzel
and @
brokenairplane
?
http://t.co/CrFJ8Mx
#
mathchat
#
elemchat
8:06 pm
rodaniel
:
@
john_at_muuua
or they can write a description, as long as it can be followed. Very little rationale; mostly steps #
mathchat
8:06 pm
john_at_muuua
:
@
rodaniel
If a student produces something effective, does the process matter? #
mathchat
8:06 pm
ColinTGraham
:
@
john_at_muuua
Finding mistakes because you've checked your working is part of maths, but not the beall and endall #
mathchat
8:07 pm
rodaniel
:
@
john_at_muuua
I would argue YES, they haven't solved all of the worlds problems, yet have they? #
mathchat
8:08 pm
ColinTGraham
:
@
john_at_muuua
If it was copied or derived from another's work, it could still be effective... should that be allowed? #
mathchat
8:08 pm
rodaniel
:
and I would love it if they learned a process that they can apply later when the time is right, #
mathchat
8:09 pm
rodaniel
:
@
ColinTGraham
aren't they doing that everytime they solve a 2 step linear equation? #
mathchat
8:09 pm
john_at_muuua
:
@
ColinTGraham
is creativity part of maths? Copying from another student, NOT plaigarism can lead to interesting collaboration #
mathchat
8:10 pm
LesLinks
:
@
john_at_muuua
Maybe they did have a process, they are just not aware of it yet, and teacher is not either.. may need too teaseout #
mathchat
8:10 pm
ColinTGraham
:
@
rodaniel
That comes back to Bloom and understanding when to apply being higher level than being able to... #
mathchat
8:11 pm
ColinTGraham
:
@
john_at_muuua
Creativity in mathematics  over 50% of mathematics was created after 1945... using maths creatively something else #
mathchat
8:12 pm
ColinTGraham
:
@
LesLinks
Everyone has a process  either something learned or something that needs to be discovered. But how often do we compare #
mathchat
8:13 pm
ColinTGraham
:
@
rodaniel
The question is what is it allowable to reuse/plagiarise/derive from vs. what should be done from scratch? #
mathchat
8:13 pm
john_at_muuua
:
@
ColinTGraham
In contrast language was created...er... longer ago but still manages constant creativity. is the issue the product? #
mathchat
8:13 pm
rodaniel
:
Question for group, what processes are you currently using w/ students to create equations in problem solving or is it a focus? #
mathchat
8:14 pm
rodaniel
:
RT @
ColinTGraham
: @
rodaniel
The question is what is it allowable to reuse/plagiarise/derive from vs. what should be done from scratch? #
mathchat
8:14 pm
john_at_muuua
:
What exactly is a mathematical product? #
mathchat
8:15 pm
ColinTGraham
:
@
john_at_muuua
That comes back to my opening question, John! Most would probably see an answer as a product in maths #
mathchat
8:16 pm
ColinTGraham
:
@
rodaniel
I'd prefer to question with students whether or not creating equations is necessarily the most effective process to use #
mathchat
8:17 pm
rodaniel
:
@
john_at_muuua
I focus on having students create lots of products. I like having students solve multiple ways... #
mathchat
8:18 pm
rodaniel
:
... create problems that utilize multiple representations, include written descriptions of their thinking... #
mathchat
8:18 pm
LesLinks
:
@
ColinTGraham
Ya it is important to compare learned process with discovered or created process, as one might benefit fromthe other #
mathchat
8:18 pm
john_at_muuua
:
@
ColinTGraham
an answer with a definitive measurable terminal result. But what if it's not terminal or definitive? #
mathchat
8:18 pm
rodaniel
:
@
ColinTGraham
Valid, but is creating an equation ever a valid process? #
mathchat
8:19 pm
ColinTGraham
:
@
john_at_muuua
That's the kind of thing that makes a lot of people hate maths, because it doesn't provide the answer... #
mathchat
8:19 pm
john_at_muuua
:
@
rodaniel
nice thinking. If that differentiated or simply alternatives? #
mathchat
8:19 pm
LesLinks
:
@
ColinTGraham
Some students arrive at products, and cannot verbalise how they got there.. #
mathchat
8:20 pm
ColinTGraham
:
@
LesLinks
So with those who can't verbalise routes to a solution, maybe we should be exploring other methods of communication #
mathchat
8:21 pm
john_at_muuua
:
@
LesLinks
@
ColinTGraham
Is verbalising a mathematical skill or a language skill? #
mathchat
8:21 pm
ColinTGraham
:
@
rodaniel
Valid if the equation makes computation more efficient or is needed as a step towards something greater... #
mathchat
8:22 pm
ColinTGraham
:
@
rodaniel
I always see equations as shorthand notations of an abstract concept which needed to be communicated to someone else #
mathchat
8:22 pm
rodaniel
:
@
john_at_muuua
They need to learn what they know, so their choice, but expectation is always mult. approaches #
mathchat
8:22 pm
ColinTGraham
:
@
john_at_muuua
Well, I always argue that mathematics is the language of abstraction (and patterns and the universe)... #
mathchat
8:23 pm
rodaniel
:
@
ColinTGraham
I look at my SEM stats class and the equations and it is important that I can translate their meaning, skill I need #
mathchat
8:23 pm
ColinTGraham
:
To come back to an earlier point  what role does content play in the way the curriculum is designed  is it productfocused? #
mathchat
8:24 pm
rodaniel
:
SEM structural Equation Modeling, #
mathchat
8:25 pm
john_at_muuua
:
@
ColinTGraham
I agree. All that 'correct answer' stuff distracts from the art behind the numbers. #
mathchat
8:26 pm
ColinTGraham
:
@
john_at_muuua
In English, for example, you can adopt a prescriptive or descriptive approach towards grammar. Not so in maths #
mathchat
8:26 pm
LesLinks
:
@
john_at_muuua
well, good question, perhaps both. Some students work through better by 'saying' than 'writing/figureing.. vsva #
mathchat
8:26 pm
davidwees
:
Of time and technology 
http://is.gd/gQoxO
#
edchat
#
mathchat
8:27 pm
rodaniel
:
@
ColinTGraham
Yes, but if the product is more than just an answer then I'm OK with that, I don't believe it has to be just one way #
mathchat
8:27 pm
john_at_muuua
:
@
LesLinks
In English we assess Speaking and Listening. Can assess a whole text via speech. should maths do that? #
mathchat
8:28 pm
ColinTGraham
:
One point which came up on Thursday was: is part of the problem too much focus on subjects post11yo #
mathchat
8:28 pm
rodaniel
:
@
john_at_muuua
Question is how to do that reliably, almost impossible to do so with statistical reliability #
mathchat
8:29 pm
rodaniel
:
We tried to do group problem solving in Kentucky in 90s, and it couldn't be validated, and was thus dropped #
mathchat
8:29 pm
ColinTGraham
:
@
john_at_muuua
This also raises the point of validating qualitative vs. quantitative output #
mathchat
8:30 pm
rodaniel
:
Gr8 conversation, have to go to a meeting, thanks for the opportunity! #
mathchat
8:31 pm
ColinTGraham
:
@
rodaniel
You're welcome, Roland. See you again sometime! #
mathchat
8:32 pm
john_at_muuua
:
@
rodaniel
'This also raises the point of validating qualitative vs. quantitative output', to RT @
ColinTGraham
#
mathchat
8:33 pm
ColinTGraham
:
One of the main problems/challenges we face in education is that the system is designed towards producing qualifications #
mathchat
8:33 pm
Janshs
:
@
rodaniel
sorry just saw this #
mathchat
I fervently believe that the aha! moment rules ;)
8:34 pm
Linda_Pilko
:
RT @
ColinTGraham
: One of the main problems/challenges we face in education is that the system is designed towards producing qualifications #
mathchat
8:35 pm
ColinTGraham
:
@
Janshs
How does the 'aha' get incorporated within the curriculum, or is it just reliant on teachers being observant...? #
mathchat
8:35 pm
ColinTGraham
:
@
john_at_muuua
What would an 'aha' moment be for a student in English? #
mathchat
8:37 pm
Janshs
:
@
ColinTGraham
this means we r torn between supporting sch results (important for stdts) and our love of Maths (sorry love again) #
mathchat
8:37 pm
john_at_muuua
:
@
ColinTGraham
'aha' is when abstract ideas become concrete. #
mathchat
8:38 pm
Janshs
:
@
ColinTGraham
tricky .. does PoS encourage aha moments? #
mathchat
8:39 pm
ColinTGraham
:
@
Janshs
School results are important for schools, not students... Students get too focused on grades because product is focused on #
mathchat
8:40 pm
Janshs
:
@
ColinTGraham
ah *but* surely level 2 quals open doors for them??? #
mathchat
also having been to sch w/ good rep?
8:40 pm
ColinTGraham
:
RT @
chris_1974
: @
Janshs
@
ColinTGraham
Aha moments are always possible  depends on how things presented. (no h in mathchath!) #
mathchat
8:40 pm
chris_1974
:
@
ColinTGraham
@
Janshs
but 5 A*C type results *are* important for stdts. Life chances, VI form, college places etc. #
mathchat
8:41 pm
Janshs
:
RT @
chris_1974
@
ColinTGraham
@
Janshs
but 5 A*C type results *are* important 4 stdts. Life chances, VI form, college places etc. #
mathchat
8:41 pm
Janshs
:
@
chris_1974
depends on *good* teachers then? #
mathchat
8:42 pm
ColinTGraham
:
@
chris_1974
The question is not really about whether 'aha' moments are possible, but more that curriculum should encourage them #
mathchat
8:42 pm
ColinTGraham
:
@
Janshs
Programmes of Study are designed around curricular requirements which seem to be based on assessable products... #
mathchat
8:44 pm
ColinTGraham
:
I wonder what would happen if every child were homeschooled.... how would qualifications/curricula be designed/validated then? #
mathchat
8:44 pm
Janshs
:
@
ColinTGraham
circular agrument then? #
mathchat
hmm #
fail
?
8:44 pm
chris_1974
:
@
Janshs
@
ColinTGraham
it used to be "tell them what you are going to do", "do it", "tell them what you did". #
mathchat
8:44 pm
chris_1974
:
@
Janshs
@
ColinTGraham
no space for exploration, and so no space for Aha. #
mathchat
8:45 pm
ColinTGraham
:
@
Janshs
Not so much a circular argument if you buy into it. Challenge is to find ways to deliver the curriculum more imaginatively #
mathchat
8:46 pm
chris_1974
:
@
Janshs
depends on good teaching. Good questioning skills. #
mathchat
8:46 pm
ColinTGraham
:
@
chris_1974
Very much an application of "this is what the great mathematicians worked out for you"... missing the joy of maths #
mathchat
8:47 pm
Janshs
:
for sure RT @
chris_1974
@
Janshs
depends on good teaching. Good questioning skills. #
mathchat
8:48 pm
Janshs
:
@
chris_1974
@
ColinTGraham
am a bad girl, I still think a little exploration is fun  even day before early entry exam today #
mathchat
8:49 pm
ColinTGraham
:
There are always effective ways to deliver curriculum, however tricky/inadvisable the curriculum is. What would improve curricul tho'? #
mathchat
8:51 pm
ColinTGraham
:
Final 10 minutes  any thoughts about process/product in the curriculum, or do we need a completely different approach? #
mathchat
8:52 pm
Janshs
:
@
ColinTGraham
yes completely different, but until you or me or Chris or rest are in *power* ..... #
mathchat
8:54 pm
chris_1974
:
@
Janshs
@
ColinTGraham
but I still don;t know what it woudl look like, even if we were in charge #
mathchat
8:55 pm
Janshs
:
@
chris_1974
we'd give it a good go! #
mathchat
8:55 pm
ColinTGraham
:
Wherein lies the problem! RT @
chris_1974
:... but I still don't know what it woudl look like, even if we were in charge #
mathchat
8:55 pm
cybraryman1
:
Enjoyed the discussion. The aha moment is when a student finds a solution to a problem that challenged them. #
mathchat
8:55 pm
Janshs
:
@
chris_1974
perhaps exams that showed what stdts could do rather than what they cannot? #
mathchat
8:56 pm
chris_1974
:
@
Janshs
I'm hoping tomorrows exam with functional in it may be a start?? #
mathchat
8:56 pm
ColinTGraham
:
Most of the thinking today, and on Thursday, seems to suggest that good teachers will find ways to adjust delivery for Ss benefit #
mathchat
8:57 pm
Janshs
:
@
chris_1974
let us know ;) #
mathchat
8:57 pm
chris_1974
:
@
ColinTGraham
so the question  not for next 3 mins  is how do we encoruage others? #
mathchat
8:57 pm
chris_1974
:
@
Janshs
of course. #
mathchat
8:57 pm
cybraryman1
:
RT @
ColinTGraham
: Most of the thinking today, & Thurs suggests that gd teachers will find ways to adjust delivery for Ss benefit #
mathchat
8:59 pm
ColinTGraham
:
I think the bigger question is how much of it is our problem now, many look to better teacher training, w/out taking responsibilty #
mathchat
9:00 pm
ColinTGraham
:
OK, as usual we end up asking more questions than we answer! Thanks everyone, and remember we are 1 hour earlier coz no more DST! #
mathchat
9:01 pm
Janshs
:
@
ColinTGraham
thanks to you #
mathchat
9:01 pm
chris_1974
:
Just a chance for a #
shameless
plug of my latest post  How I help students *less* in maths lessons.
http://bit.ly/chrismaths
#
mathchat
9:02 pm
ColinTGraham
:
Don't forget to vote for the next topic.
http://bit.ly/c9KL7u
Also look out for a survey I'll be doing about CPD & hashtag discsns #
mathchat
9:03 pm
ColinTGraham
:
Archive will be online in about 30 minutes. Catch you all next time! #
mathchat
9:15 pm
rodaniel
:
Gr8 #
mathchat
today! Hope all of my math friends try to join in the conversation soon!
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Does the mathematics curriculum need to be designed much more towards process rather than product?
As it happened on Monday, 8th November 2010, 19:30  21:00 GMT