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#mathchat Wiki
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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
2010.11.04 Product to Process
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Topic:
Does the mathematics curriculum need to be designed much more towards process rather than product?
As it happened on
Thursday, 4th November 23:30  00:30 GMT
11:37 pm
ColinTGraham
:
Hello, everyone, welcome to this week's #
mathchat
11:38 pm
republicofmath
:
Reflective abstraction starts with thinking about actions without actually doing them  extends physical operations to mental ones #
mathchat
11:38 pm
ColinTGraham
:
If it's your first time, welcome. Don't try to follow everything, but interact with one or two people. Don' forget the > #
mathchat
11:39 pm
ColinTGraham
:
Tonight's topic: Does the mathematics curriculum need to be designed much more towards process rather than product? #
mathchat
11:39 pm
smartinez
:
@
joe_bower
@
FUZZYPEACHES100
have you seen Kamii website? articles/games
http://bit.ly/bkFP3h
and videos
http://bit.ly/bRehmQ
#
mathchat
11:40 pm
republicofmath
:
For example, kids can count objects. Asking them to imagine counting hidden objects starts off reflective abstraction. #
mathchat
11:40 pm
padgets
:
#
mathchat
Hi everyone! My name is Sharon and I am a HS science teacher in Ottumwa Iowa :)
11:41 pm
ColinTGraham
:
@
padgets
Hi Sharon. #
mathchat
11:42 pm
padgets
:
@
ColinTGraham
Hi there!!! how is it going? #
mathchat
11:42 pm
NicolRHoward
:
RT @
FUZZYPEACHES100
Does anyone have any good articles on constructivist theory when teaching Math for Elementary? #
MathChat
11:43 pm
ColinTGraham
:
@
joe_bower
The discussions we had on reflective learning may help with constructivism:
http://bit.ly/92qzwV
http://bit.ly/dDhcJr
#
mathchat
11:43 pm
ghewgley
:
The #
mathchat
Daily is out  read this Twitter newspaper on
http://bit.ly/bMxifd
(20 contributions today)
11:44 pm
ColinTGraham
:
So, let's start with a focusing question: What do you see as typical 'products' in mathematics? #
mathchat
11:45 pm
ccampbel14
:
For the next hour my tweets will be about our topic: Should math curriculum be designed much towards process rather than product? #
mathchat
11:45 pm
ccampbel14
:
Hi, it's Cathy here from Edmonton, Alberta. Glad to join you tonight :) #
mathchat
11:46 pm
republicofmath
:
Constructivist theory posits that reflective abstraction is how all kids learn. It's a theory, not a practice one can adopt. #
mathchat
11:46 pm
padgets
:
#
mathchat
I see products as the finishing of a lab that has calculations
11:46 pm
ccampbel14
:
I think the products are the outcomes or learner expectations listed in curriculum. It is the content of what we need to cover. #
mathchat
11:47 pm
ColinTGraham
:
@
ccampbel14
Hi Cathy, long time no see! #
mathchat
11:47 pm
padgets
:
#
mathchat
I also see product as the "light bulb" going off for a child when they figure out the answer to a science problem using math
11:47 pm
republicofmath
:
Whoops, Cathy has got me back on track. @
ccampbel14
What do process and product mean in this context? #
mathchat
11:47 pm
ColinTGraham
:
@
padgets
Do you see that as a science product or a mathematics product, Sharon? #
mathchat
11:48 pm
ccampbel14
:
@
ColinTGraham
Yes, I have missed many chats lately. Pace at work has made it difficult to set aside this time to meet with you #
mathchat
11:48 pm
ColinTGraham
:
@
republicofmath
;) #
mathchat
11:49 pm
padgets
:
#
mathchat
both, I see a sense of accomplishment in both disciplines, heard from our math teacher that the more I do her job becomes easier
11:49 pm
republicofmath
:
What about a math blog written after a few weeks work? @
padgets
#
mathchat
I see products as the finishing of a lab that has calculations
11:49 pm
ccampbel14
:
@
republicofmath
I think the process, at least here in Alberta, are the 7 process skills  Communication, connections, etc. #
mathchat
11:49 pm
ColinTGraham
:
How about memorization of formulae, such as solving quadratics... is that a product or part of the process? #
mathchat
11:50 pm
ccampbel14
:
I believe the more we emphasize the process, the products will follow along with them. #
mathchat
11:50 pm
padgets
:
@
republicofmath
#
mathchat
sure, we use twiducate to blog and the kids often talk about how they figured something out, very proud
11:51 pm
republicofmath
:
Understanding quadratic formula and being able to use it flexibly would be product for me. #
mathchat
11:51 pm
ccampbel14
:
@
ColinTGraham
With understanding of where quadratics fit in math, using it to problem solve, etc. it can be both process & product #
mathchat
11:52 pm
suburbanlion
:
If by "product" we mean "answer" & by "process" we mean "how to get answer", then yes, process is more important #
mathchat
11:52 pm
padgets
:
#
mathchat
I would see it as a process :) The step by step parts are why I see it that way :)
11:53 pm
ccampbel14
:
Would process by similar to conceptual understanding and product be procedural knowledge? #
mathchat
11:53 pm
ColinTGraham
:
@
suburbanlion
But is an answer necessarily a product or just another step in the process towards an end result? #
mathchat
11:53 pm
georgewoodbury
:
RT @
suburbanlion
: If by "product" we mean "answer" & by "process" we mean "how to get answer", then yes, process is more important #
mathchat
11:55 pm
republicofmath
:
Vygotsky changed ed psych by focusing on process over product  in Ryan's sense @
suburbanlion
#
mathchat
11:55 pm
ColinTGraham
:
For me, the product is close to what @
ccampbel14
suggested: something to be assessed summatively in an examination/test #
mathchat
11:56 pm
republicofmath
:
Procedural can be conceptual. You might be thinking of instrumental. @
ccampbel14
#
mathchat
11:56 pm
padgets
:
#
mathchat
well, :) a product for me is the end result of a process, am thinking of many chem and bio happenings
11:56 pm
suburbanlion
:
@
ColinTGraham
there's more than one way to think of "product", but an "end result" seems to be the defining characteristic #
mathchat
11:57 pm
ccampbel14
:
Think that process precedes product at first. But then as students learn, processes & products become intertwined. #
mathchat
11:57 pm
ColinTGraham
:
@
republicofmath
I very much 'buy in' to Vygotsky's theories about development, more so than Piaget! I'm very processoriented #
mathchat
11:57 pm
ccampbel14
:
@
republicofmath
Yes, I think you are right. I have seen instrumental and relational, I think. #
mathchat
11:58 pm
republicofmath
:
@
ColinTGraham
But in assessing that product I want to see the process that lead to it I want a full story. #
mathchat
11:58 pm
ColinTGraham
:
@
suburbanlion
If the result is the final step in a series of steps, then I'd agreed end result = product #
mathchat
11:59 pm
republicofmath
:
I suspect product/process is distinction is not really helpful. I want deep mathematical stories that wow me. Product? Process? #
mathchat
11:59 pm
ccampbel14
:
Think our students value the product more than the process. Constant battle 2 get Ss to value the journey rather then destination. #
mathchat
12:01 am
republicofmath
:
@
ColinTGraham
Have you seen the book "I Think I am A Verb"? #
mathchat
12:01 am
ColinTGraham
:
@
republicofmath
I agree that distinction isn't so helpful, but it is prevalent & I think we need to be clear ourselves, if poss! #
mathchat
12:02 am
ColinTGraham
:
@
ccampbel14
Is it the students or is those who chose the curriculum or is it just human psychology (satisfaction of completion)? #
mathchat
12:02 am
republicofmath
:
@
ColinTGraham
Well, I have to assess it in that I have to turn in a grade. But that's based on my assessment of the overall story #
mathchat
12:03 am
ccampbel14
:
Would a processbased math curriculum be the same as an inquirybased approach? Similar across subject areas. #
mathchat
12:03 am
republicofmath
:
I agree, & I figure it's part of my mission to get them thinking. @
ccampbel14
#
mathchat
12:03 am
ColinTGraham
:
@
republicofmath
Yes, fascinating look at deeper conceptual thinking/semiotics #
mathchat
12:04 am
ccampbel14
:
@
ColinTGraham
What is semiotics? #
mathchat
12:05 am
ColinTGraham
:
@
ccampbel14
I think a danger of labelling process and product is that a shift towards the former, makes it something to assess... #
mathchat
12:05 am
republicofmath
:
Not necessarily, but inquiry based, IME, does focus heavily on process. @
ccampbel14
#
mathchat
12:06 am
ColinTGraham
:
@
ccampbel14
Semiotics basically is looking at the underlying content/concept/meaning relationship of signs and symbols #
mathchat
12:06 am
ColinTGraham
:
@
ccampbel14
If you like, semiotics is the "science of meaning" #
mathchat
12:06 am
padgets
:
#
mathchat
I would think you could use processbased math would be similiar to inquiry
12:07 am
ccampbel14
:
I also think that quite often parents expect or prefer products in math. #
mathchat
12:07 am
ccampbel14
:
@
ColinTGraham
Thanks, I have heard of semantics but not semiotics. I'm learning more than math here :) #
mathchat
12:08 am
republicofmath
:
Science of symbols  more basic than math. @
ColinTGraham
@
ccampbel14
If you like, semiotics is the "science of meaning" #
mathchat
12:08 am
padgets
:
#
mathchat
this is so cool! every time I come to mathchat I learn something new, now I know what semiotics is :) I am going to wow my team
12:08 am
ColinTGraham
:
@
padgets
The idea of inquiry or investigation or problem/project based learning is certainly concerned with process #
mathchat
12:10 am
ColinTGraham
:
@
ccampbel14
Semiotics also encompasses the use of metaphor, symbology, analogy, cultural variations in meaning etc... #
mathchat
12:10 am
ccampbel14
:
Do you think certain curriculums are more product or more processbased? #
mathchat
12:11 am
daveinstpaul
:
Math is not a product or a process so much as a way of thinking. I use math every day, but often informally or intuitively. #
mathchat
12:11 am
ccampbel14
:
@
ColinTGraham
This would include differences & similarities between British English versus Canadian English? #
mathchat
12:11 am
daveinstpaul
:
How do we convey to students and the general public that math is not just about calculation, or even about proof? #
mathchat
12:11 am
ColinTGraham
:
@
ccampbel14
My view is that anything requiring an assessment and a grade is basically productfocused. #
mathchat
12:12 am
suburbanlion
:
"Process" is where the learning happens, but it's usually "product" that gets assessed. #
mathchat
12:12 am
ColinTGraham
:
@
daveinstpaul
I'm sure noone would disagree, Dave. The point is the importance or weight given to product in the curriculum! #
mathchat
12:12 am
ccampbel14
:
@
suburbanlion
How do we assess process? I struggle with this all the time. #
mathchat
12:12 am
republicofmath
:
Sharon: semiotics
http://bit.ly/31sf0v
@
padgets
Basic to understanding how students increase symbolic competence in #
math
#
mathchat
12:13 am
ColinTGraham
:
@
ccampbel14
Difference in language is where it becomes semantics... ;) #
mathchat
12:13 am
padgets
:
@
republicofmath
#
mathchat
thank you! I will take a look :)
12:14 am
ccampbel14
:
Would it be correct to say that when we assess process it is on a continuum and prodcut is either you can do it or you can't? #
mathchat
12:14 am
BLicata
:
process is the most important, not memorization of material , the product is just a gr8 way 2 showcase ur new found knowledge #
mathchat
12:14 am
republicofmath
:
Agree. Following Vygotsky & Cronbach we need to formatively assess the process. #
mathchat
@
suburbanlion
12:14 am
ColinTGraham
:
@
ccampbel14
Semiosis is the study of cultural sign processes... semantics is the study of meaning (as a subset of semiotics) #
mathchat
12:15 am
ColinTGraham
:
@
ccampbel14
In assessing process, there is a much stronger feeling of formative assessment involved, because the process continues #
mathchat
12:15 am
republicofmath
:
@
ccampbel14
How to assess process? One semester in inquiry course, I gave credit for every relevant question asked by students. #
mathchat
12:15 am
suburbanlion
:
@
ccampbel14
I don't you should assess process, just observe it #
mathchat
12:16 am
ccampbel14
:
@
republicofmath
How do you give credit for asking relevant questions? #
mathchat
12:16 am
ColinTGraham
:
@
ccampbel14
Semiotics = semantics + syntactics + pragmatics (to use mathematical notation!) #
mathchat
12:16 am
daveinstpaul
:
@
ColinTGraham
I don't think I understand the terms of the discussion (no ed theory classes) so trying to contribute tangentially. #
mathchat
12:16 am
BLicata
:
Hearing each students thought process in math is vry hard, I have them vocalize their way through the problem & record it #
mathchat
12:17 am
ColinTGraham
:
@
suburbanlion
So if the process is going to result in a failure to produce.... how do you react in that situation, as observer #
mathchat
12:17 am
republicofmath
:
@
ccampbel14
I assess products in tests on more than a binary yes or on. However, I want to see process in reasoning. #
mathchat
12:18 am
republicofmath
:
Semiotics: what Colin said. #
mathchat
12:18 am
ccampbel14
:
@
suburbanlion
If you don't asess but observe process, do you keep track of this in some way? #
mathchat
12:18 am
ColinTGraham
:
@
republicofmath
So does process = algorithm, or is it reasoning, deduction, induction...? #
mathchat
12:19 am
republicofmath
:
@
BLicata
Great!@ I get them to write it on a Wordpress blog. Also in one class students give 10 minute talks regularly. #
mathchat
12:19 am
padgets
:
#
mathchat
love the semiotics page!
12:20 am
ColinTGraham
:
@
daveinstpaul
Most current mathematics curricula seem to be based on assessing and producing answers (products?) should it change? #
mathchat
12:20 am
republicofmath
:
Think that's the calculus discussion Dave! LOL @
daveinstpaul
trying to contribute tangentially #
mathchat
12:21 am
ccampbel14
:
@
republicofmath
Do the students get to choose whether they blog or present a talk? #
mathchat
12:23 am
ColinTGraham
:
Does your current mathematics curriculum include any requirement to "reason, communicate..." ? Is it assessed at all? #
mathchat
12:23 am
padgets
:
#
mathchat
I think so, I think it should focus on how it can be used in all areas, art, science, english, auto mechanics,
12:23 am
BLicata
:
I dont care about the answer, I am interested in the journey there #
mathchat
[Like it?
http://bit.ly/cM2yhB
]
12:23 am
suburbanlion
:
@
ColinTGraham
making mistakes is essential part of learning process. need to give them enough freedom to make them. #
mathchat
12:25 am
ccampbel14
:
@
ColinTGraham
In Alberta we have 7 processes: communication, connections, mental math & est., PS, reasoning, visualizing & tech #
mathchat
12:25 am
republicofmath
:
Yes!! Focus on #
math
as human endeavor  no such thing as failure, just failure to try. @
ColinTGraham
Should curricula change? #
mathchat
12:26 am
ColinTGraham
:
RT @
republicofmath
: Tell them that's how real life is, even in math Really! "So if process resulting in failure to produce..." #
mathchat
12:27 am
republicofmath
:
@
BLicata
I teach prospective engineers, among others, so answer is important. More important is way of thinking through problems. #
mathchat
12:27 am
ColinTGraham
:
@
suburbanlion
But making mistakes in examinations can be very costly... ;P #
mathchat
12:27 am
k_5remediation
:
RT @
republicofmath
: Focus on #
math
as human endeavor  no such thing as failure, just failure to try. Should Curricula change? #
mathchat
12:29 am
ColinTGraham
:
Maybe the problem is that mathematics should not be taught, nor geography, nor history, nor... but thinking instead... #
mathchat
12:30 am
ccampbel14
:
@
ColinTGraham
Mistakes building bridges, etc. would be more costly! Fortunately world products are ususally collaborative efforts #
mathchat
12:30 am
ColinTGraham
:
In relation to journeys: Are you a backseat driver, a map or a navigation system?
http://bit.ly/dq9goT
#
mathchat
12:30 am
padgets
:
#
mathchat
well, problem solving to get the right answer I think is part of the process to get the right product
12:30 am
republicofmath
:
Why I no longer have exams; too high stakes. @
ColinTGraham
@
suburbanlion
But making mistakes in examinations can be very costly #
mathchat
12:30 am
suburbanlion
:
@
ccampbel14
class often moves too fast to track observations formally, but I do try to modify my methods reactively #
mathchat
12:31 am
ccampbel14
:
@
ColinTGraham
I think THINKING across the subjecs should be the CONTENT and the subjects are the CONTEXT. #
mathchat
12:31 am
BLicata
:
@
republicofmath
I teach middle school, I need 2 know they can find their way through a problem & construct their own answer #
mathchat
12:32 am
ColinTGraham
:
If process is to become more important and curricula changed... that is another topic for another time! #
mathchat
12:33 am
padgets
:
@
BLicata
#
mathchat
same for me at the HS level, in my science class wrong calculations lead to funny looking graphs
12:33 am
ColinTGraham
:
OK, thanks everyone! It's that time again. #
mathchat
12:33 am
republicofmath
:
@
ColinTGraham
I think we need to teach mathematical thinking. Better problems  Ko's story  or like those of @
jamestanton
#
mathchat
12:34 am
ccampbel14
:
Think the processes are the 'enduring understandings' for our lives. We should emphasize & assess thesenot sure how 2 get there. #
mathchat
12:34 am
ccampbel14
:
@
republicofmath
Love @
jamestanton
's ideas! #
mathchat
12:34 am
suburbanlion
:
Thinking is not something you "teach", but something you "do". Teachers just provide an opportunity for it. #
mathchat
@
ColinTGraham
12:35 am
republicofmath
:
Thanks everyone for a very interesting #
mathchat
(and I thought the topic was a bit dull!! Just goes to show.)
12:35 am
ccampbel14
:
@
suburbanlion
Exactly! We orchestrate the experiences for students to think and we support them. #
mathchat
12:35 am
ColinTGraham
:
Not sure Edward deBono would agree! :P RT @
suburbanlion
: Thinking is not something you "teach", but something you "do".... #
mathchat
12:36 am
ColinTGraham
:
Archive will be online in about 30 minutes. Next week's topic vote is also up and running!
http://bit.ly/c9KL7s
#
mathchat
12:36 am
padgets
:
#
mathchat
thank you all for letting me lurk and learn, have a great rest of the week! take care :[))
12:36 am
ccampbel14
:
Thanks everyone...lots to think about! #
mathchat
12:36 am
ColinTGraham
:
The vote on change of times was inconclusive... so we will be maintaining the status quo! #
mathchat
12:37 am
ColinTGraham
:
RT @
joe_bower
: ?@
FUZZYPEACHES100
: Does anyone have any good articles on constructivist theory for Elementary math?? #
mathchat
12:38 am
republicofmath
:
@
suburbanlion
Sorry to disagree I have taught many kids how to begin to think mathematically. Then of course they have to do it. #
mathchat
12:39 am
ColinTGraham
:
@
suburbanlion
And you'd also have to include the development of critical thinking skills, reflective thinking... #
mathchat
12:42 am
ccampbel14
:
Very interesting..have to clarify my thinking with the many ideas! Think doing leads 2 thinking but we can model this 4 students #
mathchat
12:44 am
daveinstpaul
:
@
ColinTGraham
Yes. When students get correct answers through incorrect reasoning, focusing on answers reinforces misunderstanding. #
mathchat
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As it happened on Thursday, 4th November 23:30  00:30 GMT