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/bkFP3hand 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 process-oriented #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 process-based math curriculum be the same as an inquiry-based 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 process-based 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 process-based? #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 product-focused. #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 no-one 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., P-S, reasoning, visualizing & tech #mathchat
12:25 am
republicofmath:
Yes!! Focus on #math as human endeavor - no such thing as failure, just failure to try. @ColinTGrahamShould 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 back-seat 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 these-not 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