Topic (follow-up 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, semi-colons, 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 be-all and end-all #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 short-hand 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 product-focused? #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 post-11yo #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!