Topic (follow-up to Thursday, 28th October 2010):
How can we facilitate vertical (cross-curricular) integration of mathematics teaching from early years to graduate-level?
As it happened on Monday, 1st November 2010, 19:30 - 21:00 GMT
7:32 pm
ColinTGraham:
Hello everyone and welcome to Monday's #mathchat
7:32 pm
ColinTGraham:
Now an hour earlier since we went back to GMT yesterday. #mathchat
7:33 pm
ColinTGraham:
If it's your first time, don't try to follow everything, but focus on one or two people and interact with them. Don't forget the #mathchat
7:34 pm
ColinTGraham:
Tonight's topic: How can we facilitate vertical integration of mathematics teaching from early years to graduate-level? #mathchat
7:38 pm
ColinTGraham:
First, we should probably define 'vertical integration'. Some take it as being cross-curricular, others take it as cross-year/age #mathchat
7:39 pm
ColinTGraham:
First, we should probably define 'vertical integration'. Some take it as being cross-curricular, others take it as cross-year/age #mathchat
7:40 pm
ColinTGraham:
For tonight, either definition will be ok... ;-) #mathchat
7:41 pm
ColinTGraham:
Where does a lack of integration cause the greatest problems - at what age, in what subjects? #mathchat
7:46 pm
suburbanlion:
@ColinTGraham IME, lack of integration causes greatest problems in science, particularly physics & chemistry #mathchat
7:48 pm
suburbanlion:
@ColinTGraham in HS, had chem teacher get angry w/ me 4 explaining things to peers w/ calculus, which most of class hadn't had yet #mathchat
7:48 pm
ColinTGraham:
@suburbanlion Which seems strange given the large overlaps between maths and science... where does the problem lie, do you think? #mathchat
7:50 pm
ColinTGraham:
@suburbanlion Did your chem teacher want to explain the calculus later or was it deemed unnecessary...? #mathchat
7:52 pm
suburbanlion:
@ColinTGraham no, she refused to talk about rate of change from perspective of calculus. very awkward situation. #mathchat
7:54 pm
suburbanlion:
@ColinTGraham I think part of this problem is that topics like calculus are treated as "too hard": just perpetuates that view. #mathchat
7:55 pm
ColinTGraham:
@suburbanlion So a refusal to acknowledge the mathematical component of the chemistry... or was it fear/lack of understanding...? #mathchat
8:00 pm
suburbanlion:
@ColinTGraham hard to speculate why, but IMO opportunities 2 introduce math concepts like that should be seized instead of avoided #mathchat
8:01 pm
ColinTGraham:
Anyone else want to join in on the idea of subject-content teachers teaching the mathematical content for their subjects? #mathchat
8:02 pm
ColinTGraham:
@suburbanlion Particularly if the mathematics actual helps simplify or clarify or create connections within the topic... #mathchat
8:05 pm
thekizzaa:
@ColinTGraham non-maths teachers generally tend not to be confident about their maths ability and lack subject knowledge? #mathchat
8:06 pm
suburbanlion:
@ColinTGraham exactly. tchr was going out of the way to avoid using term "derivative", even tho it was most appropriate tool 4 job #mathchat
8:07 pm
ColinTGraham:
@thekizzaa So is the answer to provide training/support for subject teachers or have maths teachers teach maths for chemistry, say #mathchat
8:12 pm
ColinTGraham:
Are there any particular ages or years/grades where a lack of integration within mathematics itself causes problems? #mathchat
8:15 pm
TeaKayB:
@ColinTGraham You'd have a job convincing many of them that there /is/ any maths in their subject. #mathchat
8:17 pm
ColinTGraham:
@TeaKayB "Them" being... secondary school teachers? Have had an art teacher ask me to teach ratio/proportion to a Yr8 group... #mathchat
8:19 pm
ColinTGraham:
@TeaKayB Those subject-teachers who do know about maths content, often don't know whereabouts it is in the maths curriculum re: Yr #mathchat
8:21 pm
ColinTGraham:
RT @TeaKayB: Yep. In my experience non-teachers are largely very negative towards maths. #mathchat
8:21 pm
suburbanlion:
@ColinTGraham "formal proof" in HS Geometry strikes me as a topic poorly integrated within mathematics curriculum #mathchat
8:23 pm
republicofmath:
Yr 12 physics: circular motion. Teacher stuggled to explain accel ? velocity. I said: mutiply by i. Dismissed as "too advanced." #mathchat
8:24 pm
ColinTGraham:
@suburbanlion I would tend to agree, as well as recognizing other 'proofs' (pics) can help more, rather than deductive reasoning #mathchat
8:25 pm
ColinTGraham:
@republicofmath You might as well say that Pythagoras' Theorem is too advanced for 8 year olds, but they can still use it! #mathchat
8:25 pm
teachtgs:
@ColinTGraham Oft true there is lack of confidence. Have tried to work with stats in other subjects before... not always easy. #mathchat
8:27 pm
ColinTGraham:
Do you get the idea that integration across the curriculum is dependent more (too much) on application of maths w/out concept? #mathchat
8:27 pm
republicofmath:
Agree re geometry. IMO emphasize visual aspect & focus on age appropriate development of reasoning. Integrate K-20 @suburbanlion #mathchat
8:28 pm
ColinTGraham:
@teachtgs The use of statistics for experimental design was always an issue at one place I taught (& one I worked at b4 teaching) #mathchat
8:30 pm
republicofmath:
I think the physics teacher didn't understand complex numbers &/or vectors & dot products. @ColinTGraham #mathchat
8:30 pm
ColinTGraham:
@republicofmath I think there can be a tendency for mathematics to be over-separated into topics too, whereby a disconnect is made #mathchat
8:31 pm
republicofmath:
Well, yes! Which is why I feel vertical integration K-20 is important @ColinTGraham #mathchat
8:31 pm
ColinTGraham:
@republicofmath And they wouldn't take kindly to a student explaining the mathematics of 'their subject' to them either... #mathchat
8:31 pm
teachtgs:
@republicofmath It can be challenging in phy class when different math levels mixed, but why not show it. #mathchat
8:32 pm
ColinTGraham:
@teachtgs Too many teachers ask the question "why show it" rather than "why not"... #mathchat
8:33 pm
TeaKayB:
@ColinTGraham There are probably plenty of instances of maths in other subjects' curricular that I haven't thought about #mathchat
8:33 pm
TeaKayB:
@ColinTGraham Would be nice to have some kind of cross-linked resource. #mathchat
8:34 pm
ColinTGraham:
I got the feeling with one of my physics teachers that he would have used the maths but was afraid he'd have to explain it! #mathchat
8:34 pm
teachtgs:
@ColinTGraham I even talked about calc apps in my grade 9 math class when talking area of odd shapes. Previewing is good. #mathchat
8:35 pm
republicofmath:
I am gobsmacked - http://bit.ly/cvLzq6 -and delighted when students can tell me something about #math that I don't know #mathchat
8:35 pm
ColinTGraham:
@TeaKayB The national curriculum in the UK does do this to a certain extent, but not explicitly enough... #mathchat
8:36 pm
suburbanlion:
Would accelerating math curriculum make cross-subject integration easier? Seems like necessary math is always 1 year behind. #mathchat
8:36 pm
ColinTGraham:
@teachtgs I always find that kids are interested in short-cuts and efficient ways of doing things... i.e. application. So do it! #mathchat
8:37 pm
TeaKayB:
@ColinTGraham I'm talking about somewhere I could enter a topic & receive explicit list of relevant RL & cross-curricular ideas #mathchat
8:38 pm
ColinTGraham:
@suburbanlion In some cases, necessary mathematics can be two or three years behind. I think it's too much "why" instead of "how" #mathchat
8:38 pm
republicofmath:
Shows lack of interest IMO. Just want to get chores done:" I find kids interested in short-cuts, efficient ways of doing things" #mathchat
8:38 pm
ColinTGraham:
@TeaKayB The official Nat Curric site does this, doesn't it or I am hallucinating again? #mathchat
8:40 pm
ColinTGraham:
@republicofmath Maybe if you only teach the shortcuts without asking or suggesting an investigation of why they work... preview #mathchat
8:40 pm
suburbanlion:
@teachtgs I was astonished when I learned how Euler's formula could be used to find area of odd shaped polygons. grade 9 topology? #mathchat
8:42 pm
ColinTGraham:
@suburbanlion Even something as simple as checking for division by 3 or 9 can be an eye-opener #mathchat
8:43 pm
TeaKayB:
@ColinTGraham Doesn't appear to give any explicit examples or resources. It's all very vague, though admittedly I haven't... #mathchat
8:43 pm
ColinTGraham:
@republicofmath I meant the block for subject-teachers was them getting too hung up on the "why" and so discounting the "how" #mathchat
8:43 pm
republicofmath:
Kids in Twyford School UK delighted to try to draw K5 on torus without edges crossing. Used multiple reps of torus. @suburbanlion #mathchat
8:43 pm
TeaKayB:
@ColinTGraham ... spent a lot of time going through it. But then that's part of the problem- so many boxes to tick & hoops... #mathchat
8:44 pm
TeaKayB:
@ColinTGraham ... to jump through, developing new resources is made difficult. #mathchat
8:44 pm
suburbanlion:
@ColinTGraham yes & other division rules too! http://bit.ly/7wi6l2 #mathchat
8:44 pm
republicofmath:
Oh, sorry! @ColinTGraham #mathchat
8:46 pm
republicofmath:
Yes, I agree: it's context- dependent @jmstitt #mathchat
8:46 pm
ColinTGraham:
@republicofmath Within mathematics itself, I agree it is the 'nature' to work from and towards the "why" - as we have discussed b4 #mathchat
8:48 pm
ColinTGraham:
@TeaKayB So, how could curricula be designed which don't require different mathematical elements at the same time? #mathchat
8:50 pm
ColinTGraham:
@TeaKayB eg Art wants scale drawing and perspective, Geography wants bearings, Physics wants speed/time graphs... and all now! #mathchat
8:51 pm
TeaKayB:
@ColinTGraham No idea! Allow time explicitly for teachers to work together across departments would be a start, I think. #mathchat
8:52 pm
ColinTGraham:
@TeaKayB I wonder how much of the current mathematics curricula around the world were designed to teach maths for other subjects. #mathchat
8:52 pm
TeaKayB:
@ColinTGraham Doing it properly could possibly streamline curricular, allowing more time for depth, breadth, projects, etc... #mathchat
8:53 pm
ColinTGraham:
It also raises the question about whether or not subject specialization should be introduced at the secondary (11+) level... #mathchat
8:54 pm
ColinTGraham:
So, two main issues - there is a general feeling that mathematics is not coherent or integrated across the age groups.... #mathchat
8:55 pm
ColinTGraham:
The other issue is a disconnect between subjects because of too much specialization/lack of project/teamwork/collaboration #mathchat
8:57 pm
teachtgs:
@suburbanlion interesting idea though i wonder if it would make more of a divide. #mathchat
8:58 pm
ColinTGraham:
Any final thoughts or comments in the last 5 minutes? #mathchat
8:58 pm
teachtgs:
@suburbanlion I have used it with grade 9 before and will this year as well. #mathchat
9:00 pm
ColinTGraham:
OK, thanks everyone. Archive will be online in about 30 minutes. Now the UK is back on GMT, it may affect timings for #mathchat
9:01 pm
ColinTGraham:
So please vote on time changes due to daylight saving... http://bit.ly/9Tm2FF #mathchat #ukedchat#edchat #scichat #gtchat #ntchat #nqtchat