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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
2010.11.01 Vertical Integratn 2
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Topic (followup to Thursday, 28th October 2010):
How can we facilitate vertical (crosscurricular) integration of mathematics teaching from early years to graduatelevel?
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 graduatelevel? #
mathchat
7:38 pm
ColinTGraham
:
First, we should probably define 'vertical integration'. Some take it as being crosscurricular, others take it as crossyear/age #
mathchat
7:39 pm
ColinTGraham
:
First, we should probably define 'vertical integration'. Some take it as being crosscurricular, others take it as crossyear/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 subjectcontent 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
nonmaths 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 subjectteachers 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 nonteachers 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 K20 @
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 overseparated into topics too, whereby a disconnect is made #
mathchat
8:31 pm
republicofmath
:
Well, yes! Which is why I feel vertical integration K20 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 crosslinked 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 crosssubject 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 shortcuts 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 & crosscurricular 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 shortcuts, 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 eyeopener #
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 subjectteachers 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
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How can we facilitate vertical (crosscurricular) integration of mathematics teaching from early years to graduatelevel?
As it happened on Monday, 1st November 2010, 19:30  21:00 GMT