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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
2010.12.10 Effective lessons
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Topic:
What makes an effective mathematics lesson?
As it happened on
Friday, 10th December 2010 00:00  01:00 GMT
12:08 am
ColinTGraham
:
Hello everyone... not chatting yet? :) #
Mathchat
12:08 am
ColinTGraham
:
Today's #
mathchat
topic is "What makes an effective mathematics lesson?"
12:13 am
ColinTGraham
:
Anyone out there today? #
mathchat
12:17 am
ColinTGraham
:
OK, if noone is chatting then... #
mathchat
12:18 am
republicofmath
:
A necessary, but not sufficient, criterion is that a lesson is part of a coherent sequence. #
mathchat
12:19 am
ColinTGraham
:
@
republicofmath
Hi Gary. Coherent sequence of what? Lessons, topic, concept...? #
mathchat
12:20 am
republicofmath
:
Then, as part of a coherent sequence, an effective lesson ought to *engage* students  through activity or discussion. #
mathchat
12:21 am
republicofmath
:
Uhm ... yes! At least one, hopefully all. @ ColinTGraham Hi Gary. Coherent sequence of what? Lessons, topic, concept...? #
mathchat
12:22 am
ColinTGraham
:
@
republicofmath
When you say "effective" is that for the teacher, the students or both? #
mathchat
12:22 am
republicofmath
:
I could see a period of just calculation as being effective if it were part of a coherent sequence. Calculating for a purpose. #
mathchat
12:23 am
republicofmath
:
Is it just you and me, Colin. Do we need to get a life? !!! #
mathchat
12:24 am
ColinTGraham
:
@
republicofmath
I sometimes feel like it's just me! We do have our lurkers though! #
mathchat
12:24 am
republicofmath
:
I think both. I think students need to have bought into teacher's aims and premises. @
ColinTGraham
for teacher, students, both? #
mathchat
12:25 am
republicofmath
:
I hope there are some lurkers: I didn't even vote for this topic! #
mathchat
12:25 am
ColinTGraham
:
@
republicofmath
I feel sometimes that "effectiveness" is very much dependent on point of view. #
mathchat
12:25 am
republicofmath
:
I suspect Jerry's lurking @
cybraryman1
#
mathchat
12:26 am
cybraryman1
:
RT @
republicofmath
: I think both. I think students need to have bought into teacher's aims and premises. #
mathchat
12:26 am
republicofmath
:
Meaning assessment of effectiveness? @
ColinTGraham
feel sometimes that "effectiveness" is very much dependent on point of view. #
mathchat
12:27 am
ColinTGraham
:
@
republicofmath
Yes, what teachers see as 'effecting' their 'scheme' is not necessarily a good way to learn. #
mathchat
12:27 am
republicofmath
:
Ha, ha! Jerry: you WERE lurking @
cybraryman1
#
mathchat
12:28 am
ColinTGraham
:
Yes, but has he got a lurking page? :) RT @
republicofmath
: Ha, ha! Jerry: you WERE lurking @
cybraryman1
#
mathchat
12:29 am
cybraryman1
:
"If children cannot learn the way we teach, we must teach the way children learn." #
mathchat
12:30 am
republicofmath
:
@
ColinTGraham
Yes, see what you mean. Think teacher has right, responsibility to set lesson aims. Are students buying into those? #
mathchat
12:30 am
cmt1
:
@
cybraryman1
"If children cannot learn the way we teach, we must teach the way children learn." #
mathchat
#
education
12:30 am
ColinTGraham
:
@
cybraryman1
I agree that teachers should adjust to learning, but... what if children learn in different ways? #
mathchat
12:30 am
peterflom
:
@
mathchat
Effectiveness has to involve engagement; either lighting a fuse or kindling it #
mathchat
12:31 am
cybraryman1
:
@
ColinTGraham
We have to employ differentiated assessment and learning #
mathchat
12:31 am
ColinTGraham
:
I could spend 45 minutes of 'drill and kill' on basic arithmetic, for example. Students memorize, effective for me, but Ss? #
mathchat
12:32 am
ColinTGraham
:
@
nykat4
We'll be here for another 30 minutes or so, if you need to be distracted ;) #
mathchat
12:33 am
republicofmath
:
@
ColinTGraham
To clarify; how is 45 minutes of drill & kill effective for you? What aims did you have? What sequencing? #
mathchat
12:33 am
ColinTGraham
:
@
cybraryman1
Yes, differentiation is important. Is it effective though, for stakeholders, admin, parents...? #
mathchat
12:34 am
nykat4
:
@
ColinTGraham
Oh, there is distraction aplenty, don't you worry!! I'll have to hope there's an archive! #
mathchat
12:34 am
jofrei
:
RT @
cybraryman1
: "If children cannot learn the way we teach, we must teach the way children learn." #
mathchat
12:34 am
peterflom
:
#
mathchat
When students WANT to learn, it's hard to stop them; when they don't want to learn it's very hard to make them
12:34 am
ColinTGraham
:
@
republicofmath
I'm being an extremist here, Gary! Some people would argue that rote memorization is the (only) effect method #
mathchat
12:35 am
republicofmath
:
Want to pursue thought that effectiveness involves sequencing and then students buying into teacher aims. Then "fuse" gets lit. #
mathchat
12:35 am
ColinTGraham
:
@
nykat4
Yes, archive and another chance to join in on Monday on the same topic, Katy! #
mathchat
12:36 am
ColinTGraham
:
@
republicofmath
I can see that, but why should it be teacher aims rather than learner aims? #
mathchat
12:37 am
peterflom
:
@
colintgraham
I would say memorization is NEVER effective; except at ending love of math. #
mathchat
12:37 am
republicofmath
:
@
ColinTGraham
Well , teacher is "sensei": "born before" so experience sets goals, aims for activity. #
mathchat
12:38 am
republicofmath
:
An effective lesson is not, IMO, just going to be busy work. #
mathchat
12:38 am
ColinTGraham
:
Too often, effective and efficient are conflated into a single idea or approach #
mathchat
12:39 am
peterflom
:
@
republicofmath
When I visited Math Circle in Boston, I saw that fuse lit. Amazing what happens #
mathchat
12:39 am
peterflom
:
RT @
republicofmath
: An effective lesson is not, IMO, just going to be busy work. #
mathchat
12:39 am
republicofmath
:
@
ColinTgraham
Right! And I want to pursue idea that what should happen is students buying into, getting, teacher's aims #
mathchat
12:40 am
ColinTGraham
:
@
peterflom
Some things need to be 'known' automatically  placed in easily accessed memory. If it isn't memorization, what is it? #
mathchat
12:40 am
unwyn
:
Wisdom for all #
teaching
RT @
republicofmath
: An effective lesson is not, IMO, just going to be busy work. #
mathchat
12:41 am
republicofmath
:
Ahh!!! @
ColinTGraham
"Efficacy" is for scoundrels (and HM Inspectorate in UK). #
mathchat
12:41 am
peterflom
:
@
republicofmath
Do the students even have to be aware of teacher's aims? #
mathchat
12:42 am
ColinTGraham
:
@
peterflom
Absolutely, if you don't see the purpose of something or at least apprecitate there is a purpose, why do it? #
mathchat
12:42 am
dweksler
:
How about because it is interesting, puzzling, beautiful? #
mathchat
12:42 am
republicofmath
:
@
ColinTgraham
It's memory  but (rote) memorization does NOT lead to long term accessible memory, unless used frequently. #
mathchat
12:42 am
ColinTGraham
:
@
republicofmath
"Efficacy" is neither the same as efficiency nor effectiveness! #
mathchat
12:43 am
republicofmath
:
@
peterflom
At first they aren't. They do things, think they understand. Then, if effective, the scales drop from their eyes. Aha! #
mathchat
12:44 am
ColinTGraham
:
@
dweksler
Those aspects are ones we all appreciate, I hope, David. Are they effective though? What do we want to effect? #
mathchat
12:44 am
cybraryman1
:
@
peterflom
Students at end of lesson should come up with the aim of the lesson themselves #
mathchat
12:44 am
peterflom
:
@
colintgraham
But does student aim have to be same as teacher aim? Teacher aim: Teach group theory. Child aim: Solve Rubk's cube #
mathchat
12:44 am
ColinTGraham
:
@
cybraryman1
Or at least be able to explain how what they did helps towards the aim... #
mathchat
12:44 am
peterflom
:
RT @
dweksler
: How about because it is interesting, puzzling, beautiful? #
mathchat
12:45 am
republicofmath
:
@
CoilnTGraham
"Efficient" teachers do not uhm and ah, according to HM inspectors, but if really modelling thinking they must #
mathchat
12:45 am
peterflom
:
RT @
cybraryman1
: @
peterflom
Students at end of lesson should come up with the aim of the lesson themselves #
mathchat
12:45 am
ColinTGraham
:
@
peterflom
That is my whole point Peter. What teachers see as being effective is often different from Ss perceptions. #
mathchat
12:46 am
republicofmath
:
Got to go to help my wife with potato salad. Been instructive. Effective even! #
mathchat
12:47 am
ColinTGraham
:
So, now we have got caught up in sematics... What do you see as being an effective mathematics lesson? #
mathchat
12:47 am
dweksler
:
@
ColinTGraham
Well, if we are only using test scores to measure "effectiveness", those "artistic" concepts may be less relevant #
mathchat
12:47 am
ColinTGraham
:
@
republicofmath
OK Gary, thanks for starting the ball rolling and dragging in a few more participants! :) #
mathchat
12:47 am
peterflom
:
@
republicofmath
But, then, is it a student "aim" if its only discovered after the fact? #
mathchat
12:49 am
ColinTGraham
:
@
dweksler
I think the idea of what we mean when we talk about a lesson being effective, or 'working', is not explored enough. #
mathchat
12:49 am
dweksler
:
I've been impressed with this "philosophyofsiteessay" about math and beauty, etc.
http://bit.ly/fq2Tjq
#
mathchat
12:49 am
doctorjeff
:
What? #
mathchat
tryin' to drag in a few more participants?
12:50 am
dweksler
:
@
ColinTGraham
How about lesson study/review of student work as a path towards effectiveness? #
mathchat
12:50 am
doctorjeff
:
@
ColinTGraham
one that requires relevance to the real world. #
mathchat
12:50 am
ColinTGraham
:
@
doctorjeff
Well there are always a large number of lurkers who jump in at the last minute, Jeff! #
mathchat
12:50 am
padgets
:
#
mathchat
yep like me! :_)
12:51 am
padgets
:
#
mathchat
how are you all! just getting home too late will have to check the archives :)
12:51 am
doctorjeff
:
@
ColinTGraham
(I know, I'm a lurkin') #
mathchat
12:51 am
ColinTGraham
:
@
dweksler
Again, effective for whom? The student, the teacher, the school, the system? #
mathchat
12:53 am
ColinTGraham
:
How would you go about designing or planning an effective lesson? What would be your criteria? #
mathchat
12:53 am
dweksler
:
@
ColinTGraham
Well, if review of student work/lesson study improves teachers' practice. I'd hope students benefit. Naive? #
mathchat
12:53 am
doctorjeff
:
@
ColinTGraham
@
dweksler
it's got to be effective for the student. It's all about the student. #
mathchat
12:54 am
padgets
:
#
mathchat
student centered creating content not spitting it back out :)
12:56 am
ColinTGraham
:
"It's all about the student." Is it? or is it about grades and getting students to go to university and validating the system... #
mathchat
12:56 am
doctorjeff
:
@
ColinTGraham
the math concept to be taught is used as a *vehicle* to understand some aspect of the world around us. #
mathchat
12:56 am
ColinTGraham
:
@
doctorjeff
I'm wearing my old cynic hat with the last statement! #
mathchat
12:57 am
doctorjeff
:
@
ColinTGraham
yes, it *needs* to be about the student. Depart from that and it is a disgrace to education. #
mathchat
12:57 am
ColinTGraham
:
@
padgets
So back to the earlier mention of engagement. If students don't see the purpose/relevance then it's ineffective? #
mathchat
12:58 am
doctorjeff
:
@
ColinTGraham
I could tell. But in truth that is how the system is being driven right now. #
mathchat
12:59 am
ColinTGraham
:
@
doctorjeff
Well, I could say "preaching to the choir".... You'd see an effective lesson as one which 'subverts' to student needs? #
mathchat
12:59 am
dweksler
:
@
doctorjeff
How do we tell if it is being effective for ALL the students? 1 on 1 tutorials? #
mathchat
12:59 am
padgets
:
@
ColinTGraham
#
mathchat
for me yes, want them to be focused in what content is presented, I want them to see application in the real world
1:00 am
doctorjeff
:
@
ColinTGraham
@
padgets
yes, no relevance to vast majority of students, then ineffective, in fact detrimental to math ed. #
mathchat
1:00 am
cybraryman1
:
RT @
padgets
#
mathchat
for me yes, want them to be focused in what content is presented, I want them to see application in the real world
1:00 am
ColinTGraham
:
@
dweksler
Ah good question, David. Differentiation is important but one size does not fit all... #
mathchat
1:01 am
doctorjeff
:
@
dweksler
I cannot see how anything can be effective for ALL students, but there is a bar, and we are not meeting it. #
mathchat
1:01 am
dweksler
:
@
ColinTGraham
I agree, Colin, just makes it more challenging to judge effective math teaching #
mathchat
1:02 am
ColinTGraham
:
So, does it become something which is effective for the teacher in that most of the students learn most of the stuff? #
mathchat
1:03 am
ColinTGraham
:
So far we seem to be saying effective lessons are studentcentred, purposeful, relevant and engaging. Anything else to add? #
mathchat
1:03 am
doctorjeff
:
I think I posted this in a prior #
mathchat
, but here is my view of math education:
http://bit.ly/6MmJ4i
1:04 am
padgets
:
#
mathchat
i can take a lesson deliver it in 29 different ways, that is what tech and differentiation does, keeps me hopping but so much fun
1:04 am
doctorjeff
:
@
ColinTGraham
but what do you mean by 'learn most of the stuff'? What is the stuff?? #
mathchat
1:05 am
doctorjeff
:
@
ColinTGraham
effective is not just about whether the kids learn stuff, but what stuff we are requiring them to learn and context. #
mathchat
1:05 am
ColinTGraham
:
@
doctorjeff
'Stuff' is the vague idea we have going into a lesson that it kind of fits the curriculum we have to teach.... ;) #
mathchat
1:05 am
nykat4
:
@
ColinTGraham
Awesome!! Monday i'll definitely be there  what time? #
mathchat
1:06 am
ColinTGraham
:
@
nykat4
It's earlier, 19:30 GMT for 90 minutes. #
mathchat
1:06 am
dweksler
:
Colin, in the US, at least, I think most teachers would say "effective" math teaching leads to higher scores on state tests #
mathchat
1:07 am
ColinTGraham
:
@
dweksler
So it comes back to the idea of "Efficacy"  i.e. making certain things happen no matter what... #
mathchat
1:08 am
bszczepanski1
:
RT @
padgets
: #
mathchat
student centered creating content not spitting it back out :)
1:08 am
nykat4
:
@
ColinTGraham
Ok  that's 2.30 pm EST, so will be teaching then, but can make if for last half hour. #
mathchat
1:08 am
ColinTGraham
:
OK, last 5 minutes, since we started late, any ideas or thoughts to add about what makes an effective mathematics lesson? #
mathchat
1:09 am
ColinTGraham
:
@
nykat4
Great, see you Monday, Katy! #
mathchat
1:09 am
padgets
:
#
mathchat
please make it apply to a real world application, as a math challenged person, this would have helped me :)
1:10 am
ColinTGraham
:
@
padgets
So, "effective" for you, Sharon, means something that can help you in real life. How about anyone else? #
mathchat
1:12 am
padgets
:
@
ColinTGraham
#
mathchat
yes :)
1:12 am
republicofmath
:
And contrarywise it would have turned me off as a student @
padgets
#
mathchat
please make it apply to a real world application
1:12 am
dweksler
:
@
ColinTGraham
Seems like too many students are turned OFF to math. Having more inquiry approaches would help, I believe #
mathchat
1:13 am
ColinTGraham
:
@
republicofmath
So what would have been "effective" for you, Gary? #
mathchat
1:13 am
republicofmath
:
No, as I student I hated applications. Changed now. @
ColinTGraham
#
mathchat
1:14 am
cybraryman1
:
@
dweksler
Making math more relevant to students is important. Problembased & Projectbased learning as well #
mathchat
1:14 am
ColinTGraham
:
If I'm honest, the teaching I received must have been largely effective, since I am now a maths teacher, who prefers statistics! #
mathchat
1:15 am
republicofmath
:
@
ColintGraham
. I do not think lessons are, or can be effective for students. For me it's a teacher perspective. #
mathchat
1:15 am
dweksler
:
@
cybraryman1
Absolutely more PBL (P=project/problem) is important #
mathchat
1:15 am
ColinTGraham
:
@
republicofmath
It is an important teacher perspective, but should it be one that students are encouraged to adopt....? #
mathchat
1:16 am
LizDk
:
students actively involved in their lesson #
mathchat
, students seeing relevance in the ideas involved
1:17 am
ColinTGraham
:
OK, people. That's it for this week.... Thank you for your contributions! The archive will be online in about 30 minutes. #
mathchat
1:17 am
padgets
:
#
mathchat
thanks for letting me converse with you all, learn so much! :)
1:18 am
LizDk
:
my continual challlenge relates to making it as student centered as poss  given time constraints and lack of ideas / training #
mathchat
1:18 am
ColinTGraham
:
@
padgets
Glad to have you with us Sharon! #
mathchat
1:19 am
ColinTGraham
:
@
LizDk
That's always going to be an issue. Training is a topic for another day, I think! #
mathchat
1:19 am
LizDk
:
ok I guess I came in a bit late, will look at archive #
mathchat
1:20 am
ColinTGraham
:
@
LizDk
If you get a chance, join us on Monday for the same topic... from 14:30 EST / 19:30 GMT for 90 minutes #
mathchat
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As it happened on Friday, 10th December 2010 00:00  01:00 GMT