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 no-one 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 "philosophy-of-site-essay" 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 student-centred, 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 contrary-wise 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. Problem-based & Project-based 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