Topic (follow-up to Friday, 10th December 2010):
What makes an effective mathematics lesson?
As it happened on Monday, 13th December 2010, 19:30 - 21:00 GMT
7:31 pm
ColinTGraham:
Hello everyone and welcome to today's #mathchat
7:32 pm
ColinTGraham:
Today's topic is: "What makes an effective mathematics lesson?" #mathchat
7:32 pm
suburbanlion:
@ColinTGraham greetings #mathchat!
7:33 pm
ColinTGraham:
@suburbanlion Hi Ryan. #mathchat
7:33 pm
bartoneducation:
@ColinTGraham #mathchat In my experience it is pace, one or two key concepts and more pace!
7:34 pm
ColinTGraham:
One idea that emerged on Thursday was that 'effectiveness' may only be a teacher perspective... Any thoughts? #mathchat
7:34 pm
kevcreutz:
I read a good blog post today about what it means to be a good teacher. Can apply to math lessonshttp://bit.ly/i863QO #mathchat
7:34 pm
ColinTGraham:
@bartoneducation Pace of what... introduction, work, is the pace adjusted? #mathchat
7:35 pm
suburbanlion:
"Relevance" is an important quality of an effective mathematics lesson. Students need to be able to personally relate to topic. #mathchat
7:35 pm
ColinTGraham:
@kevcreutz Thanks Kevin, I'll put it in the links to read later. #mathchat
7:36 pm
kevcreutz:
@suburbanlion Do you think it is possible for students to personally relate to every topic? #mathchat
7:36 pm
ColinTGraham:
@suburbanlion Do you see relevance and relating as being the same, or just connected in some way? #mathchat
7:36 pm
suburbanlion:
@ColinTGraham I can see that. We tend to measure "effectiveness" by formal assessments. #mathchat
7:37 pm
bartoneducation:
@ColinTGraham #mathchat. Introduction certainly but also any teacher interaction plus ending. Work should be slower. Just my experience.
7:37 pm
ColinTGraham:
@suburbanlion Effectiveness may also be related to @bartoneducation's comment about pacing too. Speed of learning...? #mathchat
7:38 pm
bartoneducation:
And experience is mainly with small groups tutoring. Say 3-5. #mathchat So may not apply across widely-differentiated class.
7:38 pm
Janshs:
is effective same as 'good'? does the subject content matter? what do stdts think? #mathchat when I asked some they said structure & help
7:38 pm
ColinTGraham:
@kevcreutz Maybe it's the degree of relationship between the student and the topic... everyone relates at some level. #mathchat
7:39 pm
maxmathforum:
#mathchat on the subject of relevance, i really like @rileylark's blog post about it:http://larkolicio.us/blog/
7:40 pm
TAtoTeacher:
RT @ColinTGraham: Today's topic is: "What makes an effective mathematics lesson?" #mathchat
7:40 pm
ColinTGraham:
@Janshs Technically 'effective' means 'causing to happen' but is often conflated with efficiency and efficacy too... #mathchat
7:40 pm
Janshs:
@ColinTGraham does the tchr foster that relationship betwn stdt & subject? how? is that when it becomes effective? #mathchat
7:40 pm
daveinstpaul:
An effective lesson builds connections with other topics and promotes a deeper understanding of those topics. #mathchat
7:41 pm
ColinTGraham:
@Janshs I wonder if "effective" is an educator word. Students may say enjoyable, fun or interesting, or even "Aha!" #mathchat
7:41 pm
ColinTGraham:
@maxmathforum Thanks for that Max, I'll add it to the links archive later. #mathchat
7:42 pm
bartoneducation:
#mathchat. This is all about the relevance issue, I think. brilliant guy. http://bit.ly/gI3MJo
7:42 pm
Janshs:
@ColinTGraham aha! yes, def a most important thing, I would say esp for Maths someho #mathchat
7:42 pm
ColinTGraham:
@daveinstpaul Do you mean topics within maths or between maths and other subjects, or both? #mathchat
7:44 pm
ColinTGraham:
We didn't pin down what 'effective' meant on Thursday... grasping of concepts, speed of learning, understanding, covering curric? #mathchat
7:46 pm
Janshs:
@ColinTGraham I think understanding might be the key but hard to say when it has happened #mathchat
7:46 pm
ColinTGraham:
To go back to Ryan's (@suburbanlion) earlier comment... how do we measure effectiveness? Is it only valid by formal assessment? #mathchat
7:46 pm
suburbanlion:
@kevcreutz different students might relate to different topics, but everyone should have an opportunity to relate to at least one. #mathchat
7:47 pm
daveinstpaul:
@ColinTGraham I mean topics within math. It's important that students begin to perceive that math is a whole. #mathchat
7:48 pm
ColinTGraham:
@Janshs How deep does the understanding need to go? Or is that asking how long is a piece of string? #mathchat
7:48 pm
RGriffithJR:
@kevcreutz Have you seen these? Interactive Math and Science tutorials http://bit.ly/aPazAc#mathchat
7:49 pm
suburbanlion:
@ColinTGraham it shouldn't *just* be formal assessments. Behavioral observations can be a good indicator of effectiveness. #mathchat
7:49 pm
daveinstpaul:
@ColinTGraham Learning to perceive science as a whole would be even better, but I'm not smart enough to pull it off. #mathchat
7:50 pm
ColinTGraham:
@daveinstpaul Connections were certainly raised as a key point in Thursday's #mathchat would 'abolishing' topics help at all?
7:50 pm
maxmathforum:
#mathchat one way to assess is if students can tell an "understanding story" at the end of the unit: tell the concept, method, & procedures
7:51 pm
ColinTGraham:
@suburbanlion I agree, not *just* formal assessments, but my question is more about the validity of measurement of effectiveness #mathchat
7:52 pm
Janshs:
@ColinTGraham that's the Big Q isn't it? #mathchat I think maybe it's unanswerable but we can continually check for understanding along way
7:52 pm
ColinTGraham:
@maxmathforum The telling would need to be a retelling rather than a regurgitation of information, though... #mathchat
7:53 pm
ColinTGraham:
@daveinstpaul So you would see or like to see something more like the STEM approach to improve effectiveness in mathematics, Dave? #mathchat
7:53 pm
suburbanlion:
@ColinTGraham maybe we should end each class with a 20 question survey about the effectiveness of the day's lesson </sarcasm> #mathchat
7:54 pm
maxmathforum:
@ColinTGraham but the connection between concept, method, and procedure would have to be the students' own ideas/learning #mathchat
7:54 pm
ColinTGraham:
@suburbanlion The quick review of "what did you learn today?" or introducing journals for reflection may work though... #mathchat
7:56 pm
ColinTGraham:
@maxmathforum Applying procedures or 'creating' procedures in new situations maybe a sign of effectiveness of earlier work... #mathchat
7:56 pm
daveinstpaul:
@ColinTGraham I don't want to abolish topics, I'm just saying that it's important to show the connections between them. #mathchat
7:58 pm
ColinTGraham:
@daveinstpaul Certainly understanding can be deepened if connections between algebra & geometry are used more than they are now #mathchat
7:59 pm
ColinTGraham:
Let's expand the discussion a little... How would you, or could you, design an effective lesson? #mathchat
8:01 pm
maxmathforum:
backwards. start with what i want the students to understand and do at the end, then think what experiences theyll have on the way #mathchat
8:02 pm
ColinTGraham:
@maxmathforum So we could call that a goal-focused or product-focused approach? How do you choose what needs to be understood? #mathchat
8:06 pm
ColinTGraham:
Is effectiveness immediately measurable or noticeable? Should it be? #mathchat
8:09 pm
maxmathforum:
@ColinTGraham i use the curriculum and state standards to choose content/topic and solve problems to uncover the key math ideas #mathchat
8:11 pm
padgets:
RT @maxmathforum: backwards. start with what i want the students to understand and do at the end, then think what experiences theyll have on the way #mathchat
8:11 pm
DelaneyKirk:
RT @maxmathforum: backwards. start with what i want the students to understand and do at the end, then think what experiences theyll have on the way #mathchat
8:11 pm
ColinTGraham:
@maxmathforum So 'imposed' curriculum is a constraint... would you ever want to start something without a clear goal? #mathchat
8:13 pm
suburbanlion:
@maxmathforum seems like we often don't have any choice but to use "backwards design", doesn't it? #mathchat
8:13 pm
maxmathforum:
@ColinTGraham if i didn't have a curriculum to cover, i'd start with the clear goal of "learning/doing as much math as possible" #mathchat
8:14 pm
maxmathforum:
@ColinTGraham and i'd measure effectiveness that way. #mathchat
8:14 pm
ColinTGraham:
@suburbanlion @maxmathforum Maybe effectiveness comes from a 'bridging' approach with start & end defined but nothing clear btwn #mathchat
8:15 pm
maxmathforum:
@ColinTGraham the "curriculum" would start with good problems and continue with whatever the students wanted to explore next #mathchat
8:15 pm
CarissaJuneK:
@fouss, @msgregson, @druinok and any other alg 2 tweeps-any fun things for rational expressions, I'm struggling with engagement #mathchat
8:15 pm
daveinstpaul:
Yes. effectiveness is noticeable. Good teachers know when they are getting through; students know when they are learning. #mathchat
8:15 pm
maxmathforum:
@ColinTGraham I think there are experiences in between that students need to have. It's the content that I'm agnostic about #mathchat
8:16 pm
ColinTGraham:
@maxmathforum A problem-solving curriculum, which requires the discovery/use of mathematics as a major part of the process then... #mathchat
8:16 pm
padgets:
#mathchat Hi everybody! lurking this afternoon as kids work :)
8:17 pm
ColinTGraham:
@padgets Hi Sharon, better make sure they don't blow something up in the lab! #mathchat
8:18 pm
ColinTGraham:
RT @Totallywired77: @maxmathforum sorry to jump in, but in my experience a challenge or problem based lesson is far more engaging. #mathchat
8:19 pm
ColinTGraham:
@Totallywired77 No need to apologise, #mathchat is an open discussion!
8:19 pm
maxmathforum:
@totallywired77 more engaging thatn what? thanks for jumping in! #mathchat
8:19 pm
suburbanlion:
RT @maxmathforum Students think effective teachers tell the answer clearly. Teachers think students should think. #mathchat
8:21 pm
ColinTGraham:
@suburbanlion This suggests that Ss see mathematics as 'finding answers' whereas teachers see it as some kind of challenge... #mathchat
8:22 pm
ColinTGraham:
RT @Totallywired77 "asking" the students what & how they want to learn is a great start giving them ownership of their learning #mathchat
8:23 pm
suburbanlion:
@ColinTGraham they've been drilled to death by worksheets, can we really blame them for wanting the easy answer? #mathchat
8:24 pm
ColinTGraham:
Summarizing so far: Effectiveness = connections between topics, understanding, clear learning outcomes, ownership/relevance... #mathchat
8:26 pm
Janshs:
@ColinTGraham plus reflection, speculation? #mathchat
8:26 pm
ColinTGraham:
Is effectiveness in a mathematics lesson the same as effectiveness in other lessons? If not, what are the differences? #mathchat
8:27 pm
ColinTGraham:
And we could add: communicating mathematically with others... RT @Janshs: @ColinTGraham plus reflection, speculation? #mathchat
8:27 pm
frogphilp:
@ColinTGraham Variety is important - sometimes use rigid scaffold where teacher determines outcome' sometimes negotiated scaffold #mathchat
8:29 pm
ColinTGraham:
@frogphilp Variety of content, or variety of approach to a single topic or variety of lesson structure or...? #mathchat
8:29 pm
Totallywired77:
#mathchat the big picture and relating it to real life is paramount - who decides how effective learning is? SMT, staff, Ofsted, students?
8:30 pm
Totallywired77:
#mathchat In my mind I know the answer
8:30 pm
ColinTGraham:
@Totallywired77 This also raises the question: Is there a difference between short-term effect and long-term effect? #mathchat
8:30 pm
frogphilp:
@ColinTGraham Pedagogical variety. Change the way the teacher engages with the student from week to week. One approach=stagnation #mathchat
8:31 pm
Totallywired77:
#mathchat all of these ideas should not be specific to Maths - all a good recipe for accelerated learning
8:32 pm
ColinTGraham:
@frogphilp Overall lesson structure may be the same, but way of introducing may change, eg different types of warm-up, review...? #mathchat
8:33 pm
ColinTGraham:
@Totallywired77 Does this mean you see effectiveness as related to speed of learning, then? #mathchat
8:33 pm
frogphilp:
@ColinTGraham sometimes start with child's problem (re: birthday question); other times start with teacher-determined outcome #mathchat
8:34 pm
Totallywired77:
@ColinTGraham #mathchat long term effect or learning is the key, using short term techniques - learning in chunks, chunking!
8:35 pm
ColinTGraham:
@frogphilp This sounds like @Janshs's earlier comment about teacher building relationships between the Ss and the subject #mathchat
8:35 pm
Totallywired77:
@ColinTGraham #mathchat not speed of learning but accelerating secure learning and making it useful and important to the student
8:36 pm
ColinTGraham:
@Totallywired77 The challenge with chunking is preserving the wider connections between the chunks... #mathchat
8:37 pm
frogphilp:
@ColinTGraham Yes probably. I only just tuned in tonight in the middle of the interesting discussion... #mathchat
8:37 pm
57mason:
@Totallywired77 indeed, you seen this? http://www.youtube.com/watch?v=60OVlfAUPJg #mathchat
8:39 pm
ColinTGraham:
Can a lesson ever be equally effective for all the Ss? Under what circumstances, or how, do you judge effectiveness? #mathchat
8:40 pm
Totallywired77:
@57mason #mathchat yep just watched it - think all 'mathchatters' should be invited to nv4l!!
8:41 pm
frogphilp:
@ColinTGraham Lessons always relate to other lessons so can't be judged as equally effective for all students. #mathchat
8:42 pm
Totallywired77:
@ColinTGraham #mathchat Student Voice and then getting them to teach others "if you can explain it, you understand it" A.Einstein
8:42 pm
ColinTGraham:
@frogphilp Which begs the question: Who should the lessons be effective for, if not for all...? #mathchat
8:44 pm
frogphilp:
Lessons should be effective for all. #mathchat
8:44 pm
Totallywired77:
@ColinTGraham #mathchat bitesized easily accessible learning opportunities for students-they need to feel sense of achievement in 1hr lesson
8:44 pm
ColinTGraham:
@Totallywired77 I sometimes wonder what sort of curriculum Ss would design, given half a chance... would it be effective for them? #mathchat
8:45 pm
Janshs:
Dylan Wiliam http://is.gd/i2Oh5 #mathchat
8:45 pm
ColinTGraham:
I might add "effective to some degree..." RT @frogphilp: Lessons should be effective for all. #mathchat
8:46 pm
frogphilp:
@ColinTGraham My children's learning sequence was determined by the children this term. They said what they wanted to learn first. #mathchat
8:47 pm
ColinTGraham:
@frogphilp Did they have a list of things to choose from or was it completely free choice, Steve? #mathchat
8:48 pm
frogphilp:
@ColinTGraham It was a Google Spreadsheet with the question: "What do you want to learn?" I put the results in Wordle. #mathchat
8:49 pm
ColinTGraham:
@Totallywired77 Sense of achievement or some kind of success for Ss... do Ss have to measure/feel this themselves though? #mathchat
8:49 pm
Totallywired77:
@ColinTGraham #mathchat seriously whynot?? Getting students involved with designing SoW would be amazing!!
8:51 pm
davidwees:
Khan Academy New Features - "Learn" (emphasis mine) More than Ever Before http://bit.ly/hWqqt7#edchat #mathchat
8:51 pm
ColinTGraham:
@frogphilp How closely did ideas correspond to the established curriculum i.e. was choice informed? Did you feel it was effective? #mathchat
8:52 pm
ColinTGraham:
@Totallywired77 It would take a very supportive admin to allow Ss to design schemes of work for secondary level... #mathchat
8:53 pm
padgets:
#mathchat I have 45 different ways to teach a lesson and assess a lesson - students get to choose, thanks to tech it works
8:54 pm
ColinTGraham:
In the last five minutes or so, any final thoughts about effectiveness, what it is, how it's measured etc? #mathchat
8:54 pm
Totallywired77:
@ColinTGraham #mathchat true, you would need a supportive risk taking grp of staff - but that's how learning goes from good to great
8:54 pm
ColinTGraham:
@padgets One way one student, or one way one class, or a mix, Sharon? #mathchat
8:55 pm
frogphilp:
@ColinTGraham Ideas were around key skills. It was effective because it put the weakest area (division) first + Ss had ownership #mathchat
8:57 pm
ColinTGraham:
@frogphilp Was this with your 8yo class, Steve? #mathchat
8:57 pm
frogphilp:
#mathchat A lesson's effectiveness can be judged by what the student is doing and thinking about in twenty years time.
8:57 pm
frogphilp:
@ColinTGraham It's a mixed group from 8-11 #mathchat
8:57 pm
Totallywired77:
#mathchat All of what has been discussed can be achieved by using "New Technologies" in the classroom. I recommend taking a look at @nv4l
8:58 pm
57mason:
RT @Totallywired77: #mathchat All of what has been discussed can be achieved by using "New Technologies" in the classroom. I recommend taking a look at @nv4l
8:59 pm
mrgamble6:
#mathchat Great discussion. This term I let my students decide what they wanted to learn . Paired them. Gave resources. Let them go for it.
8:59 pm
ColinTGraham:
@Totallywired77 Just when the government is cutting budgets for ICT... :-( Maybe effectiveness = innovative use of techology! #mathchat
8:59 pm
mrgamble6:
#mathchat I roved, helped where needed. It was incredibly effective.
9:00 pm
ColinTGraham:
OK, that's it for another topic! Thanks to everyone for your contributions. Nice to see some new people too! #mathchat
9:01 pm
padgets:
#mathchat sorry kids needed me, it is a mix, and I am less stressed and having fun :)
9:01 pm
ColinTGraham:
Follow @mathchat to keep updated. Don't forget to vote for the next topic either: http://bit.ly/c9KL7w#mathchat
9:03 pm
Janshs:
RT @ColinTGraham: Follow @mathchat to keep updated. Don't forget to vote for the next topic either:http://bit.ly/c9KL7w #mathchat
9:04 pm
ColinTGraham:
Archive will be online in about 30 minutes or so. See you next time! #mathchat
9:05 pm
xmath2007:
@ColinTGraham What stdnts want/think should be taken w/ grain of salt. 20 yr ago nobody wanted an iPod or HDTV #mathchat
9:07 pm
xmath2007:
@ColinTGraham Good ??? What is "effective lesson"? What does it look like? #mathchat