Topic: How do we get our students to become more reflective learners?
As it happened on Thursday, 2nd September 2010, 23:30 - 00:30 GMT
11:31 pm
ColinTGraham:
Hello everyone, welcome to this week's #mathchat
11:32 pm
ColinTGraham:
For first-timers, don't try to keep up with everything, just interact with one or two people. Don't forget to use #mathchat
11:32 pm
ColinTGraham:
Tonight's topic: "How do we get our students to become more reflective learners?" #mathchat
11:33 pm
ColinTGraham:
This is a big topic! Let's try to keep a focus on reflective learning in a mathematical context! #mathchat
11:34 pm
ColinTGraham:
What do you see as the essential components of reflective learning in a maths class? #mathchat
11:36 pm
georgewoodbury:
I have had a lot of luck using Cornell notes to get my students to reflect on what we've done. #mathchat
11:36 pm
mthman:
The practice of reflecting in math needs to be a regular practice! Teacher feedback is also critical. #mathchat
11:38 pm
padgets:
#mathchat sorry I am late! I use Frayer models, semantic maps and concept maps for reflection
11:38 pm
ColinTGraham:
@georgewoodbury What are Cornell notes, for those unfamiliar with them George? #mathchat
11:39 pm
ColinTGraham:
@padgets Just in time Sharon, we're only just starting up! #mathchat
11:40 pm
ColinTGraham:
@mthman How do you see reflection as being different from thinking about problems, Ron? #mathchat
11:40 pm
mthman:
The last 5 minutes of class does not provide enough think time for reflective learners! #mathchat
11:40 pm
georgewoodbury:
Cornell notes have the note page broken into 3 sections. In section at the bottom, students summarize the page in 1-2 sentences. #mathchat
11:41 pm
padgets:
#mathchat I recently used glogster to have students do posters of a math concept in our science class they have used
11:41 pm
georgewoodbury:
Cornell notes: http://coe.jmu.edu/LearningToolbox/cornellnotes.html #mathchat
11:41 pm
ColinTGraham:
@padgets Frayer models, semantic and concept maps... links or further info, Sharon? #mathchat
11:42 pm
padgets:
#mathchat have also used webspiration to get kids to collborate with each other about how the vocab in a science relates to other subjects
11:42 pm
republicofmath:
First, and essential, step in #reflection in #math is to carry out acts/operations in imagination via recall. #mathchat
11:42 pm
ColinTGraham:
@mthman So do you build in extra time for reflective learners #mathchat
11:43 pm
Year7Numeracy:
@ColinTGraham Reflection is critical in understanding where they are at, and what to learn and improve on #mathchat
11:43 pm
georgewoodbury:
@padgets Love the glogster idea! #mathchat
11:44 pm
padgets:
#mathchat this might help to explain what I meant :- ) http://bit.ly/bqJvPj
11:44 pm
Year7Numeracy:
Self reflection is great but peer and class can be more effective-more ideas & understandings from others crystalises the concept #mathchat
11:45 pm
mathheadinc:
RT @mthman: The practice of reflecting in math needs to be a regular practice! Teacher feedback is also critical. #mathchat
11:45 pm
ColinTGraham:
@republicofmath This sounds more like teaching thinking skills rather than just reflection on learning... #mathchat
11:45 pm
padgets:
@georgewoodbury #mathchat thank you for the kind words :-)
11:45 pm
g4r37h:
does anyone use scenarios or role-play to encourage reflection? whether individually, as a group, on software etc? #mathchat
11:45 pm
republicofmath:
#reflection is as in a mirror: the inner mirror of imaginative recall in the absence of doing something. That's 1st step. #mathchat
11:46 pm
georgewoodbury:
I like writing assignments that call on students to reflect, but @Year7Numeracy has a good point about in class reflection. #mathchat
11:46 pm
mathheadinc:
Yes, what are they? RT @ColinTGraham: @georgewoodbury What are Cornell notes, for those unfamiliar with them George? #mathchat
11:46 pm
padgets:
@SarahAtInspSW thanks! here is a webspiration I did #mathchat
11:46 pm
mathheadinc:
RT @mthman: The last 5 minutes of class does not provide enough think time for reflective learners! #mathchat
11:46 pm
mathheadinc:
RT @georgewoodbury: Cornell notes: http://coe.jmu.edu/LearningToolbox/cornellnotes.html#mathchat
11:47 pm
ColinTGraham:
@mathheadinc Already explained with a link! Check the archive later... #mathchat
11:47 pm
cybraryman1:
On my Constructivist Teaching page I have some links for Constructivism in Math:http://bit.ly/ckPQUu #mathchat
11:47 pm
padgets:
#mathchat helps if I put up the link :-) heee http://bit.ly/d2Ei1A
11:47 pm
georgewoodbury:
@mathheadinc Cornell notes encourage students to think and reflect on what has gone on in class. #mathchat
11:48 pm
ColinTGraham:
Is student age important in the sense of reflecting/reviewing past topics versus thinking about the process of learning? #mathchat
11:48 pm
mathheadinc:
@ColinTGraham Just saw it, twanks! :D #mathchat
11:48 pm
ColinTGraham:
Links will be extracted later, so don't worry about checking them out now! #mathchat
11:49 pm
ColinTGraham:
RT @g4r37h: does anyone use scenarios or role-play to encourage reflection? whether individually, as a group, on software etc? #mathchat
11:49 pm
padgets:
#mathchat has anyone tried VoiceThread for reflection?
11:49 pm
padgets:
RT @cybraryman1: On my Constructivist Teaching page I have some links for Constructivism in Math: http://bit.ly/ckPQUu #mathchat
11:49 pm
republicofmath:
The ideas it affords being such only as the mind gets by reflecting on its own operations within itself (Locke, 1690, Book II, 4) #mathchat
11:50 pm
ColinTGraham:
@republicofmath What would be the second step, after recall...? #mathchat
11:51 pm
ghewgley:
The #mathchat Daily is out - read this Twitter newspaper on http://paper.li/tag/mathchat (18 contributions today)
11:51 pm
ColinTGraham:
RT @Year7Numeracy: Reflection is critical in understanding where they are at, and what to learn and improve on #mathchat
11:51 pm
mathheadinc:
@georgewoodbury I think well-formed questions could teach students to think and reflect on what they have learned. #mathchat
11:52 pm
ColinTGraham:
@republicofmath This sounds like an application of Bloom's Taxonomy in its revised form #mathchat
11:52 pm
mathheadinc:
@georgewoodbury I like the format of the Cornell notes. #mathchat
11:52 pm
republicofmath:
Child walking, pushes ball to roll ahead. As path goes up hill ball rolls back. "How does the ball know where I am?" child asks. #mathchat
11:53 pm
ColinTGraham:
@mathheadinc What age are you talking about here? When does reflection become something that Ss grasp as a concept...? #mathchat
11:53 pm
georgewoodbury:
@mathheadinc True, and I like the idea of students blogging their responses. #mathchat
11:54 pm
padgets:
#mathchat I think even a Kindergartener can tell you what they have done, when they did it, why they did it and if they could do it again
11:55 pm
ColinTGraham:
@republicofmath That is an example of curiosity, perhaps, in younger children... What is the next step in developing that? #mathchat
11:55 pm
marcelamomberg:
RT @cybraryman1: On my Constructivist Teaching page I have some links for Constructivism in Math: http://bit.ly/ckPQUu #mathchat
11:55 pm
padgets:
#mathchat, it is all about how you form the questions so they are age appropriate, drawing a picture to blogging on Twiducate, it can be
11:55 pm
g4r37h:
scenarios work. student solves problem in scenario and gets results. teacher asks why + how and student reflects while answering #mathchat
11:56 pm
ColinTGraham:
@padgets Can Kindergarteners say what they need to do to improve their learning process, though...? #mathchat
11:57 pm
g4r37h:
only issue is how 2 create a scenario thats engaging + absorbing enough to hold their attention and make them explore all options #mathchat
11:57 pm
ColinTGraham:
The message that seems to be coming through at the moment is a focus on the process on how a solution was reached. #mathchat
11:58 pm
mathheadinc:
@georgewoodbury I guess that's what the glogset could be for. I'll take a look. #mathchat
11:58 pm
padgets:
#mathchat I think they can maybe in not so many words but they can say yes or no to questions a teacher asks
11:58 pm
ColinTGraham:
@g4r37h I think @ddmeyer's WCYDWT approach offers one solution. #mathchat
11:58 pm
mathheadinc:
I think students should reflect on how they would explain a concept to someone else and then do it! #mathchat
11:59 pm
ColinTGraham:
@padgets If questions are asked by the teacher, have we moved away from reflective learning? #mathchat
11:59 pm
MichelleBurton:
I asked Ss to reflect on lesson an online google form after each class, summarizing the big ideas and asking qns they still had #mathchat
11:59 pm
georgewoodbury:
In class we teach them how and why. After the Ss practice "how" they need to reflect on the "why" to truly understand. #mathchat


ColinTGraham:
WCYDWT = what can you do with this, where Ss/Teachers are presented with a video, say, have to 'generate' the problem/solution #mathchat

g4r37h:
#mathchat that depends on the questions the teacher asks. yes or no questions are ok, but not as interesting as "how" and "why"?

mathheadinc:
RT @padgets: #mathchat, its all abt how U form the questions so they R age appropriate, drawing a picture 2 blogging on Twiducate, it cn B

padgets:
@ColinTGraham I think somewhat, but I think younger kids are better at showing what they know rather than speaking what they know #mathchat
12:01 am
ColinTGraham:
RT @padgets I think somewhat, but I think younger kids are better at showing what they know rather than speaking what they know #mathchat
12:01 am
Year7Numeracy:
We self assess after each assessment then discuss as a class areas to improve etc. Sometimes the kids learn better from each other #mathchat
12:02 am
ColinTGraham:
Is there a point where the teacher can/should stop asking questions altogether? #mathchat
12:02 am
mthman:
Ironically...my 5 y/o and I are having a reflective moment...be back shortly! #mathchat
12:02 am
g4r37h:
#mathchat if there was software available that created these scenarios (lots of different ones for different tastes), would you use it?
12:02 am
padgets:
#mathchat a math teacher on my team uses pbits problem based instructional tasks, to check for understanding, anyone else?
12:03 am
ColinTGraham:
@Year7Numeracy And you also blog your questions and responses for outside help too, Steve! #mathchat
12:03 am
mathheadinc:
Students should make up questions that they want to have answered during their reflection e.g. what happens if THIS changes? #mathchat
12:04 am
ColinTGraham:
@padgets pbits for those unfamiliar with it...? #mathchat
12:04 am
padgets:
#mathchat sure I think students should be encouraged to generate their own questions, maybe with a starter from me sometimes
12:05 am
ColinTGraham:
Does anyone use journals in Maths class? #mathchat
12:05 am
g4r37h:
#mathchat teacher can stop asking questions when they present another problem, related (but not too obviously) to the first after reflection
12:05 am
genghisjahn:
RT @republicofmath: Child walking, pushes ball to roll ahead. As path goes up hill ball rolls back. "How does the ball know where I am?" child asks. #mathchat
12:06 am
mathheadinc:
@padgets They could put them on the board to see that others have the same questions, then reflect on finding answers. #mathchat
12:06 am
padgets:
#mathchat PBITS Problem Based Instructional Tasks, she says they cause studnets to apply what math have learned in the real world
12:06 am
padgets:
@mathheadinc yep good idea! #mathchat
12:07 am
mathheadinc:
@ColinTGraham What goes in the journal? #mathchat
12:08 am
ColinTGraham:
@padgets So PBITs are an opportunity to apply what has been learned/taught? #mathchat
12:08 am
padgets:
#mathchat we are using twiducate in my science class, but have not heard of journals in math
12:08 am
ColinTGraham:
Well, that is the point... Learning journals are often used with adults for reflection RT @mathheadinc: What goes in the journal? #mathchat
12:09 am
g4r37h:
#mathchat do you prefer physical tangible pbits or would software on screens or an IWB with audio, video and different activities be better?
12:09 am
padgets:
@ColinTGraham #mathchat yes, I have done some cross curricular lessons with her and kids have done well and we know what needs re-taught
12:09 am
mathheadinc:
@ColinTGraham No really. My question is, do they write about their feeling or what they learned? #mathchat
12:10 am
georgewoodbury:
I have to run. Great job everyone. I'll be back for the archive! Another top notch #mathchat
12:10 am
padgets:
@g4r37h #mathchat I have only done physical PBITS
12:10 am
mthman:
@ColinTGraham Reflection requires careful analysis to one's own understanding...thinking about math is more reactionary #mathchat
12:11 am
mathheadinc:
@ColinTGraham Uh, I meant "not really"... #mathchat
12:11 am
ColinTGraham:
@mathheadinc If it is to encourage reflective learning, I think more on learned rather than feeling. #mathchat
12:12 am
mthman:
@ColinTGraham The main difference is time...think time (60 sec) vs reflection 5+ min #mathchat
12:12 am
mathheadinc:
@ColinTGraham Thank you, I was hoping you would say that :) #mathchat
12:12 am
g4r37h:
@padgets #mathchat interesting. would you use software aimed at PBITs if you had access to it and it was good enough?
12:12 am
ColinTGraham:
@mthman Reacting to what? Could you not reflect on more efficient ways to find a solution...? #mathchat
12:13 am
mthman:
@ColinTGraham I love journals for math, but also for good two-way dialogue (about anything!). #mathchat
12:13 am
padgets:
#mathchat could pattern it after our science journals where kids have to answer I now know, I discovered, I want to know more about
12:14 am
ColinTGraham:
@mthman Who gets to read learning journals? Would that affect things? #mathchat
12:14 am
padgets:
@g4r37h #mathchat sure, but we have a tight budget got 15% cut this year and for 9 teachers oh my it will be interesting :)
12:14 am
mathheadinc:
YES! RT @padgets: #mathchat could pattern it after R science journals whr kids have 2 answer I now know, I discovered, I wnt 2 know more abt
12:15 am
padgets:
@ColinTGraham #mathchat I think I would like to first then maybe after blacking out names maybe share
12:15 am
mthman:
@ColinTGraham Reacting to a question or call for a solution...or maybe it's semantics for me #mathchat
12:15 am
ColinTGraham:
How about a way of improving efficiency of problem-solving by using timed problems? Get there quicker = improved learning? #mathchat
12:16 am
mthman:
@ColinTGraham I read them...unless I ask them to blog about a topic! #mathchat
12:17 am
ColinTGraham:
@mthman The semantics is important here, I think, Ron. Reflection vs. Critical Thinking for example. CT is a step towards reflecn? #mathchat
12:17 am
g4r37h:
@padgets #mathchat when you say a tight budget, what are we talking about? how much would/could you pay for 8+ resources with 3 PBITs each?
12:18 am
g4r37h:
@ColinTGraham #mathchat and introduce a competitive element between the students you mean?
12:18 am
padgets:
@ColinTGraham #mathchat I am not sure about timed stuff, in science I do not do any of that what about anyone else?
12:19 am
ColinTGraham:
@g4r37h Competing against yourself is part of improvement. Being able to find a quicker way to solve a problem, for example #mathchat
12:20 am
ColinTGraham:
@padgets I am thinking here about becoming more efficient in how you design or approach a particular problem #mathchat
12:20 am
padgets:
@g4r37h #mathchat have $7500 to fund everything from chemistry to physics stuff, the Biology specimens , this also includes PD not good
12:21 am
g4r37h:
@ColinTGraham #mathchat true but i think most enjoy competing against others than against themselves. this is why F1 isnt about time trials!
12:22 am
padgets:
@ColinTGraham #mathchat I see well, I would like every problem to have some connection to a real world situation
12:22 am
ColinTGraham:
Are blogs a sustainable way to foster reflective thinking in mathematics, science...? #mathchat
12:22 am
g4r37h:
@ColinTGraham #mathchat but what is the incentive for students to shave a few seconds off how they reach the answer? you need a carrot
12:23 am
ColinTGraham:
@padgets Efficiency or cost-effectiveness is very much a real world situation, though, Sharon #mathchat
12:23 am
mthman:
@ColinTGraham "Thinking" happens in short bursts...reflection is a process that involves analysis & internal debate #mathchat
12:23 am
padgets:
#mathchat I love blogging with my kids, I get to know them and I use it to check for understanding
12:24 am
padgets:
@ColinTGraham #mathchat very true!
12:24 am
ColinTGraham:
@g4r37h I think there needs to be a design or planning stage where the Ss realize the importance of thinking through, b4 diving in #mathchat
12:24 am
padgets:
RT @mthman: @ColinTGraham "Thinking" happens in short bursts...reflection is a process that involves analysis & internal debate #mathchat
12:24 am
g4r37h:
@padgets #mathchat would you allow the problems to include exotic subjects like space travel espionage etc? or more like jane has 2 apples?
12:25 am
Year7Numeracy:
@ColinTGraham Blogs are an excellent way to sustain reflection.Check ours out!! :) At the same time, they are only 1 of many tools #mathchat
12:25 am
ColinTGraham:
@mthman Reflection also suggests looking at yourself and reviewing/checking yourself out... #mathchat
12:26 am
ColinTGraham:
@Year7Numeracy What other tools would you add to that Steve? e-Portfolios, videos,... #mathchat
12:27 am
g4r37h:
@ColinTGraham #mathchat of course. dont think such resources are 2 replace teacher skill - they merely serve as a tool for the teacher 2 use
12:27 am
padgets:
@g4r37h #mathchat no exclusions, because I would like them to be able to be creative thinkers and at the same time be critical thinkers
12:28 am
ColinTGraham:
OK last few minutes... any reflections on tonight's topic ;-) #mathchat
12:28 am
g4r37h:
@padgets #mathchat music to my ears thanks :) im working on such resources right now. your views and opinions are all very helpful 2 me
12:29 am
padgets:
#mathchat I appreciate you all sharing with a science geek, it gives me ideas to be a better teacher :)
12:31 am
ColinTGraham:
@padgets Mathematics is the language of the universe, Sharon! #mathchat
12:31 am
mthman:
AGREED - 100%! RT @ColinTGraham: @mthman Reflection also suggests looking at yourself and reviewing/checking yourself out... #mathchat
12:32 am
mathheadinc:
@mthman As in "what can I do better?", yes, excellent. #mathchat
12:33 am
ColinTGraham:
OK thanks everyone, the archive will be up in about 30 minutes! See you next time! #mathchat
12:33 am
mathheadinc:
@padgets How fun is that! Always nice to see you at #mathchat :D
12:35 am
mthman:
@mathheadinc Yes, "Can I do better?" but also...do I have a complete understanding of the issue or is there still disequilibrium #mathchat
12:35 am
ColinTGraham:
Don't forget we'll be revisiting the same topic on Monday next week! Good night all. #mathchat
12:35 am
Year7Numeracy:
@michelleburton Our class maths and science blog can be found here http://bit.ly/abeWao#mathchat Feedback always welcome :)
12:35 am
g4r37h:
#mathchat night all and thanks for the informative tweets!
12:36 am
ColinTGraham:
@Year7Numeracy Another shamless plug Steve! #mathchat
12:36 am
mthman:
@rushtheiceberg Here is the original prompt: What do you see as the essential components of reflective learning in a maths class? #mathchat