Topic (follow-up to Friday, 25th March 2011):
How do I teach to a specific, prescribed curriculum?
As it happened on Monday, 28th March 2011, 20:30 - 22:00 GMT
7:30 pm
republicofmath:
Where is #mathchat for March 28, 2011?
7:32 pm
republicofmath:
OK, I'll start. "How do I teach to a specific, prescribed curriculum?" With a distinct lack of grace on my part #mathchat
7:32 pm
republicofmath:
"How do I teach to a specific, prescribed curriculum?" I happens rarely to me - mainly when I teach calculus #mathchat
7:32 pm
ColinTGraham:
Hello everyone and welcome to #mathchat
7:32 pm
davidwees:
@republicofmath I'm kid-sitting my son & one of his friends, hence my absence from #mathchat.
7:33 pm
republicofmath:
Oi, Colin, where you been? @ColinTGraham #mathchat
7:34 pm
ColinTGraham:
@republicofmath What is it about calculus in particular that 'forces' prescription, Gary? #mathchat
7:35 pm
ColinTGraham:
Waiting for my PC to restart after updates! RT @republicofmath: Oi, Colin, where you been? #mathchat
7:36 pm
republicofmath:
"Calculus", u'grad, single to multivariable, is an "industry". Dept chooses book, engineers, scientists expect set curriculum. #mathchat
7:36 pm
ColinTGraham:
Anyone else out there for #mathchat today?
7:37 pm
Tina_Barr:
RT @ColinTGraham: Anyone else out there for #mathchat today?
7:38 pm
ColinTGraham:
@republicofmath So do you 'teach' the text, or find inventive ways to get around it/use it as a supplement? #mathchat
7:40 pm
republicofmath:
@ColinTGraham Do get round it. Most recent inventive way, Calc 3, was to get students choosing own curves/surfaces. More projects #mathchat
7:42 pm
republicofmath:
I have given up on tests and exams. Big relief all round. #mathchat
7:43 pm
maxmathforum:
hi #mathchat team... I'm here sporadically on a loose internet connection
7:43 pm
ColinTGraham:
@republicofmath If textbooks provide problems with solutions, then u'grads should be able to self-test anyway... #mathchat
7:43 pm
republicofmath:
Where are folks who voted for #mathchat topic? Dozy Doras!
7:43 pm
ColinTGraham:
@maxmathforum Hi Max, sporadic is ok, we're here all week ;-) #mathchat
7:43 pm
MrHonner:
@republicofmath I teach multi in HS and see/feel the expected curriculum, but I don't mind it. It's such rich material. #mathchat
7:44 pm
ColinTGraham:
@MrHonner Is there more expectation of specified content at HS level and beyond, do you think? #mathchat
7:45 pm
republicofmath:
@maxmathforum Will we be able to classify all sporadic mathchatterers, or do they not form a group? #mathchat
7:46 pm
ColinTGraham:
@republicofmath How do Ss choose? Is it completely free or some kind of guided choice? #mathchat
7:46 pm
MrHonner:
@ColinTGraham I don't expect my students to 'skip' multi in college, but I want them to see everything they'd see in that course. #mathchat
7:47 pm
maxmathforum:
I coach at 2 schools, one with a "problem-based" curriculum, one with a traditional curriculum. Both have their challenges. #mathchat
7:48 pm
ColinTGraham:
@maxmathforum I meant more that HS/Univ curriculum tends towards greater specialization, therefore prescription is more likely... #mathchat
7:49 pm
republicofmath:
Forgive me for seeming presumptuous, but I cannot imagine a student from HS skipping multivariable calculus in college. #mathchat @MrHonner
7:49 pm
ColinTGraham:
@maxmathforum How 'free' is the content or focus in each... one assumes traditional curric is more highly prescribed/structured #mathchat
7:49 pm
maxmathforum:
@ColinTGraham is it proscribed what students should know or how they should learn it. or does proscribing what determine how? #mathchat
7:50 pm
MrHonner:
I teach at a large (5K student) HS, and we have huge problems because teachers are not on the same page, metaphorically speaking. #mathchat
7:51 pm
republicofmath:
@MrHonner Do you teach Stokes' theorem in HS multivariable calculus? #mathchat
7:51 pm
maxmathforum:
#mathchat teachers feel the "how" is too proscribed in problem-based (and get bogged down in the investigations w/out reflection & mastery)
7:51 pm
ColinTGraham:
@maxmathforum A proscribed curriculum would be teaching forbidden things... sounds like fun! We're discussing prescribed #mathchat
7:51 pm
MrHonner:
Just saying that, although we may see curriculum as a restriction, there is something to be said for uniformity of instruction #mathchat
7:52 pm
maxmathforum:
#mathchat the "what" is more proscribed in traditional -- the skills for mastery and tchrs feel the pacing requires a "xxx" style teaching
7:52 pm
maxmathforum:
#mathchat xxx = explain, example, exercise
7:52 pm
republicofmath:
@ColinTGraham @maxmathforum No, let's go proscribed! #mathchat
7:52 pm
MrHonner:
@republicofmath Stokes, Div, Grad, Curl, all that! Like I said, though, I don't recommend that my students skip multi in college. #mathchat
7:53 pm
ColinTGraham:
@maxmathforum So the prescription in the two curricula is focused on different things... one on content, the other on process? #mathchat
7:54 pm
republicofmath:
Doesn't seem possible to me. We have great trouble teaching that to sophomores. Lacking algebra skills are killer @MrHonner #mathchat
7:54 pm
maxmathforum:
@ColinTGraham that's how the tchrs I coach feel. Hard to read the traditional curriculum and think of projects or explorations #mathchat
7:55 pm
ColinTGraham:
@MrHonner So you try to go for a 'taster' approach to curriculum? Is coverage an issue with multivariate calculus? #mathchat
7:55 pm
republicofmath:
@MrHonner How do you teach about connected and simply connected domains to HS students? #mathchat
7:55 pm
maxmathforum:
@ColinTGraham and hard to read the investigation curricula and extract the goals, big ideas, take-aways, etc. #mathchat
7:56 pm
ColinTGraham:
@maxmathforum Much of that comes from a lack of imagination or creativity on the part of the teacher, though, doesn't it? #mathchat
7:56 pm
maxmathforum:
@ColinTGraham so it's hard not to teach "straight from the book" in both cases, getting lost in details either way #mathchat
7:57 pm
MrHonner:
@republicofmath I teach at a large 'magnet' school in NYC.Students are very sharp. For many of them, really anything is possible. #mathchat
7:57 pm
maxmathforum:
@colintgraham reading curriculum is hard. lack of effective time on task, for sure. #mathchat
7:57 pm
ColinTGraham:
@maxmathforum What I found irritating was the long reading list we had at college, & lecturers then did not refer to the books... #mathchat
7:58 pm
maxmathforum:
@MrHonner do you think you could have taught it before awesome graphing technology was invented? #mathchat
7:58 pm
maxmathforum:
@ColinTGraham in which courses? #mathchat
7:59 pm
ColinTGraham:
@maxmathforum It was all the general maths courses, the Stats/Probability was different. One text would have sufficed too... #mathchat
7:59 pm
republicofmath:
@MrHonner Not getting feel for if you're teaching "techniques" such as D(x^n)=nx^(n-1) or concepts, or both. #mathchat
8:00 pm
MrHonner:
@republicofmath Very informally. We work through the ideas and techniques using simple domains. #mathchat
8:00 pm
republicofmath:
@MrHonner Multivariable calculus is a rich collection of concepts and techniques. Even Harvard u'grads struggle. #mathchat
8:01 pm
MrHonner:
@republicofmath Big ideas and techniques. Hopefully they get the rigor the next time through; same with AP Calc, I guess. #mathchat
8:01 pm
ColinTGraham:
@maxmathforum Do you think that the 'itemization' / disconnection of topics in curricula compounds the issues of teaching to them? #mathchat
8:01 pm
republicofmath:
@MrHonner Well, I congratulate you for what you're doing. How many students can cope with it? #mathchat
8:01 pm
ColinTGraham:
@republicofmath You lost me at calculus... ;-P #mathchat
8:03 pm
MrHonner:
@maxmathforum Maple / Wolfram certainly helps, but being able to piece together surfaces with limited info is a key skill. #mathchat
8:03 pm
ColinTGraham:
Does the curriculum you teach pose greater challenges for working with higher ability or lower ability students? #mathchat
8:03 pm
republicofmath:
Problem we have often is students having done AP calc in HS think D(2^x) = x2^(x-1). Just learned conditioned response #mathchat
8:04 pm
republicofmath:
@ColinTGraham Really, Colin. You are the limit! #mathchat
8:05 pm
maxmathforum:
@ColinTGraham Absolutely! I don't know if there just isn't agreement on the big ideas, themes, stories, skills etc. in math #mathchat
8:05 pm
republicofmath:
@ColinTGraham. Way I teach now is by projects - 2-3 weeks. Studio style. Low/high ability irrelevant. #mathchat
8:06 pm
maxmathforum:
@ColinTGraham but I've rarely found a textbook that was really clear about the big, big ideas that held it together #mathchat
8:06 pm
ColinTGraham:
@republicofmath Only as x→∞, Gary #mathchat
8:06 pm
MrHonner:
I see the same thing with the AP students. There's a good example of curriculum gone bad, I feel--all test prep, it seems. #mathchat
8:07 pm
maxmathforum:
@republicofmath when u teach the prescribed calc course, where do you get projects from? how do u cover curriculum w projects? #mathchat
8:07 pm
ColinTGraham:
@maxmathforum When a department chooses a text, though, you would expect it to form some kind of core for the course, wouldn't you #mathchat
8:07 pm
republicofmath:
@MrHonner Which textbook, if any do you use? (ref http://wp.me/p1mk0j-1cv ) #mathchat
8:08 pm
ColinTGraham:
@maxmathforum Moving towards a collection of 'chapters' from various texts and/or open source apps would seem a better way to go. #mathchat
8:09 pm
MrHonner:
We're using Larson this year, have used Stewart in the past. New books every few years--good way to earn a dollar! #mathchat
8:10 pm
ColinTGraham:
@republicofmath Is coverage of curriculum a challenge in a project-based approach or are other issues more important? #mathchat
8:12 pm
maxmathforum:
@ColinTGraham why? 'cause it's cheaper? or better? i kinda like textbooks when they're decent... gives us a project to tackle #mathchat
8:13 pm
republicofmath:
@ColinTGraham Don't mean to be fatuous when say given up "covering" material. Focus on teaching students. Learning goals/outcomes #mathchat
8:14 pm
ColinTGraham:
@maxmathforum Not so much cost, as allowing you to construct a course text which does clarify or highlight the 'big ideas' #mathchat
8:14 pm
mathfour:
Just happened to pop by - checking out my peop's at #mathchat. Y'all having fun?
8:15 pm
ColinTGraham:
@mathfour yes thanks, Bon! You going to join us again? We're discussing teaching to a prescribed curriculum #mathchat
8:15 pm
republicofmath:
I'm contemplating not-for-profit organization to produce open source texts and h'work grading system #mathchat
8:16 pm
ColinTGraham:
@republicofmath I think a lot of problems arise when people focus too much on 'coverage' just because it is in the curriculum... #mathchat
8:18 pm
ColinTGraham:
@republicofmath You could, for example, get 65% for a grade C by doing 65% of the curriculum in depth, rather than 65% 'skimming' #mathchat
8:21 pm
MrHonner:
Whether you value the standardized test or not, I think you need to "cover" all the material--not fair to the students, otherwise.#mathchat
8:22 pm
MrHonner:
@republicofmath A noble venture! Good luck! Free e-books will be easier than a free hw-grading system, I bet. #mathchat
8:22 pm
ColinTGraham:
RT @pawatt Doing exactly this with a group who have C's but now have chance to sit higher, pick what they can understand/replicate #mathchat
8:23 pm
republicofmath:
@MrHonner Who decides what material to cover. Isn't that the point of this #mathchat ?
8:23 pm
pawatt:
@MrHonner #mathchat some classes are just not going to get some topics so why confuse them?
8:24 pm
MrHonner:
For my school, the NY Board of Regents decides what we're going to cover. #mathchat
8:25 pm
republicofmath:
Time to go home. Let dog - http://bit.ly/fhnD45 - out for run. Thanks for conversation #mathchat
8:25 pm
ColinTGraham:
The question, given a particular curriculum, is where and how the decision is made about what to cover... ideally it should be Ss #mathchat
8:25 pm
ColinTGraham:
@republicofmath Thanks for getting things kicked off Gary, see you next time! #mathchat
8:26 pm
pawatt:
#mathchat Curriculum is an amalgamate of what they need pass a test, what they need continue studying and what might be relevant latter on
8:27 pm
ColinTGraham:
@pawatt Any curriculum should probably also allow for differentiation of ability/level too... #mathchat
8:30 pm
ColinTGraham:
@MrHonner When you say "BoR decides" that presumably means deciding on content, do they monitor if everything's been taught tho'? #mathchat
8:31 pm
pawatt:
@ColinTGraham #mathchat - agreed, actually really miss the intermediate paper
8:32 pm
pawatt:
#mathchat - and even if it has been taught, have they learned it. Scolded by a pupil for teaching from first principles, wanted answers only
8:34 pm
ColinTGraham:
@pawatt There can be that too... students/parents(?) 'demanding' that you only use the course text, teach algorithms and formulae #mathchat
8:34 pm
MrHonner:
@ColinTGraham In theory, results of the state exams identify what's been taught [effectively]. They do love drilling that data! #mathchat
8:36 pm
ColinTGraham:
@MrHonner You'd have to have extremely well-designed tests to effectively identify whether or not a particular item had been done! #mathchat
8:38 pm
pawatt:
#mathchat biggest problem is low ability groups, feel like reteaching the same topics for 5 years. They access it in lessons but not after
8:39 pm
ColinTGraham:
To summarise so far: coverage vs depth may be an issue, project-based and traditional curricula each have different challenges... #mathchat
8:39 pm
pawatt:
@ColinTGraham #mathchat examiners report is a great learning device for A level pupils, they can really spot fundamentals and misconceptions
8:40 pm
ColinTGraham:
decisions/control over content and how it is presented can be tricky, many teachers have difficulty 'combining' from a curriculum #mathchat
8:41 pm
MrHonner:
@ColinTGraham Perfect design of exams is an axiom now. Otherwise how could we link teacher performance to student test scores? #mathchat
8:42 pm
ColinTGraham:
@pawatt Teaching a group of low level learners who don't have the basics by 14 is probably the most challenging thing, I think! #mathchat
8:43 pm
ColinTGraham:
@MrHonner Interesting to speculate how much of a curric is prescribed because of how it will be examined, rather than usefulness #mathchat
8:44 pm
pawatt:
@ColinTGraham #mathchat Because the school AND the pupils will be assessed forever by the results rather than the content.
8:44 pm
ColinTGraham:
How much does pressure to 'teach to the test' affect how you approach your given curriculum and delivery of content? #mathchat
8:45 pm
pawatt:
#mathchat pupils will carry their results forever, you ever fill in an application that didnt ask for your grades?
8:45 pm
colport:
@ColinTGraham within the primary sector, you have little other option in numeracy :-( #mathchat
8:46 pm
pawatt:
#mathchat fundamentally the curriculum needs to open doors, this may be further study at the next level or yes you can do this job
8:48 pm
ColinTGraham:
@colport It's easy for 2ndary teachers to moan about reteaching primary... is the curriculum realistic for 1ary? Testing aside... #mathchat
8:48 pm
pawatt:
#mathchat of course, really good teachers get them saying 'I like this subject and will dig deeper because I want to not because I have to'
8:49 pm
ColinTGraham:
@pawatt I think most curricula are about being able to test then apply a label which says you are at standard 'X' in this subject #mathchat
8:51 pm
pawatt:
#mathchat - even standard X feels quite arbitrary. Testing will only ever be a snapshot but what other alternatives?
8:51 pm
ColinTGraham:
@pawatt Can you find ways to get that sort of motivation within, say, GCSE post-KS3, or is it too late by then? #mathchat
8:53 pm
pawatt:
@ColinTGraham #mathchat not too late, had awful lessons recovering stuff they dont get, then awesome results with avg lesson on new topic
8:55 pm
pawatt:
@ColinTGraham #mathchat Pupils see curriculum coming from you, if you can keep them with you then you can sell them anything
8:55 pm
ColinTGraham:
OK, last five minutes, any final thoughts on teaching to a specific, prescribed curriculum? #mathchat
8:56 pm
ColinTGraham:
@pawatt A lot of it is to do with building the student's own self-confidence about their ability to handle it. #mathchat
8:57 pm
ColinTGraham:
@pawatt It's also a good idea, when 'teaching to a test', to point out that some questions are there for the 'high fliers'... #mathchat
8:59 pm
pawatt:
@ColinTGraham #mathchat I suppose it is always pushing the boundaries of their knowledge while laying the bedrock at the same time.
8:59 pm
republicofmath:
You guys still going? I've arrived home, let the dog out, and had a beer #mathchat
9:00 pm
ColinTGraham:
@pawatt And regarding a curriculum as a 'final sketch' rather than a blueprint. #mathchat
9:00 pm
pawatt:
#mathchat while at the same time giving them the Grades they need. Dont forget, grades are tools too as they unlock oppurtunities
9:01 pm
republicofmath:
@ColinTGraham I have no pressure to "teach to test" because I do not give tests. #mathchat
9:01 pm
pawatt:
@ColinTGraham #mathchat like that, Ideally you have this mona lisa but your smiley face represents where you are now
9:01 pm
torquedu:
@ColinTGraham @pawatt What about a menu of skills within a subject? students work toward setting goals and finding their own paths #mathchat
9:01 pm
ColinTGraham:
@pawatt For the time being anyway... I much prefer the idea of collecting evidence of progress in a portfolio form! #mathchat
9:02 pm
republicofmath:
Holy calculators! A 90 minute #megamathchat ! #mathchat
9:02 pm
colport:
@ColinTGraham I don't think 2ndary teachers re-teach primary. The gaps are too wide, and the curriculum too narrow #mathchat
9:03 pm
stefaniegreay:
"@republicofmath: Holy calculators! A 90 minute #megamathchat ! #mathchat". <-OMG you are hilarious!
9:03 pm
republicofmath:
I can give a test with the best of them. All I discovered is that I can make test so any desired % get what I want. Clever me! #mathchat
9:04 pm
ColinTGraham:
@colport In many ways, it would be better if 2ary did re-teach/review basics though...but we wouldn't be covering the 2ary :-/ #mathchat
9:04 pm
republicofmath:
What about a spectrum of skills assessments - know how, know that, know why ... that students attend to? #mathchat
9:05 pm
kassiaowedekind:
@republicofmath What's the #mathchat topic?
9:05 pm
ColinTGraham:
@kassiaowedekind We are just finishing off! You'll have to catch us next time... #mathchat
9:05 pm
republicofmath:
Hey Stefanie, it takes one to recognize one @stefaniegreay #mathchat
9:06 pm
colport:
@ColinTGraham The gap between KS2&3/4 is big, as numeracy is delivered by 'specialists' in secondary #mathchat No simple answer
9:06 pm
ColinTGraham:
@torquedu Not possible within secondary system in England, much as we might like to...@pawatt #mathchat
9:06 pm
republicofmath:
Sort of anything you like - but teaching to fixed curriculum would be good @kassiaowedekind What's the #mathchat topic?
9:08 pm
republicofmath:
@ColinTGraham Oh no! Colin, don't go. What if we voted for you to continue? #mathchat#bypopulardemand
9:08 pm
ColinTGraham:
@colport No, I still remember the 5-year gap with a Yr9 in my teaching practice for PGCE... :-O #mathchat
9:08 pm
stefaniegreay:
"@republicofmath: Hey Stefanie, it takes one to recognize one @stefaniegreay #mathchat". Hehe...so true. So true.
9:09 pm
ColinTGraham:
OK, that's a wrap for today! Thanks for the contributions everyone... including the sporadic appearances! #mathchat
9:10 pm
ColinTGraham:
Follow @mathchat to keep up to date and don't forget to vote for the next topic: http://bit.ly/c9KL7s#mathchat
9:10 pm
republicofmath:
Heck, who needs @ColinTGraham. I think we might have more to say. #mathchat
9:11 pm
ColinTGraham:
@republicofmath Be my guests.... but don't expect it to make the archive, which I am off to do now! #mathchat
9:13 pm
republicofmath:
@ColinTGraham Oh, right! leave us "unarchived"! #mathchat
9:14 pm
republicofmath:
Have to go let the dog in #mathchat