Calculus Reflections Go For Gold!

I can't believe it was two weeks ago that I posted Calculus Food For Thought. Time flies. Anyway, I've had time for some thought and time to talk to some other teachers and my class. Here are some of my thoughts:

I've been working harder than they have; even by their own "calculations".

Their sense of preparedness to write the exam matches their estimated effort. I realize this wasn't a "scientific" data collection, nor is the analysis very scientific but these results provide some small additional evidence to what I have already long believed. Almost anyone, who is willing to try, can do advanced math. Their marks (yes I know, I haven't shared the marks with you -- and I'm not going to .... well .... maybe some averages would be apropos?) are more a reflection of their effort rather than their ability. Why do capable students consistently fail to apply themselves to doing their best work? What's the lack of motivation here? Is it cultural; a failure to appreciate the value of learning? Maybe we don't challenge them enough .... maybe I challenged them too much?

No, they were almost evenly split: Was I too hard or too easy on you? (remember, n = 15, rather small).

I think I have to emphasize more work without the calculator. 40% of the class thought so and while it's not a majority that's too big a percentage for my liking.

The next two questions were interesting (What was the best learning experience you had in this class? What was the worst learning experience you had in this class?) both in the particular answers and in the number of answers. They felt they learned the most from group work and take home assignments. A friend of mine thought the preference for take home assignments was a selfish desire for easy marks but I don't think my assignments are that easy. And, while it is possible they can copy from each other, anecdotally, I got more individual students seeing me for extra help and really learning and understanding the material when they had to do these assignments. Regular take home assignments are also a feature of math courses taught at the university level, so this is a good preparation for post secondary education in mathematics as well.

The variety of answers to the second question I read positively. Some things work best for some folks and not others; everyone learns differently. I had enough variety in the ways I presented and evaluated material so that I managed to aggravate everyone at least once. ;-)

In the class discussion we had of these last few questions, the students were overwhelmingly in favour of more take home assignments.

Right now they are working on their take home exams. (The 6 questions from Form B for you AP Calculus teachers out there.) On the exam they had 90 minutes to do 6 questions like these. I've given them about two weeks.

The standard is: Everyone must get 100% on this exam. Anything less is unacceptable. Here's why: They can get help from me, talk to each other but not show each other any written work (yes, I know, I'm naively optimistic). I'll tell them what they need to fix in order to get that perfect mark. There are no excuses for getting less than 100%. They sure are motivated to get that perfect mark; and I'm very picky about the degree to which they must explain written answers where required.

More than one student has told me this would have been an even better review before the exam. I've decided to test the theory out with my grade 12 precalculus class. I'm giving them their "Go For The Gold" assignment next week. Same conditions. The minimum expectation for everyone is 100%. Anything less is unacceptable. I will send letters home to the parent of any child that gets less than 100% or fails to hand in the assignment. It will explain the assignment (last semester's final exam, it is worth 5% of their class mark), that the child has chosen not to get the 100% mark they could have, and it will have to be signed and returned to me. Whatever mark they get is what will be recorded. And their paper will be returned to them with a single comment; Unacceptable.

I want to try this idea out with the whole department next year. We'll have two of these "Go For The Gold" assignments each semester with the standard set at 100%. I'm hoping that when we do this across the school it will create a bit of a buzz in the community. Every student must get 100% on this assignment which will be handed out on the same day with the same deadline in all our classes. I'm hoping it will change the culture of the school, get the kids focused on learning and help them prepare for and improve their performance on exams. Imagine, every math student in the school gets 100%. What impact will that have on the culture of the school? My grade 12 students are my guinea pigs this semester. Let's see if it works ....

Reflective Blogging

I just finished reading a fairly new blog; Outside [The Cave]. It's fantastic.

Steve is a teacher in Virginia. He's managed to roll a personal reflective/professional growth blog into his classroom blog. The thinking he's sharing with his class (grade 9, many of them are 14 years old) is providing them with excellent modeling of what blogging should look like a la Will Richardson. The impact he's having on them comes across loud and clear in the comments they make to his posts. And the depth of thought they contribute to developing the assessment criteria for their end of year final project is inspiring. This is what blogging should be: a community of learners reflecting on their learning, building authentic assessments of that learning together and growing in the process.

Clarence over at Remote Access a little while back posted about collecting a list of reflective teacher bloggers. I was honoured to be included in his list. I think the educational blogs fall into three, occasionally overlapping, categories:

  • »stories, sometimes rants, of things that happen in school with kids or staff, or
  • »sharing perspectives and information on the latest news in education, or
  • »reflective blogs about teaching and learning.

I'm most interested in that third type of blog. So, taking the lead from Clarence, I've decided to start keeping a links list of those blogs that strike me as most falling into that last category. (I'm still slowly working my way through Clarence's list.) I like lots of different blogs. I read over 70 feeds on a regular basis. I've noticed lots of folks generating long lists of bloggers that they like. But I think over time those lists get awfully long and unwieldy. So, all the stuff I read can be found one click away in my blogroll, but the stuff that moves me the most is in the list of Reflective Edubloggers over there in the column on the right.

A Lot to Chew On ....

I had the good fortune to attend a presentation and briefly chat with Alan November Monday night. After his 90 minute talk he left the entire room breathless.

Some of the themes and issues Alan raised:

The boomerang generation. About 30% (and growing each year) of young people, having left home around the age of majority, return home to live with their parents.

He pointed to Stanford University's Education Program For Gifted Youth (EPGY) website where he showed the curriculum available to the k-2 set for $400US. In math these kids begin algebra in grade 1. Your $400US gets you 3 years of enriched schooling online, 24/7 whenever you want it. Alan said most kids work their way through this curriculum in 6 months! This isn't fair! Education isn't just for the rich! Teachers should collaborate and create high quality, continuously evolving online courses accessible to everyone 24/7. We don't need big software packages like WebCT or Blackboard when something like Moodle is available for free.

He talked about the power of RSS in education. Giving an example of two university students; one with a bloglines account, one without. While the first, RSS educated, student sleeps, his Bloglines account pulls in the latest information from international universities all over the world. He'll use this information to write the various required papers, essays and research summaries in his classes. While the second student sleeps; he sleeps. Which student will have greater academic success? Which will learn more? Which will create, for himself, the best education he can?

Teachers missed the boat with instant messaging. The reaction of the educational community was to keep IM out of school. His 15 year old son, after hearing him talk about IM came home from school one day and told his dad he finished ALL his homework; he typically doesn't do his homework. Alan asked to see it. His son explained: "Well, these two kids are doing the math, those two the English, this group is working on science, another on social studies. When we're done we just IM each other our work." Homework becomes obsolete. (Or does it?) The school thinks this boy should be punished for not doing his homework. Alan suggests he should be rewarded for his social skills, networking ability, intelligence and innovative solution to every students' homework problem. What do you think? How should the education community react to the evolution of blogs, wikis, furl, and other social tools freely available on the internet? He pleads with us not to miss the boat this time.

Alan is advocating a cultural revolution in education. Kids have to learn how to think globally, to manage massive amounts of information and they have to be self-directed in their learning. He's saying that parents need to get their kids globally connected using blogs and wikis. The spur to change the educational system should come from the home. That's a bit of a mouthful. I have trouble getting parents to come out to see me once a semester for parent/teacher interviews.

There was lots more but this is what I'm chewing on for now.

Lots of other folks are chewing on some of these ideas too. Check out these links:

Yeah, an awful lot to chew on ....

Blog Pod

Here it is, the long promised podcast Bud and I did. Go get a cup of coffee or tea and sit down for while, we go on for about 30 minutes. ;-)

This was a real experiment for us. We were both experimenting with Skype and it's my first foray into using Audacity. We had a great talk and learned a lot about the technology at the same time.

I'd suggest leaving this window in front of the one that will open for the mp3 file you're about to hear. That way you can follow along with the links below which are arranged in the order they were discussed. I hope you find this as much fun to listen to as Bud and I had making it. Either way, let one of us know your thoughts, questions, concerns, comments, complaints, compliments, confusions, anxieties or any good jokes you've got to share. ;-)

The Blog Pod

Show Notes: The Blog Pod

Blogging on Blogging

Where Have We Heard This Before

The Difference Between Now and When

Seize The Time!

Bouncing Around

Students Wiki, Teacher's Wiki

Mr. K. I Have a Question....(^_^)

Alan November's Webcast


Writing HTML

Thanks for listening.....

Random Acts of Kindness

Bud The Teacher is doing some incredible work with his students in his blogging class, Bud's Blog Experiment. The level of reflection and maturity evinced in their posts is awe inspiring. It just goes to show what kids are capable of when their learning is facilitated by a great teacher who encourages them to take ownership of their education.

Nancy McKeand over at Random Thoughts writes:

Tyr and most of Bud's students get it. I know that Bud has worked hard to make that happen. You have to wonder what would happen if all teachers could educate their students about blogging. I think we would see some pretty incredible thinking and writing.

Anne Davies at EduBlog Insights picks up the thread of Nancy's thoughts and follows it up with a great idea.

I say Amen! I posted "All the Voices Need to Be Heard" a little while back. It was about Tyr and Moe's posts and my students reactions to the discussions. I love having all these student voices in the mix. I think that is crucial but maybe we all need to focus on commenting, in particular on our various student blogs and having our students commenting on other student blogs or our blogs. This is happening but maybe we could step it up.

I think if more of us joined the conversations on blogs with students we could really show the power of blogging. That kind of data could do more to promote blogging than anything else. Nancy has commented to my students' blogs from The Write Weblog group. She makes a difference. I think this aspect of blogging is one that we all need to think more about and make a priority. I know it takes time. I try to do it but need to do much more. I wrote to the students on the "A Look at Bullying" blog. I was astounded at their answers. Sometimes I get carried away and think that I have to comment to all the students, not just one (in a group) so I am going to rethink that and try to make one comment a day to a student who is blogging. It can be one of mine or one of another bloggers' students. One a day..... I like it. So think about it, how about committing to one comment a day to a blogging student? Let's make a difference.

That bullying blog is probably one of my all time favourite educational blogs!

Imagine all of us to working together to educate and encourage all of our students collaboratively. Think of the power available to us through blogging to really make a difference in a different child's life each day. Randomly leave a student blogger a comment each day.

I always end my classes by telling my students to: "go out there and commit random acts of kindness!" That's good advice for me too .... gotta go ....

What a Workshop!

Alan Levine is at it again! The man is just brilliant! Imagine spending a day playing with over 50 different learning object technologies. You write a brief note for each one you see. Ask the questions you have about it and describe what kind of help you need to implement it. Over the summer, you get personalized feedback with answers to your questions and concerns.

To top it all off, each little feedback sheet (low tech GPS forms -- I love the metaphors Alan uses!) you submit enters you in a draw for an iPod, a real GPS device or a USB key drive!

How do I get a job at MCLI? ;-)

Calculus Food For Thought

Out of a class of 16, 15 students participated in this survey. We started the year with 19 students; 3 dropped the course; 1 was absent the day of the survey.

With any further ado, here is the survey and the results:

How prepared were you to write this exam? (Average score out of 100)

How much effort did you put into preparing for this exam? (Average score out of 100)

How good a job did your teacher do preparing you for this exam? (Average score out of 100)
    Note: Only one student rated themself higher in question #2 (100%) than they did the teacher in question #3 (80%).

Did you have enough preparation using your calculator?
Yes 86.7%     No 13.3%

Did you have enough preparation without using your calculator?
Yes 60%     No 40%

Was I too hard or too easy on you?
Hard 33.3%     Easy 26.7%     Just Right 40%
    comments: hard in a good way; both

What was the best learning experience you had in this class?
Group work: 8
Take Home Assignments: 7
Learning new problem solving methods: 1

What was the worst learning experience you had in this class?
Too much "chat"
Not speaking up
Long class lectures
Textbook work
None (2)
Not enough time to go over work
Not enough math dictionary notes
Not enough solutions

What suggestions can you share for next year?
Finish the math dictionary
Blog for this class (2)
More take home assignments for marks (6)
Go faster at the start
Use visual pictures
More review time (2)
Use time wisely to avoid rushing at the end
More group work
Go over more homework in class
Do homework checks
Make this a full year course; i.e. meet every day until the exam

Food for thought ....

Future Reflections

My original plan when I started this blog was for this to be my "thinking out loud" space; part of my professional development. As I get caught up with other issues, like the great fun to be had at Carnivals, I find I'm not getting around to the kind of reflections I was hoping to dialogue with other teachers about. So, as a way to encourage me to "stay on task" and get help with some of the things I'm struggling with I've decided to post a list of reflections I've been meaning to blog about. Kind of like my blogging to do list. In no particular order, some future reflections I plan to get out:

  • »My students wrote the AP Calculus AB exam last Tuesday. On Tuesday we'll go over the long answer questions and I'd like to get their feedback on:
    • »Did we do enough work using our graphing calculators? Did we do enough without?
    • »We're they well enough prepared for this exam? Did I go too easy on them? too hard?
    • »What were the best learning experiences they had in our class this year? The worst? What should I do more of? less of?
  • »I love teaching but the corrections are killing me! Multiple choice questions are easy to grade, hard to make up. What would be a good balance between getting tests marked fast and giving students the opportunity to get part marks using more extended response style questions?
  • »What shape will blogging take in my classes next year?
  • »How will I adapt using our Wiki Notebook to next year's classes? Should I use the same prompts? new ones? How shall I structure the wiki for the long term?
  • »I did some great projects with my classes last semester. We haven't done any this semester. Again, the time required for corrections hangs around my neck like an albatross. There's tremendous educational value in these projects but selfishly, it takes time away from my personal life. How can I strike a better balance here?

Enough. I've got plenty to think about for the next little while....

Complimentary Wikis Get a Nod?

I think this is the teacher I referred to earlier. His name is Rob Lucas (Lucas was a famous mathematician y'know. He invented the Tower of Hanoi puzzle. ;-) This is a different fellow, Edward Lucas died in 1891.) I thought that the BPRIME wiki was ambitious. Rob thinks very BIG. He has created a wiki called The Teachers Lounge:

Over the course of last year, my first year of teaching, I spent many late nights planning lessons for the following day. During those nights, a single thought gnawed at me: Thousands of other teachers across the country were doing just as I was, and thousands more had done so every year for decades. Yet there was no way for me to fully benefit from the experience of all those who had come before.

I've created this website to change that. It's a new type of collaborative website called a 'wiki,' where most pages can be edited not just by a webmaster, but by any registered user. That means you can post lesson plans, links, handouts, PowerPoint presentations, virtually anything! And you don't even have to know HTML. Editing a page is as easy as using a word processor.

My vision is that over time, we can develop an extensive library of creative, finely-tuned, engaging, exciting lessons. If you share that vision, please register and help me shape the site, whether you're a new teacher yourself or a veteran. You can also click here to learn how to use the site or read the first post on my weblog to learn more about the idea behind it.

Very exciting stuff! Rob's vision is not only for teachers at all levels, but also in all disciplines to collaborate. The BPRIME wiki has a slightly different focus than Rob's; one which I regard as complimentary. The Teacher's Lounge focuses on what we teach, BPRIME focuses on how we teach.

There have been some exciting developments since the BPRIME Wiki went public last Sunday. I got positive feedback from three people immediately. Terry and James joined the wiki and Jonathan linked to my post and discussed another idea about how teachers can create their own textbooks. Terry shared two excellent contributions, here and here. And James has said that he's planning to share as well.

In order to "spread the word" I submitted my post to the 13th Carnival of Education. Since Sunday this site has been visited by 141 different people, 97 of whom were first time visitors. I find those kind of stats very encouraging. I'm always amazed at how many people are interested in the goings on here.

Participation Stats

  • 3/141 or 2.1% have responded favourably.
  • 2/141 or 1.4% have joined.
  • 1/141 or 0.7% have participated.

When I first put the wiki together I tried to strike a balance between my contributions to encourage participation and leaving it "unfinished" enough to encourage a larger community to take ownership of the space. I'd also like to find a way to increase the participation rate. I'd really love to get some feedback on how I can do this. Maybe this idea of mine isn't so great. Maybe I'm recreating work that's already been done elsewhere and so, the idea behind BPRIME is a little "tired." Or is this really a good idea and I'm just a little impatient. (It wouldn't be the first time. ;-))

I can hear this song playing in my head, Pink Floyd, "Is there anybody out there? Just nod if you can hear me....." ;-)


The 13th Carnival of Education is up over at JennyD's. One of the biggest yet. Lots of interesting stuff there; always something new to learn. I've got a post there this week too. Check it out; it's always worth your while. ;-)

The Education Wonks point us to a new carnival this week; the Carnival of New Blogs hosted by Pratie Place. Also full of interesting new voices. It pointed me to this post by J&J's Mom. A great read. J&J's Mom also had this music video which I really enjoyed. So this week in carnivals there lots to learn about in education, a bunch of new voices, and I learned about a musician (Gavin DeGraw) I had never heard before whose song (Chariot) I really liked .... cool.


That was the coolest thing! Bud The Teacher and I have been taking to each other for a while now and about two weeks ago started taking about doing a series of joint podcasts together. Tonight we connected for the first time via Skype. Both of us are newbies to Skype. It was thrilling to hear my friends' voice from Colorado while sitting in my house here in Winnipeg. We hit a few technical snags and just as we sorted them out Bud was called away. We're going to follow it up tomorrow or the next day and finish our series of podcasts. Bud and I will post the podcasts as we finish each one on our blogs, here and there.

Just to whet the appetites of the six of you reading this ;-) here's the list of topics we'll be podcasting about:

  • »Blogs and Blogging
  • »Wikis
  • »Podcasting

That last one will be very postmodern -- podcasting about podcasting. ;-)

I have some reservations about podcasting, but I have to tell you, they're really fun to do .... especially collaboratively. ;-)

Students Wiki, Teacher's Wiki

I've been trying to get my Pre-Cal 40S class to participate in a wiki to enhance their learning. We've migrated from JotSpot to because JotSpot's beta period is ending and they're going commercial. As I've mentioned here earlier; it didn't take off. Well, the Pre-Cal 40S Wiki Textbook has become the Pre-Cal 40S Wiki Notebook. Already one student has tried their hand at it and I hope it will grow.

As a matter of fact I was really impressed with this student's contribution. It had been made anonymously because he couldn't figure out how to login (a problem we've already solved). Terry Kaminsky over at the GCHS Math Blog had suggested that I try starting the kids off by beginning the solution to one of the problems. When I first read it I thought it might be Terry. ;-) The solution was correct, well annotated and beautifully presented. I did notice one small transcription error that I left for the students to correct, thinking that had been part of Terry's plan. When I mentioned the work done on the wiki in class I said I thought it had been done by a visiting teacher only to be corrected by the student who had actually written it! You should know that this student is a fairly recent immigrant to Canada and is learning English as a second language. He has really taken to blogging and is obviously getting a lot out of our blog supported class. I'm really proud of him. He impresses me on a regular basis with his enthusiasm for learning and the vibrant way he expresses himself on our blog.

I'm still encouraging the wiki's use in class by pointing out to the students that the wiki can grow into a fantastic study tool for the final exam in June.

As I continue to think about the learning possibilities inherent in collaborating via wikis, it occurred to me that there should be a wiki where teachers gather and collaborate. I've lost the site where I was reading about a first year teacher blogging about staying up late preparing lesson plans, musing about how first year teachers all over the world are "recreating the wheel" every day. Wouldn't it be great if there was a place where we all could share and learn from each other's work? Sounds like a wiki to me. ;-) Another source of inspiration comes from James Tubbs over at The Future of Mathematics blog with this post on solving one-step-equations.

I've mentioned here previously about how the folks in my department are hoping to improve student performance at our school through improved pedagogy. To that end we have our first interschool math department workshop on June 1st. The working title is the BPRIME Workshop; Best PRactices In Mathematics Education. As a way to foster community amongst the group of teachers I'm working with I've created a wiki called the BPRIME Wiki. It's a place for us to share teaching ideas, best practices, and research articles and websites. Originally I had intended the BPRIME Wiki only to be used locally, but now I realize, that's too short sighted. While the wiki is geared towards math teachers, good teaching is good teaching, and we can all learn from each other, regardless of our specializations. So, here it is, my open invitation to teachers everywhere:

An Open Invitation to All Teachers: Come visit the BPRIME Wiki. A collaborative effort to collect teaching ideas and strategies that exemplify best practices in the teaching of mathematics at all levels. While the emphasis of this wiki is on mathematics this exercise can help all of us improve our craft. Every contribution you make encourages other people to do the same. Give a little bit, get a lot.

You can self register for the wiki, although registration isn't required in order to participate -- but you should get credit for the contributions that you make. I encourage everyone to register. Also, please feel free to copy, link to, and redistribute this invitation far and wide. The more of us that work together on this the better it will be and the more we'll all learn.