The Best Hour

Jim Wenzlof pointed me to this web cast by Alan November. WOW! That was the best professional development hour I've spent since I saw Will Richards presentation on RSS: The New Killer App For Educators over at the Learning Times. (Well, now you've got enough links to keep you busy learning for the next little while .... enjoy! .... I did. ;-))

I love seeing technology used as an educational tool. I've long felt that the internet is the single most underused such tool. Some folks think that using a computer is using technology, and on a basic level, I suppose it is but there is so much more to it than that. The key idea here is the internet as a tool; something that is used to accomplish another larger goal. Most people look at the internet as a place to access or consume information. A better use of the internet is as a means to manipulate information to expand the circle of a one's own knowledge. That comes across loud and clear in Alan's web cast.

Alan begins by talking about a "global work ethic" that consists of three parts: (1) Information Literacy, (2) Global Communication Skills (did you hear the whisper .... b l o g s ...), and (3) Self Directed Learning and Work (b l o g s .... there it is again ....). From this introduction he takes us on a journey through the web, while we watch him on video, and teaches how to effectively manipulate search engines, understand the grammer of web addresses and critically evaluate the the various sordid, sundry and excellent information available to us out there on the web to inspire kids (and us) to become life long learners. Best of all, the means he uses to teach us, the web cast, is a great teaching idea for any of us to use with our own students. Imagine video taping (tape .... hmmmm .... wired? tired? or expired? see Alan Levine's presentation) your class and then posting it on the internet accompanied by a series of links to support the content you're covering in your lecture. Suddenly, a dry lecture has taken on an exciting interactive look and feel.

Y'know what? Stop reading me, go watch Alan's webcast; you'll see what I mean. You won't regret it.

One last thing (sorry to keep you). Alan is following this web cast up with a live interactive chat on May 3. Something not to miss. Ok, get out of here ....

More About the Fearful Student

Here's the whole story:

About two weeks ago my Pre-Cal 40S (grade 12) class was working on our review web site. As usual, I was circulating to give some one-on-one attention to those students that most needed it. I came across one girl who appeared to be really struggling with one of the questions in the Trig Identities review. As I watched her from a distance I could tell she was getting frustrated. I went over to her, crouched down so that we could talk at eye level, and asked: "Are you having trouble with that one?" She said yes. I started asking her some leading questions to help her find her way through the problem when I got this creeping feeling that she was getting tense and anxious. I thought she was just frustrated; anxious about not being able to solve the problem. I don't know what it was, but that wasn't it. I asked her if she wanted me to help her with the problem or if she'd would prefer that I just go away. She said she'd prefer if I just went away.

Now I suppose she might have been uncomfortable that I was physically too close to her. Maybe she was intimidated by my crouching down to talk to her at eye level. I don't know. Whatever it was, it wasn't the math. How am I supposed to help a student learn who gets flustered by my standing near them and talking to them? How can I give a stuggling student the one-on-one attention they very much need (and which I can rarely give) without standing next to them? How does a struggling student learn when the simple proximity of their teacher makes them nervous? Now, maybe the idea of man standing close to her discomfitted her. That's possible. But this young lady has been in my class before (grade 11). She struggled there too. I had given her the same kind of help, crouching down at her desk, many times before without this sort of nervousness entering the picture. What was different this time?

I don't have a definitive answer but I've got a pretty good idea what the answer is.

Last week, this same young lady came to see me while I was working in the computer lab on a prep period. She needed my signature to drop the course. I asked her why she's dropping the course and she said: "The math is too hard."

"Can I ask you a couple of more questions?"


"Have you been doing all your homework?"

"No. Not really."

"Have you been reviewing your notes daily, as we discussed at the begining of the course?"


"Have you been meeting with a study group at least once a week as I suggested when the class began?"


"Have you made a point of asking me, or a classmate, for help when you had trouble understanding what we had done in class?"


"Have you been using our blog regularly?"


"I think your poor performance in this class is a reflection of your effort rather than your ability. I think you're a very smart girl who can learn the math. You just didn't try. You might want to consider taking this course again; but this time, put in the effort."

She was relieved I signed her paper.


A few days ago a student came to see me about dropping my grade 12 precalculus class because she said the "math was too hard" for her. I've been meaning to follow up my previous post with that story and my thoughts about it but I just had an epiphany with three other kids in that class that I've got to get out! (More about the fearful student later.)

My grade 12 precal students are my blogging guinea pigs. I'm learning more each day as I try to accommodate the technology and find meaningful, relevant and curricular based applications of it. About 3 or 4 years ago I created a review website to support this course. As the class works through it I go around to give one-on-one individualized attention to those students that most need it.

Today, I also took the opportunity to make an encouraging comment to three students who haven't yet earned their blogging mark for any of the units we've covered so far in the course. What has really bothered me about these three is that they are among the most mathematically able students in the class. Here's what happened:

The first girl is Cambodian. She's an excellent young lady yet she rarely says a word. I've been hoping that using the blog would give her a voice in the class. To date, no such luck. She shared with me today that she would be embarrassed to write something on the blog where everyone would know who she was and what she wrote. In our two minute conversation I asked her how she would feel about using a "code name" that only she and I would know. That would give her the anonymity she craves with her classmates, her the opportunity to enhance her learning, and me some insight into her thinking and the ability to recognize her for it in terms of her blogging mark. Fantastic! One problem solved.

Sitting next to her were two Chinese girls who have also been regularly missing out on their blogging marks. As we discussed it they told me they had trouble understanding the text on the blog and, moreover, had trouble writing in English. So, I copied some text from the math problem they had on the computer screen, went to Google, clicked on the [More] link, scrolled down and clicked on the [Translate Tool], pasted in the text, selected [English to Chinese] then clicked [translate]. The looks on their faces were priceless .....

I'm going to see three blog posts in the next few days for the very first time .... ba da ba ba baaa! I'm lovin' it!

A Deeper Issue

I had a really good class the other day with my grade 11 precalculus students; but it didn't start that way.

We're working on analytic geometry, the link between algebra and geometry. Anyway, in this particular class I was teaching them how to find the shortest distance between a point and a line in the cartesian plane. (ASIDE: I also told them the cartesian plane is named after Rene "I Think Therefore I Am" Descartes and how he died because Queen Christina of Sweden wanted to learn calculus at 5am .... math is full of these interesting little anecdotes .... more on this in a future post. ;-))

So there we were; looking at the point P (0, 0) sitting at the origin; the line y = 2x - 10; and a little green line I called d trying to figure out how to calculate the shortest distance between the two -- the length of d. I asked the class for suggestions on how to proceed and was met with 28 blank stares.

This happens to me a lot. I ask for student input and I get the "wall of silence." At times like this I pull out an idea I learned years ago from reading this book. I was also inspired by an in-service our school had last week with Caren Cameron. She gave us a number of suggestions similar to this:

I ask all the students to take a piece of paper, fold and tear it into four pieces, and pile them up on their desks. I then ask them questions throughout the class which they have to repond to by writing their responses. A response is required, even if it's "Mr. K. I have no bloody idea what you're talking about!"

In this class I asked them to reply to two questions:

  • »Is it possible to solve this problem? Do we have enough information? Yes or no.
  • »If you could change or add one thing about this problem to make the question easy to answer, what would it be?

I told them they had 90 seconds to write their answers and gave them 60. I also told them I didn't want anybody's name on the papers -- while a response was required they could remain anonymous.

I collected the papers, shuffled them and gave a pile to each of two other students who picked out three or four at random while I did the same. Wow! From about 10 randomly selected replys I learned that some students thought the problem was solvable but they weren't sure how to proceed; some thought there was not enough information to answer the question; some wrote (what seemed to me) random scratches on the paper; some said "Mr. K. I have no bloody idea what you're talking about!" and a few of them said: "Well, if we know the coordinates of the point where d meets the line we could use the distance formula."

Fantastic! I now had enough feedback from the class to clear up some misunderstandings and the students came up with the key to the solution to the problem.

More than that, after using this written reply technique a couple of more times the students started volunteering verbal suggestions to my questions and one of them came up with a novel solution, using trigonometry, that I hadn't thought of!

More and more I find that the main obstacle to students' learning is shyness. Many times I've addressed this specific concern to them. I found that blogging about it helps them open up a bit, nonetheless, "the wall of silence" quickly pops up again.

After the tremendous success I had using this style of questioning I'm committed to using it more. However, I'm concerned that it will get old fast. I need more tools like this in my toolbox. I'm open to suggestions folks.

There's a deeper issue here too. How many of our students are capable of doing well in math, even going on to advanced math, but are hindered by shyness? How many students have failed math courses because of the paralyzing fear they have of asking questions, fearful of looking "stupid" in front of their classmates? How many of our students who get up the courage to ask their teachers questions, during or after class, end up nodding unknowingly because they can't maintain the inertia necessary to get the answers they need? What's the failure rate due to shyness and what can we do to overcome it?

Do we really need another reason?

Two days ago Apple released this announcement (emphasis mine):

Mac OS X Server v10.4 “Tiger” will also ship on Friday, April 29. The next major release of Apple’s award-winning, UNIX-based server operating system, Tiger Server integrates 100+ leading open source projects and standards-based software applications and more than 200 new features including native support for 64-bit applications, ideal for high performance computing; iChat Server to deploy secure instant messaging within an organization; Weblog Server to publish and share weblogs (blogs); and Xgrid to turn a group of Macs into a virtual supercomputer.

With the widespread use of Apple products in education I can't wait to see the changes this new(?) technology will lead to. Apple always seems to be leading innovation in the use of personal computers .... did anyone really need another reason to get a mac? ;-)

New Math Blog

There's a new math blog! It's called "Shapes, Patterns, and Proofs - Oh, my!" A geometry teacher, Mr. Fort, down in Georgia. He's got a blog set up for each student in the class. Here are his instructions for the students taken from his First post:

My idea is for you to post at least two blogs each week for the rest of this year. One blog must be a reflection and the other blog will be a response to a blogging prompt.

From reading his student's blogs (accessible from his) he seems to have them repond to prompts he gives them in class.

Along with Mr. Kaminsky's GCHS Math Blog this makes three math blogs that I know of. The word is spreading .... if anyone comes across more of these please let me know; I'm always looking for more good ideas to help my students learn. With three of us blogging now I hope to see a growing community of math bloggers and maybe even math wikis. Research supports the idea that collaboration enhances learning. Let's all collaborate. ;-)

More Mad Minutes

I've been working my way through the 9th Carnival of Education which pointed me to Mentor Matters exhibit. She wonders "how and why do teaching strategies common to the first grade classroom get blacklisted?" She goes on to say:

We got to this discussion because in meetings with upper level grade teachers, it became clear that our students’ basic math facts skills are weak. The idea about conducting daily Mad Minute timed practice tests came up as one intervention strategy. One of the veteran teachers remembered several years back teachers were told not to time kids; timing caused a stir among parents and therefore, some school leaders. So no more Mad Minute.

Brian J. Beck, an Engineering student, comments: "The problem is that you need that basic arithmetic as a stepping stone to understanding higher level concepts, and also for use in science." I couldn't agree more.

In all the classes I teach I explicitly tell my students we begin each unit learning the algebraic massage necessary to solve more interesting problems. Some examples:

  • »Exponents and Logarithms .... "Y'know how scientists say one dinosaur lived 1.5 billion years ago but this other one lived 2 billion years ago? Well, how do they know? Were they there?"
  • »Probability .... "Y'know how when you go to the doctor for a really important test and you call him up for the results and he says: Well, we have to do some more tests. Why are doctors so cagey?
  • »Differential Equations .... "Y'know how on all those police shows the coroner arrives at a murder scene and says to the detectives: The victim was murdered yesterday between 2:00 and 2:15 am. How does she know that?

These questions and more are answered at the end of each unit. But in order to get there we first have to learn the basic skills. Work through the blood, sweat and tears of manipulating the numbers and learning the basic calculations necessary to answer those questions. Students need competance and confidence with basic skills before we can even discuss sophisticated concepts and applications in more interesting problems.

To all of you teaching kids in the younger grades. Please, please, please don't give up the Mad Minute. You're giving them one of the special gifts only a teacher can give: the tools for success in the grades that follow; you're making a difference.

Stirring the Pot

All's quiet on the wiki front. I'm not happy about that. It generated a little excitement when I first published it. I got email from couple of teachers who thought it was a great idea and wanted to join in the fun. Both also said they would be passing on the address to other folks they know and I'm confident they did. But if you go look at the recent changes on the wiki .... there are none except the ones I've made.

Hmmm .... how to make this technology work. Accessability isn't the issue; the wiki's wide open and all my students have internet access at home or at school. I read some comments over at Bud The Teacher's wiki that perhaps people were hesitant to edit someone else's work. Maybe that's an issue here. The students see it as my wiki, not theirs. Ok, so how do I convince them that it really is theirs? Maybe the issue is my own impatience; maybe they need more time to absorb and accomodate the technology; more time to reflect on what or how they wish to contribute?

Maybe I set it up all wrong. Essentially, I took the learning outcomes prescribed for each unit and pasted them as headings in each unit's wikipage. Maybe I need to give them a different sort of prompt to get things going.

I recently posted about the wealth of things to learn in Alan Levine's post on the Learning Objects workshop he facilitated. Tonight I tumbled down the rabbit hole to this article excerpted below (emphasis mine):

To truly empower students within collaborative or coconstructed activities requires the teacher to relinquish some degree of control over those activities. The instructor’s role shifts to that of establishing contexts or setting up problems to engage students. In a wiki, the instructor may set the stage or initiate interactions, but the medium works most effectively when students can assert meaningful autonomy over the process.

Epiphany! That's it! Maybe I have gone about this all wrong. Instead of posting a dry list of learning outcomes I'll post one or two interesting problems that we learn how to solve in each unit. The students would then be challenged to solve the problem. In the process, they would have to explain the steps they took to do so, including:

  • »all calculations done. They should be annotated so that another student who missed class the day the material was taught would be able to replicate the work. [basic skills, low level thinking]
  • »what do the numbers mean? Interpret the results in light of the problem given. [applications, higher order thinking]

I don't know if this is the solution but it's worth a try. I'll try to get started this weekend; get some feedback from the kids next week and see if it makes a difference.

An Impact to Aspire To

Wow! I smiled for 15 minutes straight. Great teaching tips from a teacher par excellence as described by a former student .... 25 years later!. Mr. Cappucci; I've never met him, but what an impact he made! Something to aspire to ....

Check out the 9th Carnival of Education. There are gems in every edition.

Curious Things at the Muddiest Point

I wish I could work in the same building as Alan Levine. Not only because I think he's a brilliant teacher but also because he's regularly involved in facilitating exciting and innovative professional development opportunities for educators.

Two days ago he blogged about a Dialogue Day on Learning Objects, Wikis, And Other Curious Things; a full day workshop on learning objects. That particular post is rich with links to learn from. I clipped a copy of it in my Bloglines account and still haven't finished reading through all the facinating things Alan points to. Each link I followed lead me down a rabbit hole of curious things to learn about.

Alan invited Brian Lamb from the University of British Columbia to lead the workshop. One of the coolest things Brian did was to set up a wiki with a page titled MuddiestPoint: "our mid day check in on what participants want to learn more about." Sometime during the morning sessions the workshop participants all had a chance to edit that page. Brian then addressed those issues in the afternoon sessions. It's not just the content that's amazing, it's the medium!

Another reason I like Alan Levine is that he likes Canadians. ;-)

Alan and Brian are two teachers making a difference .... I wonder if we could get them to come to my school .... what a great day that would be!

iPods Making A Difference

Not too long ago I made my first audioblog or podcast. The tenor of my comments were that I saw only limited benefits to audioblogging and in fact felt as though there was greater learning value in writing. This evening I came across this article at Apple Hot News some of which is reproduced below:

The entire Duke University class of 2008 received Apple iPod digital devices as part of a university initiative to encourage creative uses of technology in education and campus life. This mix of pop culture, information technology and pedagogy has generated enormous interest from other educators as well as news media.

Here's another article about how Duke University is using iPods.

Hmmm .... rethinking my position ....

A Different Kind of Carnival

About a week ago I stumbled across The Education Wonks Carnival of Education. I had the good fortune to have one of my posts here publicized there in the eighth edition of the carnival. Next week brings the ninth edition. Check it out for a variety of differenct perspectives from the edublogosphere. EduWonk's invitation is reproduced here:

An Invitation: All writers and readers of education-related posts are invited to contribute to the ninth edition of The Carnival of Education. Please send your submissions to: owlshome [at] earthlink [dot] net. We should receive your contributions no later than 10:00 PM (Pacific) Tuesday, April 5, 2005. The Carnival midway will open here at the 'Wonks Wednesday morning. Get our easy-to-follow entry guidelines here. View the latest edition of the Carnival there.

You might also want to consider submitting a post from your own blog....

Something to Improve Math Instruction

Nancy McKeon has a post over at Random Thoughts that raises an issue I think math teachers all over the world face:

I suspect the problem goes far beyond our country's minority population. I see it in the students in the college where I teach. Many of the students do not come to college prepared to do college level math. I am talking here about white male students coming out of Louisiana high schools.

As the article says, we have to do something to improve math instruction and help all our students with math. The decision at my school has been to lower expectations. We will no longer require students to take a college algebra class, opting to offer a more "practical" type of math instead.

Somehow, I don't think that is the answer.

To be flip, I think the "answer" is to raise the bar, not lower it. Not being so flip, the answer is more multifaceted. We've had a similar problem at my school and we've decided to tackle it on several fronts.

Encourage more students to take advanced math. Success is most dependant on effort and the willingness to learn.

Improved student performance through better pedagogy. We learn from each other by observing each other's classes. We collectively implement a research based teaching strategy each year. We choose and deliver workshops to each other. (Teaching strategies, overcoming test anxiety, whatever we determine our students need from us.) And we market and encouage students to sign up for AP courses.

We've also reached out to our Jr. High feeder schools to work collaboratively. Toward this end we have a full day workshop together, just the math folks, once each year .... well .... actually, this is year 1. ;-)

Anyway, that's the plan. Time will tell if it makes a difference.

Nancy also says that her school is looking at offering "a more practical type of math" course in the place of algebra. That's not such a bad idea. Not every high school student will go on to post secondary studies or pursue a career that requires knowledge of advanced math. I think these students most need to know the mathematics necessary to be responsible citizens: probability and statistics.

In Manitoba all students take the same math course from K-9. In grades 10-12 they self select one of three paths: Precalculus (exactly what it sounds like), Applied Math (the focus is on solving problems in context with the aid of technology so that students can focus on understanding and working with mathematical concepts), and Consumer Math (has a little bit of algebra and trig but mostly focuses on the mathematics of income and debt, mortgages, investments, statistics, taxation, etc.). There are problems with this system, but it does have the virtue of recognizing that students pursuing different career paths require different types of mathematical knowledge.

Another thing that would really help this situation would be college and university professors communicating to curriculum designers exactly what skills they find students lacking and help the high school curriculum designers create a curriculum that matches the needs they identify.

Our curriculum is about to go through another major revision. I understand that there has been a consultation among educational professionals at the different levels. I hope the result is a positive one.