Monday, January 31, 2005

Researching Electronic Portfolios

Good post over on Electronic Portfolios for Learning about some research taking place on electronic portfolios. It mentions the real goal of using them:
"...student learning, engagement and reflection, not HTML coding, hyperlinking and design."

More reason to be using blogs as the "digital repository" for portfolios. Hopefully, through my informal research, I'll be able to live up to that goal.

Wednesday, January 26, 2005

More Classroom Uses of Flickr

Let me tell you how much I love Flickr! Several nights ago I was busy late into the night (well, midnight) exploring the site and generating all sorts of ideas for using the images on this site in my classroom.

Let's begin with the tags section of the site. I'm currently in the middle of a unit on geometry so I was interested what I might find in the architecture and buildings section. Here I found a cornucopia of photos containing parallel and perpendicular lines, geometric solids, & symmetrical buildings, all in a real-world context. An image like this one could be posted to a discussion forum or group blog to elicit discussion about symmetry.

While exploring the above tags, I came across the urban and street tags. There were photos that illustrated the above concepts. However, it wasn't until I came across a photo that took me to the squared circle group that I really got excited. Thinking of problems that related to the photos was incredibly easy. I started blogging the best of them as I went so that I wouldn't forget them (see a few below). The rest I put in my favorites. So many concepts could easily be covered through these photos--fractions, concentric circles, and more.

So I know I can take the pictures from the site and use them elsewhere, but how could I have my students actually find their own photos on the Flickr site? I thought a tag scavenger hunt might be interesting. Give the kids a concept and have them search under related tags for photos that illustrate that concept. The only problem with this activity is that some of the photos are titled with inappropriate language or have inappropriate content. A solution might be to have students do a favorites scavenger hunt. If you have a concept in mind, like parallel lines, search for photos that contain examples of parallel lines and add a ton of them to your favorites. When mixed with the other photos in this page, students will have to look closely to find the pictures that best illustrate this concept. When they have found one, have them blog it with a short description.

Monday, January 24, 2005


Originally uploaded by .lou.
Imagine the circle is rotated so that the arrow is facing right. Describe the amount of the rotation in degrees. How would the word hot appear?

Sunday, January 23, 2005

3 Central Angles

Originally uploaded by N-ino.
3 congruent central angles are pictured. Find the measure of each angle. Please include an explanation and an equation.

Big Tire

big tire
Originally uploaded by byrdiegyrl.
Describe how you would find the area of the tire. Please include the equation you used.

Sunday, January 16, 2005


Liked Will's post on Weblogg-ed about Podilicious: imagined social search engine and clips manager for the Podosphere. The design of Podilicious is based on successful social software such as (its namesake), Flickr, and Furl.

So I thought of a tool that I would love to have--InspireNote, based on Webnote, a tool for taking notes on your computer during a meeting, class, or any other time that you have a web browser available. The difference here is that instead of the notes appearing as post-its, they appear as symbols like the ones in Inspiration. In fact, InspireNote would perform all the same functions that Inspiration does--linking symbols, rapidfire brainstorming, adding URLs--only through a web browser.

For those of us who see the world better visually, this would be an amazing tool. We would be able to open a couple of tabs in Firefox, and as we came across interesting quotes and other information, we could copy from a Web page on one tab and paste them into InspireNote, open in another tab, making a graphic organizer with the information.

Now I'm no developer, but I would love to see somebody out there take on something like this!

Thursday, January 13, 2005

Extended Responses-What We Like to See

Here is an example of a great extended response (unedited):

Derived Measurements Extened Response

Marks heart beats 16 times in 15 seconds. Atthat rate, how many times will it beat in one minuite?

Mark's heart will beat 64 times in a minute(64 BPM). I got this by knowing that 15 multiplyed by 4 is 60 and thats equal to one minute(Because there are 60 seconds in a minute). Then I multiplyed 16 times 4 and thats 64. Thats how I got 64 as the solution.

Tuesday, January 11, 2005

I Love Flickr

Just subscribed to the Flickr blog. It's neat to see the photos that other people are posting to the site without having to browse the actual site. Of course, as a teacher I immediately began to think about how I can exploit this wonderful resource. There is so much potential for having students get really creative snapping photos with digital cameras and then having them write about the subjects. I just wish there was more time for this sort of thing.

Monday, January 10, 2005

More Nonfiction Writing for Center for Performance Assessment

More from the Center for Performance Assessment on nonfiction writing. Research on over 130,000 students from"90/90/90" schools (90% free and reduced lunch, 90% ethnic minorities, 90% achieving high academic standards) over a four year period revealed five common characteristics of high achieving schools:
  • Focus on academic achievement
  • Clear curriculum choices
  • Frequent assessment with multiple opportunities for improvement
  • An emphasis on nonfiction writing
  • Collective scoring of student work
The report states that in virtually every school they evaluated, students scores on creative writing were significantly higher than those of narrative or informative writing. As a result, teachers in the successful schools placed an emphasis on informative writing. They used a single rubric for scoring every piece of student writing.

So why did the nonfiction writing produce such positive results? Written responses " students demonstrate the thinking process that they employed to find a correct (or even incorrect) response to an academic challenge." They "write to think" and gain the opportunity to "...clarify their own thought processes." This type of writing was also beneficial for the teachers as they had the opportunity to gain valuable diagnostic information about their students.

These results reinforce most of what I have been writing about (particularly in the blogs section of my Web site)--students need to be writing in the mathematics class, and using blogs is a great way to get them doing it. Hopefully there is somebody out there who will take notice.

Student Extended Responses

First period extended responses have been posted. I have added a few to my blogroll for easy viewing. On Friday, we developed a rubric that we will use for the remainder of the year to assess each extended response. Here it is:

  • Is it clearly written?
  • Is it sequential?
  • Do I repeat myself?
Math Language
  • Does it use math terms?
  • Does it use them correctly?
  • Did I remember to include my solution?
  • Is my solution correct (or does it at least make sense)?
  • Did I use information from the problem (tell what I know)?
  • Did I give examples (when needed)?
As you will notice, there are no symbols, diagrams, etc. The purpose of these is not to show work, or computations, but to express the process in words, a highly metacognitive process. I cannot express how important this is for my students. They RARELY give any thought as to how or why they do anything in math. These explanations force them to go deeper into the process involved in solving problems.

Completion of the extended responses is followed by another important step, self - evaluation. Before publishing, I ask students to once again look over the checklist, focusing on Communication and Solution. I ask them to make sure they understand their own writing and that they have included their solution with an appropriate unit (two things that students often forget).

Thursday, January 06, 2005

Extended Responses in My Class

Yesterday I began my experiment with having students write extended reponses in their blogs. Well, almost. The blogs don't come until Monday. In class yesterday I had my students score explanations from students of a problem we solved in class on Tuesday. Each explanation could given one of three scores: 3-excellent, 2-good, 1-fair, 0-poor. Each student was also required to provide a comment or two telling why they gave it that score. The plan is to use these comments today to build a rubric for a 3-excellent extended response and have students refer to this as they write future ones.

Today I will assign the problem and have the students solve it in class. Monday they will enter their solutions into their blogs. Here is the problem:

Mark’s heart beats 16 times in 15 seconds. At that rate, how many times will it beat in one minute? Be sure to include the appropriate unit.

The standard is select appropriate units for measuring derived measurements. For example, MPH and RPM.

As with any experiment, several questions have surfaced. How will I grade these? If students use symbols, tables, diagrams, or certain mathematical notation that can't be found on the keyboard, how do I get that into the blog? We'll get to those on Monday.

Wednesday, January 05, 2005

The Latest Furl Entries

Using Blogs as Portfolios to Increase Student Math Scores on State Tests - In Practice

In my last entry I gave several reasons why I think having students write in blogs would be an excellent way of increasing math scores on state tests. The premise behind this conclusion is that writing in blogs would help students when they are confronted with extended reponse items, or questions that require an explanation as part of the answer. As part of this assertion I described many valuable features of a blog that promote the growth of student writers--the ease with which one can receive feedback through comment links, providing students with an audience through the Internet, and observing growth throughout the school year by collecting all the entries on a single Web page. All of these are features that make blogs perfect for use as digital portfolios. Perhaps, then, I should revise my declaration and state that using blogs as digital portfolios would be an excellent way to increase math scores on state tests.

So how would this look in practice? I think every student and teacher should be set up with a blog account. Teachers could give students an extended response item to solve that fits into the curriculum begin studied at the time. Students would work the solution individually, with partners, or in groups. Once a solution is found, the students could then post an explanation of how they solved the problem as an entry in their blogs.

The extended response is now available for feedback. During this feedback period, teachers can comment on the work by clicking on the comment link. Another option might be to assign a partner to each blogger and have them comment on the entry. After feedback is given, students could either revise the entry at that time, or use the information to improve upon the next entry.

This cycle--solving a problem, posting an explanation, receiving feedback--continues throughout the school year. The entries will accumulate and eventually form a body of work that will show how the student's writing has progressed over the course of the school year. This type of portfolio is known as a growth portfolio.

There are so many questions that still need to be answered (and generated). Future posts will consider them.

Tuesday, January 04, 2005

The State Test, Blogs, and Digital Portfolios

This coming February I'll be presenting "Web Logs in the Mathemtics Classroom" at the Ohio SchoolNet State Technology Conference. My session will focus on using Web logs as digital portfolios to increase student's scores on the state test.

The premise here is that there is a great deal of writing on the mathematics portion of the state test. In Ohio, questions that require a great deal of writing are called extended response items. These are typically the questions that students struggle with the most on the state test, particularly in my school district. As a result, their test scores suffer.

Obviously, the solution to this problem is to have students write more in math. At the Future of Math Web site, I describe several forms of writing that could be used in the mathematics classroom: journals, learning logs, math autobiographies, and explaining solutions to problems. For the purpose of improving test scores, teachers must focus on having students solve--and explain the process involved in--problems. But this type of assignment must be more than a token assignment thrown in once a month, or as a word problem at the end of an exam; it must drive the mathematics instruction in each and every classroom.

I have come to believe that blogs hold incredible potential for improving student writing in mathematics, specifically peformance on extended response items. There are several reasons for this. One is that blogs allow others to easily provide feedback. By clicking on the comments link at the end of each entry, teachers can provide students with information on how to improve their writing on the next entry.

Blogs furnish students with an audience. Residing on the Internet, a blog can be read by anybody with an Internet connection. Every entry is open to criticism from teachers, parents, administrators, and other students.

Blogs also allow students, teachers, and others to see progress throughout the school year. As they are updated, all previous entries remain on the page so that by simply scrolling, students and teachers are able to see the entries for the entire year. The whole year's learning is on one screen, similar to a whole year's learning in the contents of a notebook or portfolio. This leads to the next important point, and the topic of my next entry, using blogs as digital portfolios.