Links for the Week: H20 Playlist, Scribe Posts

Current Fascination

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I really like the idea of creating playlists on H20. It makes building a list of resources quick and easy, and best of all, the list is online. My first H20 playlist: Top Ten Sites for RSS and Podcasting. I've been working this one up for a presentation I'm doing at a conference next month (SOITA). Instead of passing out handouts, I plan on directing participants to this playlist. There aren't ten sites there yet, but plan on all of them being there before December 5.

A Podcast You Must Hear

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Check out this excellent podcast with Barbara Ganley coming from EdTechTalk.com. Barbara discusses her experiences using blogging with her students, and believe me, she is doing some incredible things. During the cast, Will Richardson and his Executive Ed.D class at Seton Hall tune in and ask Barbara some questions.

Teaching Tip for the Week - Scribe Posts

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Blogs have yet to really catch fire in the math world. However, there are a few teachers that have really taken this publishing format and put it to work in their classes. I'm impressed with a lot of the ideas I see coming from A Difference, and in particular, Scribe Posts. Here is how a scribe post is described:

The original assignment was simply to post a brief summary of what happened in class each day. A different student is responsible for the daily scribe post and they end their post by choosing the next scribe.

According to the post, not only have the students really benefitted from these posts to the class blog, but so has the teacher, Darren Kuropatwa, a math teacher from Canada.

When a student is scribe they take particularly good class notes and think deeply about what they learned that day. The process of writing their scribe (we've created a new use for that noun) forces them to reflect on their learning and work to articulate the lesson as though they were teaching it.

and

There have been tremendous benefits to me as well. I've become a better teacher. I know that someone is going to write about what I do in class each day -- I had better make certain that they have material to work with! ;-) The scribe posts have allowed me to see how and where students are struggling with the material.

I have set up a community of classroom bloggers over at 21Publish. My students are blogging in math, social studies, and language arts. The only problem is that all of the blogging takes place during school hours. I'd love to see them begin to consider blogs as something more than just a tool to use at school, but also as something that helps them learn outside of school as well.

H20 | blogs | math | podcast

News from around the Net

I subscribe to several eNewsletters, read many blogs, and listen to a variety of podcasts. Below are some of the best new resources I've learned about recently:

• podOmatic - PodOmatic inc provides a revolutionary new service that enables anyone to easily find, create, and distribute podcasts. podOmatic will host your podcast with 250mb for free and provide online recording tools so all you need is a microphone. And if that's not enough, iTunes support is built right in. I tried it out the other night and creating a podcast doesn't get any easier! (Thanks to TILT for this one)
  
• clusty - I'm really excited about this one! Clusty is a search engine that organizes search results into hierarchical clusters. I played around with this last night and my first impression is that this may more appropriate for classroom use than other search engines due to the clustering of results. No more endless searching looking for relevant sites! (Found this one on Ideas and Thoughts from an EdTech)
  
• H20 Playlist - An H2O Playlist is a series of links to books, articles, and other materials that collectively explore an idea or set the stage for a course, discussion, or current event. This site is perfect for the person who likes to present at conferences but doesn't like to waste paper for handouts. Direct participants to your H20 Playlist.
  
• PowerMediaPlus - Similar to unitedstreaming, this site gives you access to digital video, audio, images, and more. No personal experience with this, but I have been using unitedstreaming and I have to say that I love it!
• Antsmaching.org - Threw this one in here for fun. If you're a Dave Matthews Band fan, you need to check this site out. Here you can download live shows from the band for free!

Enjoy!


education | teachers | math | podcast

Links for the Week: Assessment Resources & MyMathTutor.com

Assessment is one of my favorite topics to write about. I believe that implementing an effective system of assessment in the classroom is one of the keys to improving student achievement. Below are links to some resources on assessment FOR learning, also known as formative assessment, or student-involved assessment.

• The Qualifications and Curriculum Authority (QCA): Assessment for Learning - Great overview with many downloadable materials. Definitely download and read: Assessment for Learning: Beyond the Black Box.
  
• Assessment Training Institute: I attended a year long training program from this group and I have to say it was amazing! It changed the way I teach. Subscribe to the eBulletin and check out some of the group's articles under the resources link.
• Center for Performance Assessment: Ever hear of Doug Reeves? Enough said. Click on the link and spend a few hours here.
  

Link of the Week - MyMathTutor.com

From the site:

MyMathTutor is a web-based learning or eLearning program designed to supplement traditional course materials and classroom instruction. Our system is centered around video tutorials that show how to solve various math problems in an easy to follow teaching style. We leverage Internet technology and streaming video to bring an effective and affordable learning system to math students.

The videos on this site cover Pre-Algebra through Trigonometry and are about 6 - 10 minutes in length. To watch them, you'll need Real Player 9 or higher. Textbook author Charles P. McKeague is the instructor in all of the videos.

Future of Math Back Up

After several weeks of being down after my host deleted my files, the Future of Math website is back up and running. Here you'll find resources to help you get started using technology in your mathematics classroom. The URL for the site is futureofmath.misterteacher.com.

My First Podcast!!

Reflections from the OCTM Conference

This past Thursday and Friday I presented a couple sessions the Ohio Council of Teachers of Mathematics Conference in Dayton, Ohio. Although it was a pretty small conference in terms of attendees, I had a decent turnout for both of my sessions. There were also several other good sessions, but I was particularly impressed by one.

On Thursday, I learned about the "3 Blocks"--Presenting Indicators, Practicing for Mastery, and Independent Practice--Framework for teaching math that is used in Dayton Public Schools. In developing this framework, the creators--two teachers from the district--hoped to have teachers across the district following a similar plan of instruction for each math class period.

The block that should begin each class, Presenting Indicators, was the one that hit home with me. Much of what the creators said should take place during this time was based on the work of Rick Stiggins, a man whose work I base a lot of my teaching on. In a nutshell, there should be a strong focus on having students "decompose" the state indicator (objective), which is written on a sheet of newsprint or the chalkboard, being taught before beginning the actual practice part of the lesson. In other words, students should know exactly what it is they are expected to learn. As part of this process, the indicator is presented and students, with the help of the teacher, underline the skill words and circle the concept words. For instance, in the indicator add and subtract whole numbers using regrouping, we would...

• underline add, subtract, and regrouping.
• circle whole numbers.
  

Ultimately, the teacher creates a word wall using the words from the indicators. As a result, students gain a stronger handle on mathematics vocabulary.

There was far more to the Presenting Indicators block--spaced review, problem-solving practice--but it was the decomposing that I think I will implement as soon as possible. I had been thinking for some time about how important it is for students to learn the "language of math." This session convinced me of it.

Welcome!

Links for Visual Classroom Participants

For a complete list of the links from today click the link below:

• Visual Classroom Links
• Even More Great Links!
  

Using the Internet to Acquire Digital Images for Classroom Use

The Internet is a gold mine for finding digital images to use in your classroom. On numerous occasions I have found photos from Google or another photo site and used them on worksheets, in a blog entry, for writing prompts, or for something else. Below are some of my favorite sites for finding photos to use in the classroom.

1. Google Images.
   
2. Flickr - Millions of users, million of photos. This is Web 2.0 at its finest. This photo sharing site allows users to tag their photos, or add keywords to them when they upload. When you search for photos here, you enter a tag into the search box and any photo that has been tagged with that keyword is returned. Tips for using Flickr:
   • Try a tag search for math nature and you will get photos from folks who have tagged photos with those words. Go to the site and try this.
   • You can also do a group search for photos. Do the same search from above and your results will show groups who have uploaded photos with the theme math nature.
3. KidsClick - This page contains links to special image databases under the following categories: Art, Astronomy/Space, Animals, History/Society. Some of the links include Astronomy Picture of the Day, FWS Image Archive, and American Memory Collection.
4. Yotophoto - From the site: "Yotophoto is a search engine for free-to-use stock photographs and images. These are images that are either in the Public Domain or released under generous Creative Commons, GNU FDL or similar licenses."
5. Stock.Xchng - This site is full of stock photos for professionals. It is still full of photos that are great for classroom use.
6. PixelPerfect - Another site meant for professionals but full of of photos appropriate for classroom use. This is a comprehensive site on digital photography with tons of information on cameras, reviews, links, and more.
7. Pics4Learning - A copyright free image library for teachers. I can't say I'm real high on this one--there just isn't the depth here that you'll find in the sites above.

By the way, the above information is copied word for word from my Website Future of Math: Digital Cameras.


Technorati Tags: education | teachers | flickr | internet | photography | Pics4Learning

Section 2 - Analyze

Use of images can involve many kinds of analysis on the part of the student. Our goal is to get them to see mathematical concepts in real-world images.

Assignment # 2 - Creating assignments for students.

1. Go to the Visual Classroom Photo Site and browse the images there. I have put a question or assignment under each photo. Remember, you are the student. Do you see the concept that I see in the image?
   
2. After you have seen enough, come back to this site, click on the comments link, and provide the rest of the participants with two assignments that you could create for students.
   

Section 3 - Create

Educational activities often involve products. Word processing software makes it easy to incorporate digital images.

Assignment # 3 - Create three "concept cards" from three digital images from the Visual Classroom Photo Site. A concept card is a document (or web page) that contains an image with a description or definition of the concept pictured. Follow the directions below to download the images and add them to an Appleworks document.

1. Find an image that you like and position your mouse over the photo.
2. Press the control button on your keyboard and then click your mouse.
3. A menu will pop up - select DOWNLOAD IMAGE TO DISK (IE Explorer) or SAVE IMAGE TO DESKTOP (Safari).
   
4. A navigation window will pop up - give the image a new name and then save it to the desktop. Repeat with two other images.
   
5. Open an Appleworks document.
   
6. Go to the FILE menu and select INSERT... In the bottom right of the window, select ALL AVAILABLE.
7. Find the image you want, click on it, and then click INSERT. Your image should appear in your document. From here, you can add the text that describes the image and apply any formatting you would like (center, increase size, change font, etc.).
   

Section 4 - Communicate

Products are not always meant to be read only by a teacher, but can also be communicated to a larger audience. In the following assignment, you will take your concept cards and create a slide show for the other participants to view.

Assignment # 4 - Create a slideshow that communicates what you learned in your project to the group.

1. Make sure each concept card is on a different page of your document. Center each image and its description.
   
2. Go to the WINDOW menu & select SLIDE SHOW... Click START to begin the show. Hit Q on your keyboard to end the show.
   
3. Move around the room to view others' slideshows.

More forms of communication:

• Web pages - Does your district provide you with web space? Use it to publish student work. Imagine how excited students and their parents will be when they see their work on the Net!
• Bulletin Boards - Put student work with digital images on a bulletin board.
  
• Hallway Displays - Display student-created concept cards in the hallway.
  

Back-to-School: New Printables and Math Tools

Printables for Digital Cameras, Blogs, and Spreadsheets

I have started the process of creating printables to help teachers get started with weblogs, digital cameras, and spreadsheets in their math classrooms. The printables are located on the individual pages on the Future of Math website and include:

• Writing Prompts for Math
• Using Blogs in the Math Classroom
• 38 Uses for Digital Images in the Math Classroom
• How to Make a Graph Using a Spreadsheet
• Writing Formulas for Spreadsheets

There are many more to come. The printables are in PDF format so they are platform independent.

Math Tools: A Great Web Resource from the Math Forum

If you are interested in bringing technology into your math classroom but aren't sure quite where to find good resources, look no further than Math Tools from the Math Forum. Math Tools is a website that contains "...a wealth of resources designed to help you use the power of interactive software to enhance the teaching and learning of mathematics." This digital library includes, but is not limited to, the following resources for math teachers:

• Tools for many different technology types: graphing calculator, handhelds, and computers, including Cabri, Fathom, Flash, Shockwave, Java applets, Java script, Sketchpad, with more to come.

• Lesson Plans: Many tools have lesson plans that were written to give a teacher an idea of how the technology can be used within a mathematics curriculum.

The Math Tools website has two main features: A catalog of resources and a discussion forum. You can browse the catalog by choosing the grade level or math course that you teach, the resource type (lesson plan, tool, etc.), and the technology you would like to use (graphing calculator, Java applet, etc.). There is a resource for every type of math taught at the K-12 level (some topics have over 40).

Upon registration (registration is free), you will be able to save resources, locate and keep a Friends list of other users, and post to the discussion forum. The discussion forum allows registered users to discuss topics in the catalog with other educators. Registered users can also contribute a resource that they have created to the site, a great way to share your work with others.

How do you measure your impact?

This past week I decided to leave my job teaching seventh grade math at Verity Middle School in Middletown City School District, just north of Cincinnati, OH. I spent the first five years of my career at Verity and I have to say that it was difficult to leave. In my new position, I'll be teachinig sixth grade at Wyoming Middle School in Wyoming City Schools.

Although I was happy as can be in Middletown, I couldn't pass up the opportunity to work in Wyoming. You see, the students in my new district typcially are members of families with highly educated parents who stay involved in their education. As a result, the district boasts extremely high-achievement rates, some of the best in the state. On the other hand, the district I am leaving is an urban district with a high percentage of students receiving free-and-reduced lunches. Furthermore, parent involvement is low and test scores reflect this.

So it seems my reasons for making the switch are obvious--wouldn't everyone love to teach in a district similar to Wyoming, where parent involvement is high and student achievement is consistently near the top in the state? Well no, there are many who may read this and say that they would much prefer the challenge of teaching in Middletown. It would be much more rewarding to make a difference in the lives of children who often have so little. How much of a difference can one make in a district like Wyoming, where 95% of graduating seniors attend a four-year college?

I started thinking about this question the other day and a few thoughts came to my mind. First, and maybe I'm wrong about this, I don't think I made much of an impact in Middletown anyway. In five years there, I can't recall having more than just a few students who I really developed GOOD relationships with. And guess who those students were? The high-achieving, highly motivated ones with whom I instantly developed a positive rapport. I had much in common with these students--a strong desire to learn and be challenged, a killer work ethic, and the drive to be successul. In other words, the type of student that I enjoyed teaching was exactly the type of student I will be teaching in Wyoming.

My second thought came in the form of a question--is it possible to make a positive impact in the life of a child, even if he comes from a great family? My answer is yes. Every child has their challenges, and teachers can help them overcome those challenges. I may have a few students this year who excel academically, but need help socially. I may have a student or two that hate to read. What if I could find a way to ignite a passion for reading in these students so that they become avid readers? Or what if I have student who is in to alternative activities--skate boarding, heavy metal music (I also reached a few of these kids in Middletown)--and as a result has few friends. What if I could find a way to relate to him/her?

I guess my main question is, how do you measure your impact as a teacher? I believe that not every child in a high-performing district is destined to be successful the moment they leave the womb; even these kids need the support of a caring teacher somewhere along the way.

Every teacher has a job to find out where they can make the biggest difference and search for a way to get there. Maybe my place was Middletown, but I'm pretty sure my place is Wyoming. Beginning this August, I'll find out.

The Best Professional Development

If I had remained at my position in Middletown, I would have been taking over the algebra and geometry courses. As I have never taught these courses, I brought the textbooks home for both courses so that I could sharpen up over the summer. Last month, I took a position in another school district, and sadly, it is not one teaching algebra or geometry.

I am still reading the books though (I'll return them in August) and I have to say I am learning A LOT! Not only am I (re)learning some great math, but I've been able to reflect on my teaching of mathematics, and the teaching of mathematics in general. Here's what I discovered...

• about my teaching: For years one of my approaches in teaching fifth, sixth, and seventh grade students is to have my students complete an activity which requires some inductive reasoning. They often struggle with this. After studying the geometry text, I now know why--students are not ready to learn this way until they reach high school. There is a chapter devoted entirely to inductive and deductive reasoning in this text. If they have to be taught this in a geometry course (normally taken in the tenth grade), then they are definitely not ready for it in the intermediate grades.
  
• about math teaching in general: As I said above, I am learning a great deal through studying these texts. I have learned something about my students--I can now see why they have difficulty reasoning. It has also been interesting to see what concepts my students are working towards in the higher grades. In other words, I can now see exactly how the math concepts I am teaching at my level will help them with higher-level mathematics. Some of the concepts that I find so simple, like parallel lines, are extremely important in more advanced mathematics (proving a parallelogram is actually a parallelogram). I have come to find that this learning experience has been better than any workshop I have taken. Learning higher level math, or at least higher than the level I teach, has been the BEST PROFESSIONAL DEVELOPMENT I have ever had, and it is my contention that it is the best professional development for any teacher of mathematics. If we are to improve math instruction in this country, we must have teachers who have a deep knowledge of the math they are teaching. For instance, if a second grade teacher is teaching students how to recognize patterns, then he/she should know how this knowledge will help them when they tackle patterns in algebra.
  

During the school year, I receive registration forms for many math workshops. I have seen the materials for many of these workshops--they consist of games and other gimmicks that teachers can use to help students "learn" math. Instead of increasing teachers' knowledge of the math they teach, the facilitators of these workshops arm them with silly tactics to help students to memorize procedures and pass standardized tests. I say we do away with this type of professional development, and begin requiring teachers to take advanced math courses so that they have a greater understanding of the math they teach, not of gimmicks and games.

Future of Math Featured in Math Forum

Just received an email from Suzanne Alejandre over at the Math Forum @ Drexel informing me that my website, Future of Math, is being featured in the latest Math Forum Electronic Newsletter. It's an accurate description of my site, hope it brings some traffic.

This once-a-week newsletter is a good, quick read with information on workshops, news from the site, and links to VERY interesting math sites. It's pretty much what I would like this blog to become. I'd like to see them add an RSS feed to it--that would be nice.

Teaching Probability with Tree Diagrams (Reflection)

Tree Diagram
Originally uploaded by Misterteacher.

We're finishing a two week unit on probability in my 7th grade classes. This year students had to make the jump from finding simple probabilities to computing compound probabilities (two tosses of a coin instead of one). Students were to use a list or tree diagram to find the sample space (total outcomes) and all favorable combinations (such as the number of times 2 heads and a tail occurs when tossing three coins).

Making tree diagrams has been extremely difficult for most of my students. They are having trouble even knowing where to begin with the diagrams. For instance, when calculating the sample space for tossing three coins, instead of branching out from a head and tail on the first toss, they might begin with three outcomes (two heads and a tail) and add three branches to each of those (to designate three coins being tossed).

To eliminate confusion next year, I am definitely going to create tree diagrams with blank spaces (see example) for each problem they solve and just have them fill in the blanks. This seems like the proper amount of scaffolding they will need to eventually create their own.

Flickr for Teachers: Teachers Sharing Sets

It's become quite common for teachers to share effective or innovative lessons through their blogs. This morning while I was helping my first period class complete a project on probability, I thought of another great way to share ideas--through Flickr sets.

Throughout this week I had been taking photos of my students in various stages of the project so that I could have them post the photos to their blogs with a summary of their experiments (this would be considered an artifact in project-based learning). I took seven photos in all and decided to create a set that I could link to in future blog posts. As I worked it occurred to me that with the visuals and the descriptions below them, this would be a very effective way to share ideas with other teachers. If I wrote about this project in my blog, teachers would only be able to read about it. With Flickr, teachers also get a visual representation of what they would be reading on the blog.

So check out my probability project set and consider sharing your innovative classroom lessons in this manner. You also might want to join the Flickr for Education Group and start sharing ideas there.

Categories: Education | Flickr | Math | Classroom

Math Solutions - Solving Word Problems

I finally got a chance to read the latest Math Solutions Online Newsletter. Regardless of what grade level you teach, there is some great information there. In the Q & A section, there was a great tip for improving students' ability to solve word problems. From the site:

My students seemed to have the greatest success with word problems when we spent time having them develop the word problems themselves. There was something about having to construct their own problem that led to a greater understanding of already-constructed word problems. The concern was not doing the computation, but rather understanding what the problem was asking them to do.

In order to better understand what problems are asking, provide students with some information related to a concept you are currently teaching and then have each student complete the following steps:

1. By yourself, write a question that can be answered from the information posted.


2. In your groups, read your questions aloud and discuss whether they can be answered.


3. In your groups, brainstorm as many questions as you can that can be answered from the same information. Write them on one sheet of paper.

After these steps, students can then present their questions to the class and have the rest of the class answer them. Today my classes are looking at double bar graphs that they have created from data they collected yesterday. Instead of just asking them questions about the graphs, I think I'll have them develop the questions themselves. This seems like a more engaging technique that will get them to think about the graphs more.

Categories Education | math | classroom

Probability with Virtual Manipulatives, Blogs, & Spreadsheets

stickorswitch
Originally uploaded by Misterteacher.

Need a highly engaging way to teach probability? Take a trip on over to the National Library of Virtual Manipulatives and play the game "stick or switch," a takeoff on the game "Let's Make a Deal."

Just like the game, this virtual manipulative allows students pick a door to find a hidden prize. And also like the show, another door will open to reveal a less than desireable prize. Students can then choose to stick with their original choice or switch to the other unopened door by clicking on the either of two buttons (stick or switch).

I'm using this game to teach experimental probability. After an introduction to hook the kids and discuss the probability involved, I allow them to play the game on their own, keeping track of their choice (stick or switch) and whether they won or lost. Tomorrow they will create graphs of the results on a spreadsheet and blog the results and conclusions. Look for them in the next few days.

Hotmath helps students excel on state exam

From eSchool News Online:

Hotmath helps students excel on state exam

May 1, 2005

California teachers using Hotmath.com to help their students with math homework say the tutorial web site--which recently took top honors in several categories of the latest eSchool News Readers' Choice Awards--has helped their students pass the math portion of the California High School Exit Exam in impressive numbers.

Results from California's 2003-2004 exam indicate that the statewide passing rate in mathematics was 74 percent--but 80 percent of students passed in the 122 California high schools that have made Hotmath available, according to data from Hotmath Inc. The results in Los Angeles suggest an even wider gap between schools that use Hotmath and those that do not. In the Los Angeles Unified School District, the district-wide pass rate was 58 percent. The rate jumped to 77 percent for the 13 Los Angeles high schools that use Hotmath.

Founded in 2000, Hotmath provides explanations and worked-out solutions to the odd-numbered problems in more than 60 popular math textbooks used in grades 6-12.

Consequential? Just because Hotmath was available, does that mean teachers used it? Don't we show students how to solve problems on the chalkboard everyday? Too many unanswered questions here.

Links:

Hotmath.com
http://www.hotmath.com

Future of Math in Connected Newsletter!

This month's Connected Newsletter lists Future of Math in its A+ Web Gallery: Sites That Get Our Highest Recommendation. I like this quote from the article:

This site breaks new ground by using a variety of exceptional techniques to enhance understanding of mathematical concepts.

Nice to know when your hard work is recognized.

Math Solutions Newsletter

Just received my summer edition of the Math Solutions Online Newsletter. This is the professional development service founded by Marilyn Burns. If you are k-8 teacher, this newsletter is definitely worth checking out. There are sections on lesson plans, frequently asked questions, and inservice updates. If you have never taken a Math Solutions inservice, this section is definitely worth looking into. I have taken three now and each one has forced me to rethink the way I teach math. I'm sure my students have benefited tremendously from the knowledge I have gained from these workshopes. You'll also want to check out the Math Solutions publications, they're some of the best in the business.

Categories: education | math | teacher

Book Review Day

It must be book review day in the blogoshpere. I've already three book reviews and it's not even 10 a.m. yet. Anyway, I've posted a link to each one over at the Future of Math: Interesting Links blog. If you haven't read a book review yet today, I highly recommend clicking above. All three would be books that I would gobble up, if only I had the time.

An Online Math Revolution

One of my goals this year was to use certain technologies--blogs, discussion forums, digital images, spreadsheets--in place of traditional methods to enhance student learning of mathematics. As part of that goal, I wanted to share my thoughts and discoveries with other teachers, particularly math teachers, in hopes that I would be able to persuade more of them to also begin using these tools in their classrooms. I also wanted to connect to more math teachers in hopes of discovering other teachers who shared my goals.

The results are in. This blog has increased in subscriptions from under ten at the beginning of the school year to 18. Not an incredible leap, and definitely not a huge number of readers (considering Weblogg-ed has over a thousand!), but there is something to be happy about here. Many of those subscribers are math teachers and they also have blogs. These teachers are also having their students complete some innovative projects in their classes using the same technologies I am using. One of these teachers, Mr. Kuropatwa, has even created a new project for teachers, the BPRIME (Best PRactices in Mathematics Education) wiki. From his latest blog post:

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.

I plan to give a lot. Projects like this will help continue the Online Math Revolution which is in its early stages. Math teachers unite! Let's work to make sure that our friends who continue to rely on traditional outdated methods are enlightened. Spread the word through your blogs, speak at conferences, volunteer to lead workshops, and network, network, network!

A New Blog

Each day I read multiple blog entries from across the blogosphere that I would love to link to and comment on. Lack of time forbids me from doing this. Then I came across the kottke.org remaindered links weblog. From the site:

Remainder n. "Something left over after other parts have been taken away."

I post several of these a day. You can think of them as the clicktrail of my journey through the Web.

Well, I thought of a way to post my own clicktrail. Using Bloglines, I plan to use the Clip/Blog This link at the end of each interesting link I read but have no time to write about to create a remaindered links weblog. I read a lot of blogs and articles each day and I feel that this blog could be helpful to many. Click Future of Math - Interesting Links to read and subscribe.

Flick for Teachers: Blogging Photos Part 2

In my last Flickr for Teachers post I outlined some ways that teachers can enhance student learning using the blogging feature of Flickr. The focus was on using photos as writing prompts in group, or class blogs. This post will focus on using photos from a class Flickr account in individual student blogs. The information presented below will be based on an article by Diane McGrath in the April 2005 Connected Newsletter titled 7 Tips for Successful Project-Based Learning. I've chosen a few of the tips from the article that I think Flickrblogs (a new term?) support. Here they are:

• Tip one: Blog as an Artifact
  
• "Students construct an artifact to help make their thinking visible, discussable, and revisable. It may be a physical object, multimedia, or a concept map." In our case, the artifact would be a photo, or a series of photos, that students have taken that display their learning during a project and blogged from Flickr.
  
• When they post the photo as part of a blog entry, students can also provide a description and a series of links to related material on the web.
• The blog makes the artifact visible to the whole school community.
• The comment link assures that the artifact is discussable.
  
• Tip Four: Blogs as communities of learners
• "Design your classroom to be a community of learners." The Flickr site maintains that its goal is to "...help people make their photos available to the people who matter to them." In other words, the goal is to create a community of people interested in sharing their photos. Blogs also support communities; in fact, one could argue that the purpose of blogs is to support the development of communities.
  
• Tip Five: Blogs are technology tools.
  
• "Learners can use real adult tools to...design artifacts." Based on the article, Flickrblogs would be great tools for expression, communication, and particularly cognition (tools that make thinking visible and fixable).
• Tip Seven: Blogs provide real audiences.
• "Students conclude their project with a presentation to a real audience."

I'm feeling some serious inspiration after writing this post. I'm seeing a project on probability that students complete on a Flickrblog coming up here in the next few weeks. Next up, sets in Flickr as artifacts of project-based learning.

Categories: education | Flickr | blogs | classroom | math

Linear Patterns: Flickr in Practice

With all these posts about Flickr, I figured I might actually start a classroom blog where I post a problem of the day (similar to think again!) several times a week and have my students respond through the comment link. I was able to get in a couple of these this week.

My first impression is that it's going to take the kids a while to get used to the routine--the first problem took the whole period in each class and the second problem took about 25 minutes! But doing this is going to help me achieve a few goals:

1. Get my students to write about math more often (when this is a requirement).
2. Get my students to think about how they are solving problems.
3. Elicit somewhat of a classroom discussion through the blog, almost like a silent discussion. After posting, students actually want to read about how other students solved the problems. This has similar benefits to an actual discussion--students get to read about the different strategies that one can take to get a solution to a math problem.
4. Discover an effecient form of assessment. When I scrolled through the students' responses to the problems, it was very easy to see where there were misunderstandings and note them so that I could correct them later.
   
5. Review prior learning.
   

I plan to continue this through the end of the year. Check back for more problems.

Categories: classroom teacher math

One-Step Equations

Today's topic: one-step equations (54 + x = 96).

Students can easily solve a problem like the one above, but as we know, at this level (7th grade) they must learn to follow the steps needed to solve an equation: using an inverse operation, balancing the equation, and simplifying. My students are struggling with this.

I think I have found a very effective way to help my students remember how to solve one-step equations. It is quite simple and uses a mnemonic device to help them. Take the process above and use the first letters of each step to make the mnemonic: IBS - inverse, balance, simplify. Then when your students are having difficulty, or you are going over a problem with the class, simply say those three letters, IBS, throughout the entire equation solving process. Post them around the room, have students write them on their papers, and, once again, say them aloud as often as possible. It's amazing how when a student sees or hears IBS, they are able to figure out what the next step is in solving the equation. The mnemonic has two additional benefits:

• It forces them to write each and every step instead of doing the math in their heads and then writing the solution.
• It makes them use the vocabulary associated with equation problem solving process.
  

Categories: education classroom math

Future of Mathematics: The Website

Future of Math: The Website has undergone some needed updates...

• A new look--simple and refined. I don't know how to create CSS, so I tried to come as close as possible with a simple table with gray borders.
• A new page--Digital Portfolios.
• I'm adding a list of links from my Furl archive to each page so that there is constantly new information on each topic covered on the site. By the way, you might want to check out the archive and subscribe. I'm up to 418 sites now!
  

If you've never been to the Future of Math website, here's a rundown of what's on it.

• A great About page which describes my philosophy on using technology in math.
  
• An extensive page on blogging in the mathematics classroom. Here you can find my blogroll.
  
• A page on using digital images in the math classroom.
  
• A page on spreadsheets.
• A page on discussion forums which is badly in need of updating (I'm in the process).

Flickr for Teachers: Blogging Photos from flickr

Once a classroom account has been set up with flickr, a teacher and his/her class(es) can begin the process of uploading photos and then using them in the classroom. One of the best ways to use these photos is to blog them. Flickr allows you to set up your account so that you can select and post a photo to any number of blogs. So if your students all have blogs, they can post photos from your Flickr homepage to them and use them for a multitude of different assignments. If your students do not have individual blogs, or if a group blog is being used as a class blog, then a host of other types of activities exist.

Following are suggestions for using a Flickr library as a tool to enhance classroom blogging. The suggestions are divided into activities for group blogs and those for individual student blogs.

Group Blogging with Flickr - In the classroom, a group blog is one that is administered mainly by the teacher. It is meant to build a community of learners by having student work published in a single place so that other members of the community can view it. Integrating digital images brings a new dimension to the group blog as the information is no longer just textual, but is now also visual.

• Writing Prompts
  
• Problem of the Day (or week) - Having students solve a problem (or problems) on a daily basis is a routine activity for most math teachers. It helps teachers to assess, review, and enrich the math curriculum. In a group blog, a problem is posted for students and they post their solutions through the comment link. Adding digital images from a flickr account allows a teacher to ask a wider range of questions because they can then use details from the image to eliminate much of the verbal description that would be needed without it.
  
• See Think Again! for a few examples
• Here's one on transformations.
• One on central angles.
  
• Journal entries - Of all the forms of writing in math, the requirements of a journal may be the most ambiguous. Entries can be as diverse as you wish, from justifying solutions to describing one's feelings toward math. A possible use of Flickr might be to take photos from classroom activities, blog them, and have students summarize the activity illustrated in the photo.
• Inquiry projects - An excellent example of using a blogged photo to get students to research a concept is at the Pre-Cal 40S blog.
  
• Blogging Photos from Your Favorites - Because Flickr is an online community, you have access to the photos of all Flickr account holders (as long as they wish to make their photos public). As you browse others' photos, Flickr has a feature that allows you to add those photos to a favorites page. Once there, you can blog those photos and use them for all of the activities above.

More Examples

If Kayla eats 1/4 of the pizza and David eats 2/3 of what is left,
how many pieces will there be when they are finished?
(from permanentennui)




What would the next three squares look like in the pattern above? Describe the pattern.
(from misterteacher's photostream)

That's it for this entry. Next up, suggestions for using photos in individual student blogs.

Flickr for Teachers: Your Own Personal Web Page

Click on the about link in flickr and here's what you'll find:

"Flickr - almost certainly the best online photo management and sharing application in the world - has two main goals:

1. We want to help people make their photos available to the people who matter to them.
2. We want to enable new ways of organizing photos."

If classroom teachers could take those goals and put them into their own words they might read:

1. I want to make my classroom photos available to members of the school community including parents, administrators, and other stakeholders.
2. I want to have a place to store my photos, regardless of platform, and use those photos in engaging classroom projects.
   

Building on the first goal, a great way to use flickr in the classroom would be as a homepage that documents the events of a particular classroom throughout a school year through digital images. Once a teacher creates an account on the site, the URL can be made available to parents and other members of the school community so they can watch the school year unfold in photos.

Here is how it might work:

• Our Class - Mrs. Jones is a third grade teacher who is great at keeping contact with parents. At the beginning of the year she takes photos of each student in her classroom and uploads the photos to the classroom flickr account. In addition, she takes the biographical information she collects on each student and adds a description of each student under their photo. Mrs. Jones then creates a set titled Our Class or Who Are We? using the photos and descriptions. Now parents can come to the site and page through the set to learn a little something about the students in their child's classroom. They can also add an inspiring comment for their child.
• Field Trip - Last Thursday Mrs. Jones' class took a field trip to the local natural history museum. With flickr in mind, Mrs. Jones snaps several photos of students at various exhibits with a digital camera. By Monday, she has uploaded the photos and created a set titled Field Trip to the Natural History Museum.
  

The possibilities are endless--photos from class parties, a science fair, class projects, assemblies, and on and on. Using flickr is more effecient than creating a web page and then taking the time to update it when new photos are added. Using flickr, you simply upload the photos, add a description, and the page updates itself.

So this ends chapter one of section one. Next up, enhancing learning through the blogging of photos from flickr.

Flickr for Teachers

for teachers

Sometime in the next few days I plan on beginning a concept album with the above title. As you know if you read this blog, I love flickr. Since discovering this site, I have thought of, and blogged, multiple uses for it for teachers. The songs on this concept album will each describe a different use for flickr in the classroom, with an emphasis on the mathematics classroom.

Let me stress that this is not a how-to--you will not learn how to upload photos or tag images. The information will be restricted entirely to classroom uses of the site. Below is a table of contents, which I'm sure will change in the coming days.

Table of Contents

Using Photos from the Classroom

• Your Own Personal Web Page
• Photos from the Classroom
  
• Blogging Photos from flickr
  
• Problem of the Day - see past blog entries
  
• Sentence Starters
• Journal Starters
• Sets - Creating Books
  
• Vocabulary Books - Patterns & Functions
  
• Real World Connections - Bring life to a concept
  
• Narratives
• Slide Shows
• Presentations from Projects

Using others' Photos

• Favorites
  
• Problem of the Day, Vocabulary, Real - World Connections
  
• Tags

Online Collaboration

• Groups

Tools

• "Send to Flickr" Bookmarklet
• Sky's the Limit!
• Social Studies - maps, presidential photos, historical photos, geography, culture photos
• Math - figures,
  
• Language Arts - photos that evoke emotions, authors, symbols, settings
• Science - concepts, scientists, tools,
  

Teaching with (Digital) Video Part 2

In my last post I introduced the concept of using (digital) video to enhance teaching and learning in the mathematics classroom. This post is a follow-up and will describe curriculum integration strategies for video, ideas from my classroom, and list some other uses of video in the classroom. Finally, check the list of links in the following posts for further information on video in the classroom.

Curriculum Integration Ideas -

• Digital Video Editing -
  
• A Day with Fractions - From the Apple Education Website, this video, actually a collection of still shots, was created by second graders from California. The video allowed the students to demonstrate an understanding of fractions and time concepts learned in class. As you watch it, think about how through making the video the teacher has given students the opportunity to see fractions in the real world. You can also see how they are connecting fractions to related concepts, such as percents. So how do you utilize digital movie making in the classroom?
  
• As a form of assessment--using it to evaluate student knowledge of concepts like fractions?
  
• To enhance student learning?
  
• Or as part of an entire unit, a unit in which the video was completed over a long period, with scenes added as students learned more about the concept?

• Streaming Video - In my last post, I linked to an article about how short video clips that reinforce key concepts are effective in increasing student achievement. This article was based on a study of students in California. Sixth-grade students whose teachers showed them video clips during instruction improved an average of five percentage points more than students in a control group on a test to measure comprehension of state mathematics standards. Eighth-grade students improved an average of three percentage points more than students in the control group. The approach these students' teachers used was to incorporate approximately 20 standards-based, core-concept video clips into their daily lessons. The clips came from the unitedstreaming video-on-demand service.
• BrainPop - There are over 50 animated shorts at this site covering five different strands of mathematics--algebra, geometry, data analysis, number operations, and problem-solving. As I stated in my last post, this site is powerful because it brings sound and animation to the concepts. Although you could not teach your entire curriculum with this site alone, the mini-movies here bring life to the static images that reside in textbooks. Classroom uses:
  
• Introduction to a unit--a way to give the students a little background before jumping into a lesson.
  
• Reinforcement--teach a lesson, and then have the students watch a related movie to reinforce their learning.
• Intervention--some students just don't get some concepts when they learn from a textbook. Perhaps the movies here could be another way of reaching these students.

From the Classroom -

• Alphabet Geometry - Transformations--slides (translations), flips (reflections), & turns (rotations)--of geometric figures on a coordinate plane have a place in the 5th, 6th, 7th, and 8th grade math curriculums. From my experience, it seems that younger students have a difficult time visualizing where on the coordinate plane a shape should end up after it has completed one of these changes. Because of this, I created a set of Flash movies that show block letters (polygons) undergoing these transformations. Classroom uses:
• This past year, with 7th graders, I had the students watch the movies and actually draw what they saw after each movie was complete. They also wrote the definition of each.
  

Other Resources -

• Videoblogging - videoblogging.info, Freevlog

See the next entry for a list of links to video in the classroom websites.

Teaching with (Digital) Video

So this is the first of my concept albums that I spoke of in my previous post. This one is titled Integrating Video into the Mathematics Classroom and will consist of 6 songs. This album kicks off a new direction for the Future of Mathematics. I’m not going to be writing so much about the events of my classroom, but more about the world of math and how it is affected by new technologies.

Introduction - Our classrooms are populated with students whose learning styles vary greatly. Some are visual, others auditory, and still others kinesthetic. Therefore, if our goal is to reach every learner in our classrooms, we must see to it that we are incorporating activities that reach the diverse learning styles of our students. This type of effort must not be ignored in the math classroom in particular, where students are often bombarded with worksheets and problems from the textbook.

One way to promote learning for multiple learning styles is through the use of video. By bringing sound, animation, and interactivity to learning, streaming video, Flash movies, and digital video editing software allow students to experience concepts in new ways. Open a textbook or hand out a worksheet and all you offer your students is a static image of the concept on a piece of paper. Take the concept of transformations, for instance. In a textbook, students only see the before and after versions of the transformation. However, with a Flash movie, students can see the transformation actually take place.

This album will focus on the use of video--digital,streaming, and Flash movies--to improve student learning in the mathematics classroom. Below, and in future posts, you will find curriculum integration ideas, links with more information, information on the best products for integrating video, and more. Enjoy!

Articles -

• Video on Demand Boosts Students' Math Scores - (eSchoolNews Online)

  "Short video clips that reinforce key concepts are effective in increasing student achievement, according to a second research project. An earlier study found that video can improve learning in science and social studies. Now, brand-new research shows judiciously selected video clips also can produce statistically significant gains in algebra and geometry scores."

• Macromedia Flash as a Tool for Mathematics Teaching and Learning - (School Science and Mathematics)

  "Macromedia Flash is a powerful and robust development tool. Because of its graphical, sound, and animation capabilities (and ubiquitous browserplug-in), major companies employ it in their website development (see www.nike.com or www.espn.com). These same features also make Flash a valuable environment for building multi-representational "movies" (a Flash term analogous to "applet" in Java) to illustrate mathematical ideas or simulate mathematical situations."

Products -

• BrainPop.com is a large library of short educational movies created with Flash animation. Topics from all subject areas are described by young Tim and his robot friend, Moby, in often humorous ways. These jokers demonstrate difficult subject matter like scale drawing in real life situations, which helps students who are having difficult time understanding these concepts from traditional instruction.
  

• iMovieHD - iMovie allows your students to capture, edit, and enhance their own curriculum-based movies. Incredibly simple to use, it also allows them to combine all of their materials and research, including: photos, images and video from the Internet, scanned images, audio files, and their own narration. If your district uses Apple computers, iMovie is definitely worth looking into.
• - Pinncale Studio 9 is similar to iMovie--your students can easily capture, edit, and enhance video with it--but is only available on the Windows platform.
  
• unitedstreaming - "unitedstreaming is a digital video-on-demand service brought to you by Discovery Education."

That's it for song number one for Teaching with (Digital) Video. Later this week I'll post the songs Curriculum Integration Ideas, From the Classroom, & (Digital) Video Links.

Great Idea: Blogging a Concept Album

Concept Albums and Blogs is the latest post from the Read/Write Web blog. What an interesting idea, one worth pursuing.

At the risk of going off-topic, I'm currently deeply into IMHO the best album I've heard in years - Green Day's American Idiot. It's a concept album and I often wonder how such a thing could be done in blogging. It's common wisdom that a focused blog is the best way to gain a following in the 'sphere. But I reckon bloggers could complement their chosen topic by producing concept-driven 'blog albums' from time to time.

While I encourage ambitious bloggers to be topic-focused, variety is the spice of life. An excellent way to keep things interesting is to explore a different concept every week or month (or whatever time period suits you). I have to keep reminding myself of this too. As I said in the Sept 03 post:

"Perhaps I'll start writing weblog "albums" - there'll be about 10 posts per album and each album will have a different unifying theme."

What an interesting idea, one worth pursuing. All of our blog posts fall under one category or another. It would be interesting to really focus on one topics for an extended period of time, becoming a pseudo-expert on it through some research, and writing several posts presenting our findings to the blogosphere. Heck, our blogs could become destinations for others looking to find out information on the particular concept we choose for our albums.

For instance, let's say my concept album focuses on using digital images in the classroom. Through my research, I uncover articles from online journals about this concept, discover books about digital cameras, find related information on websites, and read about products that facilitate the use of digital cameras in the classroom. I can then take that information and turn it into posts with links to articles, book reviews, links to camera reviews, and other resources, all around a unifying theme.

I sense a new direction...

SAT and Blogs

Check out this post from the K-F Libra/Tech Blog titled Blogging Will Help with the New SAT. The first line seemed like such common sense to me.

I am sure if teachers incorporate blogging into their curriculum the angst over this new writing component will eventually disappear.

I can imagine that angst is the proper word for what most of the students feel as they confront this section of the test. 25 minutes to read the prompt, decide a viewpoint, plan, and write the essay, all while trying to vary sentence structure, use clear and precise vocabulary, and leave time to check back on what you have written (Collegeboard.com). But what if students had a great deal of practice with this type of writing ahead of time? Would the angst still be there?

I agree with the post--if teachers were to incorporate blogging into their curriculum, in the form of short, timed writings, then students would go into the test prepared. Of course, this type of blogging would also prepare students for the state tests which, at least in my state (Ohio), they are required to pass to graduate.

It seems that everywhere I turn these days, there is another reason to bring blogs into the classroom. I have been writing for several months on the effect of nonfiction writing on student performance. The type of writing this new test requires--supporting a certain viewpoint--is precisely the nonfiction writing that needs to be practiced in each and every subject area, particularly math, science, & social studies. What better way to do it than to have your students practice this through blogging! I can't believe that none of the educational bloggers out there have picked up on this.

I can imagine SAT practice sessions based entirely on blogs. They sessions would consist of an hour-long class with a portion given to instruction, a portion given to writing a timed essay, and a portion on evaluating other students' responses. Or wait a minute, maybe this should be a standard lesson that all classroom teachers use on a regular basis.

Spreadsheets Day Two

Just finished the first full period of having my students find surface area of six figures by way of spreadsheets. I learned quite a bit in just one period.

First, as with most of the technology that I bring into the classroom, all the skills my students are learning today can be learned through less invasive means. As I said yesterday, anybody can the find surface area of a figure with a pencil, paper, and calculator. The great thing about the spreadsheet though is that it also acts as an organizer. Students are able to see how the figure (in our case, a prism or cube) is divided into six sides, each having an area. Also, by putting the areas into the cells, their work is not a jumbled mess on a piece of paper. Spreadsheets are also a tool that students need to learn to use to function in the some of the professions they may work in some day. When finding surface area, they master a simple function, the =sum(A4..G4) function. Obviously, you must master the basic before moving on to the more complex functions.

Second, I've learned that the spreadsheet must be one of several tools used to teach surface area. Students MUST have experience with actual three-dimensional objects (have them cut out a 2-D net and tape it together) if they are to learn this concept at all. When shapes are on paper, it is difficult for them to perceive that the shape has a length, width, and a height and even more difficult to figure out what they measure of each is. But when they are holding a 3-D shape, they can turn it in their hands and make the connection between what they are holding and what they see on the paper.

Spreadsheets--Surface Area

I've decided to conduct another technology experiment with my lab rats, I mean students. I just finished introducing surface area (actually review, they've had it since the fifth grade) to my first period class. Instead of teaching it the old paper-pencil way, I'm going the spreadsheet route. I'm feeling that by giving them a worksheet with several problems and having them use the spreadsheet to find the surface area, they will learn the procedure as well or better than they would with a calculator and pencil-paper.

Why? For one, the spreadsheet gives immediate feedback. If they don't write the function for finding the surface area correctly, the number they are expecting to get will not appear in the cell where the sum goes. Another reason is that students can't be on auto pilot when they use the spreadsheet. With each new problem, they write the function for finding the sum of of the areas they have entered, once again going over the procedure again in their head. However, hand them a worksheet and calculator and their actions seem to be automated--no thought required, just the tapping of keys and the moving of a pencil. Finally, it is was immediately apparent that many of my students thought this was somewhat exciting--giving the spreadsheet the command and having it give the result, knowing they had done it correctly. Far more motivating than the same old pencil-paper and calculator math of old.

A Victory for the Good Guys

A few days ago, Will stated "The battle for the 'Net is about to be engaged..."

Well, victory number one for the good guys has occurred. I just learned this past week that I'll be teaching a graduate course on blogs to the teachers in my district this coming June. After viewing my session (Web Logs in the Mathematics Classroom) at Ohio SchoolNet in February, the district's coordinator of instructional technology (CofIT) was impressed enough to put me on the schedule. My session also got me an article on the district's web site.

Now this entry is not about tooting my own horn, but to explain how interest in web logs and technology beyond Powerpoint is growing in my district. I must say that the CofIT really seems to have a proper vision for integrating technology into the classroom. Now if our school levy would just pass this May, I might be able to keep my job and enjoy contributing to this vision next year.

Virtual Manipulatives

This past Tuesday our school had its first annual (hopefully) family math night. 15 families (a good turnout for our school) rotated through six stations, each lasting 15 minutes, learning about state indicators through interactive activities.

From the time the idea for a family math night was pitched, I knew that I wanted my station to involve the use of technology. But it wasn't until about a week from the big night that I decided on using virtual manipulatives. What a wonderful choice!

Virtual manipulatives weren't something I had used in my classroom before. I'm too busy using blogs, flickr, and discussion forums to find time for them. Nevertheless, I decided that I would teach transformations using the manipulatives from the National Library of Virtual Manipulatives. This site is loaded with manipulatives spanning all grade levels and areas of math like geometry, algebra, number operations, data analysis, and measurement. Each manipulative comes with instructions, a lesson guide for parents and teachers, and challenges.

At my station, I instructed my students on the three most important transformations for this age group--translations, rotations, and reflections. With the virtual manipulatives, the kids were able to transform the shapes and see the results. This is powerful stuff, considering that textbooks only offer students a before and after image, there is no movement.

In my search for the perfect activity, I came across other sites with virtual manipulatives:

• NCTM Illuminations
• Manipula Math with Java

Although I am now sold on virtual manipulatives, I do have some recommendations for their use. Using these in class requires a great deal of advance preparation. You must know EXACTLY what each one does and have a list of questions ready to ask students as you teach. I had the benefit of using a projection system so that students could see what it was I was asking them to do. I can't imagine trying to teach a lesson using virtual manipulatives without one.

More Reflection

I've overwhelmed myself all year long trying to be superteacher. So now I've decided to just focus on two main goals for the rest of the year:

1. Blogfolios - Continue to have students add entries to their blogs so that they can improve their writing.
2. Assessment - Use assessment for learning to increase student learning. I've been trying to incorporate new assessment strategies all year long, but other distractions (like trying to make every lesson an innovative masterpiece) have kept me from implementing them fully. So my goal is to give more short-term assessments that consist of one or two word-problems and then base my teaching off of them.
   

That's it. No more worrying about whether each lesson is problem/project-based/hands-on/visual, kinesthetic/blah...blah...blah...

Reflection - Learning Math Through Writing

I am really struggling with problem of how to get my kids to best learn the material I am teaching them. The day following a homework assignment is the toughest. How do I assess if they understood the homework? How do I tell if it is time to move on? These are the questions I have been faced with since the start of my career and yet I think the answer to both may have been in front of me the whole time--have them write.

Last night's homework required students to make conversions in the metric (3,000 mm = _____ m) and customary systems (108 in = _____ yd) using proportions, something entirely new to them. This is a multi-step process: set up a ratio for the unknown, set up a ratio for the base conversion, make them into a proportion, cross mulitply. It hit me that if the students can describe the process that I just described, and support it with reasoning, then they know how to do the homework. So I think I'm going to scrap the "share your answers and with a partner and choose a problem that you both struggled and we'll go over it on the board" approach. Instead, I'll have them write the process in words and go from there.

Blogfolios - What I'm Learning

I'm finding out what a great form of assessment these blogfolios are. Unfortunately, I'm finding out the hard way--by seeing how poorly written my students' extended responses were today. This is the third extended response entry they have written and for quite a few of them, their worst. But even this dark cloud has a silver lining: due to the lack of improvement on this entry, I now know many things about them, and this process, that I did not know before:

• Wanna know if your students have a good command of the vocabulary associated with a particular concept? Have them write about it. This past entry--the old so-in-so is so tall and casts a shadow a certain length while a lamp post is a certain height and casts a shadow a certain length problem--required students to write about corresponding sides on similar triangles. I think I saw one paper the whole day that used the word corresponding.
  
• You can pass out worksheets all day long, but they are best used for practice, not assessment. I've learned more from assigning a single word problem about what my students know of similar triangles and using proportions to solve them than I would have if I had assigned a page full of drill and practice problems. The main thing that I've seen is once you change the context of the problem, all the skills you thought they had suddenly disappear. So how do you change this? Like I said, you have to drill and practice so that the kids learn the skill. But you also have to provide them with many problems that diverge from the basic practice problem and require them to use those skills in a real-world context.
  
• Assign a worksheet, the kids practice the skills. Assign a word-problem, and they have to use problem-solving strategies to solve it. The particular problem that I have been speaking of throughout this post required students to draw a picture. How many drew it? Very few. So to get students to practice these strategies, and to recognize appropriate times to apply them, assign more word problems.
• Students are having a difficult time explaining the problem-solving process in words. Their explanations leave out a lot of steps, and when they include all the steps, they are seldom explained sequentially. As I helped a girl get her steps in order, I had her begin by numbering the steps 1 - 4 and then writing a brief phrase explaining what she did for each number. This way she could see a numbered order of steps. After she completed this, I then had her type the steps as sentences. It helped her a lot. Guess how I will have my students write their next entries.
  

So I have some ideas of how to improve this whole blogfolio process. Next time, I'll have my students revise today's entries, publish the revisions, and then have them compare them to the nonedited entries below them. Hopefully, they'll see some major improvement.

Blogvangelism at OSN Conference

Blogvangelism at OSN Conference
Originally uploaded by Misterteacher.

A little edification for the folks in Ohio. I'll have the whole presentation ("Web Logs in the Mathematics Classroom") ready for download on my web site by this Monday.

Great Article on RSS

I added a link to David Warlick's blog, Exactly 2 Cents Worth, in my previous entry. After I posted, I decided to check out some of his previous entries. One in particular, RSS is the New WWW, contains a fantastic description of RSS--how it works and some of the ideas that he has for it's future. By the way, ever check out PiNet?

Live from Ohio SchoolNet

T minus 20 minutes and counting until the start of my presentation "Web Logs in the Mathematics Classroom." I'm not expecting a huge turnout--2:00 is the last session of the last day. I figured that I'd take some time to jot down some thoughts and observations from this conference.

After scanning the session titles and descriptions for the Ohio SchoolNet Conference, I 've come to this conclusion: social software and the Read/Write Web have yet to catch on here in Ohio. Only two sessions (that I noticed) addressed these concepts: my session and another one by David Warlick on wikis and discussion forums. By the way, Warlick's session took place at the same time mine did (rats!), so no report on what he talked about.

In the exhibit hall, the themes were high stakes test simulations, data analysis, & content management systems. USE MY SOFTWARE AND YOUR KIDS WILL PASS THE STATE ACHIEVEMENT TEST! It's sad that so much time and energy is being wasted on getting kids to pass these tests. Imagine what technology we could have for the classroom if the minds that developed these products were not consumed with aligning software to state curriculum, but with creating engaging technology that didn't turn the computer into a drill and kill death machine.

FutureofMath -- iPod Version

FutureofMath -- iPod Version
Originally uploaded by Misterteacher.

iPod addicts: If you think, like I do, that Apple's mp3 player and all things associated with it are the essence of coolness, then this one's for you.

I created this one with Macrodmedia Fireworks (no iPodmyphoto.com here, though I'm sure their version would've been better).

Future of Math on the Road

I just found out that I'm going to be teaching a graduate course at SOITA this summer titled Digital Portfolios. In it, I'm going to talk about using blogs as digital portfolios. I'm going to be doing a quite a bit of blogvangelism in the coming months. Here are the stops:

• Ohio SchoolNet State Technology Conference (Wednesday, February 16)--1 hour lecture titled Web Logs in the Mathematics Classroom.
• Workshop at SOITA (Monday, March 14, 4 - 6:30)--Hands-on wkshp on using blogs, Furl, flickr, and wikis in the classroom. Title is Great Web Tools for Your Classroom.
• Workshop at SOITA (Tuesday, April 12, 4 - 6:30)--Hands-on wkshp on titled Using Web logs in the Classroom.

If you happen to read this and you're from Ohio, be sure to stop in.

Teaching Translations

Wow. Everyday in my class is a real eye-opener. The latest unit I'm teaching is one on transformations--slides, flips, and turns. To do these well, students need knowledge of graphing x- and y-coordinates. This is a skill that is taught from the fifth grade and I still have a good number of students who can't do it. And most of those that can simply go blank when the coordinates are for points on a shape (like quadrilateral).

So for next year, I have some recommendations for my teaching of this concept:

• Really dig in deep to make sure students have a strong background in graphing coordinates, beginning with the x- and y-axes. Last year (when I taught fifth grade), I copied two number lines onto two different transparencies. In the middle of each number line, I placed a zero. On the left side of the zero went the negatives and on the right, the positives. I introduced each one by itself. One I kept horizontal (x-axis), the other I turned so that it was in vertical direction (y-axis). After a brief explanation of each one, I combined them so that my students could see why the numbers going right (x-axis) and up (y-axis) are positive and negative when going left (x-axis) and down (y-axis).
  
• After teaching the axes, really drill the actual graphing of coordinates. My students are having a difficult time reading the grid (for example, counting over 3 and up 1 for (3,1)). I guess the best way to do this is by relating it something they know, like a street map or Battleship (but most tell me they played that in 6th grade!) But the biggest problems lie with graphing a shape!
  
• Connect the translating of a point to adding and subtracting integers; perhaps even teach the two together. My students had a TERRIBLE time with integers. So maybe when they translate point A (3, 1) four units to the left, they can see that they are going in negative direction. Therefore, to get the new coordinates, they need to subtract 4 from 3 (3-4 = -1).
  

This post was mostly for me. Hopefully, I remember to look back at it next year.