Something, but I'm not sure what...

Today my 4th period Fundamental Geometry kids were playing an online game called "Banana Hunt". It entails estimating the measure of a given angle which can be anywhere from 1 to 359 degrees. The assignment was to go to the site, play the game until a total of 35 bananas was gained within one 10 turn session - not easy. After this they take a screen shot of their score and "turn in" the file as part of an Edmodo assignment.

Now to say that to achieve any sort of positive educational experiences with this group of kids is difficult would definitely be an understatement...but anyway. Two of my students in the front of the room (both of which are not taking this course at grade level and they're not gifted) were playing the Banana Hunt game and doing quite poorly at first until one of them finally got 37 bananas. This success infuriated the other student.

"What? No way! I hate this game!" he said.

I asked, "You wanna cheat?"

"Really? Can I? How?"

"Here use this?", as I handed him a protractor I cleverly had on hand.

"How do I use this?" he uttered.

"I'm not sure; you'll have to figure it out." I replied as I left his side to help another student whose browser had frozen. A few minutes later I hear "Ha, 47 bananas." from the student I just have the protractor to.

"No way!" was the exclamation from the "protractor-less" student. "Give me one of those!"

So I gave him one, and the competition continued. Other students took interest and naturally asked the same. It wasn't too soon before the general buzz in the room was: "This is so much easier!", "Why didn't you just give me one of those to begin with?", "What's the highest number of bananas now?" They were motivated, challenged, and accomplishing the learning goal: measuring an angle up to 360 degrees with a protractor. What had just happened? I must admit, I ended the period very proud of the students and somewhat proud of myself. If I could just figure out the recipe of the instructional "tricks" that were somehow implemented and repeat it again...What a great year this would be...

I know it could have just been a good day for the kids. Sometimes luck is on a teacher's side, but what if...

Here is the link to this activity should you wish to check it out: http://bigmacmath.wikispaces.com/measuring_angles

Homework: The Trials of Best Practice (Part I)

So what is this set of homework procedures I mentioned in my last post? Well here it is, and the story behind its development.

As I believe homework is meant to be used, I initially wanted to assess the students ("formatively" speaking) on their ability to practice whatever mathematical techniques I desire them to posses at an independent level. With knowledge of their capabilities, I could then scaffold the intensity of instruction from this baseline. So I thought that giving students a short assessment at the end of the week containing all of the main goals of each of that week's homework assignments was the way to go. There were several problems I and other colleagues saw with this set up that lead to an improved final plan.

Initial concerns regarding the fact that there were several issues developed by assessing students on a Friday. In our district, the Friday schedule for students is shortened by one hour to allow for common planning time for staff at the end of the day. Although offering an end of week summary has its merits, adding a weekly assessment at this time made me feel that new or continuous instruction or student participation in ongoing projects would take a back seat to this initiative. Also, I've always felt that assessing within the week something was taught drew too much on information stored in the student's short-term memory; a location where content is easily forgotten.

Bump the assessment to Monday was my solution to both of these issues. Since a weekend's time will have passed, now I would be assessing students based upon the content that was stored within their long term memory; a place where thoughts tend to "stick". Of course, what about content that never made it to long-term storage? Since I wanted a procedure that would give the students an academic incentive to do homework beyond getting a simple check for completion; I thought, why not let them use their homework solutions to take the assessment? This would then offer them a chance to use homework as an assistive tool. Additionally, this would allow the students to utilize their homework to associate forgotten information with whatever bits and pieces of last weeks content made its way to long-term memory storage. Since brain research has shown that associating new or forgotten information with long-term memory improves retention, I thought I had a winner. Still one issue remained.

A colleague pointed out, "What if a student learned the content so well, they didn't need to utilize their homework as a crutch to demonstrate mastery on these Monday assessments? Would they just simply stop doing their homework?" I thought, "So what; as long as they learned the content, what does it matter if they do their homework?" After some debate, I was eventually convinced that accountability for timely completion of individual out-of-school assignments was an important goal of assigning homework. So now while students complete the Monday homework assessment, I have the time to check their assignments for completion and enforce accountability.

So in short, here are the procedures:

1. Assign homework.
2. Next day give the answers and allow time for questions.
3. The following Monday give an "open homework notebook" quiz based upon the prior weeks assignments. "How did you get..." journal style questions work best.
4. While the students take the quiz, I will visually check that the necessary assignments are complete which will contribute to two points on the assessment.
5. Give back the assessments the next day and modify instruction as needed.

As the first summative assessment for my students slowly approaches, I plan on reflecting on the continuing successes and/or failures of these procedures in a later post. Right now, the Monday night grading is a bit much, but I think it seems to be worth it. I am already farther ahead in content than I was in previous years which will hopefully allow more time for experimenting with new methods of teaching and learning that I've been wanting to try.

Homework: Guilty of Worst Practices

In years past I had utilized what I thought was an effective procedure of assigning and assessing my students' homework. I assigned problems on a regular basis - usually after they observed something I wanted them to practice - checked it the next day for completion (not accuracy), and went over every problem on the board. I would call this the traditional "fast glance" process of assigning and assessing homework as it was the consistent and speedy method used when I was in high school some 20 years ago.

This method's biggest benefit was the amount of time it saved me both in and out of the classroom. I had thought about collecting and grading homework each time I assigned it, but the amount of paperwork and grading time was soon overwhelming. "Or" I could perform a deeper look as I walked around with my clipboard of +1's, +1/2's, and 0's, but this would take up too much instructional time. With time on my side because of the "fast glance" method, I continued with the hopes that it was adequate enough.

As I reflected over the years, I made sure that what I assigned was what I assessed - that was never really a problem. I gave all the classic speeches regarding my expectations for student homework with the hopes that it would be enough to motivate students to give out-of-class practice their best shot. A burning question still remained, "Why were students who completed their homework on a regular basis failing tests?"

Here is what I've determined so far:

My students would quickly learn how much "stuff" needed to be attempted to pass my "fast glance" technique. If I called them on an inaccuracy; of course "I didn't understand it" was the excuse. Without fail I always replied, "Don't worry, I'll go over it with the class soon." So here I was attempting to further explain a mathematical topic to a student that really didn't "get the problem wrong" because they didn't understand the steps in the solution. They didn't get the correct solution, because they never really attempted the problem thoughtfully. Something must change. I am convinced that realizing the students' absence of thoughtful practice will lead to an answer to my question: Improved procedural measures in handling assigning and assessing homework will lead to increased summative assessment grades.

Additionally I realized that the "quick glance" method inherently modeled very low expectations. Why would a child without the intrinsic motivation to complete homework do so just so I can look at it quickly and do the assignment for them anyway by going over it? I laugh now at all of the upset speeches and tirades I've made preaching the significance of homework when what I was really doing was constantly demonstrating its insignificance through my verification process.

I must change this practice, but what set of procedures has all of the pieces I need? I want a method with time benefits and accountability measures that are motivational; not to mention formative and flexible. After some deliberation and thoughtful input from the members of my professional learning team, I think I have a potential solution soon to follow in my next post called Homework: Trials of Best Practice (Part I).

The Secret Number Game

Logical Reasoning (The Secret Number Game)

Many in-services ago, a colleague shared with me a neat little game called "The Secret Number Game". It was a great way to engage students and incorporate introductory experience with the dreaded mathematical proof. For this activity I focused on the flowchart style of proof.

Here is how it works:



After it appears that the students get a grasp of the rules, I pair them up to play the game against each other. The intent of this activity is to get each of them to create a flowchart proof that will allow another student to guess their number based solely on looking at it without the "answer bubble" filled in.

It took some students a few tries to get the type of flowchart that I wanted: one where a number could be found by looking at the organizational structure and connections. Proofs developed by a "lucky guess" or complete process of elimination really don't serve the purpose of this activity, so tables and flowcharts created this way were asked to be "tweaked" or done over.

For the big finish I asked the students to place their name and flowchart proof on a 1/2 sheet of paper with the "answer bubble" empty and crumble it up. Armed with these, they threw them at each other, uncrumbled, solved, and checked their answer with the original owner of the flowchart.

In retrospect, the students seemed to enjoy this playfulness and movement of the activity, and I would encourage you to give it a shot when and if you teach the basics of Flowchart Proofs.

Presenting: Archimedes

Web 1.0, Web 2.0, Web 3.0 Hike, Hike, Hike!!!

I think that in order to understand what Web 2.0 really represents, it is helpful to know what its predecessor offered and its future will bring. Web 1.0 was called the "read" web. Read in a sense that the majority of the content was only available for the casual user to view. The ability to contribute content to the internet was only available to those with the skills to create webpages and the web space to publish it.

Allowing the average user to contribute their personal or professional experiences or opinions to the web marks the onset of the "read/write" web or Web 2.0. Now through the use of blogs, wikis, interactive multimedia, the average web browser could contribute information to the internet via numerous forms of multimedia. Additionally, the ability to contribute to the world-wide web has spawned an insurgence of social media sites (Facebook, MySpace, Twitter) where electronic synchronous or asynchronous communication can occur.

The next step in the evolution of the internet will involve ideas surrounding what will be called Web 3.0. Also known as the "Intelligent" or "Semantic Web", meaning that searching the web becomes more personalized and suitable to your needs. For example, if you wanted to search for a pizzeria within 5 miles of your location using current web technology, you would need to search using the keywords "pizzeria" and your location - Scranton for instance. From here you will more than likely get results that are from well over 100 plus locations. With the semantic web, when you search you would only need to search for the keyword "pizzeria" and you would receive results based upon your previous search history, likes and dislikes, information regarding your favorite foods, personal budget, and even omit locations that won't take your American Express card. Check out this video the get the lighter side of what you could experience in the future...

Checking Out Web-Alert

Web-Alert is a website that allows you to receive updates via SMS text messaging to your cell phone. Simply go to www.web-alert.com, enter the url of the site you wish to follow for new content, and/or type in an optional keyword. I am not sure if this is working yet, but I will post a comment to this message if it does... Key word: web-alert

For Education As For Business

Through following various friends on Twitter steeped in the contributions online social media is playing in deploying product interest; I am noticing bits and pieces of best practices educators may implement when utilizing social technology within their instruction.

A recent post from The Conversation Agent's blog called The Hardest Thing to Manage: Our Own Ego discusses how managing our ego plays a critical role within the pursuits of presenting ourselves online. The section I found of most interest regarded a gist from Guy Kawasaki's book: The Art of the Start. The Conversation Agent's summary of Kawasaki's 7 milestones that apply to business and any the educational connections I perceived are as follows:

1. Prove your concept - Define your goals for allowing students to participate in a web-based social activity. Is simple formative assessment the priority? Do your interests surround building a collaborative community? Is student participation meant to be isolated (classroom-based) or open (cross-classed)?
2. Complete design specs - Which social media tool provides you with features that meet your goals? If your goals are collaborative in nature, perhaps using Google Docs is best. If academic honesty is of high concern, the traceable features of a Wikispace may be a reliable option. If a more global experience is necessary, ePals or TakingItGlobal might suit your needs. Collaboration with peers highly web 2.0 literate or a district instructional technology coach is highly recommended at this R&D stage.
3. Finish a prototype and show it around - I tell my teachers, "Try to break it." What ever tool you decide to use; you need to master its features before requiring the students to do so. Since the participatory nature of these forms of online media is difficult to test alone; try to bring in the assistance of your colleagues. This collegial assistance can certainly offer both extrinsic and intrinsic benefits beyond learning a new technological tool. Depending on your school social climate, attempt to utilize administrators and the school board membership in testing your educational "prototype".
4. Raise capital - Pretty obvious application here...Utilize the synergy you have built in the demo stage to motivate interest. Of course free is best...
5. Ship/show a testable version to customers - Start with a class of students you can provide your with honest feedback. The respect you have gained with your students and their levels of maturity can go a long way. Time to cash in... It's also time to consider if you as the classroom leader are providing the students with intrinsically motivational reasons to participate in your choice of online social tasks.Ship/show the final version to customers - After you have defined your goals, found the right "tool for the job", mastered it use, evaluated and discovered how to generate student interest; it's ready to deploy on a larger scale.
6. Achieve break-even - On the first attempt and at an absolute minimum, expect the students to learn as much from their utilization of your chosen form of social media as they would have without it. Quickly raise the bar from here. Scaffolding your approach with students inexperienced with applying social media to an academic and problem-solving scenario should yield better results than throwing them into the deep end and hoping your instructional goals don't drown with them.

As business procedures change, so must the business of daily classroom activities. Maintaining collegial relationships via online social media (Twitter, Facebook, MySpace, etc.) with any professionals outside of the teaching and learning community has never been easier and as beneficial to lift the shroud of how education should align with authentic "real world" operations.