21st Century Math Teaching

Kinesthetic Geometry Vocabulary

2010-11-03T13:43:00.000-07:00

As an ongoing initiative to further integrate technology, mathematical vocabulary, and fun into the math classroom, my Basic Geometry students created a series of multimedia presentations utilizing the various terms being used in a learning unit on special pairs of angles. For this activity students were required to plan, communicate, rehearse, and execute organized arrangements of students on the gymnasium floor into representations of geometric objects. Hopefully through the kinesthetic nature of this activity, students can achieve better recall of the geometric terms used and even greater understanding of their properties. Here is a sample of their fantastic work:

Special thanks to the Physical Education teachers that helped me organize this activity, and Mr. Brain Gannon (twitter @bpgannon) for sharing this great idea via twitter.

PSSA Testing Week

2010-04-15T16:21:00.001-07:00

Well our high school is at day two of our state mandated testing - the PSSA's. So far the PSSA testing has gone quite well.

The students have been very cooperative with the promise of early dismissal and entry into a contest based upon their levels of success. I'm not sure the prize drawing has the intended effect due to the fact that this is not an immediate reward since kids have to wait for thier score to be determined, but perhaps it can serve as a motivator for next year's juniors when they see the prize drawing - time will tell. I'm not a big fan of prizes as motivators, but it seems to have positive effects in some arenas.

-- Posted From My iPhone.

Location:Great Bend,United States

BlogPress

2010-04-11T09:57:00.001-07:00

Checking out the features of BlogPress - an app from Apple's App Store that allows the posting of blog entries from a mobile device. It has features that include:

-moble posting to multiple blog platforms
-auto video embed through YouTube from video library
-shoot instant video and post
-insert videos from camera, device photo library
-linking to picasa and flickr accounts
-Twitter and Facebook integration

Here is a video of my daredevil daughter:

My son getting his teeth cleaned by Aunt Stacey.

-- Posted From My iPhone.

Location:Lincoln St,Dickson City,United States

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

2009-09-28T19:10:00.000-07:00

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)

2009-09-05T18:31:00.001-07:00

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:

Assign homework.
Next day give the answers and allow time for questions.
The following Monday give an "open homework notebook" quiz based upon the prior weeks assignments. "How did you get..." journal style questions work best.
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.
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

2009-09-05T17:54:00.000-07:00

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

2009-08-28T09:52:00.000-07:00

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

2009-07-29T10:45:00.001-07:00

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

2009-06-03T21:18:00.000-07:00

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

2009-05-11T07:45:00.000-07:00

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

2009-04-17T05:25:00.000-07:00

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:

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)?
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.
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".
Raise capital - Pretty obvious application here...Utilize the synergy you have built in the demo stage to motivate interest. Of course free is best...
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.
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.

2009-03-21T11:54:00.000-07:00

What Is Substantive Conversation - ScribeFire Test

2008-12-29T09:12:00.001-08:00

Does classroom talk lead to sustained conversational dialogue between students, and between teachers and students to create or negotiate understanding of subject matter?

Explanation

In classes with substantive conversation there is considerable teacher-students and student-student interaction about the ideas of a substantive topic; the interaction is reciprocal, and it promotes coherent shared understanding. This element describes the extent of talking to learn and to understand in the classroom.

Features of substantive conversation include:

INTELLECTUAL SUBSTANCE: The talk is about subject matter in the discipline and encourages critical reasoning such as making distinctions, applying ideas, forming generalizations, raising questions. It moves beyond just the recounting of experiences, facts, definitions, or procedures (e.g., technical language, analytical distinctions and categories being made, levels of differentiations between types and arguments stated, grounds for disagreement stated).
DIALOGUE: The conversation involves sharing of ideas and is not completely scripted or controlled by one party (as in teacher-led recitation). Sharing is best illustrated when participants provide extended statements, direct their comments, questions and statements directly to others, redirect and select next speakers.
LOGICAL EXTENSION AND SYNTHESIS: The dialogue builds coherently on participants' ideas to promote improved collective understanding of a theme or topic. In short, substantive conversation resembles the kind of sustained exploration of content characteristic of a good seminar where student contributions lead to shared understandings (e.g., teachers and students may make principled topic shifts, may use linking words, make explicit references to previous comments, and may summarize).
A SUSTAINED EXCHANGE: This extends beyond a routine IRE (initiate/response/evaluate). This can occur between teacher and students or student and student and involves several consecutive interchanges. Dialogue consists of a sustained and topically related series of linked exchanges between speakers.

In classes where there is little or no substantive conversation, teacher-student interaction typically consists of a lecture with recitation where the teacher deviates very little from delivering information and routine questions; students typically give very short answers. Discussion here may follow the typical IRE pattern: with low-level recall/fact-based questions, short utterance or single-word responses, and further simple questions and/or teacher evaluation statements (e.g., 'yes, good'). This is an extremely routine, teacher centered pattern, that amounts to a 'fill in the blank', or 'guess what's in the teacher's head' format.

Continuum of Practice

Virtually no features of substantive conversation occur during the lesson. Lesson consists principally of either a sustained teacher monologue/lecture and/or a repeated IRE sequence with little variation, or conversation which is not substantive.

Features B (dialogue) and/or C (logical extension and synthesis) occur and involve two or more sustained exchanges.
All features of substantive conversation occur in an ongoing and sustained fashion, extending across almost all of the lesson, with both teachers and students scaffolding the conversation.

Example

A year 8 integrated Maths and Science class was divided into groups. Each group spent a period building animals to certain design specifications. The animals were given names by the students. Discussion was then held about classification systems of the animals. The teacher then distributed a classification system that he had created.

In groups of four the students then moved from table to table where the 15 animals were set up and had discussions about the animals. On a sheet they classified the animals according to the system the teacher had given them. When all the animals had been classified by all groups, the teacher held a whole-group discussion of the classification by each group of each animal. Interesting discussions ensued in respect of different classifications by some of the groups of the same animal.

This discussion covered issues of measurement, including very sophisticated discussion about exactitude, angle of viewing the animals, injured animals, error in measurement generally and its sources and so on. In most instances within these conversations students were initiating the dialogue and other students were providing the frameworks upon which the groups were constructing their collective understandings of the topic.

Content from: Queensland Government Educational Site

Alternative To a Poster Project

2008-12-16T12:56:00.000-08:00

There are few educational tasks more tedious than keeping track of several classes worth of poster projects. They are bulky, unportable, many parents hate them, and invariably they fall apart once the Elmer's glue loses its grip.

Now you don't need to "loose your grip"; www.glogster.com/edu is an excellent resource for students to complete an online poster project rich with multimedia and creative opportunities. These projects now become portable, open up new avenues for creativity, appeal to our "21st Century Learners", and can include an audience far beyond the brick and mortar of our classrooms - "the web".

Unless you like getting glitter all over your desk...

Check out this example of a poster or "glog" I created based upon Dr. Martin Luther King, Jr. It used resources readily available on the web, and took about 1/2 an hour to create.

Before I request unblocking it for the students, I am looking for some input on how you might use this resource in your classroom...Comments welcome...

Animoto In the Classroom

2008-12-09T11:55:00.001-08:00

Animoto is a cool website that allows you to upload a bunch of pictures or PowerPoint Slides. It mixes them, creates animations, and then balances the animations in relationship to the beat of music. Here is an example:

I am trying to figure out ideas where this can be used in your classes, but I am having trouble discerning a legitimate reason to do so. A reason besides, 'cause its cool...Any comments are welcome...

PSSA Open-Ended Question 1

2008-11-18T20:30:00.000-08:00

Julia created the coordinate grid below to identify the locations of her house and her friend Carol’s house. Julia’s house is located at (155, 102). Carol’s house is located at (493, 388).

A. What are the coordinates of the midpoint between the girls’ houses? Show all your work and explain how you know your answer is correct.

B. There is a straight path between the girls’ houses. If Julia and Carol meet at the midpoint between their houses, what distance would each girl have to walk? Round the answer to the nearest yard. Show all your work and explain how you know your answer is correct.

Please recall that you will receive your grade for this assignment by utilizing the PSSA Open-Ended Math Scoring Rubric...

Blogger-rithems

2008-09-24T19:20:00.000-07:00

Of course we all know how literacy across the curriculum is a drum that has been beaten for many years now. Not to say that it isn't important, but how can I bring literacy into my math class that is authentic and engaging to my students?

I can have the students write out procedures in journals, hand out little scraps of paper for students to summarize today's lesson as an exit pass, practice open-ended questions graded by the light of some type of rubric...Yawn...When was the last time you heard a student yell, "Sweet, another math problem where I get to explain the what, how, and why I did each step of some archaic conundrum!" What are these students learning? That they can score a 1 out of 5 when math and literacy cross paths...Do they really digest the red remarks we leave them to help them improve?

We can model the correct outcomes and demonstrate "how its done", but are these students learning how they "solve a problem" or how you "do a problem". Isn’t' literacy about their ability to express their own thoughts and emotions in the written word. Yes, I said emotions. Why can't we bring some emotion into the math class? The question is how?

The reason for all of this ranting is the result of a failure on my part to try to engage students in a way I have never tried before. I asked students to post comments to a written prompt using a blog. It seemed harmless enough, but I don't think I asked a very good question on my first attempt. I asked, "Describe something you really do well. It could be anything from starting up World of Warcraft on your PC to baking your grandma's famous meatloaf; as long as it is a multi-step activity. Not only should you describe each step in detail, but how and why you perform each phase of your activity."

Some of the students did an excellent job. Being located in a very rural community several students posted excellent comments on such items as how saddle their beloved horse; other students gave detailed explanations on how to cook the "World's Greatest Mac and Cheese", how they first learned to swim, etc. I could tell by their enthusiastic comments that some real emotion was exercised.

...but many students missed the point. About half of the comments posted appeared to be stolen out of a cookbook. There was no emotion. The response to "why I did each step" was also missing. How can I classify these "Vulcan-ized" comments to an authentic experience when there were little to no feelings drawn upon? I can see now that an initial failure I presented to the students with was the lack of intrigue or passion I conveyed in my initial posted question. It was dry and boring.

Now I am at a crossroads...Do I bail out now before I invest any more class time into this potentially year-long project, or tough it out? I guess I wouldn't be rambling on and on if I had planned on giving up...but again, what do I do now?

My current thoughts are leading towards replying to each of the student’s comments and asking them to "re-tool" their thoughts and describe some activity they love to do. Hopefully then I can draw some connections between their comments and math literacy. I hesitate to do this until I get responses the students seem to "care" about. What do you think??? What would you do next???

Community Service with Web "to point, oh"

2008-04-23T19:42:00.000-07:00

After punching the hell out of my keyboard, I hate Explorer 7.0, a computer miracle occurred. I must have smashed the right keys and a site called Math Is Fun jumped out at me. Come on though; Math is Fun, really? Forgiving such a blatant disregard for a young child's idea of fun, I checked the site out anyway, and behold; the Math Is Fun Help Me Forum.

Before I get any further, I want to bring up the idea of community service for a moment. Beyond being an aweome thing to do, many schools are incorporating community service as a graduation requirement. It is also a necessity to students petitioning and maintaining membership in the National Honor Society. So why not incorporate online collaboration into this.

Any form of tutoring qualifies as community service, but it is usually limited by the buildings the tutors have physical access to. Lets use the strength of a sweet blog to break down these physical barriers, and teach 21st Century skills at the same time. Again, for an example of what this can look like, go to the Math Is Fun Help Me Forum.

Imagine students from your school helping the "mathematically challenged" across the continent creating contacts that could very well last beyond high school. Nice. Think of the number of Facebook/My Space pages kids visit on a regular basis already, and “why” they visit them. The "why" scares me a little bit. Through scholarly pursuits, such as online tutoring, students may change their creepy “why” to more academic/collegial reasons.

I am proposing our district form an online tutoring club with myself in charge of monitorig the web discussions for content accuracy, phishing, bullying, and general nonsense. The biggest problem I foresee at this point is getting the word out to students from other schools once this service becomes available. Any ideas??? Comments welcome…

In the beginning...

2008-04-05T07:00:00.000-07:00

Many of the preiminary ideas I plan to post are collected from the myriad of professional development opportunities that have been made available due to the rising demand of Web 2.0 usage in today's school system. My first challenge to all math professionals reading this blog is to begin to investigate and search for as many professional opportunities they can find.

The conundrum here is: much of what I've learned through out the past year was not from the presenters or assignments I had to endure...and trust me using the word endure is being polite. Just view this video to see what I mean...

It was through meeting with other teachers, sharing email addresses, Skype contact info, bitching (a very powerfully underrated collaborative tool...lol), and following up to maintain contact. Throw them questions, share ideas; presentations are just the tip of the iceberg when it comes to professional development. I just wish presenters would realize this.

Stay tuned for some tips you can use in your math classroom.