Capstone for Things 15-21

Capstone Reflection for Things #15-21

I see my use of the screen-casting and virtual classroom technology growing a lot over the next several months. I like the idea of having my classes available to those who could not attend and for those who need to review concepts. I see a lot of potential for a virtual classroom semester review before the semester final. We will do some review in the classroom, but there is always a sizable demand for reviewing the material before the test.  Recording this year’s session (usually on a Saturday) will allow those who could not attend a chance to hear the same material as those who could. It’s possible that the review would be then online for next school year’s final.

I also like the visual learning tools – presenting the same information in a radically different manner that is intriguing enough to awaken the students’ intellectual curiosity. Part of learning the material in math/geometry is getting a lot of exposure to the material and becoming comfortable enough with the material to expand concepts and figure out new problems based on those learned principles.

As for Marzano, there are a number of the initiatives that are in play when using these tools:

Reinforcing Effort and Providing Recognition: these tools provide interesting ways for students to put forth more effort to learn the material. Also, having students use some of the tools and present material is an effective motivator and provides recognition for their efforts.

For Summarizing and Note-Taking, these tools give students an additional opportunity to observe the concepts and work additional problems. Also, having students put together some of the visual learning tools is a way of taking notes, writing out concepts and tying them together.

Highlighted in this section is Using Non-Linguistic Representations. Creating a Bubbl or Gliffy diagram helps translate words and concepts into a graphical representation of the interrelationships existing in the material. Having students put the representations together should help them organize their thoughts and increase the depth of their understanding.

The Michigan content standards (and the upcoming core curriculum) include doing proofs in Geometry. A vital part of that process is for students to learn and use postulates and theorems (along with a few definitions). Using the visual learning tools and assigning partners of students to present diagrams and word clouds of specific theorems for presentation to the class meets a number of the NET-S standards:

Creativity and Innovation (creating original works, using models to explore complex concepts)

Communication and collaboration (creations would  be shared with the class – postings on GoogleApps. These projects would encourage critical thinking, or at least provide the basis for critical thought to begin.

These applications provide a lot of room for application, experimentation and learning – much of it coming from your own efforts. The amount of online research into your subject is mind-boggling (and in some ways, counterproductive) – but the opportunity is there to keep on learning and growing, either as a teacher or a student.

Thing #21 - Screen-casting

For my screencast, I used Camtasia and presented a triangle proof - one of the longer proofs that require students to add material and think about how to get from the simple areas to the more complex line of thought. We are just reaching the point where students have enough confidence to complete simple (5-line) proofs on their own. As we move forward, the proofs increase in complexity, drawing on the full semester of geometric activity, since we have learned postulates and theorems from Chapter One onward. To begin seeing the more complex connections, students have to work through a lot of proofs and learn a lot of postulates and theorems. They then have to draw on that knowledge and determine how to put the items together in a logical sequence. It takes time and practice.

I can see me doing several "Proof-Casts" per week and posting them on Blackboard. I posted the first one today - which was actually my second "take" on the screen-cast. For the first screen-cast, I presented the lesson live with a full (28 students) classroom. I generally have a lot of give-and-take with the students as we go through something complicated - trying to lead them into each conclusion to determine the direction for the next line in the proof. I showed the video to a fellow teacher and, while the message was good, the presentation was lacking a little bit. The first screen-cast had an incredible amount of background noise, such that it was difficult to focus on the message. I will also need to balance the on-screen marking with the animations of PowerPoint - you cannot do both at once effectively. More underlining while making points would be useful as well. Also, the camera positioning was poor - I need to find a better way to place/mount it for the best picture.

I see many screecasts in my future...

The URL is: Blackboard video post

Thing #20 - Visual Learning

I put a Bubbl diagram together on the topic of Triangle Proofs:

I also did a tagxedo of one of the Triangle Proof theorems:

These visual learning tools offer unique perspectives on educational themes - perspectives that are engaging enough to rouse curiosity from a student view - trying to "get" the message. As educators, we are competing for the students' attention, curiosity and time.  These tools are an additional avenue worth pursuing to facilitate learning new, and sometimes uninterestion topics.

The Bubbl diagram is a nice way to organize a concept overview and show students the links to related items and to tie those items together.

The tools are helpful because they are graphic, visual, intriguing and informative. The idea is to pique the students' interest and to increase their knowledge and understanding. These graphics provide a different pathway into the students' brains and hopefully open the right portals for education to occur. I can see me using these tools and projecting them onto the Brightlink screen during my classes. I can also see assigning students to put together their own Tagxedos and showing them to their classmates on the big screen. They could also be printed out and displayed in the classroom.



The screen shot of my Tagxedo reflection:

Thing #19 - Virtual Classroom

Currently, I extend the classroom using Blackboard.  Assignments are posted, extra help is posted, some answers are posted as well. I would like to extend further by putting course content online.  Some fo the content will be as screen casts using Camtasia and some will be the posting of presentations used in the course.  I would like to conduct review sessions live online (using something like AdobeConnect) - but my Geometry classes include 110 students, which would require a pretty hefty licensing fee. I am planning to do the reviews as screencasts as well - it would give the students the ability to listen several times over with a lot of visual material to help out.

As a student Navigating the Land of Online Learning, it seemed that being informed about the course, the computer, having an internet computer, how the course is valued by the school and knowing the rules of the course all contribute towards a successful conclusion  of the course. One item not mentioned is that the student must be motivated and interested - the student needs to put in the time and effort to complete the course. What is necessary:

Dealing with asynchronous classes.
Having internet access. Mac? PC? Both?
Finding the course that you need or really want to take.
Finding the parameters from the teacher
Keep parents in the loop
Check on the cost, if any

I would hope that online courses would help grow a students creativity and capacity for innovation, but realistically think that it would be hard to grow in this manner individually versus being in a group setting.

Certainly, Critical Thinking, Problem Solving, and Decision Making would be part of any class - we hope to be creating tomorrow's thinking adults. As for  Technology Operations and Concepts, certainly just completing and participating in an online course implies a level of competence in the technology area.

Thing #18 - Staying Informed

I selected the iGoogle RSS aggregator because our school is integrating Google Apps as a resource/tool for teachers and students, so it seemed logical to stay in that arena.  I signed up for a number of math-related sites and will be curious to see what turns up (not much so far, but it's early). These updates will help me stay current, review new ideas, highlight issues, identify resouces that all could be used to improve my pedegogy. As a teacher, you never stop learning.  The RSS capability of iGoogle will help facilitate that learning by providing new material to absorb.

Thing #17 - Research and Reference Tools

I went on both InfoTrack Junior and Student editionsl and entered math terms to see what would arise. The answer is not much - the databases seem to be geared for research in other areas. Both sites came up with similar references, probably indicating that I would need to better understand the database to craft my queries more appropriately. For my classroom, I did not see much in the way of useability. There were some interesting articles that had little to do with my request and I would like to go back and read them. The results seemed to be mixed - various articles from various sources around the web - largely credible sites with a mixture of education/peer-reviewed articles with articles from mainstream periodicals. I did not see any credibility problems in that search.

Screen shot of Junior Edition:

Screenshot of Student Edition:

Advanced Research.

I went to the Educators Reference Complete and did a search on teaching ADHD students and got more information than I could absorb in an evening. The articles appeared to be education-oriented, peer-reviewed or education industry publications with a high degree of credibility. A number of the articles contained strategies to be tried in the classroom.

Work Cited 1: Using the Educators Reference Complete, I did a search on Math Lesson Plans and got a few (not a lot) interesting hits. The citation for the article is:

For thWork Cited - 2, I selected an article on a topic that I have used from Mathematics Teacher, one of the journals from the National Council of Teachers of Mathematics discussing a new method of teaching proofs. The BibMe citation is:

Dirksen, Jennifer, Nathaniel Dirksen, and Ivan Cheng. "ProofBlocks: A Visual Approach to Proof ." Mathematics Teacher Apr. 2010: 571. Print.

Thing #16 - Professional Learning Networks

LearnPort has a good variety of courses and educational connections - plenty of online courses to take, opportunities to earn SB-CEUs, commity rooms, peer net capabilities, lesson plans and more. Looks like a great resource. Some of the 21 Things-type topics are listed in my screenshot.

Facebook is great for social networking. I suppose I could see a use or two in a math classroom, but I would be afraid that the postings would largely be teenage social angst and, other than getting to know the students better, I feel that Blackboard offers more in the educational arena.

Joined MACUL - we'll see if they accept me...

ISTE has a lot to offer in the technology area - for $95 -  implementing NETS, forums and groups to belong to, a collection of webinars, a collection of the standards - along with additional resources to assimilate technology into the educational arena. "Teacher Educators" looked like one group that I would be interested in. My contributions would be based on actual experience in the classroom and in dealing with technology integration into the math curriculum. I am willing to try new things and, as with most teachers, willing to discuss the experience and offer feedback. I am a technology mentor at my school and would like to keep up with the latest and greatest.

Thing #15 - Productivity Tools

I took the Capstone Word document that was pasted into the previous blog and converted it to a PDF:

I use pdfs all the time - most students can easily download or view the documents. Also, students cannot easily edit the documents, so they tend to keep their integrety over time. This does not influence the instruction in the classroom, but rather helps students outside the classroom. For my students, I often post additional work that they can do that relates to the current and/or previous lesson. This helps the students who need additional exposures to the information get the help that they require.

The Capstone paper was then converted to an mp3 (it did a reasonable job converting to voice). Other formats available include .pdf, .txt, odt, .pcx, .png, ps:

Public calendars keep everyone informed - parents like to know when tests are coming up, when projects are due, what section are we covering, etc. Students can check to make sure they are on schedule. Colleagues can check for scheduling meetings.  It's just one more tool in this age of tons of information.

Capstone for Things 8-14

Capstone Reflection for Things 8-14

A number of these technology applications will immediately fit into and be used in my classroom. One application that really stands out is the Prezi presentation package. The one-page graphic organization format is very powerful in conveying a cohesive packaged idea, where the various strands and tie-ins are readily apparent – giving the student an immediate visual overview of what’s included and how it ties together. The mapping process is extremely flexible, allowing you to visit and re-visit concepts. Just the process of mapping the items lets you organize your thoughts, forcing the presenter to put together a cohesive package rather than a stream of consciousness. On the flip[ side, the one page organization lets the presenter put together a stream of consciousness, random thoughts and even a little bit of chaos – ensuring that you can immediately include thoughts and ideas to be revisited, improved and logically mapped when you are ready to put the presentation together.

Even the presentation mode helps.  It is an eye-catching process as the presentation winds its way through the field of thoughts and concepts with the ability to highlight even the smallest point in a manner that will help the students visualize and internalize what you are presenting.

I can envision using this to teach a proof – organizing the thoughts that occur randomly into individual little units and then tying them together as a finished whole.

There are a few features lacking – like having items fill in spots as you talk about them (like the listing of items in a proof), but there is much that this program has to offer.

The next application that I see myself integrating into the classroom is Quizlet – the flashcard program. I use a Jeopardy template for reviews, but can see where the flashcards would be useful and different – and available at home for students to look at on their own. The cards are easy to set up, the quizzes are easy to use – I just need to put a couple of sets together to get the feel of the program.

The flashcards force you to be succinct and precise to capsulate the concept and present it for review. This not only helps the student remember it more easily, but also helps you consider how you present and discuss various concepts – and how much it takes to break things down into bite-size learning bits.

A third tool I envision using in the classroom is the National Library for Learning Manipulatives.  This site has quite a few math concepts incorporated into individual packages suitable for showing to an entire class or for signing up for the computer lab and having students explore the concepts and manipulatives on their own. A number of the manipulatives that I tried will require at least some teaching and/or discussion of what is being show to get the full effect of the exercise and to totally understand what is happening. This makes it possible to also tie the concept together with the course material to reinforce the learning process, provide additional exposure to the material and leverage the hands-on experience.

Using these technology applications will help to address a cross-section of the nine Marzano effective learning strategies:

The most significant is that I will be using a lot of nonlinguistic representations – the flashcards, prezi presentations and the manipulatives all include a lot of images that directly relate to the subject matter.  Since we already do quite a bit of work linguistically in the classroom, these resources will serve to broaden the students’ exposure to the material and provide an alternative way to learn and retain the concepts.

The flashcards will help provide cues focusing on what is important to remember and providing the mental link to that knowledge. Prezi will provide some of the means to use advance organizing to preview concepts and link it to prior knowledge.

The flashcards will also help in pointing out the similarities and differences in various concepts – one example would be in the determination of congruent triangles – exploring the differences and similarities of SSS, SAS, ASA Congruence Postulates and the AAS Congruence Theorem. This is especially true because the concepts are displayed graphically – allowing  visual interpretation of the relationships and the naming of the Postulate/Theorem involved.

I put together a lesson using the Prezi tool to show the concepts involved with the Perpendicular Bisector Theorem. Two sections deals with prior knowledge – one ties it to previous lessons in Geometry, the other ties it to the Pythagorean Theorem learned in middle school.

The lesson helps students meet some of the G2.3 Michigan Curriculum Standards”

G.2.3.1 Proving triangles are congruent (SSS, SAS, ASA, AAS, and HL)

G1.2.5 Solving multistep problems and constructing proofs about the properties of medians, altitudes, perpendicular bisectors to the sides of a triangle and the angle bisectors of a triangle.

Perpendicular lines are found in many of the objects that we work with in geometry.  Students need to use this information in proofs and in problem solving. They have to know how the use of perpendicular lines generates right angles and right triangles – including isosceles triangles. Also, perpendicular lines are used to create parallel lines.

All of the proofs are multistep problems – some more so than others. As proofs get more complicated (starting towards the end of Chapter 4), the steps involved in solving the problems become more complicated.

Thing #14 - Online Video and Audio Resources

There are several ways to integrate video and audio resources into my classes.  First is to use the Brightlink projector and sound system that exists in my classroom. Since most classes  are taught using this equipment, this would not be unusual. However, integrating web-based programming would be new. The manipulatives (easy for you to say, Ron) that can be found in the National Library of Virtual Manipulatives are nice tools that offer a way to visually observe while testing out different object movements. They can certainly be shown to the class on the Brightlink. However, I believe that the students would be better off doing some discovery learning on their own - so I would prefer to have students manipulate the manipulatives on separate computers in a computer lab that I would reserve for a class. Take the transformations manipulatives listed in the high school section under Geometry - there are rotations, translations and reflections illustrated.  One of the biggest problems with students in this area is visualizing what should happen to the objects, once given a set of instructions on how to move them.

The manipulatives let students pick the objects, move them in a variety of ways and explore the options. They are easy to use. However, there is some additional information that needs to be added by the instructor, so that students can be guided into looking for the right information.

These are largely visual items without audio tracks - but effective nonetheless.

The emphasis in math would be for more video-oriented material (vs audio material) - I am hoping to impart images of math objects to my students.  Screen shot:

MathTrain.TV appears to have a lot of potential, but I have not viewed a lot of the videos due to a lack a available free time (there's this computer course that I am taking...). I plan on going back over the course over the Christmas break and discovering/exploring what's available. If there's an appropriate video, I will incorporate it into the lesson.

Thing #13 Online Interactive Learning Tools

My house:

My Mom's house (Placemarked):

Quizlet:

I created a set of flashcards that depict the various elements that students must know and identify to use those elements in proofs. They are the items that students add to the analysis (not the "Given") items. I plan to use them as a quick review several times before the test. I will have students add the appropriate markings to the drawings on the cards to help display the information. I also plan on using the games and quizzes, but find that I need to describe things better before I go there.

Thing #12 - Evaluation and Assessment Tools

Google Form Survey Results:

A powerful tool - I did not have to ask anyone to respond.  The students who were going on Blackboard noticed the survey in the Announcements and filled it out!  Great for feedback, judging comfort levels and opinions on the class. This tool has a lot of potential for such feedback and making adjustments to focus on specific areas and also to deal with non-educational issues affecting students.


Rubric using Rubistar.

The lesson I used the rubric for is a two/three person team putting together a geometric proof on a whiteboard, such that they can show it to other students and explain their proof. (Different groups have different proofs.) This proof session was done with limited reliance on me to help them. The rubric helps me focus on the items I wish to measure (even after the countless questions and interruptions that occur) and a reminder to check on everything. It is also a tangible record of the work that the student achieved and the level at which they are working.

The rubric:

Data Tools.

We (Catholic Central HS) are heavy users of Infinite Campus.  The program houses transcripts, medical and learning alerts for the teachers, schedules, personal and demographic information and grades. Parents and students have online access to grades. Teachers can send blanket e-mails to students and parents.  Before school starts, I go through all of my students' profiles and look for pertinent medical and learning process items that might have an effect on student performance. Students are flagged, a very brief notation of a condition or preference is noted - you follow up by going to the guidance counsellors' office.

While we have reviewed and analyzed the MEAP data in the past, the Catholic Secondary Schools are opting to not participate in the testing this year - so that option is disappearing.

However, we do use many common assessments, we analyze test data for specific feedback and are increasingly looking at alternative assessments to gauge learning in our students.

Thing #11 - Presentation Tools

I put together a Prezi about the perpendicular bisector theorem and its converse (along with a little bit on using the theorem). The curriculum standard most strongly associated with this is:

G1.2.5 Solve multistep problems and construct proofs about the properties of medians, altitudes and perpendicular bisectors to the sides of a triangle, and the angle bisectors of a triangle. Using a straightedge and compass, construct these lines.

The URL for my Prezi is: http://prezi.com/bpds_orhbznh/perpendicular-bisectors/ and it looks like:

Prezi is an incredible presentation tool - I loved the one-page organization and the ability to emphasize points in different manners by creating different paths to different levels. Powerpoint has its strengths - mre formatting options, a little easier to control and know what is going to happen as you put it together. Also, it's a program I know well, it works with some other tools that I have (Camtasia) - I have a very high comfort level with PowerPoint. Powerpoint achieves some of its flash via animations.

Prezi's one-page organization lets you consider the interrelationships that exist between the points you wish  to make - and make it easy to revisit those points to provide enough emphasis for students to remember the information. Prezi's appeal is the ability to zoom in on little details within the larger picture - and then to zoom out an put it all together. The visual graphic organizer should help students organize the information in their heads. I can envision reviewing points once a presentation is finished by using the single page view and zooming in where appropriate.

For students, it can help organize their thoughts by allowing them to put all of the information on a single page, move it around and then tie it together logically.  You have to think about the process and the items involved and how it should be ordered and presented. It's a way to organize complex situations with various inputs and reach a logical conclusion. I can envision assigning my Algebra 2 students to put a Prezi together on all of the methods of solving quadratic equations and pointing toward the answers that were asked for (vertex, zeroes, maximum, minimum, discriminant, etc.)

Zoomit is an interesting little add-on.  Occasionally, you need a larger picture or additional emphasis and this is an easy way to get there. For some learners, you need to isolate pieces of the picture and talk about that point specifically - this will help achieve that. It also takes away the "I can't see it" response that occasionally arises.

The timer will also be useful...

Zoomit page:

In this example, it allows the students to more easily see how to read the protractor so that they can figure it out on their own.

Thing #10 Digital Story Telling

I used Voicethread to create a video on angles and angle measurement that can be found at: http://voicethread.com/share/1590869/ .  The video is also posted on my BlackBoard Geometry page in the Announcements section.

The storyboard I used as a general outline is:

Digital storytelling can be used to demonstrate concepts that can be videoed, but not easily duplicated in the classroom - how angles are used in building construction, or showing the curvature of the earth when talking about arcs. The storytelling can also be used to explain concepts - such as in my video - with voiceovers, music, video, graphics, and web resources all compiled in one presentation to provide images along with the standard textual representations (testbooks) that are currently the primary source of information.

It was not easy showing this to a peer, since it was a first effort on a program that I haven't used before.
She did like the use of the architectural drawings to illustrate the concepts. She thought that the voice comments were a lot more effective that the written comments - you can focus on the slide and not have to read the comment, then the slide. She also thought that both my delivery and the presentation could be a little more animated. Having said that, in general, her comments were positive (surprised me, I can think of a lot more things that I could add, but the program is limited in what one can do with it). This program gets more interesting if you can upload animated videos and go from there.

I love the concept and have written down ideas for use with Camtasia,the Brightlink and recording the lesson as I teach it in the classroom - coming soon to my Blackboard site. I can envision absent students viewing the entire class and even those students who were there going back and reviewing concepts/lessons.

Thing #9 - Digital Images

I used the Piknik site to upload and edit a picture and also to create a slide show using pictures uploaded from http://www.pics4learning.com/ - the Pics for Learning site.

Original Photo:

Edited Photo:

Edited photos can be used a lot in Geometry to illustrate geometric relationships that exist in architecture and in nature to emphasize a point or to put a "real world" spin on the topic. Students can then associate an image with the concepts, find the similarities and look for those relationships on their own.  Adding fun details enhances the experience - students notice the enhancements, point them out to their fellow students and are more likely to talk about the image and remember it - along with its geometric relationship.


The slide show is at http://www.picnik.com/show/id/11168560124_9LhRm/t/perpendicular-and-parallel

Thing #8 - Copyright and Creative Commons

My ten question quiz turned out to be a 12 question quiz. It seems that most of us have been a little brainwashed and intimidated by what we have heard to be the copyright law without understanding Fair Use. It is interesting to compare the broad, legal discussion of fair use and its implications and then to go to the industry-sponsored web site and view their self proclaimed limitations ("Multimedia Fair Use Guidelines"). It is comforting to know that we are not breaking the law in doing our best to educate our students. We have a lot of internal resources that are available only to our students and are fairly well protected in what we do. All of the people I talked to were aware enough to be cautious when generating material for general public consumption, but again, everybody thought that most of those limitations remained in the educational arena.

No one that I talked to knew about the Creative Commons process - most aren't really worried about copyright protection. However, as we generate more and more resources in-house, perhaps we need to pay attention to this...

Creative Commons License:

Capstone Paper - Things 1-7

Things 1-7 Capstone Reflection

As I work my way through the 21 Things, it becomes apparent that I can’t help but use the applications in the classroom to improve the learning experiences for my students.

A great deal of the technology presented thus far will make its way to the students via Blackboard.  I have posted several links to my Blackboard page and will post more in the near future. In class, I will visit the sites and show the students how the sites work and what they can learn/reinforce using the sites. I will also let the parents know that these resources are available and of educational value for their students.

I will continue to use the Blackboard site to provide resources to the students, such as homework assignments, worksheets, solutions and key concepts sheets. I have debated whether I post my classroom sessions (currently on PowerPoint) or even additionally, should I record the audio and some classroom video and post the classes themselves online.

I also see that some of the resources and techniques presented will be used in teaching the lessons.  I use an interactive Brightlink projector that I use every day and I have sound capability that I rarely use. I will use the text-to-speech application this week – I believe it will enable me to differentiate major concepts and increase the engagement of the students.

Improvement in my own practices will come from using the above sources and also from continuing to expand the resources available.  This course is providing the direction to continue to look at a number of educational resource sites for additional applications and to further explore the web for items that can be used in the classroom.

In providing additional resources online for students to turn to, I can offer students opportunities to achieve a better and deeper understanding of concepts. For my Informal Geometry students, the three digital manipulatives on transformations will greatly help those students who do not visualize spatial orientations. These students generally do not “see” how the figures interact and where they should end up. For my Geometry students (including the Informal ones), the “That Quiz” application provides not only a current resource to enhance current learning, but also a resource to review prior learning to reinforce those topics.

I envision using those review sites towards the end of the school year for my geometry students as they head into Algebra 2/Trig. They often arrive in an Algebra 2 classroom having totally forgotten many of their Algebra 1 concepts (like graphing lines, factoring numbers, and exponents). Perhaps our math department should put together a list of recommended activities for students to prepare for the next school year over the summer.

I can see that some of the applications will enable group projects to be more collaborative as students will not have to be in one place to get things done via Google Docs.

I am certainly addressing the value of homework and practice with the use of Blackboard for organizing the homework and providing additional resources for students to revisit the material. Having links to sites that provide the material and extra practice should help those students who like to learn independently or via the web and to those students who need multiple exposures to the material before they gain a working knowledge of it.

The web resources will help in student visualization (Marzano’s Using Non-Linguistic Representations), which is an extremely important skill in Geometry. It helps the students understand how everything fits together if they can visualize it well. Importing these visualizations into my lessons can only help further the students’ understanding – which can be additionally reinforced by the online activities they can do at home as discussed above.

I will be assigning a project, due at the end of the semester, for students to make a music video of a math concept (a formula, a postulate or a theorem). The video will need to be between two and five minutes long and can be any music form (rap being the easiest of the genres). The collaboration and cooperative work in putting the video together will need to be documented via Google Apps – a script, picture of the group, listing of meeting times and places (all of our students have accounts) along with filling out a form delineating their efforts, the group participants, the math behind their video. A short slide presentation of the math concept will be required.

I will then have our school’s video news include the top several videos in a series of their broadcasts.

This project will meet several of the 2009 METS standards for Grades 9-12 students:

9-12.CC.2 – use available technologies to communicate with others on a class assignment or project. The students have access to Google Apps and will be required to use it in several aspects of the project – filling out a planning form and a completion form, submitting their script and putting together a presentation of the math principle involved.

9-12.CC.3 – collaborate in content-related projects that integrate a variety of media – audio, video and print (perhaps graphic) media will be involved. Most of our students have access to enough technology to get this done – a percentage have posted YouTube videos (and we will discuss what is appropriate to post and what type of information stays with you for a lifetime…)

9-12.CC-4 – plan and implement a collaborative project using telecommunications tools – this could come into play, and I will talk about and show them one or two ways to do this (certainly Skype is conducive to this sort of activity).

It is interesting and challenging to take advantage of the technological tools that we have for our use – and to consider adding additional tools. (I really like the Adobe Connect meeting tools and am considering adding that to my classroom.)

Thing #7 Face of your Classroom

The main face of my classroom is done using Blackboard.  All of my classes are included. Postings include daily homework assignments, copies of worksheets, solutions to problems and occasional key concepts pages. Most of my work is done in Powerpoint and converted to pdf's for publication.

I have added links discovered in this course to my Blackboard site, found at http://blackboard.kentisd.org/.

I also took a shot at developing a web page on weebly.com at http://ccmathisfun.weebly.com/. Thus far, I have only done the first page and am considering whether I want that type of web presence. I have done a lot of work on the Blackboard site and my students are aware of the site and they use it frequently. Creating an open web presence is something that I have considered in the past, started in the past, and left unmaintained in the past.  The advantage is that you have a community face to the classroom and its activities.  The disadvantage is that it has to be currently useful. I find that Blackboard allows me to be current without a lot of effort - it seems to fit my needs and the needs of the students for now.  As for Catholic Central, I am one of the few heavy users of the program.

Students find it convenient and useful. They refer to it when they need it and occasionally I will post extra assignments and work.  Screen shots follow:

Blackboard:

Web site CCMathisfun:

Thing #6 Digital Citizenship

The first site I looked at is the Dihydrogen Monoxide as a threat site.  It does help going in that I knew that DHMO is just another way of saying "water" (H2O) - once in a while I get to put my Chemical Engineering degree to work...

The site is well done. However, the credibility quickly drops when Wikipidea lists it as a hoax, along with the standard hoax sites. Clicking on the credible list of links and then cross-checking DHMO comes up empty.  The site provides links, but there is no association between them.

Accuracy:  statements are made (DHMO causes car accidents) without substantiation. There's nothing behind the statements.

The site appears to be updated daily - nice touch.

I can see how people could be fooled by the site, but a quick check in the real world sets things straight pretty fast.

The second site I visited was the New Hartford, MN site. There are credibility issues on the main page - "Updated January 1 and June 3 of this year", the main city URL takes you right back to the same page, there is no "East Green Earth River" and a quick MapQuest shows that New Hartford, MN is a country intersection, with farms on all sides of the road - no river, no bridges, no people.  None of the schools exist.  Pretty easy to write this one off on credibility, accuracy, date.

2.  At Catholic Central, we address moral and ethical issues head-on.  I have discussed cyber bullying, displaying personal information on the web, and acceptable use several times with our students.  When we talk about getting on the web, youtube, facebook, etc., we discuss these issues along with what the students should be doing on those sites.  Two activites: class discussion and the signing of acceptable use contracts by the students.  This is becoming a broader issue as we are going wireless campus-wide, so the issues are getting greater administrative attention as well.

Thing #5 Differentiated Instruction and Diverse Learning

Differentiated Learning Assignment

In reading the key elements that guide differentiation, there are a number of them that I incorporate into my classes:

Pair and group learning:  I have individual and group whiteboards that are used for pair and group work. I find them especially helpful for multi-step processes (like proofs in geometry or completing the square in Algebra 2). Also, students often work in pairs to complete in-class problems that demonstrate the concepts that were introduced earlier in the class.

Identify Key Concepts - students are shown the concepts visually on the Brightlink - often in word, picture and number forms. Examples are given for them to explore (with the ability to ask their neighbor or me) and then the concepts are again discussed.  The following day, key concepts are reviewed along with the homework that was assigned.  Several days later, the concept is again reviewed in the warmups.

Provide multiple media and formats - my presentations are digital, there are worksheets that go along with the material, additional "reteaching" worksheets are provided online, concepts are presented in words, pictures (when possible) and numbers. We use whiteboards individually, in pairs and in groups.

I give "mini quizzes" on key concepts that allow the students to focus on one concept, check their understanding without a major impact on their grade.

Diverse Learning Assignment

Visiting the Using Technology to Support Diverse Learners, I found several math manipulative sites including http://nlvm.usu.edu/en/nav/vlibrary.html and the NCTM site (Illuminations) that provide interactive visual representations of math concepts.  I found several on the Pythagorean theorem - several students are having difficulty doing the various calculations - they would benefit by spending 15 or 20 minutes with the application. There are also a number of students who have trouble with transformations that could use these digital manipulatives to see and understand those concepts. I have several students who have difficulty visualizing spatial orientations and the movement of objects who will benefit from using those sites. I plan on assigning specific and open-ended tasks that they can use to explore those transformations (rotations, glides and reflections).

Universal Design for Learning Assignment

I visited the Universal Design for Learning: Strategies and Tools and clicked on the Math Support section. After exploring several of the tools, I took a longer look at the "That Quiz" tool.  I found that it would be an exellent tool for my lower level Geometry students to choose topics and choose the level of difficulty.  The problems were appropriate and accurate - they come in "quizzes" of 10 questions each and, while timed, allow students to work at their own pace. This would be a great computer lab tool or an independent study tool.

Text-to-Audio Conversion

Once you get going, it's hard to stop. I tried NetTrekker, Natural Reader and AT&T's demo.  AT&T had the best pronunciation of math terms and also had a feedback area for getting pronunciations corrected. (We'll see if they do it.) I can use this in my lessons as an emphasis area - instead of me reading a theorem or key point, the software can do it. I see it as one more way to change up the pace of the presentation and keep students engaged. I found that you could change the pronunciation a little bit in NetTrekker by changing the spelling of the words involved (specifically "congruent").
Screen shots:

Thing #4 Thinkfinity

The first activity that I chose (and there are enough to choose from) is the Box Plot graphing activity, found at Box Plot Graph. It is one of the math activities that is located on the NCTM site.  The activity draws the box plot from a set of data. It also calculates the mean and the quartile ranges (the numbers listed under the plot).

This is a useful representation for several reasons:

1. It is large and easy to pick out the points - nice for projection onto a screen.
2. The students can enter their own data and observe the plot.
• Seeing the concept in action is useful - this is not a normal way of thinking about or representing data.
3. There are several activities listed next to the graph. They are activities that the sudents can do to gather appropriate data to create a graph.
4. There are things you can add to the presentation - the ordering of data and dividing it into the quartiles - that can be done on the whiteboard alongside the projected graph.

I would have the students do one of the data-collecting activities, enter the data into the computer, write out the data and organize it on the whiteboard, show the quartiles and compare it with the graph and the data calculations made by the program.

The second activity is called "Congruence Theorems and is a visual representation of the ways in which triangles can be shown to be congruent.  Congruence Theorems lets a student identify the parts of a triangle needed to establish congruent triangles. The student then gets to construct a second triangle using the original information to see if they used information guaranteeing congruence. In a lesson, I would have groups of students choose triangle parameters and demonstrate congruence (or not) to the class. It would be nice to get a computer lab and have students explore several specified configurations and then do a number of explorations on their own - with a small writeup of each configuration and which ones worked versus which ones did not. Screen shot:

Thing #3 - Communication Tools

Skype is a powerful communications tool in that it incorporates video along with the audio and personalizes the experience.  It is easy to see that you could bring personalities into the classroom and make subjects real to the students - providing a real-world connection to the subject at hand.

In Geometry, one could bring in an architect to discuss angles, objects, the golden ratio, etc..  In Algebra 2, you could access a research biologist to discuss data collection and analysis or a NASA engineer to study launch paths, gravity effects/equations and other parabolic motion paths. I have a projector and sound system in the classroom and am working to get Skype working there.

I am wondering how dangerous it would be to open a Skype chat some evenings for homework help or test review -- it would be OK for the 20 who get in, but what about those that don't?  Also, just getting set up the first few times would take a while.  Probably good for smaller classes and difficult for the larger groups.

I like the backchannel chat because it allows you to discuss, think and contribute without interrupting the presenter and slowing down the presentation. It also gives the presenter a chance to get feedback immediately or after the fact - their choice.

Below is a screen shot of a converstion that I had with my senior-in-college son (Tim) - he finished his last final before break today. Jing would not let me take a screen shot of conversation in full screen mode - it backed out of the full screen as soon as I clicked on the capture button.

Thing #2

The above (brief) lesson plan was done using a template that I created (and shared on the Catholic Secondary Schools Google Apps site).

Obviously, the sharing of documents and techniques using Google Apps is a valuable tool.  Users can access the site when they need it, edit the document to add utility and effectiveness  and share results with other users.

For educators, sharing and editing of documents opens the door to increased collaboration.

I see applications with group projects and forms - in Geometry, I do one major group project per semester.  Google Apps will let me assign students to groups without considering geography (many of our students do not live near each other), but rather abilities.

I can see applications for group homework (doing proofs) or even individual work.  I am wondering how to manage such things (I have 112 Geometry students and 46 more in other classes).

Catholic Central has assigned gmail accounts to all students and we are set up for using the Apps.

I also see some downsides - the system kicked me out at least 10 times on different computers (I am running them side by side) with similar error messages.  I had to finagle the downloading of my template and had trouble downloading all templates.

I have sent a collaborative document to a colleague and am awaiting a response.

The resulting document is shown below:

Thing #1 - Keyboard Shortcuts and Delicious

The Jing capture of my word document is above.  I used shortcuts to right-align, center-align, underline, italicize, 1.5 line spacing and single-line spacing. It's interesting that the italicize shortcut worked here!

When doing a lot of Word document processing, the shortcuts save time and energy because your hands never leave the keyboard. A second benefit would be that you would see the formatted docment as you type, rather than formatting the document after you are done typing - which is my usual way of getting things done.

Finally - while I probably do not do enough Word documents to get good at a lot of shortcuts, I have used the "Windows E" shortcut three times since it was mentioned!

Delicious (used keyboard shortcut!)

My Delicious address is: http://www.delicious.com/robertjkoch

I found that my searches gave me sites that are relavent to my subject area - versus having to wade through a standard Google-type search where you have to look at a lot of different sites to find useful material.

Also, organizing my educational sites in one place will make it easier to find the sites I need and easier to share them with my fellow teachers.

Thing 00 - Second Post - Blogs!

A good blog contains information worth sharing - topical, important, personal, etc. It should be written with a target audience in mind. Good blogs are well-written, concise, organized and current.

A blog could provide students with suggestions, tips, study points -- anything that could enhance the lesson and provide multiple exposures to the material (important in math). A blog would enhance my existing web presence well beyond my faculty picture by providing an interactive resource for students to obtain additional information, to exchange information and to provide feedback to me: what they understand, where they need additional help.

Blogs are obviously an easy way to publish (just hit the "Publish" button!).  However, simply publishing isn't everything: as a blogger, you need to attract readers -- otherwise, it's pointless.

21 Things - Getting Started (Finally)

Some new experiences - like setting up and updating a blog - are part of what I expect to get out of the "21 Things" course. Along with that, I am constantly looking for ways to incorporate technology into the classroom.  I have an Epson BrightLink projector and use it for 90% of my class presentations/lessons.  This is the first year that I have had access to interactive presentation capabilities and I am on a steep learning curve, but see the need for additional skills to enable me to further enhance my lessons.

Also, perhaps some "different" ways to contact students and perhaps push material to them...