The Technofication of a Lesson

According to the Montana Common Core State Standards, the Pythagorean theorem is a critical area for eighth grade students.  It is also a concept that is used in many real life contexts.  For example, a 22-inch TV has a diagonal length of 22 inches, which is the hypotenuse of a right triangle.  Also, painters and construction workers need to know the size ladder to use to get to the top of a wall.  Geologists use the Pythagorean theorem to find the center of an earthquake.  Surveyors use the theorem to calculate the height of a mountain.  Triangulation is a more complex version of the Pythagorean theorem that helps pinpoint locations on earth.

There is no doubt that it is an important concept for success in adult life.  However, the traditional method of teaching it would most likely involve direct instruction.  A teacher would demonstrate the skill; students would practice and then there would be a quiz.  See original lesson plan. 

Substituting technology still keeps the lesson direct instruction but it is more engaging and interesting for students.  See substitution lesson plan.  Augmentation cleans up the substitution plan but still only enhances the original direct instruction plan.  See augmentation lesson plan.

Student Work - Google Earth

To transform the lesson, one has to think outside the box.  Flipping the classroom is one such idea.  In a flipped classroom, the direct instruction is done outside of the classroom as homework.  Students watch videos that introduce concepts.  In class, students work on activities or investigations that apply those concepts.  For a significant redesign from the original lesson see modification lesson plan.

Student Work - Wheel of Theodorus

A Menu is not a new pedagogy.  It has its roots in the elementary classroom’s stations.  However, redefining a menu takes the best of the old pedagogy and makes it rich with technology.  A menu is a way to organize the classroom for instruction that includes problems, activities, games and investigations.  It allows students to have choice that helps them work within their own strengths as well as challenges them to step outside their comfort zone.  An internet-based menu uses their world to help students have success.  The menu in my lesson is located on a Google web page so that students have access to it anywhere.  It consists of an appetizer, a main dish and a dessert.  The appetizer introduces the Pythagorean theorem.  The main dish consists of activities and investigations that use and apply the Pythagorean theorem.  The desserts allow students to be creative with triangles.  For a more in-depth description see redefinition lesson plan.

Most students are highly motivated as they work their way through the menu.  They begin by watching several YouTube videos that reinforce their fragile understanding gained from watching the stop-motion movie that I created to introduce the topic. (The Pythagorean Theorem Movie).  The students are required to choose two main dishes.  A favorite activity is the Pythagorean Triples and Google Earth Activity.  When students get to the desserts, the have a good grasp of the Pythagorean theorem and are ready to have some fun.  Since I have used and revised this menu, I have never had a student fail the culminating quiz. 

The Pythagorean Theorem Movie

This assignment from my Education Technology class was to create a video.  I choose stop-motion animation.  It was more difficult than I anticipated but I learned lots!

This file contains the movie, the lesson for creating a stop-motion animation and a rubric for grading the movie.

                                         

Best Water Bottle Ever - Digital Imaging

 Assignment 1:  Take 20 pictures of a handheld object using various angles, backgrounds, perspectives and settings.

 What I have learned or relearned about taking pictures - 

I own a Panasonic DMZ TZ4 that I purchased several years ago.  I stopped using it because I was unhappy with the pictures that I was getting from it.  What I learned is that it wasn't the camera, it was the operator.  The first thing I did was re-read the manual.  My camera has a multitude of options that I still don't understand.  The three most important settings are Intelligent auto, normal picture, and scene mode.  The intelligent auto does all the work for me.  It reads the scene and makes all the optimum settings automatically.  The normal picture setting allows me to take pictures with my own settings.  There are all kinds of things I can change.  For scene settings, the exposure, coloring, light, etc are set for certain scene types.  I don't know what I was doing before but with all these options I know I can get some great photos again.

Here are some composition tips that I have picked up:

1.  In general, don't center the picture.  Use the rule of thirds.  Your primary points of interest should sit along third lines.

2.  Pay attention to the background!  Plain backgrounds are best.

3.  Pay attention to the light.  Where is it coming from?  Sometimes shadows add interest and sometimes they are distracting.

4.  Only use flash if you have to.

5.  Shooting with the sun directly behind you makes for a flat photo.  Have the sun come from the side or better yet shoot in the shade.

6.  Limit the palette to one or two colors that are predominately featured.

7.  Try interesting angles.

8.  Frame the subject with something in the foreground to show depth.

9.  Move in close to fill the frame.

The most important tip I found was to STOP chimping (checking the photo on the back of the screen) and take lots and lots of photos!

Assignment 2:  Editing

For this assignment I had to take 5 pictures and change them from their original.  I made an album but couldn't figure out how to post them as a slide show so I have posted each original photo and how I changed it.  I used Picasa for the editing and although they have a lot of fun features for manipulating photos, I kept losing what I had done.  Clearly, I have a lot more to learn.

 

 

 

 

Assignment 3:  Turn 2 photos into Art

Original photo for  Art photo

For larger version:  Water Bottle Art

To see art version of original photo:   Water Bottle Art 2

The Legends of Archimedes

The first podcast assignment was to research a person that was famous for something; create a script and then a podcast with at least 3 sound effects (I hope that you can hear the crackling fire).   I had fun with this assignment and I hope you will enjoy hearing these stories that I discovered about Archimedes.


                          

I think I will try podcasting again...

A Conversation About Division

For this week's assignment, I tackled podcasting.  I now have great respect for sound men because this was harder than it seems.  The following podcast is a conversation with my friend Sue Harding.  She and I often have math ed conversations but this one is much shorter - about 6 minutes - and slightly scripted.  The questions we discussed are:

                   1.  What is division?
                   2.  What does the Montana Common Core say about division?
                   3.  Is it important to teach long division?
I admit that I don't have all the answers but I hope you enjoy our conversation.

What is division?

                                    

 Here are two pencasts that will give you more information about what was discussed in the podcast.

Division Models                                                                                Partial Quotients Strategy

 

5th Grade Division Strategies

If you are interested in better quality Math podcasts, the MathGrad is highly entertaining.  I'll post the link in Awesome Links.

 

Google Earth

Google Earth is a virtual globe and map.   It uses images from satellites, aerial photography and geographic information systems.  It is a free program that lets you fly anywhere on earth.  It has many uses.  Here are just a few.

This week we used Google Earth in several assignments.

1.  National Parks powerpoint.  I tried to narrate some of this but the audio did not come through so instead I just added music.  Hope you enjoy learning about some of my favorite National Parks.

2.  Google Earth Tour - In Anticipation of Summer 2014.
Again I tried to add audio but again it eluded me.  You will have to download this and view it on Google Earth. 

  

 3.  From Birth to Kalispell.  This picture is suppose to show my birthplace to my current home.  I wasn't actually born in Sacramento, CA but my family moved there shortly after my birth.  The red lines show the few side trips I made.  I lived near San Jose and then in Hawthorne, Nevada.  I also lived in a few towns in Oregon - all along Interstate 5 and then finally made it to Kalispell where I have lived for the past 25 years.

4.  Pythagorean Triples and Google Earth Activity

Pythagorean triples are whole numbers which satisfy the Pythagorean Theorem.  In this activity, students use Google Earth to find three places that appear to form a right triangle.  For the complete instructions see "Awesome Links" on the right.  

Just How Smart are Smart Pens?

A Smart Pen is a pen with a microphone, built-in speaker and infrared camera that records what you hear or say and links it to what you write and draw.  I have been using mine for several years to create pencasts for my students.  A pencast is an interactive flash movie of your handwritten notes and audio.   However, there are many other educational uses for the smart pen.

In this collaboration project, my teammates and I researched and wrote about the smart pen.  We created an introductory document that tells about the smart pen.  This is accessible to the right in Awesome Links and in the box.com folder below

We also created a powerpoint presentation that gives ideas for how to use it. (See below and in box.com)

 Also available in the box.com folder is an assessment and the summary for the assessment. (see below). 

All new technology experiences problems.  However, none of my pencasts have faded.  Some of the older ones have minor glitches but my middle school students tell me that they like my pencasts better than Khan academy so I must be the one who is smart!

My latest crusade...

This is now personal.  Two of my grandkids are being terrorized by timed tests!  Not only are the tests creating stress and anxiety but also both of them have adopted the false adage that in math, “faster is better.” I am compelled to find out more.

Brain Research

Recent studies have found that kids with the highest amounts of working memory are the ones that are the most susceptible to math anxiety.  Stressful math situations compete and sometimes take over the working memory.  Previously known facts are no longer accessible.  Lack of confidence takes over and the “I’m bad at Math,” attitude sets in.  Students who have the potential to take mathematics to high levels spiral into math aversion.  Yes, there is a physiological reason not to give timed tests, but what does the Common Core say?

The Truth About Timed Tests by Tracey Carisch

The Role Played by Timed Tests in the Development of Math Anxiety by Jo Boaler

Common Core

Second graders must know from memory all sums of two one-digit numbers (2.OA.2) and third graders must know from memory all products of two one-digit numbers (3.OA.7).  But nowhere does the common core give a time frame.  After reading Progressions for the Common Core State Standards in Mathematics K-5 Operations and Algebraic Thinking, it is clear that fluency is important but “this is not a matter of instilling facts divorced from their meanings, but rather as an outcome of a multi-year process that heavily involves the interplay of practice and reasoning.” (pg. 19). 

Bill McCallum, one of the authors of the Common Core, addresses this question.

“It was not our intent to dictate the pedagogical method.  It is no accident that the standard says ‘know from memory’ rather than ‘memorize’.  The first describes an outcome, whereas the second might be seen as describing a method of achieving that outcome.  So no, the standards are not dictating timed tests.  Some curricula might go that route; others might encourage students to build up their knowledge of number facts another way.”

    

Alternatives

So what is a solution?  Luckily one of my granddaughter's teachers agreed to the use of flashcards with her Mom.  But how does a teacher with a classroom full of students guarantee that they “know from memory” their facts?  Any suggestions?

The journey begins...

A little Math humor...