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?