Symbols

Which symbols are precious to you?

How do symbols gain value?

How are symbols created and when are they no longer used?

In my job as a mathematician and teacher I am surrounded by symbols.  We use symbols to make things more efficient, bring attention to items for future reference, to abbreviate ideas, and to represent other things.  Google defines a symbol:

I am struck by the reference to musical notation as the notes on a page represent a tone and length of that tone but is it really MUSIC?  No, the power to music comes from listening to it.  Are musical symbols necessary?  In some cases, yes.  I think it is amazing that Pachelbel’s intentions for the sound of his piece is probably the same now at the 100 weddings this weekend as he originally intended it to sound in the 1700s.  Without these symbols, that tradition might have been lost. 

I think it is amazing in mathematics that by noting this:

that the observer will know that I intend for lines l and m to never meet, EVER.  After establishing that, we have a whole slew of other ideas to show and prove.  Simple lines on a page take the place of words and meaning, as long as you understand what my symbols intend.  Symbols take on meaning only when the inscriber and the observer “know what you mean”.  Unfortunately, to the casual observer, some of this meaning is lost if you don’t know what I mean.  Thus rendering the symbol useless.

We place so much emphasis on symbols such as our flag, a cross, a star, a rainbow triangle, a plus sign, and the list continues.  We assume that other parties “know what you mean” by displaying these symbols.  But do they?  To show our dislike for an idea, we may dishonor, erase, or disrupt the symbols associated with these symbols.  When symbols we hold with high regard are treated in this way, we react with knee jerk reactions.  Why?  These symbols are just that – symbols.  Symbols may represent these real feelings and ideas, but the symbols themselves ARE NOT WHAT THEY REPRESENT.  Before we get up in arms about how a symbol is treated, we need to reconsider those feelings and realize that just because the symbol was treated in such a way, it does not take away from the essence and being of the thing the symbol is intended to represent.

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What is Data? What is GOOD Data?

I miss teaching statistics sooooooooo very much.  I have to work hard to try to get the class BACK at my school because statistics are literally EVERYWHERE and the class is required for so many careers these days.  Everyone wants to be data driven and make decisions with data in mind.  We are looking for improvement and maximization or minimization.  We are looking to see if there is a significant difference which is literally the culminating topic for most statistics courses.

Today during our weekly late start Wednesday professional development session more “data” was distributed to our staff about attendance and discipline.  I really appreciate the transparency of our administrative team with this distribution.  Anytime I am presented with data I want to know more about it before I make any judgments.  I wonder if my students look at data with that same lens or if that is something that I need to teach to them.  When I do get the opportunity to teach statistics as a course, our first unit is all about data and what data is.  So I pondered the question for myself:

What is data?

I began thinking about a definition that we develop from class about the fact that numbers become data only when we have a context.  Google says:

When you actually dive into the definition of data, you are almost forced into considering the following:

What is GOOD data?

Now THAT is tricky because now you have to make a value judgment.  Or do you?  Does just putting it in context make that value judgment for you?  Can what I consider GOOD data to me be just mediocre or bad data to you?  As an educator, what do you consider to be GOOD data?  Why?  How do we get others to consider this when they present data?

I wonder if people think that I am being “type A” or a “B*&$%” when I ask about the who, what, when, where, and why of the data that I desperately want to know before making any data minded decision.  I won’t stop asking though.  It is important and I want others to see the importance too.  Without that information, how can you know if you have GOOD data?  I guess for me, GOOD data can satisfy all of those questions and provide a good basis for decision making that will allow the most positive outcomes to occur.

“Upside Down” Triangle

I’ve incorporated Which One Doesn’t Belong tasks into my bellwork.  I love how they fit nicely into my Geometry lessons about definitions and saying what you mean and meaning what you say.  Given the image below, I was not expecting my students to write what they did about the upper left corner image.

Students wrote some of the following statements:

• the only upside down one
• it is the only regular triangle <— especially shocking since we have worked with the term “regular” in this class already
• the only normal one
• different shaped triangle

I was shocked at how many students referred to the triangle as “upside down”.  It really made me think about how we represent triangles to our students.  I plan to do more work with showing multiple representations and pressing students to work on how they verbally express themselves.  How do you address this issue of “right side up” in your class?  I think it is really important especially when we head into concepts like area and perimeter.

My Teacher Hacks Contribution

I love hacks.  Especially teacher hacks since they usually involve making my school life easier/more efficient/cost effective.  Below are some of the hacks that I use on a regular basis.

1. ) Mail Merge

Mail Merge is a command that you can do in Microsoft Word.  If you have ever wanted to quickly address a memo to individual students and include other information (like their first period classroom number for delivery) this hack is for you. I use this a ton to contact my extra curricular team.  I also use it for my information sheets (I like to have a paper version of what you see online to write on while talking to parents on the phone).

First, make an excel file that includes header titles in the first row.  If you use PowerSchool, you can obtain this list through the reports function. Then, open Word and select Mailings.

Select Start Mail Merge>Letters.

Then Select Recipients>Use an Existing List and locate the excel file you created in the earlier step.  Then start making your master document and

Insert Merge Fields

such as Name or Period as you go.

Finally, Finish and Merge.  I usually select the option to edit individual documents if I want to see what things will look like before I print.  Since we have student aides who will deliver the notices, I sort the list according to their first period room number to make delivery more efficient.

2.)  1 Quick Share on Google Drive

My document camera is no where near as crisp as my personal phone.  Additionally, our school uses older PCs with Microsoft products which precludes me from using Air Drop to share student work but I have found a nice workaround (I wish I could give credit to the blogger who wrote about it, so if you know that person, let me know and I will credit them here). When I want to show student work, I do the following.  I take a picture of it with my phone.  Then click export.

Then select Google Drive (I have the app on my phone)

Then select 1 Quick Share (named as such so it shows up first here)

That folder is bookmarked on the internet showing in my classroom so that all I have to do is click and the picture is ready for viewing or for inserting into my SmartNotebook.

3.) Export SmartNotebook to .pdfs and Save to a Folder Linked on Schoology

I was not a fan of SmartBoards originally.  I believed them to be overpriced whiteboards.  Then with the advent of better software and apps such as Desmos and Geogebra, I have come around to appreciate the power of dynamic demonstrations and the ability of my students to touch the math.  Now all of my lessons are made on the Notebook software.  At the end of each period, I select Export to pdf and save the file to a Google Drive folder that I have shared with my students on Schoology (previously I would just share the link with a bit.ly or through PowerSchool).  Now when a student’s IEP calls for providing them with the notes from class or when a student is absent, I can easily direct them to the notes from class and I do not have to keep updating the link.

4.) magnetic tape

Most white boards and chalkboards are magnetic.  Having magnetic tape allows you to stick almost anything to the board for easy access.  I put this tape on the back of my hallpass and it is stuck to the blackboard near the door so I never have to even touch it. I’ve used it on clipboards, dry erase markers, the daily period start and end time schedule in a plastic sleeve.  Basically anything that you would like to have at your fingertips while near the board.

5.) Extra Copies Bin with 31 Hanging Folders

I keep a bin of 31 folders for each class.  At the end of the day, any extra copies go in the folder with the date on it.  Students who are absent need only go to the date that they were absent and get the copies they need.  When I get to that date the next month, I recycle what ever is left over.  I also link a digital copy of anything that has been copied into PowerSchool so that if we happen to run out of copies, a student can make their own copy through the link.

6.) Word Wall with Definitions

I had a conference with my administrator several years ago.  I knew that my district really wanted us to have word walls but I hated the idea of giving up prime wall real estate for just words on a wall.  Together, we came up with the idea of having the word on a flap that could be lifted with the definition hiding beneath.  Genius. Now my word wall had “meaning” and I didn’t mind giving up the real estate since there was more of a purpose to the activity.