Year: 2013

Categories
Technology

T^3 Conference – My First Look at the iPad App

The 25th annual Texas Instruments Annual conference started today, and after an inspirational opening by Leland Melvin, I was eager to get to my first session on the new Nspire iPad app.  I think I am currently in my “stubborn” stage…refusing to pay to buy this until I understand its worth.  So, for now, I will sit back, try to learn, and gauge the reaction of the room.  The app is currently “on sale” at a price of $4.99, which is $25 off the regular price.  Whether the regular price is way to high, or the sale price is too low….I’m not sure yet.

The icon for various page types (calculator, graphs, geometry, etc) will be familiar to those who have used the Nspire computer software.  Also, a short introduction / tutorial is provided, but what fun is that?  Today’s presenter was Andy Kemp, who led us on an hour-long tour of the features of the new app.

A math keyboard is provided, and seems to be designed to have a different look and feel than the standard iPad keyboard.  Templates for things like fractions, matrices and derivatives seem to be intuitive.  Also, some buttons can be held and pressed to give extra functions.  Holding down the cos key will give a menu for sec, and their inverses.

Ipad app

“The ability to move the graph around with your fingers and manipulate it is what is fundamentally different”.  The function rule will change as the graph changes.  This is nothing much different than the handheld, but the transformations are much smoother with the ability to drag with fingers, rather than using the closed hand tool.   A variable button allows us to recall previous functions, and use them to create new functions.

I do appreciate and like how the sliders work on this app.  The slider box can moved and resized much more easily, and the settings can be changed by holding down on the slider box.  Also, the animation feature is much more obvious and easier to implement.

Here’s what I don’t quite understand.  To find roots of a function, TI still wants me to identify a lower and upper bound, after which it will then search for roots. This, to me, is not as convenient as the Desmos calculator, where landmark points are identified easily, and can be turned off if I like.  Not sure I understand TI’s obsession with requiring boundary selections.

My first impression is that I would use this more than the teacher software, which to me is often clunky and slow.  I like that I can create files which can feature graphs, data, and functions.  And TI continues to update its arsenal of activities and files.  So, eventually, I will probably relent and purchase the app for my ipad.

Categories
Algebra Middle School

Follow-Up on Math Term Expungement

In a comment from my recent post “3 Phrases From Math Class we Need to Expunge“, Tina from the blog Productive Struggle shared a Google Doc she has been assembling of terms and “tricks” we all could evaluate in our math courses.

Tina is requesting 3 categories of entries:

What tricks do you hate when students shout out?
What words do your students use without understanding?
What notation do you wish students started using earlier?

Here is the link to the document: Tina’s Google Doc

My favorite so far is Tina’s idea to introduce subscript notation for sequences and series earlier in math courses.  It always surprised me how much trouble that was for my 9th graders….silly almost.

Categories
Algebra Middle School

3 Phrases from Math Class we Need to Expunge.

A brief twitter exchange last night between myself and the great NY math educator Mike Pershan caused me to get off my rear to assemble a post which I had kicking around my head for some time now, a list of terms and shortcuts we use in math class which, while well-intentioned and used everyday by many math teachers, aren’t necessaily helpful in causing kids to understand their underlying math concepts.

Twitter

In a recent in-service with middle-school math teachers, I used a video by Phil Daro (one of the authors of the Common Core math standards) to have colleagues reflect upon the practice of “answer getting”, short-term strategies employed by teachers to get students through their immediate math assessment, but with little long-term value in math understanding.  Click on the “Against Answer-Getting” tab for the video.

So, here is my first list of nominees for elimination, and some strategies for helping students develop underlying algebraic ideas.  It probably won’t be my only list, and I welcome your candidates and thoughts.

SAME-CHANGE-CHANGE (aka KEEP-CHANGE-CHANGE):

This is a device I often see in pre-algebra classrooms, often times as a poster for easy reference, other times as a mantra for the students to help complete worksheet problems.  From the site Algebra-Class.com:

TIP: For subtracting integers only, remember the phrase

“Keep – change – change“
So, we have a short and snappy device which helps us with just one specific type of integer problem.  It’s not wrong, just too specific, and do students understand why it works?
What to do instead:
Let students develop their own summaries of integer problems, and create their own posters which describe their findings.  Use integer zero-pair chips or online applets, like from the National Library of Virtual Manipulatives (search for “chips”).  Number line applets can also help students visualize addition and sibtraction problems.  Have students write stories about given integer and subtraction problems, and have students peer-assess work for proper use of math terms.  Eventually, have students debate the possible equivalence of integer pairs:
  • 5 – (-2) and 5 + 2
  • a + (-b) and a – b
  • a – b and b – a

FOIL

The ad-laden math site Coolmath gives its own snazzy description of foil:

We’ve got a cool little trick called “FOIL” for multiplying binomials….it’s really just an easy way to do the distributive property twice, which would be really messy and confusing to do.

YEY!  You mean I can multiply stuff without that nasty and scary distributive property, without actually talking about the distributive property!  Yey shortcuts!  I’m in! {insert sad face}

Folks, ditch FOIL, and use the opportunity to talk about the double-distributive property.  Re-write the binomials as an equivalent expression and multiply.  Set the stage for factoring and note how much more understanding factoring by parts takes on.  And, now we can tackle those “messy” trinomials too.

CANCEL (LIKE) TERMS

Try this exercise tomorrow: take a class tht has been through Algebra 1, and as an opener tomorrow ask them to explain what the phrase “Cancel Like Terms” means when dealing with a rational expression.  Or, if that is a bit too scary, simply ask your students what it means to recude a fraction.  This is a nice activity to do as a Google form, and have students assess the explanations.  Many students will give an example as a definition, which is not what we are looking for here.  How many students discuss factors, GCF’s, numerators or denominators?

Reducing a rational expression means to divide both the numerator and the denominator by the greatest common factor of both numerator and denominator.  (Incidentally, also try having your students provide steps for finding a GCF.  This one also reveals what your students understand.)  The great part about this procedure for reducing is that it works equally well for each of the following expressions:

To many of our students, cancel is digested as “cross-out stuff”.  We have better vocabulary for it, so let’s encourage its use.