Month: September 2012

Categories
Uncategorized

Tech Tools for Math Class

Below is a post I wrote for the blog portion of the Siemen’s STEM Academy website.  The site is filled with lots of great, free, STEM resources for educators, including lesson ideas and archived webinars.  I hope you can find a use for this great information in your classroom!

DISCOVER AMAZING TECH TOOLS FOR MATH CLASS:

It’s the new school year.  You have that new projector and touch board, or maybe you have new tablets for your students.  It’s time to get interactive with your math lessons.  So, what to use to get your students to experience mathematics, and move away from worksheet math?

The National Council of Teachers of Mathematics continues to add applets useful for grades K-12 in its NCTM Illuminations resources area.  The applets run on Flash and include:

  • Algebra Tiles – build, manipulate, and evaluate algebraic models
  • Fraction Models – sliders allow you to explore multiple representations for fractions, decimals and percents.
  • Factorize – explore numeric factors and their relationship to length and width

NCTM has also added a new area of downloadable Common Core Math Tools, which require java to run.  Sample lessons and how-to pages are included to get you started.  In the iTunes store, NCTM has also provided free apps geared towards elementary grades:  Pick-a-Path,  Okta’s Rescue, and Math Concentration.

Desmos Online Calculator – a favorite of mine, a tool I have posted about before, and its care-takers continue to seek your feedback to make this graphing utility better!  It has a fast, simple interface, and you can find maximums, minimums, and points of intersection with a single click.  This tool is ideal for class presentations.  A free registration allows you to save your documents.  Runs great on the iPad!

GeoGebra – a simple tool for interactive geometry, constructions, and measurements, but can provide tables and graphs for algebra class as well.  Works as a java applet, but can also be downloaded as a stand-alone program.  The caretakers are working towards an iPad app.

Sketchpad Explorer – an old favorite, the Geometer’s Sketchpad, moves to the iPad with this free app, available through iTunes.  Students can tap, drag and play with interactive sketches which come loaded with the app, or link to your iTunes store account and upload your own creations to share.

Interactivate – from Shodor, this ever-evolving collection of Java-based courseware has something for all math classes.  Learn about estimation through a virtual model of a forest fire, search for patterns in the multiples of Pascal’s Triangle, or investigate the Mandelbrot Set.

Categories
Geometry

What is Three?

A middle-school teacher’s family emergency pulled me into the classroom last week to teach an honors Geometry class to 8th graders.  Geometry…sigh….the course I always put on my “please do not ask me teach this” list during my time as a high school teacher.  And since it is the start of the year, the class is learning basic terms and definitions, all the great stuff I dreaded as a teacher.  Oh, and I have 10 minutes to plan before the kids walk in.  Ready?  And scene…..

This is the 3rd day of school.  Students have been exposed to the class rules, some algebra review, and textbooks look clean with their grocery-store paper-bag-covered  exteriors.  This is the first real geometry lesson for these kids.  I am their first impression of geometry, and the precision and argument they will experience.  No pressure.  Today’s lesson: basic vocabulary and terms.  Let’s look at the terms we need to understand by the end of today.

  • Undefined Terms: point, line, plane
  • Ray
  • Segment
  • Collinear / Coplanar points

How nice.  I drew the short straw.  Essentials of geometry vocabulary, and I get to be the boring guy.  Not the role I was born to play.

And just what are “undefined terms” anyway?  According to the textbook, these are terms which we understand, but don’t need to define.  Seems a bit hinky to me…

So how to build some discussion, based off previous knowledge, and ease our way into a structure for geometry?  As students entered, I had the following warm-up ready as they prepared to take notes:

DEFINE THE FOLLOWING:

  • Three
  • Line
  • Odd number

After some initial snickering about my strange challenge, the students took to their definitions.  So, how do 8th grade geometry students on the first day of class define “three”.  A similar response was given by a number of students:

It’s the number between 2 and 4

Thankfully, a few students identified the flaws in this definition: that, first, there are an infinite number of “numbers” between 2 and 4, and that in order to understand this definition, you need to understand what 2 and 4 mean, which seems unreasonable if you don’t know what three means.

So, should we consider “three” to be an undefined term?  Are we OK with NOT having a formal definition of “three”?  What do we need to consider?

Do we all understand what three means?

Yes, when asked to represent 3, everyone in the class demonstrated the same understanding of its quantity.

Would we expect any alternate understandings of the term, if we asked others?

Doubtful.

Would having a definition increase our precise understanding of three?

Nah, I think we all get it.  Three is three, and that’s that.

Stooges

This discussion turned out to be a nice opener to the traditional undefined terms in geometry: point, line and plane.  And hopefully a good start as these students begin to experience the logical structure of geometry.

Tomorrow, ask your students to define “Three”.  Would like to hear what they say.

Categories
Technology

SMART Notebook for iPad

This weekend, I had my first chance to toy around with the SMART Notebook app for the iPad ($6.99).  My colleagues and I have a a nice bank of Notebook files we use, particularly in geometry courses, and I am most interested in utilizing the portability of the iPad to allows students to interact with math lessons.

IMPORTING FILES:  One of the issues I have with my iPad is how difficult it can be to work with files.  But using DropBox along with the Notebook app worked quite well.  I saved a few files I use from my desktop computer into DropBox.  Choosing one of these files in DropBox on my iPad, they were recognized, and I was given the option of opening them in Notebook.  Clean and seamless.

dropbox

The instructions file included with the app also gives you guidance on how to save and open files directly from the SMART Exchange.

WHAT TOOLS DO WE HAVE?  Once a file is opened, you have a “lite” version of the SMART Notebook software.  Available tools are pen, eraser, text tool,and  photo import.  Some of the more popular and creativity-inducing features, like screen shade and the magic pen, are not available.  No drawing tools either.  Essentially, it seems easier to prepare a document on your desktop, then move them to the iPad.

Tree

Like any iPad app, Flash animations will not run, which is a bit of a downer here.  If I am thinking about ways I would like students to interact using the iPad,the manipulatives like category sort, vortex, and pairs would be most useful.  But we can still make good use of drags and movement.

angles

Protractor

WRITING NOTES:  If you are like me, then writing on the iPad is a new experience.  For small groups, my fat fingers may be fine to communicate ideas.  But the idea of the infinite page we have come to know from Notebook does not seem to be a feature here.

Fat Fingers

Equation

In the end, this app is really SMART Notebook “lite”, with the ability to look at files you have already created, edit and share them.  I see this as a nice formative assessment tool for classroom.  Imagine a Notebook file with a number of practice problems or challenges, and passing the iPad around to have students contribute their ideas.  Connecting to a projector, a class discussion of student work could then be held, as students appraise each other’s work.  I’m excited to try this with a class and observe their response to this tool.

Here are some other reviews of the Notebook app: