Month: March 2013

Categories
Technology

“Wow” Moments with Wolfram|Alpha

The Siemens STEM Academy offers great resources for teachers, from lesson plans, to blog posts from teachers, to fantastic free webinars.  Full disclosure: I have written for the STEM Academy blog, and been a part of the Academy summer program…but I am but a small fish in a cool ocean of resources!

This week, the Academy hosted a free webinar featuring a demonstration of the dynamic knowledge provided by Wolfram|Alpha.  Having used Wolfram Demonstrations before in my classroom, I was looking forward to learning more about this search tool.  Crystal Fantry provided an hour-long overview of this exciting resource, and ideas for classroom uses.  It’s amazing how many “wow” moments I have these days with the new tech tools our students can have in their hands, but this one goes beyond that.  Knowing that students have access to resources like this should cause us all to think about our roles as math teachers / facilitators….this is a game-changer!

So, just what is Wolfram|Alpha?  The site is simple, just enter what you want to search for, and off you go…but this tool is so much more than that.  The “about” from their website provides some insight:

Wolfram|Alpha introduces a fundamentally new way to get knowledge and answers—not by searching the web, but by doing dynamic computations based on a vast collection of built-in data, algorithms, and methods.

So, what the heck does that mean exactly?  Let’s learn by diving in.  And while you can use Wolfram|Alpha for far more than math, this is a math blog so let’s focus in on some math….

Try this: “y=2x +3”.  Let’s start with something simple…what does Wolfram|Alpha give us?

WA1

Fun stuff.  A nice graph, the domain, and alternate form.

How about this: “3x+5=2x-9”

Also nice, a plot of the the functions.  And the equations’s solution..but what’s this…a “step-by-step solution”?  If you are logged in (free accounts) you can step through the solution:

WA2

So, what happens now when you give that worksheet of equations to solve for homework?

There are a lot of other neat computations to explore, try some of these as starters:

  • “y=(x+2)(x-3)”
  • “inverse y=x^2+3x+1”
  • “sin(x)+cos(x)=1”
  • “Integrate x^2 dx from 0 to 5”

WA3But Wolfram|Alpha goes beyond quick lists and computation.  How about “Pascal’s Triangle mod 5”. Or “triangle sides 3, 6, 8”, or try the elusive 17-gon, and see the many facts to check out.

A TOOL FOR RESEARCH AND GENERALIZATION

I have only scratached the surface of the many features, and there are also lots of nooks, crannies and links for you to explore.  I’m eager to use this tool with students as a means to research new ideas, and make some sense of their characteristics.  For example, let’s think about domain and range, as I ranted about in a previous post.  I like that Wolfram|Alpha expresses domains using set notation, and this is a great opportunity to have students research new functions.  Most of what we do in Algebra 1 deals with linear functions, so we get a lot of “all real numbers” domains.  Expose your students to non-linear functions, once they know how to make their x,y tables.  Try these:

  • y = 5 / x
  • y = rt (x-2)
  • y = 1 / (x^2 – 9 )
  • y = 2^x
  • y = x^2 – 4

And what to do with these new functions?  Let’s place them into categories, share our findings, and communicate our ideas.  Give each group 2 or 3 new functions to look at and share their findings on www.padlet.com.  This site, formerly called WallWisher, allows everyone to contribute their ideasd and move them around the canvas.  Here’s a sample of my function domain wall, click the link to contribute your own, play around the wall, and double-click in any empty space on the canvas to contribute.  Or sign up for a free account and create your own wall.

Padlet

Thanks to Kyle Schutt (@ktschutt) and the gang at Discovery Education for providing these great webinars.  Be sure to check out the Siemen’s STEM Academy blog for more great resources, blog posts, and archived webinars.

Categories
Middle School Technology

Probability Openers – Separating the Possible from the Plausible

A recent problem I reviewed from the Mathematics Assessment Project (MAP) caused me to refelct upon the coverage of probability in our classrooms.  The website provides sample tasks and assessment tools for schools and districts as they adjust curriculums to match the Common Core.  In the standards, probability begins to take center stage in grade 7:

Investigate chance processes and develop, use, and evaluate probability models.

Probability is treated like the ugly step-sister in many math courses: ignored, shoved to the side.  Look at standardized testing results, including AP Statistics, and you will find that probability standards often produce weak results.  The isolated fashion with which we treat probability is certainly not helping.  Let’s develop strategies to not only re-think probability, but to encourage communication of ideas and develop understanding.

I have taught probability at many levels: as an 8th grade teacher, as an AP Statistics teacher (and reader) and as the author of a Prob/Stat course delivered to 9th grade students.  This year, I taught my first college course in Statistics, where the problems with probability persist.  The picture below is from my college Stat 1 class, which you can also see on the great site Math Mistakes, by Mike Pershan.  Visit and provide your input:

Conditional

Here are two activities I hope you can use in your classrooms to help fight the probability battle.

“WHICH IS MORE LIKELY” OPENER:

The Core Standards provide a framework for our students base knowledge of probability:

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Before we can start diving into formulas and fractions with probability, we need students to understand, and be able to express, whether an event is likely or not likely.  For simple events, like flipping a coin or drawing a card, this can be an easy discussion, but what happens when we start talking about complex events, like flipping multiple coins, tossing 2 dice, or choosing a random car from a parking lot?  Download my Probability Opener, which asks students to assess events and compare their probabilities.  Answers are provided.  The events start off innocently enough, but soon meander into more complex tasks, where students are asked to identify the more likely outcome:

You roll the dice and move your piece in the game of Monopoly…

A:  You end up on Boardwalk

B:  You end up in Jail

This is also a great activity if you have a classroom clicker system, or for Poll Everywhere if cell phones are allowed.

SPINNER BINGO

This activity is an adaptation of a Spinner Bingo problem from the Mathematics Assessment Project site I mentioned at the top of the post.  Visit the MAP site for not only the task, but a rubric and samples of student work.

The problem presents a scenario where students are asked to assess a spinner game, and bingo cards created for the game.  Read the files given on your own, but here is a quick summary:

  • 3×3 bingo cards are filled out, using non-repeating numbers from 1-16.
  • Two spinners with 8 equal spaces numbered 1-8, are spun, and the sum computed.
  • Players mark off their bingo cards if the sum appears on their card.

This is a nice scenario, so let’s adapt it and use it as our unit opener.  Having students play a game, and develop and justify a strategy, is a great way to get started.  Here is a lesson guide I have written to help you get started.  Also, the site Unpractical Math provides a virtual spinner applet you can use.  It’s often easier to just dive in and play, so here is a brief video demo of the game and how you can play it in your classroom:

Please let me know if you use either of these activities, and would appreciate your feedback. Thanks.

Categories
Technology

Dive Into Screencasting

Looking forward to an afterschool session tomorrow on screencasting.  I have done a number of screencasts, using different (mostly free) products, for many educational purposes.  Sometimes, I use screencasts to explain class problems, so students can review procedures.  Other times, I have made screecasts to demonstrate ideas for colleagues, like Flubaroo, Google Drive and Sketchpad.  Here are some resources for both my district colleagues, and my blog friends.

PRODUCTS FOR SCREENCASTING:

Screencast-O-Matic:  Free sign-up, requires java, and can upload directly to YouTube.  15-minute screencast limit.

Jing:  Free download and sign-up.  5 minute screencast limit.  Share to twitter and Facebook.

SMART Notebook:  I’m always surprised when colleagues don’t realize a recorder comes with this software.  Create wmv files, which upload to YouTube.

doceriDoceri:  Free for the iPad.  I love sitting on my couch on a Sunday morning and crafting a lesson at the touch of a finger.  Program “stops” into your playback, and record your voice over the playback.  Uploads to YouTube.

TIPS FOR SCREENCASTS:

Making a video which will be useful to the viewer can take practice and patience.  Here are a few tips I have for somebody new to the screencasting game:

  1. Keep it short and snappy.  Think about your message, and deliver it succinctly.  I have not run across many people looking to rewind and replay my mad ramblings.  Try not to improvise or go off-message…which brings me to…
  2. Write a script, or at least an outline.  Think about the bullet points you want to cover in your screencast, jot them down, and stick to the script.
  3. Rehearse the script.  For me, this means simply going through my bullet points.  What are you going to say, in what order, using what resources?
  4. Rehearse the timings.  When I first got started making screencasts, this was something I often did not think out enough, and now obsess over.  What do you plan to show on your screen?  What pictures, website, programs or applets should be open?  Don’t wait to hit record before opening a program, which you know will choose that moment to act up.  Have everything minimized and ready to go, and do a run-through.
  5. Be prepared to start over.  I need to start making a director’s cut version of my mistakes in screencasts.  Quality matters.  Fortunately, with a screencast, you can start over and make it better.

Here are some sites and articles which are also helpful to the new screencaster:

Teacher Training Videos: a wealth of videos which walk teachers through the basics of many tech tools.  Find screen capture tools near the bottom of the page, on the left.

Educause – Why do screencasts?  Mike Ruffini promotes the benefits of creating screencasts, along with strategies for implementation and evaluation.

Turn To Your Neighbor blog – a quick-start guide to getting started with screencasting.  Includes a pdf of the quick-start guide.  Great suggestions for the new user.

TeachThought – How to Screencast Like the Khan Academy.  Has overviews of products for the advanced user (read: not-free).  More insights into the benefits of screencasts.

STEM Fizz: The Friday Institute for Educational Innovation.  Not necessarily dedicated to screencating, but good ideas for flipping the classroom and the rationale behind this practice.

When you have recorded your first video, and you start populating the YouTube channel, let’s embed those videos in blogs and webpages to share with the world.  Here is one on the plug-in for Google Drive, called Flubaroo, which has proven popular as an easy tool for educators.  I like to think I have gotten better since this video, one of my first.  And I have also learned the value of a quality microphone.