Tag Archives: wolfram

Use Appropriate Tools Strategically

This semester, my Algebra 2 students will be exposed to a wealth of math tech tools.  Graphing calculators will be a big part of what happens in my classroom; not only because they are great tools for discovery, but also because I feel some responsibility to have students understand the appropriate use of these tools as they head towards AP classes.  Forcing a tool upon students because it will help them on a test is weak, I know…I cry myself to sleep sometimes…though I do rely on the technology to craft discovery moments in my class.

But I also want my students to experience other tools, like the Desmos calculator (which we will use later for the world-famous Conic Sections project), Geogebra and Wolfram|Alpha (reviewed earlier here on the blog).  So, how do I get my students to experience all of these tools, and start to make measured decisions about how and when to use them?  Hey, we have a Standard for Mathemaical Practice for that!

CCSS.Math.Practice.MP5 Use appropriate tools strategically.

Lost in the great stuff on precision, modeling and reasoning is this awesome nugget, with a specific focus on tech tools:

Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

Nice!  Exactly what I am looking for!  So, how do you do that?  How do you get students to start comparing and assessing tools?

Here is the day 1 assignment I gave to my students in Algebra 2, as posted on Edmodo:

Write a product review for the Desmos online calculator. Consider its pros and cons, and whether you feel this is a site you would recommend to others. One side of a piece of paper MAX. Screen shots allowed and encoraged. Can be turned in via hard copy, or electronically.

Thats it.  Go ahead, kick the tires, and tell me what you find.  I didn’t make students aware of my on-going man-crush with Desmos or that I had done a webinar for them.  I had no idea what I was going to get back.  And since I stress written communication in my classes (moreso, I suppose, than many math teachers), this gave me a first writing sample to analyze.

The results were largely encouraging.  While many students focused solely on the graphing of functions, some students demonstrated evidence of digging deeper, looking for characteristics which make Desmos unique.  Some snippets:

Unlike the normal graphing calculator, it graphs your equation as you are typing it and allows you to delete parts of the equation if your graph isn’t what you wanted it to be. Desmos also provides the general equations for many different lines, parabolas, and other more advanced graphs.

The example graph list on the left side of the screen acts as a jump start and learning tool to give confused students a boost in the right direction.

It is quick, simple, and efficient to use and is recommended to all users that seek a tool for graphing. The designs are not distracting but sleek and a simple white to emphasize the purpose of the tool, for math and nothing else.

The Desmos is different, its not complicated at all, it can do so many things that most calculators can’t, and it’s free. The fact that Desmos is free is really what makes it so much better than all of the other because you don’t have to shell $120 out of your pocket for a calculator that has all the same capabilities that Desmos has.

But not all is sunny, as some students noted some “Cons”:

With the internet calculator, there is the obvious issue of no internet, no calculator. Also, I found some buttons were tough to get to such as the “pi” key which required me to press several buttons in order to get that one.

One last thing about the calculator is the fact that it can be downloaded as an app, but only on apple products. For android users, like myself, you would have to use the calculator through the internet which isn’t as easy to use as through an app.  Also, the app is accessible without wireless internet connection, but android users need the wireless connection to use the Desmos calculator.

All told, a good first writing assignment for my students, followed by some discussions of tools and their appropriate use.  As we travel through Algebra 2, many chances to compare tools, and discuss the best tool for the job.  Looking forward to doing another product review, using Wolfram|Alpha.  Stay tuned.

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“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.