Category: High School

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High School Technology

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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Algebra High School

Talking Inverses and the Enigma Machine

Here is a challenge which has appeared on my classroom board, in various forms, over the past 10 years:

Board

Can you decode the message?  In 10 years, I have given out zero gift cards….so good luck.  More info on this challenge below.

A trip today to the Franklin Institute science museum in philadelphia reminded me some of cryptography nuggets you can use in math class; in particular, discussion starters for inverses, and code-breaking using matrices.  One of the first artifacts we encountered in the exhibit was the Enigma machine shown below, which I fawned over like a teenage girl at a One Direction concert.

Enigma

The Engima machine is a coding machine, used primarily during World War II, to both code and decode messages.  Messages were typed using a standard keyboard.  The electric signals from the keyboard passed through a system of rotors and plugs, and lit up a letter, which was recorded.  There were a number of variations of the machine over the war years, and the Allied forces employed many mathematicians, many working through Blechtley Park in London, to intrcept and de-code messages.

Consider this intercepted message:

LXFAVPBNAQMHIZJPBMMRCSWOI

How would you even start to decode this message?  Does a one-to-one correspondance seem reasonable?  How else can letters be coded?

You can try your hand with some coding using this Enigma Simulator, which shows the coding rotors, inputs and outputs.  But here’s the neat thing about the Enigma machine: the machine is used to both code AND decode messages, using similar procedures, which are outlind here.

Flowchart

So, now you have everything you need to decode my message it seems.  You have a message, and a device.  Oh, but those pesky rotors.  If they aren’t set correctly, then the machine is of little help.  Working through this issue was the task of many of the mathematicians during WWII.  And I want you to be successful!  Set those pesky rotors to R-J-L (my initials), and start typing!  You can also copy and paste the message, but it is far more fun to watch the rotors do their work as you type.

Embedded in all of this crypography history are some neat math discussions:

  • After looking at some messages and their coded outputs, is there a ONE-TO-ONE correspondance here?  For example, does the letter E in a coded message always map to the same decoded output letter?
  • Are there any patterns we can use to help decode the message? Any predictable behavior?
  • A message is coded using a rotor setting.  Then this coded message is typed, using the same rotor settings, and we get back the original message.  The Enigma machine is its own INVERSE!  How exciting is that!  How many ideas or devices do we know of which are their own inverse?

Here are some sites with additional information relating to the Engima:

Exploring the Enigma, from +Plus Magazine.  Good student reading, with guiding questions.

This Numberphile Video has a demonstrations of the gears and plugboard of the Enigma, and some explanation of combinations.

In my next post, we’ll look at Hill’s Cipher, a cryptography application of matrices, and think about my Best Buy challenge!

Categories
High School

A New Start for The Blog?

So, the name of this blog is “MathCoachBlog”.  I picked the blog name about a year-and-a-half ago, as I was working in my district’s curriculum office, and hoped to use this forum to share ideas, resources and experiences.  I treasure the opportunities I have had to share with others, the kind feedback people have given me about many of the activities, and the many friends I have made through this blog and twitter.

But here’s the thing: I’m not an academic coach anymore.  After 2 years working with some great people in my office, I have chosen to go back to the classroom.  This was purely my decision, and I am looking forward to implementing many of the ideas and resources I have been encountered in the last 2 years.  I’m thinking of it as a mid-career re-set, and in some ways I am more energized to teach classes than I ever was before.

But the blog….keep the name?  Change the name?  Keep it?  Change it?  We’ll get back to that….

This week, I had to set-up a new classroom for the first time in a long time.  I was in the same room for 13 years before, and had to pack a lot of stuff when I moved into an office.  So, time to dust off the cobwebs, think about what’s important, and do some moving-in.  Here are some elements I like to have in my classroom.  What are some neat things you like to have to create a positive classroom culture?

I like to tell a lot of stories in my class, think about anecdtoes from previous years, and keep in contact with as many former students as I can.  For AP Statistics, the “Wall of 5’s” has always been a topic of conversation, and a goal for many students who strive to eventually be “immortalized”.  It’s a nice hook the AP classes.  Thanks to my colleague Joel, who kept the wall alive the past 2 years, and has now made a duplicate wall for his classroom.

Wall of Fives

Along the same lines, I like to have lots of pictures from previous years around.  Many of these are from our annual Stats Fair, and are great conversation starters.

Stats Fair

The Wall of Badges: more chances to talk about my experiences as a Siemens STEM Fellow, an AP reader, and conference junkie.

Badges

Cool art.  Escher works always generate buzz.  Now with 100% more Legoes!

Escher

T-shirts from math contests our math club has attended provide just the right amount of geek-pride.

Shirts

And finally, the oragami art a graduate made for me is the best gift ever, and gets it own spot in the room.  Special appearance by John McClain – a “Secret Santa” gift.

Oragami

So, about the name of the blog…  Since I announced my return to the classroom, I have had lots of conversations with colleagues in my department, and know I am blessed to work with many fantastic people.  Sometimes we don’t agree on things, and that’s healthy.  And I’m thrilled to be able to implement so many of the great new things I have learned, and continue to share them out to you.  So, I’m no longer a coach in my district, but I think that, in many ways, I way wind up being a more effective coach to my friends online through the sharing of classroom ideas.  So, MATHCOACHBLOG LIVES ON!

Also, it’s sort of a pain to change the name,….so there ‘s that.