NCAA Tourney Simulation 2015

Following a process similar to last year's, I used the fan picks on Yahoo Fantasy Pick 'Em as a "true proportion," assigned integers according to those percentages for each team, and then used the randInt( function on my TI-84 to generate a number.

As an example, in the 2nd round game of Butler vs Texas, I assigned the numbers 1-60 to Butler (as the higher seed), and 61-100 to Texas. The number generated was between 1 and 60, so I chose Butler.

This year's simulation had Arizona upsetting Kentucky in the Final Four and Duke taking the championship in the final.

Here's the whole simulated bracket. Click the image for a larger view.

Algebra on a Chromebook: Google Search Math Tricks

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Need a calculator?
Need a graphing calculator?
Need a unit converter?
Need to calculate a volume?
Need to calculate an area?
Need to find the measurement of the side of a shape, given one of its volume or area?

Your students (and you) can use Google Search to perform all of those tasks without ever leaving the browser window. Does it take the place of having a standard, standalone, scientific calculator? Of course not.

However, knowing these Google search math tricks help me to work more efficiently when I'm in the flow of a project. Having a browser window open is ubiquitous to the modern computer experience, so as often as possible, it makes a lot of sense to me to utilize what I've already got open and available. If I can perform the task without going to a specific online calculator or grabbing my physical calculator, it just makes sense.

So what all can I do?
1. Perform calculations the same way you might on a handheld calculator.
You can even do square roots or logs if you know the proper notation.

2. Graph equations of functions. 

Include a comma between equations to do more than one. Trace for specific values by hovering your mouse cursor over the function.

3. Calculate the volume or surface area of a 3D solid. 
Just type in volume formula of _________. Cone is shown here, but also works with cylinders, prisms, spheres, and pyramids.

4. Calculate the area of a 2D shape. 
If you only search, "area of _______," it will return the formula and give you a text field to enter your dimensions, but you can also specify a dimension in the search. In the example below, I specified a radius of 4 by including "r=___"

5. Convert units 

This is super important for project-based learning, "real-world" problems, or gathering information for 3-act math stories.

The drop-down menu that is currently on "digital storage" below also has options for temperature, length, mass, speed, volume, area, fuel consumption, and time units.

How Do You Define a "Calculator"?

As our technology shifts from being based on hardware (music player, camera, "computer," telephone, datebook, notebook) to based around software (all of those things living on your smartphone or tablet), we've also seen a shift in the tech capacity of our classrooms.

Humor me for a moment and tell me this - which of the following are "calculators?"

All images under Creative Commons license

Did I surprise you with any of those choices? There is probably some debate between #6-8, and the thought of 1 and 2 being very useful to you might be amusing, but my point is that what we call "calculator" has evolved to match the power of our technology. 

Most everyone I teach with grew up with access to a graphing calculator (even if it was a TI-81), so its quite natural to have your students use it in the same way, but there was a lot of debate in the 80s about whether or not kids should be using calculators, and then again in the 90s about kids using graphing calculators. 

To me, the next phase in this discussion is the use of physical calculators with algebra solvers or apps like PhotoMath (which I wrote about here) or HomeworkSolver (picture above as #8).

Similar to how students hover over the problem with their device's camera in PhotoMath and identical to how a student would use Wolfram Alpha, students enter the equation to be solved and what is returned to them is a step-by-step solution that gives them the value of the variable.

I found a kid using this app a couple of weeks ago while he was working on practice solving some level of inequalities. The discussion went something like this after he came to show me all of his answers.

"I'm done, Mr. Baker"
"Cool. Next time, do that all by yourself."
"What do you mean? I did do this!"
"Nah, man. I watched you over their on your phone looking at the answers."
"This is just a calculator!"
"No, calculators just do things like 9*6=54"
"You CAN do that on here." [which wasn't a lie]

I was kind of stuck. He was right. I finished with what I feel like is a cop-out answer: "Well, you can't use that in here." That's fine that I set that rule for class, and I am responsible for making sure this kid can solve an equation in Algebra 1, but it ignores the real debate.

What constitutes a "legal" calculator in your classroom? 

• Is it scientific? (Better stop giving those order of operations problems, and operations with integers, then.)
• Is it scientific with a muli-line display? (Don't assess your kids ability on fractions, then. Those have a fraction button. They also simply irrational numbers.)
• Is it a graphing calculator? (Are kids "cheating" then if they use their calculator to produce a graph on their paper "by hand?")

Let's frame it in the context of our real job - which calculator best prepares our students for the "real-world" ahead of them?

If I'm answering that question for myself, the least I get to is to allow graphing calculators at all times, and I'm still on the fence about algebraic calculators. We need to change what we ask of kids in our curriculum, because we can't erase the technology.

Simulating the NCAA Tourney with a Random Number Generator

It's "Big College Basketball Tournament" time, everybody!

(When I remember to get it in on time) sharing your bracket for the NCAA tourney is always an easy way to get conversations going with a lot of my students, which is especially good because right before Spring Break is when some of my students want to talk to me the least. :)

I did some research on building a "probabilities of the NCAA tournament" project a few years back, but it seemed kind of impossible, and not totally worth it when weighed against other curricular demands.

So, I scaled back expectations and started with having fun with it myself. Using the probabilities from the user picks on CBSSports.com's bracket manager, I simulated the outcome with a random number generator (from mathgoodies.com), and chose the victor from there.

BRIEFLY, MY PROCESS

Had this been the number generated for the game above between Oklahoma and North Dakota, OU would have been the winner because 33 is between 1 and 76.

RESULTS
To my pleasant surprise, the method produced a rather conventional bracket, while still making some fun, plausible upsets. As I'm writing, the first day's games are about half done, and the bracket is holding its own against most anyone else's.

5 Ways to Pwn Your Math Homework With Google Search

I couldn't finish my homework because I didn't have graph paper.
I couldn't finish my homework because I didn't have my graphing calculator.
I couldn't finish my homework because I didn't have my calculator.
I couldn't finish my homework because I don't know how to use my calculator.
I couldn't finish my homework because I don't know how to convert units.
I couldn't finish my homework because I didn't have any examples.

You've only got to teach math for a few weeks before you've heard every one of those excuses. No one answer is going to be good enough for the kid that goes through all of those, but you can use a simple Google search to perform many necessary tasks to "pwn" your homework and save time.

All of these tips work simply by typing in the search box on Google.com, or using the "omnibox" on browsers like Chrome and Firefox.




1. Calculate.
Typing in calculations such as -1*-3 pulls up an onscreen scientific calculator that gives you an answer and allows you to continue with my calculations.

2. Find and print graph paper.
Your teacher does it this way often, too. :)

3. Graph equations and trace for points.
No need to even go to a graphing calculator app or website. Trace along the line to find intercepts, coordinates, and other key features.

4. Convert units.
You may still need to show your work (especially if you're in a lesson on the topic), but this will at least check your work.

5. Solve systems by graphing multiple equations at once. 
Separate with a comma. Trace along the line to the intersection and approximate the coordinates.

BONUS: Find a video tutorial without going to YouTube.
Many graph or calculation searches will also bring up relevant video results that you can play from the search screen.

For more info, all of the documentation about the Google calculator and grapher can be found here.

The Next Step: Re-wrapping Within Your Instructional Context

We had our fall open house last night, and during the "hour" my Algebra 1 parents were in the room, I was sharing with them my philosophy on graphing. Basically, that wherever, whenever possible, I want kids to use technology to make their graphs so that they can do all the state-standards-type activities: analyze slopes,  make predictions, relate what's going on in an equation and/or table to the behavior of the function.

I set a rule for myself last winter. "Never graph linear equations by hand." This was an easy line to draw in the curricular sand of Algebra 2 because the kinds (theoretically) already had a strong background in graphing linear equations, understanding that the coefficient of the variable was the slope, and how to articulate that between coordinate points.

Can I just as easily draw that line in Algebra 1? Do I believe as firmly in the value of conceptual understanding over procedure, or will I make the (perhaps) easier decision, teach a step-by-step process, and pass the conceptual buck on to the next teacher? (By the way, does anyone feel like the times you most often make instructional concessions against your better judgement for a student that the kid quite frequently ends up being in your class the next year)

So there I was, about to make a grand statement to parents about how their kids were never going to make graphs by hand, and I had to stop short. I literally stopped the sentence.

"I don't know," I said. "Its been a few years since I taught Algebra 1, so there are some things I'm trying to remember..."
"But, the content is easy, right?" a parent asked off to the side.
"Well, yes, but I have to conceptualize it differently between Algebra 2 and Algebra 1."

Is it wrong for there to be a difference, or must we always view our instruction within the context of our course/students' prior knowledge/school environment? Understanding when to re-contextualize that information and tailor it to those students in that year is what I've been learning about math instruction the last year. Lots of people can pick up math content. If content knowledge were most important, wouldn't a student ideally be able to teach an Algebra 1 course after they had mastered it?

The first time you teach a new course (or return to one you haven't had for a few years), there's a temptation to expect that once you reacquaint yourself with the content, that the rest of the year will work itself out. Of course a master teacher is a content expert, but even more importantly, they are adaptable and flexible to make instructional design decisions that they're willing to abandon if the delivery is not appropriate for their students' context.

Co-Teaching for Relevance with WordSift.com and Data

Relevance seems to be a theme this week. Touche', Dr. Hopper.

Yesterday I wrote about my frustration with what I thought I was highly relevant lesson and the varying degrees that my students bought into the premise and were engaged in our graph/function activities. Since relevance is an area of focus our building principal is leading, I shared the post with him to get some feedback.

He made a great point that while I had, indeed made a great attempt at relevance, relevant to me doesn't always translate to relevance to my students. Something I'd kind of observed but had not solidified - kids don't really buy picture packages anymore, they just opt for the CD files. Truthfully, I should have been alerted to problems when I had to explain how buying photos works... LOL.

Today in my Algebra II class, I revisited a tool that I piloted first last Thursday to try and steer my Applied class's inevitable preoccupation with Valentine's Day into math activites.

The Tool

Wordsift.com from Stanford University is no ordinary word cloud generator. Beyond the basics, WordSift allows you to highlight tags by subject relevance, and creates a concept map of related topics to generate ideas for further research. Here's a video demo from a science class for more in-depth info.

Obviously, my Applied class loves math!	A concept map about sleeping
This was right after lunch. :)

The Catch

If this were, say, a creative writing class, we could have then found interesting ways to express our feelings about love or food, or had it been history we may have looked at food in a given period or place. But this is MATH CLASS, where cool ideas and easy ideas rarely intersect. :) How do I incorporate co-teaching and relevance into analyzing polynomial functions?! My book has several problems like this:

Sure, they're "real-world," but you're not getting any extra points with your students for engaging them with topics they're waiting to sink their teeth into.

Using Data

 My go-to relevance kicker in math class is to go to the data, so I sent my little darlings on a data hunt to make line graphs on a topic of their choosing.  Here's where things are going to get "ugly:" even after your students get to make a choice about their topic, they're going to have to evaluate that choice for usefulness. Whenever they asked me if the set they'd found would work, most of the time all I had to ask was, "If that's your set, what are the IV and DV?" When they realized they couldn't (usually because they were dealing with a qualitative variable), they knew to move on. Here are the rest of my instructions for the assignment.

The Key

It came as no surprise, but when I tried this the first time with Applied and "love," even after we were a little more specific and looked for things like marriage, divorce, or # of teddy bears sold over a period of years, without prior planning, the kids were kind of sinking in the entirety of the internet. The fixated on answers from Answers.com that were less than reliable. To find more success and ensure more viability of datasets, here are some good places to get started:

Data Sources

• Misc., random topics (but a GOOD variety)
• Carnegie Mellon Data and Story Library
• People in different countries over time
• Gapminder.org
• People, Weather, Defense, Business in the US
• Business and Finance in the US
• Sports records over time
• TI Data Sets for uploading with TI Connect 
• (Most Statistics textbook websites will have accompanying dataset files. These happen to come from WH Freeman, The Practice of Statistics, 4e)
• Generate your own with the TI CBL or CBR
• How-to's here and here

Extra guidance: Gapminder is most extensive (and has some amazing visualizations. Bonus video showcasing those here). The Census Bureau has an amazingly sortable index on business and industry time series and trend charts. I'd lean toward going here for the most user-friendly (although perhaps less customized to student interest) experience.

Census Bureau's Index

Adaptations for YOUR class:

Using data sets to enhance the relevance of your students' problem sets and studies is not something I think you're going to be able to do every day. Some days, you're going to have to provide direct instruction building up to your relevance piece, or more focus practice building on their work from a previous project or activity. What's important to remember is that the extra choices, evaluations, and connections that your students have to make when it does come time to incorporate datasets is going to pay off in the end as you build your automatrons into independent learners and thinkers.

iOS Ed-ssentials: "The Only Math [Apps] You'll Ever Need"

I picked up this book at a garage sale a couple of years ago. 

The Only Math Book You'll Ever Need: Practical, Step-by-Step Solutions to Everyday Math Problems.

Sounds promising, right? In fact, I think I'm going to use at least one section in here about mean and median next week in my Applied Math classes as a Think Aloud activity (my previous Think Aloud experience here) The real problem with this book as "the only math book you'll ever need," is that many of the sections in the book are all over simple numeracy skills or operations that anyone with a pretty basic mobile phone can have done for them. Here's a quick summary of topics in the book that my basic, feature phone can do:

• Tipping
• Unit Conversion (measurements)
• Unit Conversion (time)
• Percentages

[These aren't even covered in the book, but I just found out my LG Cosmos Touch can also give me trig and inverse trig ratios, factorials, permutations, combinations, nth roots, logs, and natural logs]

Needless to say, any of the sections that are heavy on computation tips and low on concepts are easily, and wisely replaced by modern technology.

Without further ado, here's my [short] list of "The Only Math Apps You'll Ever Need". If you're looking for yourself, your child, or your MS and HS students, I would start here.

MyScript Calculator, by Vision Objects : I found this one just last week, actually, and there was a tiny bit of a learning curve getting the app to recognize my numerals, but it took out a step for me between writing my work and entering into the calculator. It also tries to guess what you're calculating, and automatically computes what the operations are equal to (saving you keystrokes)

Free Graphing Calculator, by William Jockusch: This app is good as a graphing utility; I like the colors, I can zoom and manipulate the axes with ease, but I really like this app because it has a built-in reference library for basic formulas and mathematical definitions, axioms, and laws. A digital formula sheet, if you will.

Graph, by VVImaging, Inc: All the statistical graphs and data analysis you can't do with Free Graphing Calculator is covered here.

I made the choice NOT to put a regular scientific calculator on this list because I feel like its important for students to continue to carry those in their bags for assessments. Going on the assumption that your students will have traditional calcs with them, then, you don't need them on your devices.

Next in the series, I'll reveal my essential note-taking apps.

Do you agree, or disagree? Could you keep your list to three, or are there other essential math apps for you?

New Semester Resolution #1: Innovate Like Its 1992 (or, Do Your Students Still Make Graphs By Hand?)

1. Raise your hand if your students love making graphs by hand.
2. Keep your hand up if all of your students are proficient at producing graphs of equations (especially anything past linear functions)

Still have your hand up? Okay... Maybe this post isn't for you. Just kidding - universal appeal here. Several years ago I picked up the 1992 NCTM Yearbook at a massive used book sale held yearly in St. Louis. Every archived article in this yearbook was concentrated on using the power of calculator technology to enhance students' understanding of numbers, operations, and functions, and moving instruction beyond simply replicating graphs. Yearly we have conversations in my Algebra 2 PLC over how we're going to get our kids graphing quadratics and describing transformations of the accompanying graphs and equations.

As you may have also experienced, students often get caught up in making the graphs and sometimes never even make it to the transformations (which puts a wrench in the cogs of your lesson). Do your state standards say anything about students constructing graphs by hand from tables? Do the CCSS imply any graphing by hand? (In fact, Mathematical Practice Standard #5, Use appropriate tools strategically specifically expects that students will use technology for their graphing.)

Graphing by hand - right up there with top hats, saloons, and spitoons.

Being able to sketch a graph after using a graphing calculator or spreadsheet program is different work than what my students usually do with functions. Using technology to grab a graph and then use it in modeling doesn't eliminate necessity of my students' knowledge of the graphing, and it probably demands more.

When my students graph by hand, I usually...

• Pick "easy" equations that have as many integers as possible in the features
• Use "small" numbers
• Don't require students to manipulate the scales on their axes.
• May or may not know who actually has an understanding of "rate of change" on that function they just graphed beyond the fact that they used "rise-over-run"

When we use technology to generate graphs, students must...

• Trace graphs to find features (intercepts, zeros, maxima, minima)
• Have an awareness of the domain and range the want for their function ("I didn't get anything on my graph when a put in the equation")
• Know the scale of their axes in order to judge reasonableness of their graph to the situation they are attempting to model (A strangely high/low y-intercept of a linear function over time when students input "1999" instead of years after *)

So why do we still so often require that students are able to construct graphs by hand? Is it a filter for straining the "good" students from the "poor"? Is it "good to know?" I don't know that many people could legitimately give me a case for the necessity of a student being able to make a graph by hand without any assistance from a calculator, software, or web-based utility, like the Desmos calculator (of which I recently blogged about if you didn't catch it.).

More than TWENTY YEARS later... we're still having this discussion. In fact, one of my favorite Google+/Twitter follows, +David Wees also blogged about it earlier this year and made some valid points in favor and opposition. Is one barrier to education reform/relevance that we're holding onto too many they-should-know-this-because-we-did skills in our curricula? Will this be the year you finally give in to technology's relentless march? :)

It will take some editing of my assessments, but I am going to allow (and encourage) my students to use technology to graph EVERY instance it arises this coming semester.

Are you ready for 1992? I encourage you to join me in this challenge!

The (Math Teacher's) Student Holiday Gift Guide

If I had my druthers, here's what I'd love for all of my Algebra 2 students to have under the tree on December 25th, (or some other time this holiday season) separated into categories:

STOCKING STUFFERS (Aunts, Uncles, Cousins, Friends)

• Highlighters
• Great for placing emphasis on steps, color coding elements of formulas, or triggering reminders of side-notes the student took during class
• Grid paper notebooks
• I had my students purchase grid paper composition books (or notebooks) this year, and it changed my teaching to be able to have them sketch (appropriately neat) graphs in their notes without having to have coordinate grid squares handy every day. Also, the students didn't have to tape/staple said squares into their "regular" notebook. Graphs, equations, and charts are all right next to each other, all in context.
• Personalized pencils
• My mom bought me 2 pencils when I went off to college that had "Charles" written on the side of them, and I cherished them so much I couldn't bear to sharpen one until this past summer. They sat in my desk waiting for that right moment for about 10 years. So.... having a lot of personalized pencils would have softened the blow of using them the first time. As far as my students, I've kept track of the pencils alright, and my students need some help in that department.
• Zebra mechanical pencils
• These metal pencils have a feel similar to using a pen, and for reasons similar to the pencils listed above, your student will probably keep track of this longer (and feel more important). I hunted a Zebra ballpoint down for a week once in high school.
• Erasers (Magic Rub)
• Mathematics and problem solving can be messy work - I always feel more ready to make mistakes and try a ton of different approaches when I'm working in pencil with a great eraser, than with ink. Finality is fantastic, but kids need to be okay with starting over sometimes.

---

UNDER THE TREE (Brother, Sister, Close Friends, Mom, Dad, Grandparents)

Books

If the only place my students ever read about math is in their textbook, they're always going to think no one really does anything with math.

• Freakonmics: A Rogue Economist Explores the Hidden Side of Everything (Levitt and Dubner) 
• Superfreakonomics: Global Cooling, Patriotic Prostitutes, and Why Suicide Bombers Should Buy Life Insurance (Levitt and Dubner)
• The Number Devil: A Mathematical Adventure (Hans Magnus Enzenberger)
• Euclid's Window: The Study of Geometry from Parallel Lines to Hyperspace (Leonard Mlodinow)
• Cartoon Guide to...
• Calculus (Gonick)
• Statistics (Gonick and Smith)
• The Manga Guide to...
• Calculus (Kojima and Togami)
• Linear Algebra (Takahashi)
• Statistics (Takahashi)
• How to Lie with Statistics (Darrell Huff)
• Math Doesn't Suck: How to Survive in Middle School Math Without Losing Your Mind or Breaking a Nail (Danica McKellar)
• Kiss My Math: Showing Pre-Algebra Who's Boss (Danica McKellar)
• Hot X: Algebra Exposed (Danica McKellar)
• Any sodoku

Electronics

• TI - 36X Pro ($18.97) or Casio FX-300ESPLUS ($12.99)
• These beefy scientific calculators are closer to what scientific calculators in 2012 should be. Can do most statistics, trigonometry, and functions work a graphing calculator can besides the graphing, yet comes in under $20, probably less than you might spend on some of those books.
• Casio Prizm FX-CG10 Color Graphing Calculator ($108.35)
• I've said before, I'd rather students not have to carry a dedicated calculator, but I beg of you, save $40 and buy the top of the line Casio graphing calculator instead of the Texas Instruments. This Prizm has the same functionality as the TI NSpire CX, at a fraction of the cost. 
• I would buy my own children a Casio for literacy reasons, as well. Most math teachers are still largely unfamiliar with how the menus on Casios function and are organized, so a student with a Casio has to be skilled at reading and following manuals. I've seen some kids sink because of this, but it wasn't because they couldn't, but because they wouldn't. I like knowing I'm nurturing young technical readers.
• Livescribe Echo Smartpen ($75.99)
• Not just a pen, the Livescribe will record audio, and track pen movements when used with the dedicated notebooks (yes, I know, another investment). 
• Livescribe pencasts are the selling point for me. You could use anything to record audio, but the pencasts can be replayed on a phone, tablet, laptop, or PC and students have their very own Khan Academy-style videos.
• Apple iPad Mini ($458) or Amazon Kindle Fire ($199)
• Everyone knows that tablets put learning in the palm of your hands. I may not be reading books all the time, but I'm definitely reading more content (blogs, professional websites) since my school district gave me an iPad last September, and students are going to need them in college, anyway.
• Moleskine Evernote Smart Notebook ($24.95)
• Evernote is fantastic for curate material and easily search text and notes later on, but not everyone wants to take notes on a tablet or laptop all the time. This notebook has special paper and tagging stickers that, when paired with a tablet or smartphone, allow you to upload those handwritten notes into your Evernote account and search/catalog however you please. 

Value Above Replacement: Sabermetrics for EdTech

Have you seen the movie, read the book, or heard of Moneyball? Here's a quick primer if not - be sure to keep reading after the excitement of this trailer. :)

Billy Beane, real-life general manager of baseball's Oakland Athletics, was faced with a challenge I'm sure you recognize: get a ton of performance with what never seems like enough money. Knowing he was never going to get ahead (or feel satisfied) trying to make conventional, "sexy" decisions, Beane recruited a statistician to go behind what his scouts' eyes were seeing, and make his personnel decisions based on parameters, or metrics, that were going to provide the most improvement for the best price. Generally, this outlook in baseball is referred to as sabermetrics, and is first attributed to Bill James.

the specialized analysis of baseball through objective evidence, especially baseball statistics that measure in-game activity.

I very simply substitute "technology" for "baseball" and "learning" for "in-game activity" in the above definition from wikipedia and I have definition for the principles we should be following when we choose technology tools for purchase on any level, and when we plan our everyday lessons.

the specialized analysis of TECHNOLOGY through objective evidence, especially TECHNOLOGY STATISTICS that measure LEARNING.

I'll be the first to argue in favor of spending as much money as possible on district technology budgets, but only if an actionable research plan has been followed first. Bad money spent just takes away from sports, theatre, music, teacher salaries, etc.

My favorite sabermetrics stat is WAR - Wins Above Replacement. (Here's how Baseball Reference calculates) Basically, WAR aims to compare any baseball player on a team against what an "average" player at the position would do. How can we apply that to education technology? I don't have numbers for it yet, but using my new sabermetrics definition for technology, (and some intuition and reflection), I can compare any piece of technology against the "average" instructional tool or method.

Wet-erase overhead vs. SMARTboard

iPads vs. laptops vs. computer labs

Graphing calculators vs. Graphing software

Graphing calculators vs. graphing by hand

student clickers vs. paper response cards

students on whiteboard apps vs. small, physical whiteboards

The observations would be simple, the CHANGE or DECISIONS would be more difficult. If the technology method as you're applying has insignificant statistical difference between traditional methods, then you have 2 options:

1. Transform the way you use the tool, get new data, compare again
2. Pass on that tool and continue using the "old" method

Its usually fairly easy to justify purchase or use of technology, even if students are more successful. Our culture ingrains within us such a reverence of new technology that often the first impulse is not to question the technology, but rather, search for other factors. The students? The teacher? Hour of the day? Grade-level?

Could you commit to making anti-technology decisions in favor of future, more capable tools or un-flashy, proven methods? What's the VAR of that technology in your classroom?

Desmos Updates Web-Based Calculator: Ready to Ditch Your Old TI?

Desmos, Inc, creators of a great online graphing calculator just updated the interface and functionality of their web-app, but is it enough render other apps or traditional calculators obsolete?

There are advantages to your students utilizing web-based, iOS/Android, or physical TI (or Casio) graphing calculators, so if you've got the resources, use them all!

Software, hardware, and mobile apps all have their place in 2012 maths education.

Appropriate Uses:

Desmos (and other) online graphing calculators

You live on the web, you work on the web, you publish on the web. Why are we still forcing our students to make and analyze function and statistical graphs on a separate piece of hardware and (at best) uploading them to PCs via USB? 

Especially with Algebra 1 or Geometry students, I feel like there is a ton of instructional time spent just teaching navigation through menus and screen on traditional calculators. The beauty of the Desmos interface is that almost every utility your Algebra students might use is all together. Equation editor, tracing, and graph view doesn't require any extra keystrokes. Instructing use of the Desmos Calculator is usually limited to answering "How do I add a new equation," and "What do you press for the exponent?" and the students quickly figure out the rest as they play.

Editing equations on this web-based graphing calculator also seems like training wheels for other math software like Mathmatica, Wolfram Alpha, or Geogebra

The real power of Desmos, is how they've built sharing right into the app. 

With a button that looks VERY similar to the Google Docs share button, you've given a hypertext link, mail link, embed code, and image download. Very flexible!

You could:

• use the sharing feature to upload your own graphs onto your class website
• post to your class social media pages
• embed into assignments/quizzes/exams

Your students could:

• Share on wikis
• Share on discussion/message boards
• email you
• email each other
• Post on their social media accounts

Mobile Apps or Software Based Calculators

I haven't really found one that has anymore functionality than the free Desmos calculator, but these are handy to have on my iPads or the math computer lab for when the network is down. The practice of typing mathematical equations is also important for success on our Missouri Algebra I EOC. It'd be a shame for our students to score poorly because of the technology instead of a lack of knowledge. 

Students are also always willing to download a free version to their mobile devices. Searching in your app store will get you one of several free or cheap options. The favorite for my class iPads is (you'll never believe it) "Free Graphing Calculator". My preferred software for high schools is the open source GeoGebra platform. It is very similar to Geometer Sketchpad, which is written into many textbook's curriculum, and (like Sketchpad) also has an archive of lessons and resources.

Traditional graphing calculators (TI-83/84/NSpire or Casio Fx or Prism)

Students taking standardized tests still have no other options for their graphing/statistical needs than the golden standard dedicated graphing calculator. It seems obsolete and an inefficient use of resources to me, but its also irresponsible to neglect training on operation (and encouraging/requiring students to use them). If your math students are spending all of their time sketching simple graphs on their ACT, SAT, or AP (or your Praxis II) scratch paper, they will run out of time to do the analysis that is truly required on the assessments. Until the testing companies find a way to block students' use of other apps during testing, laptops, tablets, and smartphones will continue to be banned from the testing environment.

Besides testing, endurance also lies on the side of TI. Although it seems crazy to me that they still sell TI-83s for 80-90 dollars, that's actually great for your attempts to integrate the technology into your classroom. The keystrokes for most basic functions on TI or Casio hardware haven't changed since at least 2000, so you can reasonably use class sets your school has previously purchased within the past 12 years. Can you imagine getting a reasonably similar experience for your students between a 2000 iBook and a 2009 MacBook (The year before TI-Nspire was introduced). We have almost 40 old TIs we still use in a bind.

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What's your preference for your students' graphing needs? Given limited instructional time, which approach would you prioritize?

Guns Don't Kill, People Do (or... How It Should NEVER Be About the Device)

"Interesting how students really are involved when you throw a device in their hands."

I hear, read, or see something similar often from policy makers, parents, or teachers, or admin. Don't let them know, but I disagree. Not that technology and mobile devices aren't an iceberg of opportunity to enhance instruction, increase efficiency, and expand spheres of influence, but that the devices themselves bring it.

I feel like the entirety of my Master's program of study was an emphasis on that point. Computers don't help kids learn, teachers using software with clear directions, goals, and feedback do. Calculators don't help kids do math, teachers refining analytical minds do. Tablets, smartphones, clickers, and iPods don't inherently engage students in the lesson, a teacher that invites them to the learning and delivers content on the devices does.

If you're using (or investing) in classroom tech only b/c, "Kids get more engaged with a device" you're headed down an expensive road. Teenagers have short memories and fickle tastes - they'll be bored with the device itself before you're even done with the final stage of your implementation plan.

Devices come here, but YOU don't.

Think about it this way - think of the greatest lesson you've ever delivered. Think about the non-tech materials you used in the instructional plan. Was there a reading out of a book? Did students write together? When you were reflecting on how amazingly well that lesson went, and how much your students learned, did you praise the pencil? 

"I got some Ticonderogas from Target for my class, and man... those kids were so involved with their writing today."

Of course, not! High-yield instructional strategies will always be founded upon what the students are doing with the tools, not the mere existence of them.

New devices DO get kids' attention, and there is always a new level of excitement when we have some new tech toys out in class, but its all pointless if all your students got out of the day was, "We played on the iPads." The same way you can sit in front of the TV, or browse your Twitter/Facebook feed for hours "being productive," I often see a numbing effect on my students of "on-task" behavior being whittled down to not talking to anyone else or distracting others.

iPads, clickers, Smartboards, wireless tablets, and video equipment is exciting to have in the classroom, and I'm so blessed and thankful that I get to play with them so often and experiment, but the danger for me always in instructional planning is focusing too much on the tech and not enough on learning outcomes. I must take a moment to reflect on my lesson and analyze what my students need the tech for in that lesson, and what they'll be learning as a result (and communicating that expectation to the students as well.)

Agree, or disagree? What have you seen with your kids/students?

Tip Tuesday: How Do My Students Deal With Photos?

My AP Statistics kids just turned in a project Friday that required them to screen capture some plots from their graphing calculator and embed them into the narrative of their paper. There's a couple ways to accomplish that:

TI-84, USB Cable, and TI Connect Software

TI-83, Camera Phone

The method using the TI Connect software is probably PREFERRED, and it makes for a more polished product, but in my school, and probably for most schools and many students, the graph and take a picture method below is more realistic.

I had a project come in late today because he hadn't had the pictures from his calculator on Friday. When asked him why he hadn't just emailed them to himself, he said,

"Well, I don't have a smartphone, so I don't have a way of getting them off of my phone."

Sound familiar? As long as I have been giving projects requiring students make videos or take pictures, I've heard the can't-get-them-off-my-phone excuse. It's valid-ish. Not everyone has a smartphone (nor should everyone). I don't, either. That's my touchscreen messaging phone I bought on Amazon for $.01 in the photo above. What this student didn't know, and I guess is lost knowledge when most people just have their personal email attached to their mobile device, is that you can email any account with a text message. It works just like sending a text message, except you enter an email address instead of the recipients' mobile numbers.

STEPS:

1.  Take the photo.
2.  Begin a new message.
3.  Enter your own (or someone else's email address in the "to:" field

emailaddress@domain.com

4.  Attach your photos (usually this says attach in the message menus) 
5.  Attach as many photos as you need! The next thing this student did to shock me today was he ended up sending like 6 different emails to himself, one for each pic.

I attached 3 pix to this message.

6.  Wait a few moments, open your email on a computer, and save/print the image files.

Classroom Use:

This was relevant to me most recently with these calculator screen captures, but I could see it being relevant for assignments on field trips, scavenger hunts around the school, photos accompanying reflective pieces in a lit/comp course, evidence for student learning portfolios, or relevant notes for interactive notebooks (to be glued into a physical notebook OR a physical artifact uploaded to a digital notebook).

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Extra bonus: 

There are several web-based photo editors for cleaning up the images once they come from the camera phones. Here are some I've used:

• PicMonkey (used on this blog and heybethbaker.wordpress.com)
• Pixlr (express or advanced) (used often for my master's portfolio, also a Chrome and Firefox extension)
• Aviary (Also a Chrome and Firefox extension)
• Inside Google+ photo viewer (from the makers of Picnik)

Browser-based Interactive Whiteboard Software - Desmos

Have you ever...

• Panicked because your interactive whiteboard's software stopped working?
• Wished you could edit your whiteboard lessons from home without installing more software?
• Wished you could share/email your whiteboard lesson to a parent or student with the same interactivity they would have with your file in class? (NOT a pdf, .doc, or ppt)
• Wanted to embed your lesson content on your class blog or website?
• Wanted an easy to use graphing calculator online?

Web start-up Desmos recently presented at TechCrunch Disrupt with a browser-based solution to interactive whiteboard software that is not dependent on any branded hardware OR software.  Our district uses SMART Notebook and can port those lessons at express.smarttech.com, which I've used this summer on the laptop I'm projecting from that doesn't have the software installed.  It's better than nothing, but its functionality is scaled down dramatically to basically opening files, inserting text, and drawing freehand.  You can't even insert images.

The software is still in alpha testing (as of the end of May), but I've applied for an account and hopefully will be able to play before the new school year starts.

Oh, BTW, I haven't even gotten to the graphing calculator that IS already live! (Which may end up being an even bigger deal; color-coded, cartesian and polar coordinates, zooming, sharing, integration with the whiteboard app)

Here's some video:
Graphing calculator -


Desmos founder, Eli Luberoff, at TechCrunch Disrupt -


You can read the original article from TechCrunch here.

Things you might also be interested in:
Other online graphing calculators:
graph.tk - HTML 5 grapher.  Color-coding, zooming, screenshots
Graph Drawer  - color-coding, point and function plotting, save as .png, not as user-friendly

Other whiteboard tools:
express.smarttech.com - Create basic SMART Notebook files and open any previously saved
www.dabbleboard.com - Doodle freehand and make shapes, insert images, sharing