31 December 2014

Are You "Gifted"? - Try This Intelligence Test

Are you ready? 

This intelligence test measures your creativity and ability to think of multiple solutions. Play the timer below for 2 minutes, following the directions in the Google Form below. (reset the timer after each box.)


What's the Point of This?

I started reading Malcom Gladwell's Outliers this week. The basic thesis of this book is that "outliers," particularly successful or extraordinary people like Bill Gates or Andrew Carnegie are not solely the product of hard work, genius, or  go-get-ivesness, but a combination of brilliance, opportunity, and/or luck.

In one chapter he uses the case of psychologist Lewis Terman's longitudinal study of geniuses, "Genetic Studies of Genius". Terman's "termites," as he called them were children selected from prestigious families and schools for the highest of high of IQ scores. His hypothesis was that when these children grew up and impacted their professions, you would find multiple Nobel laureates, Pulitzer Prize winners, and influential civil servants.

More than 40 years into the study, his hypothesis was critiqued as resoundingly false. One contributing factor to success beyond our popular notion of "high IQ" is creativity. Successful individuals are not only "smart," but they are often creative problem solvers and abstract thinkers.

Gladwell introduces an "alternative intelligence test," that measures divergent intelligence (ability to think creatively in many directions vs. traditional IQ assessments that measure convergent intelligence, the ability to eliminate other options to a "right" answer). One of the more popular tests is Guilford's Alternative Uses Task (1967), which asks participants to think creatively about common, everyday items.

How could I use this in my class?
I think administering the Alternative Uses Task would be a great thing to do with your students when trying to unlock creativity or effort in your classroom. Many students who may feel insecure about their traditional IQ intelligence could do well at the task, opening up for you (and them) the idea of who is "smart" in your class.

Divergent thinking is important in finding multiple solutions to problems that can often get kids stuck on word problems/ open-ended problems. Knowing who the creative thinkers are in your room helps you and your students know who to go to as the "experts" when students are stuck for ideas. Facilitating these exchanges also open up opportunities for leadership beyond the "smart" students, engaging more of your students.

It could be especially interesting as an opener to presenting your students with a 3-Act Math Story.

You can find "Brick and Blanket" and four additional creativity tests on this post from 99u.com

18 December 2014

Big Macs are NOT Commutative

I went to a St. Louis Blues game with a friend recently and the team scored 4 or more goals, so everyone with a ticket stub got a free McDonald's Big Mac the next day!

When I got my Big Mac back to the math office for lunch, I opened the carton to discover that on top of my sandwich was two consecutive pieces of bread. It looked a lot like this:

source: smosh.com
Besides relevance in assembling nearly anything, many creative processes, and computer programming, order of operations is even important in our branded food products. Who wants that much bread? :)

I showed it to my friend who had stayed behind and his reply was inspiring.
"Big Macs are NOT commutative."
This image will be posted in my classroom as a playful reminder to always be considerate of those operation rules.

17 December 2014

Bowling in the Living Room

The older my daughter gets, the more I continue to be amazed at what she's capable of doing (and inspired by what my wife comes up to do with her) during home-school time.

On a random week-day this past September, my 4 year old tracked and generated her own color-coded data chart. This is especially profound for me today because I just got back my semester evals in AP Stats and a couple kids said that the times I sent them out to collect (and then use) their own data were some of the very best, most relevant lessons.

So, my wife could have picked up some colored balls or marbles and counted them in some repeated fashion that my daughter then notated on the chart she was given, but instead, they went bowling in the living room.

A simple toy bowling set we bought a couple of years ago, set up in the living room.

That face... LOL

Which pins did you knock down?

Counting the number of pins after all the trials, then drawing an illustration in her science notebook
This post probably isn't actually for teachers in an early ed or primary classroom. From all of my interactions observing my son's classroom and others in the district I teach, no one has to tell early ed and primary teachers that physical activity and tangible, concrete objects and experiences are critical to students' engagement in and memory of the content they are responsible for learning.

If you are an early ed/primary classroom teacher, let me just continue to encourage you in all of your work encouraging and promoting numerical literacy. Creating and interpreting charts to track, present, and understand data becomes more important year after year as companies increasingly use computers to track data on customer's preferences and habits, waste or excess in financial statements, student achievement on state tests (and how/why they are rising/falling), just to name a few.

If you're a part of my usual audience of middle school and high school teachers, my hope is that you'll take the same lesson I often take myself when I observe my daughter's learning - kids always start out eager to learn. They start out eager to take experiences from play and translate them into a different medium to make sense of what they just did. When everything is new, few things are "boring."

Here's my lesson from today, courtesy of Hey, Beth Baker:

  1. Involve your students in creating as often as possible.
  2. Take some time out of class to do something. 
  3. Keep pushing and seeking exactly what your students are capable of. If its something their passionate about, they'll probably surprise you.
  4. Use the normal or mundane things around you in a new way to surprise your students and bring them in.

16 December 2014

Algebra on a Chromebook: Coding with Bootstrap

Have you ever wanted to code in the classroom to integrate more STEM projects, but felt tied into making sure you hit all your required curriculum?

Bootstrap (www.bootstrapworld.org) is a complete curricular resource for math teachers who want to integrate coding into their algebra instruction and computer science teachers who want to integrate and support their students' math learning.  Students learn the logic and spatial reasoning necessary to translate into "real" coding languages while working with operations, functions, and the coordinate plane. It's a real two-for-one!

What Will I Find?
The Bootstrap website has everything you will need to implement the Bootstrap curriculum in your Algebra 1 class (except for the technology hardware, of course)
  1. Student workbook (and teacher edition)
  2. Unit pages for students to follow through and fill in their workbook
  3. WeScheme online coding environment (this is called an IDE, for "integrated development environment," which just means, "this is where you write the code for your website or webapp.")
  4. Alignment to common core standards
  5. Teacher notes (displayed on the same page students use to read instructional content)
  6. Professional development videos to help you understand coding-specific words or processes before you have to share with your class.
How Will My Students Do This on Their Chromebooks?
Some of the work in the Bootstrap units will take place in the online modules, some will be handwritten on paper or whiteboards, and some will be in an IDE like WeScheme (when kids are building their projects)

In other words, students will use their Chromebooks for viewing lesson content, collaborating, and writing their code. 

Why Should I Do This Instead of Focusing on Raising Tests Scores? Accreditation is Very Important for Us.
I believe this question can be answered with three more. How's your more traditional curriculum working for all of your student? Is everyone mastering the Algebra content? Are your students learning content for a test, or are you giving them a vision for something more?

In my personal experience, the number of students that come into my Algebra 1 class that are being successful in "normal" classes continues to fall. We still have students that can excel in those environments and can play the school game, but I see a growing divide between those and the others. Going through the laundry list of things our district is trying to target, the bootstrap curriculum gives me opportunity to still do plenty in reading technical content, writing for assessment and understanding, and providing engaging, relevant work.

How Else Could I Sell This to My Administrator and My Colleagues?
Here are some talking points that should cover most of your bases-
  • "The units are aligned to the common core."
  • "Students will have an end product to demonstrate their learning at the end of the semester."
  • "They provide a pre and post test to gather data on the curriculum's effectiveness."
  • "Coding is a highly relevant and marketable skill for getting our students college and career-ready."
  • "Feel free to come visit and ask my kids about their work at any time. :)"

Is the Bootstrap curriculum for everyone? Maybe not - if you have no interest in coding yourself, then I think you would have a hard time getting your students passionate about learning themselves. Some students are just as averse to "new" or "different" in education as your teaching colleagues, so you'll need to be sold on the idea yourself to get them on board. That's not to say you already need to know everything about coding. The teacher notes are very helpful, and I went from totally confused to amazed at the idea of "circles of evaluation" and how they can help increase my students' UNDERSTANDING of the process and necessity of order of operations.

01 December 2014

3 Act Math Story - AP Stats - Ferguson Protestors

We're discussing sampling techniques in AP Stats right now, and I think a lot has been discussed in conventional and social media since the August 9th shooting of Michael Brown about the "real" Ferguson.

I teach in the district covering Ferguson, MO, so I've had students in my classes that I'm sure can identify with the popular claim, "I am Mike Brown."

I ran across this article in the NY Post over the weekend criticizing CNN's reporting of the looting, violence, and arson following the grand jury decision on November 24th.

The question that comes to mind first when I see this image paired with this headline is, "Well, how would we know?" There are so many variables playing into reporting of the protests. Who is "from" Ferguson? What is the line between "peaceful" and "violent"? Because St. Louis County is so fragmented with numerous municipalities, is there a big difference between being "from" Ferguson and being "from" one of the numerous small cities/villages/towns that border the Ferguson city limits?

Who's "more" of a part of Ferguson, the demonstrators at night or the people that come to clean up in the morning?

As I included in the teacher notes of this story when I posted on 101qs.com, I don't know if there is an "answer" to this question, but I think its a fantastic opportunity to talk about representative sampling, potential bias, and thinking through demographic and survey data that would be relevant in painting the most "real" picture of the attitudes of Ferguson residents.

The story on 101qs with aligned common core standards and accompanying questions, notes, and resources is here:

Evaluating as a 3-Act Story
  • The image-headline combo is great for getting a reaction or response from students (perhaps too much in my specific case).
  • The question is open-ended and there are several avenues students could take to support or refute the claim made by they New York Post writer.
  • I included several potential resources, including the link to the nypost.com story, census bureau quick facts for Ferguson, MO, a survey report from May 2014 evaluating the effectiveness of government services, and a map of Ferguson breaking down the wards. There are probably a few other data sources kids might need depending what path they go down, but from the teacher perspective of someone else using it in their classroom, I think its quite useful.
  • Since there's not a specific, black-and-white answer, there isn't a lot of closure. I could include a video of Ferguson residents actually peacefully demonstrating, or the dozens and dozens of volunteers that have helped clean up day after day, but that's not as rewarding as "here's the answer. Ta-da!"

In closing I would ask you to rate by the simplest barometer of success for a 3-Act Math story: Is this "perplexing?"

29 November 2014

2-Way Mirror: What Dance Class Taught Me About "Each As My Own"

We had a motto (mission? slogan? value?) in my district 7 years ago when I began teaching that went something like, "Treating Every Student Like You Would Your Own." That's a great principle to teach by, but it only really works if whoever applies it HAS CHILDREN. Before (and even when they were still infants) I did a lot of things in the classroom that weren't necessarily bad, but that I would do differently now that I'm seeing my little ones grow as learners.

A couple of years ago, I got take my daughter alone to a make-up dance class during the week and watch through the two-way mirror. The experience was thrilling and nerve-racking, to watch your kid doing something they love, but not really getting to enjoy it with them. Obviously, I don't have a two-way in my high school math classroom, but how would that change my behaviors if I did? How would that change my parent interactions?

It BROKE MY HEART to sit there and watch Lucy struggle with something the other kids were having more success with (she's still working on the formal aspect of dance over improv, and this make-up class has older girls in it), but there were two things I see parents do that I did not feel because I watched it happen:

1. I didn't blame the teacher. We know that parents know their kids best, but that should also mean they know where their child struggles. I made a mental list of things I saw Lucy needs to work on.

2. I didn't blame Lucy or myself. I could SEE her effort, so I know that she needs more practice, and more feedback. We've all heard "I was never good at _______" be used as a reason for a child's lack of interest or success in math class. I've never had formal dance training, but I know watching that class that I want my daughter to feel good about herself as a dance student, so I'll do whatever I can to assist in that.

What the two-way mirror made me reflect about my own behaviors in the classroom is how much time I spend redirecting one student, again and again, at the expense of many others? Is that right, or not? How many chances does a kid deserve? (One of Lucy's go-to lines when she's in trouble for not obeying is, "Can I have just ONE. MORE. CHANCE?!")

I actually started the first draft of this post a year and a half ago. It was Lucy's first experience in a "classroom" and my first experience as a parent of a "student". The conclusion I would have made then was that, yes, sometimes we need to let a kid go so the bulk of the class can get a chance to learn what they need to know (In the case of the dance class, it was particular movements, in your math class, it might be solving quadratics). I think NCLB showed us that when our strength of our focus is on bringing up the very, very bottom, that rigor of instruction gets dragged down with it. 

A year and a half ago, I still wore my teacher goggles as a parent. I was disappointed Lucy wasn't keeping up, but I understood the dynamic on the other side of the mirror as the teacher repeatedly redirected her to stay on line, to listen, and to follow along. I felt more compassionate for those kids that struggle, and their parents that are doing the best that they can, but I can't say it was affecting my practice. 

This school year, my middle child, my oldest son, started pre-k in a special ed classroom at our school district's early childhood center. We've entered the world of IEPs, progress reports, and letters home in backpacks. My wife spent a day in his classroom a few weeks ago and said he spent at least a 1/3 of his time there blowing bubbles. There's a kid in his class that struggles using "safe hands" (hitting) and with general impulse control, so I'm sure that Landon gets to spend of lot of his time on choice time because he's a nice, generally compliant kid. He generally likes school, and when a lot of his time is spent blowing bubbles and eating goldfish (his speech therapist has been giving him one for each produced sound), its no wonder!

Here's what I get now about the students in my class, and their parents' expectations -
When you work out "each as my own" in your classroom, you realize that it doesn't work best for any kid for when you attempt to put all kids into a group. Some students and families are better adapting to it than others, but "getting by" is not the way that I want to remember any of my own children's experience. When I was on the parent side of the 2-way mirror, all I wanted was for Lucy to get all of her teacher's attention all of the time. No big deal. ;)

So how does that work practically?
We have the impossible task of giving each student as individual and appropriate an experience as we can. We have to go the distance for each kid as long as I would my own children. Even if my students' parents don't have time to call me or come chat with me at conferences, they still want the best for their child, so I owe that to them. 

21 November 2014

Socrative Interactive Assessment in 30 Seconds

I've written more about the Socrative app/website before, but have been tasked with presenting in a slim 25 minute window to our school staff, so I wanted to refine my experience to the elevator pitch.

Socrative is...
  • an app
  • a website
You can use Socrative on...
  • PCs
  • Macs
  • Tablets
  • Smartphones
I've used Socrative for...
  • exit slips
  • quick check-ins
  • surveys
  • test review
  • quizzes
  • unit exams
  • final exams
Socrative questions can be...
  • short answer
  • true/false
  • multiple choice
Quiz navigation can be...
  • student paced
  • teacher paced
  • randomly ordered
You could spend...
  • 5 seconds
  • 5 minutes
  • 5 hours
...preparing your assessment in Socrative.

It really is a versatile tool! For more info, read can read further about Socrative on this blog, or visit Socrative.com

18 November 2014

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.

11 November 2014

Student Tips for Dividing Polynomials by Monomials

I used one of my exit slip writing prompts today and these were the results. Some of them are actually useful, and others might only be useful to the kid who wrote them, but seeing the confidence on a kid's face when they leave knowing that they were able to give a tip about what we did in class is priceless.

07 November 2014

What's It Mean to Innovate?

Source: dictionary.com
Do you think of yourself as an innovative teacher?
What do you think of this definition?
verb (used without object)innovated, innovating.
1. to introduce something new; make changes in anything established.
It's all relative, I think. What may seem like innovative instructional methods (new, challenging to the establishment) could be common place somewhere else. What I might do with my students on my class iPads when we are writing or even drilling with interactive practice might look innovative to a teacher who doesn't have individual devices for each of their students, but would be ordinary in an established 1:1 environment.

Here's a quick list contemporary buzz-word areas of innovation:

  • STEM-integrated focus
  • STEAM-integrated focus
  • Game Based Learning
  • Project Based Learning
  • Flipped Classroom
  • Flat Classroom
  • Virtual School
  • Global Classroom
  • Parental Involvement
  • Special Needs Learning
  • Makers Spaces
  • Robotics
  • Coding
It doesn't take long reading blogs, scanning social media, or sitting at a technology conference to know that there is a wide range of implementation across education of all of the items listed above. Imagine you were in a school that does the flipped classroom very well and you were feeling very average as far as your implementation. If you were to move to a school in which NO ONE was flipping, you could make quite a name for yourself using the exact same instructional methods you had been using at your old school. When you have new skills and knowledge to share, don't you feel more innovative? I wonder if +Jon Bergmann still feels like an innovator now that he's been doing the flipped classroom for a decade. 

Do you have to be pushing the envelope on more than one of these areas to be "innovative," or just hitting one really well? Is there a layer of influence to earn the title of "innovator"? If you are the only teacher you know doing something new and no one knows about it, is it a "worthy" innovation?

Perhaps the answer is that "innovative" must be have a dynamic meaning because its definition is so subjective to its context. Remember, incandescent light bulbs were once an innovation.

Here's my own definition of innovative education technology practice as we teach at the end of 2014.

It should really go without saying that the teacher is using technology in the classroom, but where the "innovators" are defined begins in the varying degrees of student use of technology in the classroom. During an accreditation visit two years ago, we lost a lot of points for student use (or lack thereof) of technology in the building, so you don't have to be too far on the scale here to be a tech "innovator," but in a different setting, more would be required. 

So back to the "Are you an innovator" test. Let's just use the definition for where you are.
Are you making changes to what is established? Do you introduce new ideas?

28 October 2014

Pathways to Prosperity - Pathways for Teachers

I had an amazing opportunity to be a part of a program this past year called Pathways for Teachers (the professional development/curriculum writing arm of a larger program called Pathways to Prosperity.) The goal of the program is to pair up gen ed teachers with business and industry to give teachers "real-world" settings and experience that they can take back to their classrooms and use to enhance the relevance of their curriculum. The program was funded last year by+Boeing, through a partnership with +Cooperating School Districts.

We spent 2 whole days in the spring touring different manufacturing and business sites talking to workers and getting a general idea of what STEM-type jobs might look like beyond engineering. (I went to Icon Mechanical in Granite City, IL, Component Bar Products in O'Fallon, MO, Boeing HQ in Hazelwood, MO, and Ameren HQ in St. Louis, MO). During the summer, we had a week-long Pathways Institute that was designed to give us a more in-depth look at ONE site we had previously visited, training in developing project-based learning units, and time to collaborate and write the units.

I spent my externship day in the summer back at Ameren HQ downtown for what I thought was going to be a day of attempting to integrate electrical theory and problem solving into my Algebra class. What I came away with was several next-day applications for statistics and graphical analysis that completely caught me by surprise. Believe me when I say, real people do stats. Excel was EVERYWHERE (as were awesome 3 monitor setups at like every desk.)

After the day at Ameren, I worked 2 1/2 days with two other teachers from my school creating a project-based learning unit integrating everything we had learned at our individual externships. Collaborating on the project was a great experience because justifying decisions to my teammates and bouncing ideas off each other to solve different problems that arose in the process made for a better project. As just a small example, in the unit, students are grouped into teams and each student is given a job with an individual rubric. Giving specific tasks to kids in groups was not something I'd ever tried to tackle on my own, but we became our own support system. Its always harder to back down from makig innovative (hard) changes when you're got a buddy in the trenches with you.

Today I have the opportunity to share my experience with the this year's round of teachers - here are my slides.

Created with Haiku Deck, presentation software that inspires

23 October 2014

The PhotoMath App is Good, and History Says Its Here to Stay

In case you haven't heard about it yet, there is a new education app for iOS and Windows Phone devices called PhotoMath. Most basically, the app utilizes the camera on your device to recognize numbers and letters, runs an algorithm, and then displays a solution on the screen. From there you can follow the solution it generated step-by-step.

Here it is in action.

There are two ways to respond to the Photomath app, really. One is a reaction of fear, and the other one of promise.

This app is really cool,  people! The computational power behind pointing a camera at an equation or expression and having it solved or simplified step by step for me (nearly instantaneously) should really impress us, right? My hope is that the PhotoMath app and it's future iterations will be the disruption in math education we've been looking for. How much longer can classrooms ignore the technology and force students to solve everything by hand (and then stop there)?

Let's look at a brief (and roughly estimated) timeline of math technology in education:
  • 1970s: 
    • Computers are cool and all, but we mustn't let them replace the computational and arithmetic skills of our students. What if the technology goes away?
  • 1980s: 
    • Handheld calculators are cool, but we should only give them to students once they've learned their math facts anyway. What if the technology goes away?
  • 1990 and 2000s: 
    • Graphing calculators are a great tool, but students still need to know how to do it all by hand. What if the technology goes away?
  • 2010s: 
    • That's really impressive that you can make full color graphs on your smartphone/tablet, zoom in and out, change axis scales, and locate points of interest with a swipe and a pinch, but they can't use those on "the test," so they aren't worth the time.
    • Wolfram Alpha can solve equations for you? That's a really cool tool for college students to use as they explore upper-level mathematics. I hope my kids don't find that and cheat. Besides they need to know how to solve equations for "the test."
  • 2014: The PhotoMath app

What side of history will you be on?
As I noted in the timeline above, technology to solve our kids' equations on their homework has been in their hands or laptops via Wolfram Alpha or CAS graphing calculators for years already. The PhotoMath app makes it even easier to access that power, but I think your attitude toward Wolfram Alpha should mirror the opinion you ultimately take of PhotoMath. Will you embrace the technology and lead conversations and work to push for lessons and assessment in your school that expect more of students than x=_____, or will you wait for someone else to make that decision? I think history foreshadows that you'll be dealing with it eventually, anyway.

Special Right Triangles - Really?

What's in the list you keep (internally or physically) of things we still traditionally teach in our math courses that just feel "wrong" in 2014?

Memorizing formulas is probably one of my least favorite things, and I know I have that in common with my students, so wherever and whenever possible! I like to teach them the concept on a pattern level or with strategies that have more than one application. In other words, if the only reason for me to teach it is to maybe get lucky and steal a question or two on a test, then I usually won't stress it.

I was having a good week with my Applied Math class. The kids have been more or less focused recently, and we were all getting along. Kids love Pythagorean Theorem, for some reason. Right up there with "y=mx+b!" It's hard to find a kid who at least doesn't think they know how to use it. Taking advantage of those good vibes, I would have rather rolled on into circles, but the ugly special right triangles lesson stood in my way.

I went through the trouble of having them use Pythag the night before to actually solve the SRTs, and my first example showed them again how they can just use Pythag on any right triangle to find a third side. Good feelings were still flowing, and then our first question from the book had a 60 degree angle and ONE side. "Try and do THIS ONE with Pythagorean Theorem," it seemed to taunt me. I took the bait and walked the class through the relationships. And one by onem my confident students fell to the wayside, and my focused, eager students started to check out. 

So, why? Why invest time in a chunk of knowledge that isn't necessary if you know  Pythagorean Theorem or basic trig ratios?

Here's a note sheet I plan to share with my students tomorrow to articulate the alternatives again.

21 October 2014

"We Just Want to Be Comfortable"

I went to the St. Louis EdSurge Summit at Ritenour High School Saturday afternoon. The event featured dozens of #edtech startups with tables sharing their product and passions, and a terrific keynote to end the day from Google Education czar +Jaime Casap, but what impacted me most was the student panel hosted in the auditorium after lunch.

The second question +Chris McGee posed to the group was, "If you had unlimited funds to set up your ideal learning space, what would you include?"

Accounting for my typing speed on an iPad, here are their responses:
  • A desk with matching pencils and notebooks, picking where you sit, no desks in rows or columns 
  • Students feeling comfortable, couches EVERYWHERE, because everyone loves couches, it's just uncomfortable sitting up in a desk - I can focus better on a couch
  • ATMOSPHERE, as inviting as possible, simplicity and complexity in a way to get things done
  • We DONT fall asleep on the sofas, it's not just the classroom, it's the teacher too, if we're in a cozy classroom the way we think and work will change
  • Availability of being able to choose our tools for what we want
  • Students interacting with teachers when districts are hiring new teachers
  • I think I focus on my work better when I'm working on a computer or tablet
  • LIGHTING is a big part of atmosphere for relaxing 
  • I can stay more organized with the laptops instead of using my binder.
Do you put as much thought into the layout of your room as you do the color on the walls, the alignment of your posters, or the security of your teacher desk?

I have a couch that I salvaged out of the "surplus: send to plant" storage area 2 summers ago that I put toward the back corner of my room in what I named the "collaboration corner." It's a decent space. I have a rug we were done with at home, a coffee table that I salvaged from somewhere else, and a few clipboards to write on. The only problem with the collaboration corner is that it's in the back corner. I don't feel like I can manage the students there when I'm at the front of the room at the SMARTboard (which is something else to consider anyway; should I be up there enough for it to feel like a problem?) or speaking at a student's desk in the front. So what happens? The collaboration corner hasn't hosted very much collaboration the past year and a few months.

So what's the plan? I'm gonna double down on the commitment to the collaboration corner and move the couch toward the front of the room.

Do you ever feel this way about the things those students shared? You want to believe what they're saying, that they're totally committed to those statements and that in the environment they described they would all be creative, productive little problem solving machines, but your experience with that starts to psych you out.

My hope is that moving the couch out of the back corner will separate the kids seeking the couch to hide out from the kids who just want to get in a spot where they can hunker down and work. The funny thing is, I thrive in the same environment with the same level of trust. I've convinced my curriculum coordinator to let me and a colleague go work at Panera Bread Co. this week on a website for the district rather than sitting at the table in his office. I'll sit there and drink somewhere between 6 - 9 cups of coffee, spread out my things, jam to some music, and crank through that work.

Here's where my put couch on Monday. You've got a week, kids. Show me what you've got.

19 October 2014

Algebra on a Chromebook: LucidChart Diagrams

I've heard more than once that laptops or Chromebooks in a 1:1 environment get relegated under the desk during math class because the classroom teacher struggles with finding ways to integrate the technology into what is usually a much more hands-on process with graph paper, pencil, and exercises.

I think the easiest answer is to have kids using the laptops for watching videos, looking up examples on webpages, or drill and practice on websites. The sexy answer is to have kids engaged in problem-based learning, integrating their math work into relevant reports, graphs, images, and presentations, but first you would have to also sell problem-based learning on the teacher.

In between the easy answer and the sexy answer lies LucidChart Diagrams, whose collection of education templates can facilitate note-taking, critical thinking, the problem solving process, organizing and summarizing, sequencing, and concept mapping.

Let me show you briefly how a student could use LucidChart Diagrams to integrate writing and list the steps to solving an equation.

You can find LucidChart Diagrams in the Chrome App Store

After clicking on "Create," this box pop-ups, giving you a selection of templates. There is an extensive "education" collection.
This is the "sequence chart" which you could use for any technical writing task. 

Your next task is inserting an image of a worked out equation for students to write about. Scroll to the bottom of the menu on the left and select the plus icon to add an image. This box pops up in which you can do a Google search or upload your own (student or teacher created)
Here's what mine looks like after resizing the image some and inserting each of my steps. (click to zoom or pop out to new tab)

mind mapping software

Other charts you might use - 
  • Venn Diagrams
  • Cluster/Word Web
  • Compare and Contrast
  • Concept Map - use to connect similarities and differences in characteristics of functions
  • Planning Chart - problem solving or think alouds
  • Vocabulary Chart - visualizing unit vocabulary, grouping similar/related words
  • T-chart - change the headings and use as guided notes/interactive notebook. students import images of examples and type in on the right side.

17 October 2014

That Common Core Subtraction Problem

Its hard to have NOT seen a variation on this problem over the past year.

The basic premise is this: Students are presented a subtraction problem, but instead of performing the traditional stacking/borrowing algorithm, evil public school common core teachers force students to jump through extra hoops. Students add chunks of numbers to the lower value to get to multiples of 5, 10, and then the higher value in an effort to find the difference between the values.

Every time I see this shared on social media its from a politically conservative non-educator using it as a tool to illustrate how big government getting its hands into our locally controlled schools makes things unnecessarily complicated (and ultimately, worse).
Here's the problem with using this ONE standard to characterize and criticize "common core math" - its the same thinking that our students and families use when they say things like, "all I need to be able to do is count my money. I don't need ______."

This question is meant to address a 1st grade standard about operations and algebraic thinking. The point is getting kids to understand multiple ways to manipulate numbers.
CCSS.MATH.CONTENT.1.OA.C.6Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). (source: corestandards.org)
Before you're ready to confirm your contempt for core standards, think back to your own math experience. I've found that most "non-math" people often prefer problems and learning environments in which there is more than one "right" answer. The point of this question is to build mathematical thinkers that can adapt their thinking to look for solutions when their first or second attempt is unsuccessful.

11 October 2014

2 Exercises for "Relevant" Proportion Solving in Algebra 1

One of the first things I realized after becoming a math teacher in my very first Algebra 1 summer school course was that students love to cross multiply. You stick a fraction on the board and ask something like, "Okay, what next," and you will most certainly get some kids that are dying to cross multiply.

Kids that only know how to cross multiply love to get exercises like this:
And they're probably even pretty comfortable with this:

But things might start to fall apart sometimes when students have to set up the proportions themselves in a situation not neatly laid out for them in "word problem" format.

Here are two such attempts that I used in my Algebra 1 class this past week. One is about troop reduction in Afghanistan, and the other is about "total percentage of weight loss" and trying to win the reality show The Biggest Loser.

  1. You could increase the rigor in both of these problems if you did not initially give either of the numbers I hand out (8000 and 51%, respectively) and instead, had your students figure out what number would be relevant to finding a solution that would satisfy the problem. After deciding what information was needed and/or relevant, students could do a web search to find the information for themselves. 
  2. Have an extension question exploring these ratios in a different way.
    1. The Afghanistan troop numbers could be compared to Iraq or previous deployments this century in Afghanistan.
    2. The Biggest Loser problem could ask students to compare Jerry to other seasons to see if he would have won those years. You could have students set up "teams" of Biggest Loser contestants and find the proportions of weight loss necessary to defeat other fantasy teams from previous Biggest Loser seasons.

10 October 2014

10 Writing Prompts for Exit Slips

Exit slips are, of course, a great means of quick, formative assessment over your day-to-day lessons in class. Writing is a means to trigger students' brain to memory and learning connections. Let's do 'em together!
  1. "Describe something you previously misunderstood about _______ that was clarified in this lesson."
  2. "Give two tips for remembering how to _______."
  3. "Give a title and two section headings to your work/the notes for today's lesson."
  4. "How would you describe today's lesson to my five year old when she asks what the kids learned today?"
  5. (After putting up the graph of a function with each axis labeled): "What would this graph tell us about the relationship between the variables?"
  6. Have students answer any of the unit essential questions (this is good for PLC pre and post data, too)
  7. "How did something we learned about ______ help your understanding of ______ today?"
  8. (After putting up a solution to an exercise). Evaluate this student's work. If the student was wrong, make an inference about where he went wrong or what he needs to relearn.
  9. Did today's class rock or suck? Explain your choice with two reasons.
  10. Make a list of as many content-specific words we used today. Define their meaning in the context of today's lesson.

09 October 2014

Student Tips for Simplifying, Multiplying, or Dividing Radicals

To wrap up the lesson today, I had my students try to process their learning with an exit slip giving two tips for simplifying, multiplying, or dividing radicals.

Some of them referred to some notes we had written yesterday, some referred to something I'd said in the last couple days, and some used a kernel they'd picked up during class today that helped it click for them. We had a successful day, I think.

The "or dividing" is awkwardly  tacked onto the end of that heading because after I wrote "2 tips for multiplying or simplifying radicals," someone piped up, "Can we do dividing, too?" You win, students - its your class. :)

29 September 2014

#FLIPCLASS Tip: Organize Your Videos by Standardizing Links

I've written previously about organizing your videos per unit or chapter in a playlist, and of course, you can send out your videos via Remind, post them on Edmodo, have kids subscribe to your Youtube channel, or host them on your own website, but here's one more idea (that I think is more user-friendly if you're keeping accountability via kids notebooks instead of online).

Use a link shortening app or website like Bitly, customize the shortened links to your name and objectives, and follow the same pattern for all of your videos. Aligning your links' names to objectives or standards already listed in your syllabus will help students and parents match up which video goes with what needs more work or is to be made up.

Here's what I mean - I have a shared syllabus with 3 other teachers in my department for our Algebra 1b course.

Rather than simply posting my videos to Youtube and then sharing out a long, randomized link, or even YouTube's shortened version, I take each url and shorten to bitly.com/baker_starks_**, where the end of the link is a number that corresponds to the standards listed in that image above. So, if you go to bitly.com/baker_starks_5, you get my video on the Distributive Property.

But if you're posting the link on Edmodo and Remind, what does it matter that you've shortened it?

Good question, reader. Do you students ever tell you they "lost the text from Remind" or "couldn't login to Edmodo?" Following a standardized name for your links gives you another defense and the student another chance to get their notes done because if they remember the suffix you always include, they can make some guesses as to the ending.

Why not just name the videos as the standards are worded on your syllabus?

Bitly links must be unique, so only one person in the world can "own" the link to something like bitly.com/orderofoperations. You might be able to sneak in some, but I'd bet at some point you're going to run into a naming issue and have to deviate slightly from the way it was written on your syllabus. Then you've made it HARDER to find that video, instead of easier.

23 September 2014

Have You Heard of "Twice Exceptional" Students?

I read this account (via Quartzof a NYC public school student who is exceptionally gifted intellectually, but (in part because of his intellect), was really struggling with attention on class, interacting with and understanding his peers emotionally, and otherwise doing "school" activities. Ordinarily, these behaviors would sound alarm as a child probably in need of an IEP and special accommodations, but because of his strengths elsewhere, the necessity for services and supports are either masked or compensated for by the student, or ignored by his teachers.

This boy's experience was a representative anecdote for what educational psychologists are calling "twice exceptional" children - children who may be traditionally "gifted" in one area, but in desparate need for interventions and supports in areas of the school environment. (Special Ed Manual from Idaho Dept of Education) This boy's story went on to recount bullying the boy ended up enduring even in a "gifted" classroom and a general dislike and failure of school. He had taught himself to read before he was 4, but was regressing in a classroom setting he struggled to adapt to and cope with.
Do you have any students like this?
Have you ever assumed that a bright student must also work well and lead in a group setting? If you've seen the Steve Jobs biopic or are familiar with his story, you've experienced this fallacy)
Have you ever been surprised that a student on your IEP list in a co-taught special ed classroom might be need the most support emotionally or behaviorally, but ALSO be the most gifted intellectually? (That IEP stigma can stick hard, can't it?)
Do you ever find yourself giving "gifted" students a free pass on other aspects of learning and growth? 

Thinking through my own experience working with these students (and maybe even reflecting on myself as a student), let me share with you some tips for supporting the needs of "twice exceptional" students and engaging them in your classroom.

1. Don't assume that your "smart" or "honors" students must also have the best behavior.
Honors students may need your PBIS measures and expectations reminders, too.
If you're struggling with a student's behavior, you may be particularly frustrated that he or she isn't being a "leader" for the others. Thy may really WANT to be "good," but be unable to for some reason (and this probably frustrates the student, too.)

2. Focus on educating the WHOLE student. 
Kids that are exceptionally gifted in one subject math give up or accept that others are (and will always be) weaknesses. As the student stresses one and ignores the other, the divide between strength and weakness will only widen. Find nuggets a student can mine and go further. If you really believe that your students should be life-long learners, then no matter how bright your student may be he or she STILL has things to learn - things to learn from YOU.

3. Have a conference with parents early I'm about ways they would like to see their child receive extra support or be challenged to improve. 
Whether or not they can EXPRESS it in edu-speak, they have goals for their child's interventions. One of the most shocked/delighted reactions I can remember at parent-teacher conferences was when I told the parents of a student with a 36 on the math portions of the ACT that I was really wanting to work on his writing and communication of all the math he could perform operationally. 

4. Let the genius/crazy happen as it wants to.
Resist the urge to fit your twice exceptional students into whatever mold you want to see them in as "successful." If they're introverted, don't force group work on them. (But find ways to force interactions on them in more digestible nuggets). If your student has noise or sound sensitivities, be prepared to adapt your lecture/lesson to that student being able to isolate themselves when they're overwhelmed, but still continue learning activities. Give a student's work time to bloom and come to a full realization before you shoot it down. I've dismissed several "bad" drawings from my 4year old in this manner that after I listened to her explain it, I saw her reasoning and artistry more clearly.

5. Be proactive in your support. 
Conference ithat he student and acknowledge that you understand and are aware of their needs, but also that you have a plan of x, y, z for them as a student in your classroom and in your subject. Engage them in that journey.