Reflecting on Another Year

This month marks another full calendar year teaching in a juvenile corrections facility. To compare this  current moment to last year on this day is a lesson in contrasts. My current roster shows only three students I had on this date a year ago. The classroom has been upgraded with a projector attached to the  ceiling, a new Smart Board and wireless internet (password protected and only for use by myself or with myself and a student for a specific learning purpose). I use iPads and can seamlessly integrate technology and mathematics. I'm now teaching the second iteration of my video game design class.

It's not only the tangible changes that exist, there are also changes invisible to the eyes. In a word, I feel a lot more confident, perhaps even comfortable. I don't say this in a way that makes it seem like I know everything, or just sit back and rely on a curriculum (I don't), but as a way to say, I can do this job and I do it well.

One of the most important changes over the past year has been to consistently seek out trainings which pushed me to become more creative, and blend together technology and education. It is really easy to say, let every kid use a computer or iPad. The question then always becomes how do I make this meaningful in my classroom, and how do I squeeze out the best of what these technologies offer.

It isn't easy. It took a training in Limestone, Maine at the Maine School of Mathematics and Science for me to really rewire my brain with all these technologies. It took another training at the conference for New England Mathematics Teachers in Vermont to connect the dots with Common Core.

All of these changes over the past year has improved the quality of education here greatly, and make this an exciting place to teach and learn. The nature of teaching in corrections though is it can all change suddenly, as a result nothing is taken for granted. I have to stay flexible and open minded to be successful here.

The evolution of being a teacher here has really run the gamut over the past couple years. I started out in a classroom with no technology, where our only resources were textbooks and each other. Piece by piece technology was added, then training and support.

My hope also by writing this is to help demystify a bit what education can and should look like in a corrections facility. There is no doubt it can be difficult, but I believe it can and does work effectively for a great number of students. My plan is to write a bit more about this in the coming weeks.

Using Illustrative Mathematics

Illustrative Mathematics is a website I have been using on a near daily basis to focus on specific standards and concepts with students. The advantage of using this website is I can easily pull up a problem for each student. Each student I teach is on their own individualized curriculum, thus it is time intensive designing activities and assessments for every student on every day.

www.illustrativemathematics.org

Illustrative Mathematics provides guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards.

Typically I will search through their database, find the right illustration and print out the first sheet to the size of an entire piece of paper. The problems have 3 or 4 parts usually so they can be time intensive, draw upon numerous skills and involve having to make charts of graphs. Here are a few examples:

1. Kimi and Jordan

This problem I use with students who are beginning to make the transition from Pre-Algebra to Algebra. The rates have context. The tables are laid out in a readable format. Students with experience generating equations won't have much trouble. When it comes to sketching the graphs, students can use the tables or the equation.

2. Adding Fractions with Common Denominators

It is easy enough to give students a worksheet with 20-30 problems adding fractions with common denominators. Once a student realizes the mechanics of the exercise, this should be done rather quickly without much thought. I love how this problem slows that process down. There is again a context, the answer isn't a whole number, the answer has to be translated into a meaningful number and then a picture has to be drawn which should clearly determine whether the student is comfortable with adding fractions or merely grasps the mechanics of adding the numerators.

I highly recommend checking out this site and adding it to your teaching repertoire. It is a definite time saver and comes with high quality questions that demand going beyond the simple mechanics of mathematics.

A New Year, A New Puzzle

Hello everyone and Happy New Year.

I thought I'd start us out light today with a problem that has been giving some of my students all sorts of fits. As usual, I try to offer absolutely no help, but if you have a struggling student who is just about to give up, ask them how much each section should add up to. That might do the trick.

The Bank or the Mattress?

A large proportion of students I teach have personal finance experience. I use this term loosely of course, the experience tends to be related to illicit activities and usually ends unsuccessfully. Unsurprisingly then, pretty much everyone I am teaching is either broke or owes money in the form of restitution payments to victims and/or the government. One of my goals in this facility is definitely to teach students how to manage money efficiently, and this works perfectly in tandem with Pre-Algebra and Algebra students.

I provide a number of scenarios for students.

Scenario 1

You are given $10,000. You decide to keep $5000 in cash and hide it under your mattress. You take the other $5000 to the local bank and open a savings account that promises a 5% interest rate a year for 15 years if you don’t touch the money. 

I love this scenario because my students have an idea in their head that cash is king and using banks means you could lose your money. I love to watch their reactions as they calculate how much their $5000 is worth after the 15 years.

Some questions for them to consider:

1. At what time during the 15 years does your bank account grow the fastest?

2. What would happen if you left the money in the bank for another 15 years?

3. What are the pros and cons of having your money in the bank? Under the mattress?

The last question can really be the most interesting. Students live under the misconception the bank can take your money, or if someone robs the bank you will lose your money, or the bank could simply steal it. This is a great opportunity to investigate what the FDIC guarantees. Then take all these ideas suggested about banks, and show how they really apply to the mattress, plus the associated lump you have to feel everytime you lay down.

Scenario 2

This one is a bit more realistic

You are currently broke but interested in saving money in hopes of becoming a millionaire. When you are released from the facility you begin working full-time hours and decide to put $100 a month in a bank account no matter how much you need it. The bank gives you a 5% interest rate compounded annually.

1. How long will it take for you to become a millionaire?

2. After 10 years, what is the difference between the amount of money set aside in the bank, and that same amount of monthly money if it hadn't been put in a bank?

3. What if the interest rate increased to 8% after 5 years?

4. If you started with $1000 in the bank, would this make much of a difference twenty years later?

I love the direction of the these graphs, students see right away what is happening and then quickly start introducing hypothetical situations. They start saving $200 a month at the beginning, change it to $500 a few years in the future when they figure they have a higher paying job. Pretty soon the "million dollar date" is dropping from 50+ years down to 36 years, and maybe below 30. Strangely becoming a millionaire doesn't seem so far fetched.

A lof of skills are included in this lesson. Percents, linear equations, non-linear equations, forecasting, budgeting, graphing. This is the type of mathematics that really gets me excited with all the questions we can ask, test out the new scenarios, and see how it turns out.

Last but not least, don't forget to mention they have to pay taxes on all this interest. I have no intentions on being called out for missing that slight detail years from now!

Fun with the Olympic Rings

I'm constantly in the process of generating content for mathematics class. I like to focus on one problem which incorporates a lot of different skills and comes with a number of questions exploring the problem. This type of problem solving is more aligned with the Common Core, and ties in learning from all over the curriculum. The belief is it creates learning environments which engender thinking, and move away from the more formulaic mathematics courses.

This type of teaching in a juvenile corrections facility can be a bit of a struggle at first. Many students I meet and teach are struggling learners who need to relearn the foundations before embarking on such tough problems. These open ended problems can be confidence killers, and students want to shutdown before they even start because there isn't an obvious solution with an obvious pattern of strategies to follow.

To this I say, too bad. If there is one thing I am preparing these kids for upon their departure from the facility, it's the real world. And we are not talking about the type of world where everything will be easy and readily available for them. It will be a struggle. They will have to work harder at both school and jobs to just keep up with their peers. They will have to constantly be making decisions and looking out for themselves, because there is no support for them.

When students start with me they will be challenged, they will have to think, be creative, explain how they are approaching tasks, ask for more information, ask for resources, in essence, makes things happen. This means as a teacher you have to be flexible, you have to let students test ideas even when you know they are wrong. You have to keep them motivated to keep working through the problem after experiencing failure. It's not easy.

Today's problem is another geometry problem. It's a simple diagram of the Olympic Rings with questions attached. There are no numbers provided, no strategies delineated, nothing except a few challenging questions. I'll offer little to no assistance to students, unless they ask for resources. I imagine a ruler and some trigonometry can do the trick. The first challenge I foresee is deciding whether the rings are equal, then where the midpoint of the circle is, then how to decide how to measure the length of the arcs, and then the angle of the arcs. Every student should have a different solution at the end of class.

The Housekeeper and the Professor

The first question I get when I tell students we are reading a novel in mathematics class goes something like this, "Mr. Cimato, this isn't English class, why are we reading?" There is typically agitation in their voice. They can hardly believe I would consider violating the sacred silos of education. Most mathematics classrooms subscribe to this theory, maintaining dutiful focus on the concepts they are tasked with. This game occurs in schools across the country, with teachers pretending only their subject exists, and students going along as to minimize the thought and effort required to succeed.

When our classrooms operate in this manner, we are making one of the biggest mistakes possible. We are tasked with bringing the real world into the classroom, integrating with technology, and making meaningful connections in our classrooms. While reading a book as part of a mathematics class isn't exactly ground-breaking, it provides a different access point for students, and ties together two unlikely subjects.

The post of this title, "The Housekeeper and the Professor" is a book by Yoko Ogawa. It takes place in Japan and tells the story of a housekeeper, her son and the housekeeper's client, a mathematics professor. The professor is anything but ordinary, an accident has crippled his short term memory, allowing him to only remember the prior 80 minutes. This part of the book is the hook, students are immediately drawn in on this rhetorical situation. What would my life look like if this happened to me? What challenges would I face? What would be advantageous about this?

Ogawa writes in such beautiful prose, the housekeeper has to introduce herself and start anew everyday with a man who can't remember her face. The professor uses mathematics as a way to break the awkwardness of the situation. The housekeeper, a poor mathematics student all her life, plays along to appease the the professor and hope to stay in his good graces. Along the way she realizes something most every mathematics student wishes. She can ask him to clarify certain topics, can ask him to explain examples repeatedly, and doesn't feel the wave of embarrassment from not catching onto a topic straightaway.

Many students identify with the housekeeper because they also struggle and are maybe hesitant to ask for help when their peers are already moving ahead. One of the advantages of reading this book is the professor actually teaches and lays out the mathematics. The levels oscillate from simple operations to highly complex mathematics.

I have found reading this book with struggling students has produced great results. Students want to learn and use the mathematics from the book. Students also enjoy the story which makes for excellent literary discussion.

In Loco Parentis

  Quick quiz for all of the teachers out there - WHAT DOES "EN LOCO PARENTIS" MEAN?  What is this little phrase all about?  What types of burdens and blessings does it carry?  At first sight, and embarrassingly enough, during my first education class in college it appeared to mean 'the crazy parent.'  The most reliable resource on the internet, Wikipedia, indicates that 'in loco parentis' refers to the assumption of some degree of parental responsibility of a an institution or non-biological parent.  By the end of this post, you might favor my original definition!

  I teach Biology and Environmental Science to the greatest group of students anybody could ever imagine.  Granted, some of my students have attempted murder, some have attempted rape, others enjoy a good fire every now and again (at the expense of others), and the majority of them have lived their lives on some type of mind altering substance (not to mention shared their blessings with others for a small fee)- but, hey, we all make mistakes.  I walked into my Biology classroom with the idea that I was going to change some kids!  I was going to make a difference in their lives.  These kids were going to be better off because of me!  I would liken my first day teaching youth in a detention facility to the births of my children.

  Susan Maushart speaks of birth as, "...the only way to gain control is to lose it..."  On my first day of teaching, as well as the birth of my first daughter - I HAD A PLAN!  My plan was great, NO my plan was AMAZING.  There wasn't going to be a student that could escape my grips without totally converting to the societal definition of success and happiness.  My plan was scheduled, my plan was flawless, I had truly thought of all of the little bends and curves that might befall me during class.  My plan was weak, hummm, nope it was just SHIT.  My attempt to control my situation, my surroundings, my classroom, my students' learning was not going to be successful on that day or any other.  I'm not sure if you are seeing a pattern in my writing, but the underlying theme was "my."  I was the center of my planning on that first day, and on that first day one of my first students let me know that I was not going to be the first person to control her actions.  She flew the coup, I hit my 'man down' button, and resigned myself a failure at teaching the 'hard-to-teach.'

  The birth of my first child had more similarities than differences.  At the birth of my first child, I had a date all picked out for the induction, I had a plan to avoid medications and interventions, I relied on myself for my planning and thought little of the advice of others, and stepped up to bat with confidence.  It wasn't less than 28-hours later that I had my daughter by my side in the warmer after multiple interventions, increased Pitocin doses, an epidural, and a quickly developing bought of post-partum depression.  I had relied on myself, my plans, my ideals, and discounted the opinions, experiences, and expertise of others.  I had ruled out the natural plan of the little person inside and the inability to control her.

  In class, I quickly learned to absorb the advice of everyone surrounding me.  Beware, this is DANGEROUS.  Absorbing something doesn't mean that you don't discard it later if you don't find it to be helpful - and discard bits you must!  Above and beyond listening to my principal, receptionist, maintenance men, fellow teachers, and guards I learned to listen to my students.  I dropped the pride, picked up a solid brick of humility to keep my feet on the ground, and started fresh.  I listened to their stories, I listened to their past experiences in school (or HUGE lack thereof), I listened to their desires, their interests, and I listened closely to them on the days that they told me to, "Fuck off."

  As my journey 'in loco parentis' went on, both with my children and my students, I learned that being a parent, or in lieu of a parent, is not about control.  My classroom became student centered, student directed learning (with a little guidance from  me - hey, I'm a little controlling), and I fell in love with their strengths and their weaknesses.  My students and my children have taught me more than I have taught them.  It's not just a corny saying.

  While I sit out on leave, I continue learning through my children at home while awaiting the birth of my newest child.  But, there is a piece of me that longs to be with these students that I have grown to love like my own children.  I miss the lessons that they taught me every day.  I miss the growth that I experienced at their very able hands.  I can only hope that my time with them has helped them learn a lot about science, a bit about relationships, and a smidge about the crazy parent that lives by the moto "in loco parentis."



 

Game Maker: Design and Program Teams

Since the beginning of this semester when I began teaching Gamemaker, students and I have progressively been improving our repertoire of both design and programming skills.

It is to the point now where we have pushed on to designing both the art and concepts for original games. The first couple weeks saw students working independently, trying to attempt to create a game all on their own. After this time expired, none of us really had too much to offer. One student had made phenomenal characters, another excellent environments, and yet another who could program shapes and blocks well but had no artistic ability. It only made sense at this point to shake things up and create teams with a shared goal.

Students were organized based on strength in either the design team or the program team. The teams work independently on their tasks, but have to meet together to establish characters, plot-lines, level-ups, rewards, scoring, etc. Sounds strangely familiar to the corporate world.

My job in all of this effort has been to continue teaching the programming, work with teams on solving problems as they arise, make suggestions, and continue to be inspired by the complete dedication from the students.

With a common goal, students have been working 2-3 hours a day on their tasks. Here are some of the results.

A hand-drawn boss by B.S.

Boss digitally enhanced with color.

Early sketches of our hero

Enemy worm drawings by G.O.

Animating a character in Game Maker

Beta-Testing Alien Wars

A Journey Through Punishment

Take a few minutes out of your day to watch this report profiling a group of residents from Long Creek. You will have a chance to hear from them, and learn a bit about what has led them to prison. This was accomplished through a performance called, A Journey Through Punishment.

I had the chance to see the play firsthand and had to admit it was powerful to hear these young men put their past into words. 

Link to the article: http://www.wgme.com/news/top-stories/stories/wgme_vid_19644.shtml

The trailer:

Deconstructing Number Tricks

Number tricks have been around about as long as I can remember. They usually occur in one of two varieties, ending with the number they begin with, or ending with a specific number.

Here is an example involving squares:

Example 1

And another example with basic operations:

Example 2

In both of the above cases the answer is 3, that is simply just a coincidence based on the examples I chose.

These types of puzzles make for excellent examples of simplifying expressions for an algebra class. The  puzzle involves a variable (number selected), and then a number of operations. By translating these puzzles into an expression, students can test out whether the answer will be consistent for any number picked.

Here is Example 1 again but translated into an algebraic expression:

Example 1 translated into an algebraic expression.

When students complete the expression in the last step the resulting solution will be 3. This proves any value for x will not affect the solution. Have students try it with negative numbers, with decimals, or even π.

When students get the hang of translating the puzzles into algebraic expressions and simplifying, have them attempt to create their own number tricks. I challenged a few of my students to end with numbers they began with, and end with a specific number I've chosen. They can then translate them into algebraic expressions and prove their number trick.

Here is an example a student created yesterday, "Kick In the Nuts".

And the corresponding algebraic expression.

In Their Own Words

The follow article was written by a Long Creek Student in Mr. Cimato’s math class for the May issue of DocTalk. Read the whole issue here.

By Z.G.

Through the years math class has been very difficult, not only for me but for many math students everywhere. However, things are starting to seem a lot easier thanks to the new math program in Mr. Cimato’s class— Khan Academy’s self-paced math lessons. When I asked several students at Long Creek Youth Development Center (LCYDC) how they felt about the program, many responded in a positive way. “I like the math program because it helps me move through my work faster,” said D.C. a Long Creek resident. Not only does it help students move through work quicker, but also helps them understand the work better than any text book could. It gives tutorials and shows videos on the work that is being given. This is very beneficial to students. For my personal opinion it has helped me move through math work that I’ve never seen before. Now I’ll be taking Trigonometry—never in my life did I picture myself taking such an advanced math class. This is all due to Mr. Cimato, and this new program! But like most math classes and programs, it does get frustrating and “I hate losing all my points when I get a question wrong,” said C.S., another resident. The math program is based on a point system. 

When you get a certain amount of points your bar will turn green. This is when you can advance into different math, but if you get question wrong and the bar is not green it takes all your points. This is because the program wants you to master the math problems you are working on. Some say it drives them crazy but I feel it helps because the program is helping me get better without realizing it. All I want to do is get points, and all the program wants me to do is get better with my math work.

When asked if it is harder to work with the program Mr. Cimato said, “It is more difficult because the problems are more challenging, and there are more skills involved.” This is a very different response than students had given. When asked the same question kids said it was much easier because you have to be more precise with answers and this helps to learn the work better. Mr. Cimato also said, “Using the program students get a better understanding because they spend more time on each problem. If they get it wrong they want to know why so they don’t repeat the mistake. Prior to this students would just go through the problems and not care what they did wrong.”

The math program is a computer program we use on the MacBook, and does not have a textbook. This helps because many students get upset and don’t like sitting at a desk with a book in front of them, but using the MacBook they tend to come into class sit down and get right to work. It is done at the students pace and they are not rushed. The program is not timed and gives students something more effective to work with in math class.

Introducing Game Maker

This year, for the first time I've been here, we've been given the go ahead to design and teach STEM (Science, Technology, Engineering, and Math) courses. I considered a few different options for my course, but eventually settled on one specifically drawing upon student interests and simultaneously upon my own skill-set, Game Maker. The focus of this course is to introduce students to the lengthy, tedious, and highly frustrating process of video game design.

As you can imagine with a teenage male population restricted from playing video games, interest was exceptionally high in participating. It meant the students would have to do plenty of research, play different types of games, analyze color schemes, sounds, music, story lines, scoring, etc. It also meant they would have to be exceptionally detailed, be technically proficient, creative, and be willing to work hard understanding and applying the underlying mathematics.

Not surprisingly, a few dropouts emerged over the first month when they realized it would be the most work they may ever put into a class.

Game Maker Programming Interface

Through a bit of luck and some initiative, I was able to acquire software for our Macbooks with a curriculum that included the anatomy of game design and game design itself.  This was all free which is a nice advantage to have with shrinking budgets.

In the 3 months we have been working at this, we have built a number of games including Pac-Man, Pong, Break-Thru, Helicopter and Pinball. Many of the students are now creating artwork and concepts for their own games which we plan to release before Christmas to the facility for a gaming competition.

Designing the Pac-Mac room

Aside from the technical aspects of teaching this class, there is another extraordinary angle the students and I have discovered...

We are our best version of ourselves when we are playing games. We work together showing pro-social behaviors. We believe any goal is attainable. We are disciplined enough to not give up. We learn new behaviors and apply them easily and effortlessly.

Our new goal is to figure out how to translate what we do in video games to everyday behavior.

Resources:
http://www.yoyogames.com

Exploring Perimeter

If I had to suggest one theme for teaching students who historically have difficulty in mathematics class, it would be to make learning meaningful and purposeful. The following geometry problem has a few great qualities that make it perfect in accomplishing this goal. The solution can be derived from a combination of geometric skills, algebraic skills and/or simple arithmetic. This provides a number of access points for students. There is also a part of this problem that defies explanation, and that’s the hook.

Thanks to James Tanton for bringing this problem to my attention.

Imagine having a magic rope that wraps itself around the Earth at the equator. Suspend belief during this time, and also imagine that it falls perfectly on the Earth’s surface. Mountains or oceans do not affect it. The rope forms a perfect circle. You measure the distance of this rope, which provides the circumference of the Earth, then add 10 feet to it. Your new rope is now wrapped around the Earth, and since it’s a magic rope, it also hovers evenly over the surface of the Earth. What is the distance from the ground to the rope?

To tackle this problem, most students (and teachers), begin with the radius of the Earth and then calculate the circumference. From here a student can add the necessary 10 feet, work backwards until they have derived the new radius. Comparing radii offers a solution. It looks like this.

There is absolutely nothing wrong with this methodology, but what it fails to do is unlock the beauty of this problem. What if instead of the Earth, we were adding 10 feet of rope to the circumference of your coffee cup? What if we added 10 feet to the circumference of a penny? Would you believe me if the difference never changed?

On the left side of the equation I add 10 feet to the circumference, on the right I add an unknown quantity to the radius, which represents the distance between the radii. In the second step I sub in the definition of circumference for C (C=2πr). This allows me to solve for the unknown distance between the radii, exactly 1.59154!

With this knowledge in hand, invite your students to find circular objects, discover the circumference, add 10 feet to calculate the new circle and use string to trace the new circles. Students can now measure the differences between radii and experience the beauty of mathematics.

One last thing, do you really believe the magic rope would be 1.5 feet off the ground? Mindblowing.

The Ceiling Vent

Inside the facility there is a lot of repetition: white walls, red trim, locked doors, and many ceiling vents. The monotony can be a bit tiresome when you spend all day inside. This summer I invited a few classes to explore this monotony with me. Equipped with iPads we walked up and down the halls, into units, pods, classrooms, and staircases in search of the extraordinary. Our goal was simple, to take interesting photographs and transform them into mathematics problems.

One student’s photo was a bit less than extraordinary. Actually it was really ordinary. I want to share that one today to illustrate how a simple concept can be explored.

The Ceiling Vent

The student was interested in knowing how many tiny squares precisely comprised this ceiling vent. 100? 500? 1000? More? Now this type of question might seem quite elementary. Just count the amount of squares in the width and height, then multiply, but that’s not how we roll.

Instead we came up with a rule for this problem. No counting!

Since the student had been studying ratios, we thought it would be interesting to measure the width of one cell, and then measure the width of the entire vent and divide. We accomplished this task using the GeoGebra software on our Macbooks. We then applied the same strategy to the height. Given these two numbers, we could finally multiply them to discover how many squares comprise this vent.

Geogebra Analysis

In addition to determining the amount of squares, we were also able to determine whether this vent is actually a square by our measurements.

Now if we had just stopped here it probably would have been a good day's math class, but again we are  always looking to go the extra mile. Answer in hand, we took to the halls and surveyed staff and residents alike for an estimate of how many squares are actually in the ceiling vent. We developed averages, ranges, and medians to analyze how good our local population is at estimation.

It's amazing how such a simple photograph led to another interesting day in mathematics class.