2022 #OneWord

 I have been thinking on my 2022 one word for quite a while.  Usually words come to me rather quickly. Last year, recenter, was almost instantaneous... but this year I struggled, so I decided to just do a brain dump...

As I brainstormed, there were so many words that came to mind, some of which included:

• enrich
• learn
• expand
• selfish

I really reflected upon what these words had in common.  The last one, especially, since it was really unexpected. I am not a selfish person by nature. I have always thought of myself as an everyone-else-first kind of person. So I was a little shocked when this word came to mind. 

It has been a long year. for everyone. I and I mean everyone. Teachers, students, staff members, parents, flight attendants, the medical community... everyone has been overwhelmed... Even that group of people that you think are doing really well. They aren't. They're struggling.

2020 was a horror movie. 2021 was the sequel to the horror movie. And we all know there is not a single horror film where the sequel was better than the original. 

Possible consideration for...

Still, what did my brainstorming mean?  Finally I saw the connections and a word came to me that encapsulated what I needed.

Control

2021 was out of control. As much as I tried to (and successfully did) recenter many aspects of my life including family, friendships, and running, I didn't have control over so many other aspects.  The problem was that I didn't realize (or want to admit) there were hundreds...thousands...millions of things OUT of my control... but I still wanted to control them. How many students were in class... Who was out sick... If classes were virtual, in person, or some hybrid plan. If friends or colleagues wanted to talk. or text. or video call.  I had control over none of these things, yet I wanted control over all of them.  

When I reflected over what I needed... it was control. Not control over things that I didn't have power over, but control over things I did. Control over my emotions. I'd lost that in 2021. In 2022, I will focus on what I can control:

• I can control my actions.
• I can control how I treat others. 
• I can control my responses. 
• I can control what time I go to sleep. What I eat. What I watch. 
• I can control my effort. 

2022 is all about controlling what I can control... and doing my best to let go of things that I can't.  

I don't think it will be easy. I am, by nature, a pretty anxious person. The past two years have not helped this part of my personality.

But how I respond to situations is within my control. And 2022 will be about regaining that control. 

Let's Make A Deal!

 This week's game was also based on a television game show: Let's Make a Deal!  It is a review game that covers unit rate and leads into constant of proportionality. 

Students are given two choices (which eventually evolve to three or four choices) for which is the better deal.  They then use unit rate strategies to calculate which is the better deal based solely on math. This is an important filter. We actively discuss that in real life people think about other factors besides cost - taste, quality, and so on - but for our purposes, the only factor is the cost.

Students then calculate the better unit rate and explain in a sentence, using my model if they are having trouble wording an answer. 

I then wander the room and check work.  Students know I've picked a random student and that student needs to have their work shown as well as a sentence explaining which is the better deal including the unit rate.  

If students are correct, that is if the secretly chosen student is correct, they get the point. If not, teachers get the point. 

Generally students write in cost per item ($3 per pound, $2.29 per gallon.  When they calculate the cookies, they get 0.23, which they generally write as 23 cents per ounce for Oreos. When students calculate the problem above, they get 1.69/250 = .00676.  Students are often confused how to write numbers correctly when values get more precise than two decimal places. How does it get represented? It is a great question since we never (rarely) use this many decimals for money in real life.

What does .00676 mean?  Well, .01 is one cent, so this value is less than a penny per napkin... that seems to make sense; napkins aren't that expensive... so that means it is part of a penny per napkin. So we can write it as $0.00676 per napkin or we can round and say six-one thousandths of a dollar, or six-tenths of a penny per napkin. What we wouldn't write is 6.76 cents per napkin. We then establish a class agreement that the cent sign will no longer be used, and everything will be written in terms of dollars since that is the calculation result we would get. 

I show students this real image and ask, "If you were buying things from this toy bin, how many toys can you get for $5?"  Most answer 5 toys, since the cost is 99 cents each, which is about $1.  We then look at the photo in more detail and notice that it doesn't say 99 cents, but .99 cents.  This is read ninety-nine hundredths of a cent. This means each toy is less than a penny! 

We redo the math: $5 broken into $0.99 each would be 5 parts with a little left over.  But $5 broken into part of a cent each... $5 / .0099 = 505 toys!  What a bargain!  

Not sure who would need 2600 bananas for $5... but if you are looking...

Welcome to ... The Price is Right

Good morning, readers! Currently our eighth grade class is working on estimating the value of non-perfect square roots and placing them on a number line.  This is a difficult concept for many of our students as we are introducing them to the idea of irrational numbers. Additionally, many students have the misconception that the square root means "divide by two." 

To help with this, we play a game based on a VERY popular game show - The Price is Right. 

Here is how we play.  Students are given an imperfect square (such as 40) and asked to estimate the square root.  We have a double-number line tool card which was developed by a teacher at my school to help students visualize where they are on the integer number line. Using this card, they identify the two perfect squares that the imperfect square is between. They then decide which perfect square is closer to the imperfect square.  The initial goal is for them to identify if the imperfect square is larger or smaller than the half mark.

For example, if they had the square root of 40, students would identify the square root of 36 and 49, decide that they are closer to the square root of 36, which means the value is larger than 6 but less than 6.5.  We would get estimates that range from 6.1 to 6.4. 

Once we have done a few practice problems, the game begins!

I randomly call four students to the front with their tool cards. I play the music as they 'come on down' and then display the 'fabulous new prize'

It is the BEAUTIFUL square root of 10!

The four contestants then start their work while the 'studio audience' (other students) do as well. After 90 seconds or so, I have the students in the audience start calling out bids, much like the actual game show. Contestants up front can listen to the suggestions or stick with their answer. 

Each contestant shares their answer with me and I write their estimate on the board.  I then reveal the correct answer, usually to three decimal points.  Students then have to decide who is the winner - the person that is closest without going over. 

We do this for a number of rounds and the winner of each round gets to go into the showcase showdown at the end of class.  This determines our daily winner.

It is amazing how good students get at estimating values. At first they start with one decimal point but after some time, practice, and friendly competition, they start going out to two and three decimal points. 

This strategy and game has really increased our students accuracy as well as confidence. They never use a calculator during the entire lesson and are able to estimate the square root of imperfect squares with amazing precision!  The results of the final round are below: 

After the game, we do return back to the learning target - estimating the square root of non-perfect squares. It is important to return to this, because student "H" in the image above didn't win as they had an answer that was 'over', but all four answers met the target of the lesson.  It was a good day!

#MarburnCon21

This week got to experience the wonder of #MarburnCon21.  This virtual conference hosted by my school, Marburn Academy, focused on the theme of "Closing the Gap."  It brought together researchers from across the country as well as England and Australia to share the most recent best practices, techniques, and strategies to help students that learn differently or in non-traditional ways. 

What I really love about conferences is being able to take information from these experts and filter them into two buckets - what can I do to change my own classroom in the long term and what can I get from these presentations that I can bring back to the classroom on Monday.  MarburnCon21 gave me a good opportunity to reflect on my current teachings.

Day One

The Keynote speaker, Dr. Carl Hendrick, shared so many good thoughts. He reminded us that memories are built around schema - that words in context could have different meaning and memory depending on this schema. Vocabulary is built based on this schema and novices need lots of practice as well as explicit practice to build memories - much more so than people that have previous connections. 

Dr. Hendrick also talked about authenticity in four parts: Expertise in the subject, passion, unicity (the purposeful linking of the teacher's experience with students), and building rapport. 

One takeaway from Dr. Hendrick for Monday connected to feedback. The purpose of feedback is to improve the student, not the assignment. Improving the one assignment will not transfer, but improving the student has a stronger chance of transferring to the next activity. 

Another speaker that left an imprint on me was Dr. Sarah Powell. Dr. Powell spoke on helping students with word problems - a very important part of my everyday teaching world. She opened up with ineffective word problem practice.  When I say ineffective, I mean based on long term studies, not based in opinion. 

Dr. Powell shared that attaching keywords to operations in word problems is not an effective practice. For instance, teaching students if they see "all together" they should always add. What research has shown is that students will scan for numbers, key words, and then use the clues to solve the problem without reading the context.  She shared that in norm-referenced tests, key words led to correct answers between 25 and 50 percent of the time. With multi-step word problems (the type seen in late elementary to middle school) this accuracy dropped to less than 10%.  

Instead, we have to teach our students attack strategies and help build their schema to recognize how problems should be solved. Dr. Powell also shared a great visual for students in a round table discussion after her presentation.  

Day Two

Day two continued first with Dr. Erica Lembke sharing her knowledge of data based learning decisions. Much of her presentation fell into the bucket of long-term thoughts and how I could revise my progress monitoring on various skills and, more importantly, have students track their own growth over time. 

Her presentation was followed by an amazing language acquisition presentation by Dr. Pamela Snow. First, her dedication to helping educators was shown off by the fact she is located in Victoria, Australia, meaning she was presenting to us at 2:00 am local time.  Amazing.

Dr. Snow led us down a conversation of components of language including form, use, and content. She went into biological vs. non-biological forms of language, the explosion of vocabulary between ages five and eight, and the different tiers of vocabulary from everyday oral vocabulary (expression of feelings or needs) to general contextual reading (knowing words for comprehension), to lexicon in specific classes (hypotenuse, quotient.)  

I finished my MarburnCon21 experience with information from Dr. Amber Ray as well as Dr. Elizabeth Hughes. Both of them shared many ideas that I plan to incorporate into my lessons over the next few weeks. Dr. Ray spoke on SRSD as an approach to writing, while Dr. Hughes talked about the importance of precision of vocabulary in the classroom. Dr. Hughes had many connections back to Dr. Snow as well as Dr. Hendrick, and I reflected on how as a math department we have spent the past couple of years focusing on our vertical alignment of vocabulary.  It is a great feeling now when students join us in seventh grade and say, "I'm going to plus 5 and 9" and I hear a cry of "You don't plus numbers, you ADD them!"

Thank you to all of the organizers, presenters, and behind-the-scenes members that made this event possible! 

Day One: Where Do I sit?

It was so wonderful getting back into the classroom this week for so many many reasons. One was that I got to use one of my favorite first day of school activities called silent line-up.

This activity starts by having students lining outside my classroom. From there I told them directions are on the board and once they enter the room they may not talk or write anything.  As they come in they see the desks with numbered post-its and this screen:

I usually include "no mouthing words" but with masks, this wasn't necessary.

It is always interesting watching their reactions. They first start by staring at each other. and then staring some more.  This year I actually had a student go straight to the first desk and sit down while another sat in the last desk in the room. Bold moves, I exclaim.

Eventually they find some systems that kind of works. This class saw a calendar on the wall and a periodic table. Some pointed to the numbers on the calendar while others pointed to various elements.  Other students had no idea what they were trying to communicate.  

I was born in Rubidium

After 10 minutes I gave the student in the last desk a voice so she could talk but nobody else could.  It didn't help matters much. 

Five more minutes pass and after 15-minutes all the students were seated and student #7 said, very meekly, "We are ready for greatness." I asked them to give me a thumbs up if they felt they were in the right seat. Not many did.  We went around the room and shared birthdays. The first student called out January 5th, the next was later in January.  The third student called out a birthday in August.  Moving along other students realize there are many people out of place.  

I tell them they'll have 5 minutes to figure out their correct desk and will allow them to talk thsi time.  A couple minutes later all students are back in their seats and we go around again.  Turns out we have a correct order this time and also learn that two students in this class have the same birthday! (A math lesson for another day, perhaps.)

When we were finished, I processed through the activity. I asked them how easy the activity was. Were they frustrated? Did they want to quit? Was it getting easier or more frustrating as the class went on?  We then connected it to their educational experiences, not just in math.  When they are stuck, what is their strategy? Do they sit quietly and not ask for help? Do they build their frustration? Do you wait for the one person in the class to talk?  How much faster and easier did this problem get solved once you were able to all communicate with each other?

Eventually we talk about how school can be difficult at times, but by staying silent and not asking for help it will only increase the frustration and difficulty. Many times the rest of that week a student would need help (from I don't understand the material down to I don't' have a pencil.) Usually they spoke up, but when they didn't I reminded them of this activity. 

It also benefits me in the classroom as well. I see who the natural leaders are, or who students perceive as the leaders. Which students gravitated towards each other? Which ones tried to be a tribe of one? Which tried to just be invisible?  I learned of friend groups and potential discipline issues before anyone said a single word in my class. It is a powerful fifteen minutes.

I hope that all of you are having an amazing return-to-school experience. Stay safe!

Reflections After Hitting a Milestone

Recently a fellow educator on twitter, MorganLeming3, replied to a rather fun post from Nicholas Ferroni: How long have you been in education? (only using references and not the number)

My students have this insane curiosity about how old I am. Ranges go from 30 (so kind!) to 63 (so... ummm.... unexpected?)  They try to use context clues (the age of my kids, the fact that I've been teaching longer than any student in the school has been alive...)   I run lots, so I can't be THAT old, but I have a son in college, so I have to be at least 50, but I have a daughter that is only a year older than them so then I have to be about their parents age. 

So generally I give references like that to the question posed in the twitter post.  Realizing some facts, I decided to see how long I was a teacher.

What is crazy... what I found amazing... is from the day I was born to the day I first entered my first classroom after signing my first contract is LESS THAN the number of days from that day to today. 

I have literally been a teacher for longer than I have NOT been a teacher. 

This statistic amazed me. I have literally been a teacher over half of my life. 

And that has led to lots of reflection.  I started teaching back in the late 90s - before standardized testing, before common core, before Google was a publicly traded company. I started teaching before students had cell phones or social media.  I started teaching before you could get a new overhead projector with free two-day delivery... and back when we said overhead projector, we meant this:

Say hi to Elmo!

It is amazing both how much education has changed, and how it has stayed the same over these 20+ years. We have made so much growth in understanding how the pre-adolescent and adolescent brain encodes information. We have made so much progress on understanding various learning difficulties and how to best serve students that learn in non-traditional ways. 

There are so many changes that have happened within the classroom, both with this new knowledge, and also to keep up with the latest trends. I have been teaching a while, but looking back at how much technology has changed in the past two decades, it is amazing that there is anything that looks the same anymore. What do students still sit in rows and columns? (pre-covid, that is.) Why do students still give study guides the day before tests? Why do we still punish students with lower grades for late work or for retakes? Why do we still reward students with extra points on assignments that don't connect to learning targets (one box of tissues = 5 bonus points!) Why do we still average in zeroes to final grades? Why do we still depend so heavily on worksheets (PS - if you do, I highly recommend the book Boredom Busters by Katie Powell) 

Education has so much room for growth still and I hope to witness, and even be a voice in that change, over the next part of my career. 

When Will I Ever Use This In "Real-Life".....

 The most common question I think many teachers receive is "When will I ever use this in real life???" I get this question from students, from my own kids, my wife (when have I ever used...)

First, I always find it funny that math is generally the main target for this question. The one subject that arguably is needed for any profession.  So let's look at math skills and where they are used in real life.

"When will I ever need to know that a^2 + b^2 = c^2?" 

Let's look at the skills needed to solve this problem:

1) Following Steps in Order.

In order to solve this problem you have to follow steps in the correct order. Assuming you are solving for a leg, you need to square then subtract then take the square root. If you are solving for the hypotenuse you need to square then add then take the square root. If you don't follow the steps in order, you end up with an incorrect answer. 

Now, reflect on the times in your profession or in your life you had to follow steps in the correct order to complete a task. Recently I was tasked with putting together a squat rack with a lat pull-down attachment. There were over 20 steps and hundreds of different pieces of hardware. Following the steps in the correct order was key to putting it together. 

2) Attention to Detail

Looking at the Pythagorean problem, you need to know if you are solving for a leg or a hypotenuse. You need to label your values correctly and put them in the correct part of the equation. You have to notice if you are adding or subtracting a constant.  25 + 36 = c^2  is a different problem than 25 + b^2 = 36. Students get training on noticing small details and the importance of those details. How many times have you heard someone say, "I only forgot the negative sign, why did it get marked wrong?" That one symbol is the difference between MAKING $40 and LOSING $40.  

Obviously when putting together the squat rack, this skill was vital. There were bolts of different sizes, including a 72mm bolt and a 76 mm bolt. These are almost identical in size, but different enough that putting the wrong one in the wrong place would make the equipment non-functional. 

3) Building Social Skills (especially to ask for help!) 

The math classroom is the prime place for students to practice social skills and language to ask for help - not only from an adult but also from peers. Students solving for the missing value of a right triangle can check in with each other, practicing good social questions such as, "What did you get for the answer - I got 15."  They can work on respectful dialogue when answers do not match "Oh, I got 9." From there they can use respectful, responsive language to determine who made a mistake. 

This language is a skill and needs to be taught. Students do not inherently know how to handle conflict, especially if they are the one that made an error. 

You can bet I was asking for help when I needed to attach the two vertical sides of the cage.

4) Using Resources

Sometimes you don't have the answer in your brain. Sometimes you need to use a resources. In the math classroom this can be a tool card, a notebook, a digital reference... each classroom has their own system. I can't think of a single profession where this skill isn't valued. Doctors have scores of medical text, mechanics have diagrams and reference cards for various vehicles. No profession requires you to know all of the answers to all of the questions off the top of your head. In teaching, like other professions, our greatest resource is each other - getting ideas on how to help students from other teachers that have had similar situations is vital, which connects right back to having the social skills to talk to others.

So many skills in one skill!

This is just a small selection of thoughts that came to mind as I have thought about this question. I've left off other skills such as patience and perseverance.  Math is more than a list of algorithms. The math classroom should be a fluid, open classroom with dialogue and discourse. Students should be engaged in discussion and asked to defend their answers. Incorrect answers and appropriate-levels of struggle should occur. Those skills translate to the real world in many important ways.