Lessons in Laundry

Yesterday, I got beat. Beat up? Beat down?  Beat.
My opponent? A fitted sheet. Well actually four fitted sheets.

The intimidation started days before. Both of my girls had attended a week-long sleep-away camp and came home with a pair of fitted sheets each. I washed and dried them right away. That was the easy part. Then they sat in a laundry basket staring at me for days. Snickering even. They knew I couldn’t fold them. This was a fact proven many times. Somehow though, with four together all at once, the challenge escalated from a dare to a quadruple dog dare. Finally I couldn’t take it anymore. My need for organization trumped my fear of failure. 

Maybe this was a learning opportunity? I decided it was finally time to learn how to do this right. I Googled how to fold a fitted sheet. As you might expect there was no shortage of videos, tips, and tricks. I chose a video and cast it on the big screen. I sat. I was focused, ready, and attentive. I could do this! 

At first glance, the video I selected ticked all the right boxes. Step by step, clear and succinct instructions were written on the screen, said out loud, and modeled with confidence. The cheerful, upbeat music playing in the background suggested this daunting task could actually be fun. The young woman demonstrating the steps faced the same direction I faced, gave helpful tips and reference points, and was encouraging and supportive.

In spite of all this, I could not do it.

First, I watched the video three times from start to finish. I made an attempt. Fail.
Next I watched the first step, hit pause, mimicked the first step with my own sheet. So far so good! I hit play, watched the second step and hit pause. Tried on my own… Fail. One more time… Fail. I thought maybe I could do it at the same time as it was modeled. No – I couldn’t keep up… Fail. Then I remembered the playback speed on Youtube was adjustable . . . yassssssss! With renewed optimism I tried and tried again. Fail. As my fail streak continued, the video got slower and slower and louder and louder. Fail. Fail. Fail. Fail. At the slowest setting, the cheerful music and helpful instructions distorted to a comically creepy tone. Mute. After an embarrassing number of attempts, I still couldn’t get past step three. I was hilariously inept. I sat to gather my thoughts. Clearly no amount of slowing this video was helpful. Maybe this video wasn’t as awesome as I thought? Maybe I wasn’t up for this challenge?

Reflection time. What was my next move? Accept defeat? Never! A different video? Not really appealing at this point. Maybe I needed to revisit my goal. Did I really need to fold my fitted sheets this particular way? Wasn’t my desired result just to have a neat pile of fitted sheets that would stack, avalanche proof in my linen closet? Folding this way wasn’t necessary was it? Perhaps playing around a little on my own would help.

Taking a deep breath, I took a closer look at my now crumpled lump of bed linens. The trouble really was managing those elastic – y corners. I noticed too that the sheets had some key differences. Aside from size, the one I had selected to start with had elastic all the way around, while the elastic part on the others was limited to the corners. I probably shouldn’t start with the full elastic. Hmmmmmm.

I decided to make some space and mess around myself.

Would it make a difference if I could spread out the sheet on my bed instead of trying to hold it up and fold it mid-air like a pro? Let’s see . . . I spread out the first sheet on my bed for a closer look. Folding all sides in helped hide the elastic creating a more rigid rectangle. A few more tucks, flips and folds and I had it! A neat, stackable bundle. Five minutes later, my process was streamlined and three other fitted sheets were ready for the closet. Now I won’t be making a how-to video on folding fitted sheets anytime soon, but I DID have a method that worked just fine.

This whole scenario made me wonder . . .

How many times do we, as teachers, try to make things easy and efficient for students by sharing a favorite method? Do we call it a favorite method or just say the BEST method? Or THE method? How often do we declare how simple this is with my clear and easy to follow steps? Do we model something we have done a million times and make it look so easy that it might be embarrassing if others don’t “get it” right away?

I understand the complexities of the decisions teachers make. Students arrive with varied experiences. Trying to quickly level-set and have the whole group move forward from a common starting point sounds appealing. We may favor the idea of all students completing problems the same way using the same method because it might save time, be less confusing, and guarantee that all students have at least one method that “works every time”. But is this the actual result? And at what cost?

This immediately brings to mind a situation from my early days as an educator. With the topic Dividing with Decimals on the horizon, I wanted to determine the dividing experience of my students. I thought the best way to set my class up for success would be to test the waters with some whole number dividing examples. I wanted to see what dividing methods they already employed in order to connect and build and broaden. It did not go well. For whatever reason, many of my students did not have the prior knowledge I had expected. Just saying the word division brought a change in demeanor. Some looked nervous, others defeated, some slumped with the visible groan of here we go again with this pointless drudgery. Maybe I should be playing some upbeat music in the background? 

My well prepared lesson to connect their knowledge of whole number division to decimal division went out the window. But what to do?!?  I panicked. How else could you explain my next move? 

I spent the next forty five minutes walking students through the dividing algorithm. YIKES. I chose an easy enough example, maybe something like 168 / 4, but heard myself giving random senseless directions like, “First, put the first number under this line. Next, put the second number in front of the curvy part. Now how many fours go into 16?” Even as it was coming out of my mouth, I knew I was approaching this wrong.

I powered through . . .

“There are 4! Put the 4 up here and subtract 16 because 4 fours are 16!”
With my happy singsong voice, “Now how many fours in 8? 2! 
Two fours are eight so we subtract eight and TaDa! We have our answer!” 
Blank stares, Then the questions started . . .
“Why are we subtracting when this is division?”
“We were multiplying too – where’s the dividing part?”
Then, “I don’t get it”.

My panic (and poor decision making)  continued . . .
I doubled down on working with the algorithm. 
The examples continued with me leading in my happy and hopeful singsong voice, feeding the students step-by-step instructions that got louder and louder and slower and slower. Even when students successfully managed to repeat my process and generate a correct solution, there was no satisfaction, no celebration. Just the shrug or surprise of someone not attached to the process who wasn’t ever sure if they were correct or not. 

After class it was reflection time.

Thankfully I was perceptive enough to know that the class was a complete fail. Even for those doing the steps as directed – it was a fail. Students did not understand the connection between multiplication and division. They did not know that division could be thought of as repeated subtraction much like the connection between repeated addition and multiplication. Many DID know that division could be explained through the idea of sharing where the divisor could be the number of groups or the amount in each group. So what’s my next move?

Well, I certainly knew what not to do. Step by step instructions for a procedure, without understanding why, rarely leads to long term success and retention. My persistence with drilling the steps made some students feel bored and others incapable. Presenting math as a mystical process where answers magically appear through procedures seemed like a great disservice. Turn off your thoughts and repeat mine! We don’t need to know why – just trust the process!  Just because I learned division this way, and got it (well maybe “got it” is a stretch – I could follow the steps to an answer) does not mean I should repeat this method of instruction now that I am the teacher. But what to do? It was time to break the cycle. I had some planning and learning to do.

I thought about some basic dividing examples and tuned in to how I would solve them. No long division. Not once. Instead, I broke up the dividend creating a sum of numbers that divide the divisor equally. Sometimes I broke up the dividend according to place value, sometimes not. Sometimes I used multiplication with the divisor to get as close as I could to the dividend and then dealt with the remaining portion. Still other times I created a new and simpler problem by multiplying or dividing each part of the division problem by the same number. Now how to work through these ideas with students???

I did some research. How and when does division appear in our curriculum? I reviewed the progression charts. I checked out Graham Fletcher’s Progression of Division video. How is division introduced? What alternatives to algorithms are out there in my tried and true sources like Van de Walle, Small, and Burns? After my research, it was time to plan . . .

My initial mistake was assuming certain prerequisites. It is much more productive to start super simple and build quickly with connection, meaning and understanding, then it is to fail and have to back track. Better for our confidence too!

I came up with some examples. I considered what manipulatives, materials and scenarios would be useful so students could physically engage with the problem and talk about it with their peers. How could I ramp up the examples so that the use of manipulatives was no longer convenient or even feasible? How can I connect the examples they found manageable to those just out of reach? How will I support students to record their actions mathematically so that it reflects their process and showcases a method to employ in the absence of manipulatives?

This is the work of teaching. It is not breaking down an algorithm into bite-sized steps. It is not standing at the front saying trust me and do what I do! It is figuring out what students already know and determining how to build, connect, generalize and solidify. It is finding and ordering examples that are simple to model and prove and facilitating discussion so that generalizations can be made. It is testing those generalizations with examples that are not so simple. It is finding ways to make students’ thoughts and ideas visible and accessible to others for investigating, revising, and sense making. 

What did I have to do as the teacher? First comes the acknowledgement that knowing how to divide myself is a far cry from being able to teach it. To be fair, no number of math degrees will ensure that a teacher has deep knowledge of every math topic they are required to teach. Give yourself a little grace, but don’t let yourself off the hook either. Do some research, ask others, consult the experts. Don’t pull examples from thin air as you stand in front of your class. What example should be first? Why? What comes next? How many are needed before generalizations can be made? When and how do the symbolic representations start?

Since students were happy with the idea of division as sharing, I planned to start with simple problems with small numbers and no remainders. We used counters, number lines, and open area models. Students shuffled the counters into misshapen groups one by one like you might shuffle cards. Some arranged the counters in arrays. Others jumped backwards on the number line subtracting the same amount repeatedly until they reached zero. We looked at each other’s work.  We found each part of the division equation in the picture. We discussed how the representations were the same and different. I heard myself saying things like, “So you took away groups of 4 over and over until there were no counters left? Could we call this repeated subtraction?” 

Then the numbers got bigger. I created the need for efficiency. No one wanted to divide 168 into four groups one counter at a time. No one thought groups of four counters over and over seemed much better. Students were then able to say things like, “well twenty five groups of four make one hundred. Do that first and then we just have the last 68 to sort.” Perfect opportunity to discuss the divisibility rule for 4 and why it works. Others knew that 160 divides 4, since 16 divides 4. Great opportunity for looking more closely at that idea. We looked at all our ideas and debated pros and cons. We discussed how these ideas could be presented visually and recorded symbolically knowing that showing our process in an organized way can make our thinking visible and defendable. We discussed if these processes can be replicated in order to develop generalizations used for any example.

Will we ever get to the division algorithm? Sure! But with meaning and understanding – not by repeating steps. We will dissect it and compare it to our other methods so that why and how it works is understood. And when we do, we will determine when and if it is ever useful. Depending on the numbers, other methods often work best.

Now that I have my own method to fold fitted sheets will I ever return to the step by step video that was so far out of my reach? Probably. I do love a challenge. But not yet. I know how to fold a rectangle. My approach of making the fitted sheet resemble a rectangle first is fine for now. If I ever find myself in a situation where I am responsible to fold many fitted sheets efficiently and neatly without a flat surface to lay them on, maybe I’ll need or want to extend my knowledge. But for now, I’m good. 

I did learn a lot from my fitted sheets problem. I confirmed that there are connections to teaching in almost everything I do. I reaffirmed that reducing a complicated procedure to a list of steps does not always work nor will it likely lead to long term proficiency. In fact, I vowed that if I ever find myself suggesting procedural steps or speaking slower and louder to repeat those steps I will stop dead in my tracks – my lesson likely requires an edit or complete redesign. In the end, I was able to look beyond the appearance of good teaching and define best practices. The video I chose was not a terrible video, just the wrong choice for my skill level. Ideally, teaching involves making connections to known skills and increasing complexity gradually. Deep and lasting understanding is built through defending conjectures and strategies with representations. And as I often suggest, facilitating an approach of  play…persist…prove can often achieve successful and satisfying results. The best teachers will never be replaced by a step-by-step video. These are my lessons in laundry.