Once upon a time there was a kid named Christian who came into my 7th grade math class with a number of strikes against him.
βDonβt expect too much from him,β they told me.
βHeβs slow,β they said.
βHe should be pulled out for basic skills.β (The basic skills program in our district was no solution at all. Kids went into it, never learned basic skills - and never came out.)
When Christian arrived in my room on the first day of school, he seemed shell-shocked - you know the look. He was clearly terrified by the thought of another year of math, and mortified at having an aide to help him in front of the other kids.
The year before, I had been badly burned trying to teach the basics of algebra to 7th graders who hadn't mastered the basics of addition, subtraction, multiplication and division, let alone fractions, decimals, and percentages, so Christian was actually in luck; I had decided that this year all of my students were going to be going back to the basics during the grace period of the first month or two of school. Christian would get his basic skills and be able to blend in at the same time.
I even broke protocol and asked his aide to let him work without her help for the time being. She was fine with that, and happily spent each class period on her Kindle.
Christianβs shell-shock seemed to be wearing off.
But not for long.
I had created self-explanatory practice activities based on pre-worked examples over the previous summer - John Swellerβs research into worked examples had made a huge impact on me the year before, and I was eager to try them out.
My idea was for the kids to work through these basic skills activities at their own pace with me acting not as the sage on the stage or the guide at the side, but as the βsage at the side,β available to provide in-depth assistance to individuals or small groups in response to meaningful questions that bubbled up from from students themselves.
Every day I would place copies of the activities in piles on the windowsill at the back of the room and tape the fully-worked answer key to each activity to the window above it. The students would take an activity, complete it at their desk with pencil and eraser, go back and check it against the key, and then move on to a slightly more complex activity that built on what they had learned from the previous one. They would repeat this process over and over and over again, completing as many as six or seven activities a day.
Except for Christian. His max was three activities on a good day, and his self-consciousness was starting to resurface as he watched the other students race past him.
After noticing frustration at his lack of progress one day, I asked him to meet me out in the hall for a second. This part still gets to meβ¦ I had clearly scared him; he thought he was about to get punished. I actually choked up a little as I shut the door so the other kids couldn't hear, locked eyes with him, and said, βListen to me. I donβt care how many activities you finish a day. I do not care . I only care that what you do get done gets done correctly to the best of your ability, that you learn from your mistakes when you make them, and that you ask me for help when you need it. In this class, math doesnβt need to be done quickly, but it does need to be done correctly . Deal?β
A look of relief and a sliver of a smile appeared. βDeal,β he said.
We went back into the room and he went back to work. At one point I caught him watching some of the other kids again, so I cleared my throat to get his attention, locked eyes with him and shook my head no. The sliver of a smile reappeared and he put his head down and kept going.
I considered the outcome that day to be a complete success - but Christian apparently didnβt. Meeting me at the door at the end of the period, in a voice little more than a whisper, he said, βMr. Hare, do you want me to finish the rest of those tonight?β
βOh, Christian, you donβt have to,β I replied, worried that he might be biting off more than he could chew. βYou gave me a full period of work today.β
βI want to, though.β
βOkay,β I said somewhat reluctantly as I set about rounding up the papers for him. βBut you have to promise me you wonβt beat yourself up if you donβt finish.β
He promised.
So began one of the most heartwarming episodes of my entire 30-year career. Every day Christian would complete his two or three activities during class time and then take five or six more home for unassigned homework, and the next day he would deliver the completed activities as he entered my class, with the problems he had struggled with circled, and with questions in the margins. He was confident talking to me now, and his mood in class had changed too; he was now completely at ease with his classmates, to the point of busting their chops when they tried to tease him: βSlow and right beats fast and wrong!β he would say.
One day Christianβs aide told him she was being reassigned because he didn't need her anymore. The look he gave me at that moment was unforgettable.
And then Covid hit, and I never saw him in person again.
Like many students during remote instruction, Christian became just another silent rectangle on the screen during Google Meets and just another name attached to completed assignments in Google Classroom. By the time in-person instruction had resumed, he had moved on to eighth grade.
Two years later, though, a card from him showed up in my school mailbox. In it, he thanked me for allowing him to work at his own pace, and claimed that if I hadnβt, he might have never discovered that he loved math. He also added two sentences that I'll never forget: βI never minded doing the work,β he wrote. βI just needed time to think.β
I had his younger brother Isaac in my class at the time, and he told me that Christian had managed to pull himself up into the Algebra track in high school since I had him. As only a punky little brother can, he added that he and his family were amazed because βWe didnβt know he was smart.β Apparently Christian had told his Algebra teachers that he was willing to put in extra effort on his own time in order to keep up, and this work ethic had taken him to the top of his class.
(Christianβs example had clearly rubbed off on Isaac, too; his work ethic - both in my class and on his own time - was beyond exemplary, and he pulled himself up from Partially Proficient to Advanced Proficient on that year's state test, earning his way onto the Algebra track as well in the process.)
Christianβs story opened my eyes to the potential of example-based, self-paced instruction for self - remediation . Watching him take his fate into his own hands over the seven months he was in my class was deeply inspiring.
And something else that year inspired me too. During remote instruction, I found that the activities I had used with the students in person didnβt work nearly as well when I wasnβt around to help them with them. The one or two pre-worked examples I included with each activity simply werenβt enough under these new circumstances; the further the practice problems got from the examples, the more students got stuck or left them blank.
βWhat am I supposed to do?β I heard myself saying one day while reviewing incomplete assignments. βGive them an example for every single practice problem?β
I could almost see the lightbulb over my head. βWhy not?β I thought. βI have all the time I need during lockdown.β And it would allow me to deliver more content in more fine-grained detail than ever before - and in a way that all of my students could get a hold of.
So I started churning out activities with a pre-worked example to go with every single practice problem, and loading them - along with their fully-completed keys - into Google Classroom.
This time lightning struck. Instantly my inbox started filling up with emails from students saying it was the first time they had ever understood math, and from parents thanking me for creating schoolwork their kids could learn from without their help (which was a big thing during Covid, if you recall).
More amazingly, most of my students were actually doing the work - at a time when, letβs be honest, there were no real consequences for not doing it. (Iβll never forget my principal telling me during lockdown that parents were flat-out telling her to stop calling them and that they didnβt care about their kidsβ grades anymore.)
I had been dreaming of self-remediating materials for most of my teaching career; trying to teach students with wildly varying levels of background knowledge had been deeply frustrating over the years, and trying to go back and fill in all of their individual gaps in a room with as many as 30 kids per period, 6 periods a day had bordered on the definition of insanity.
I had even tried to create a Teach Yourself book several years earlier - to no avail because I hadnβt yet heard of John Sweller or pre-worked examples.Β
My experiences with Christian and during remote instruction suggested that self-paced activity sequences based on a 1:1 ratio of pre-worked examples to practice problems might be the solution to the age-old problem of getting each and every kid caught up with the basics.
A number of years and hundreds of activities and students later, Iβm happy to report that it is.
My wife Diane works at a local community college. She frequently sees students get accepted into the program despite their inability to do math (because everyone gets accepted) and then have to take humiliating so-called βremedialβ math courses - some over and over again and at great expense. So many of them still donβt meet the math requirements for their chosen major at the end of this excruciating process, and watch their career prospects deteriorate right before their eyes - along with many of their hopes for a better life. Itβs beyond heart-wrenching.
Christian was on that track, and he knew it. It terrified him to think that he was being passed along year after year without knowing what he was doing, and that the more he seemed to be moving βforwardβ in math, the more he was actually getting further behind. That's why he worked his heart out when he got a for-real chance to catch himself up.
This next part is going to sound crazy, but itβs the truth: students like Christian are the norm, not the exception. Some of them may pretend that math doesn't matter - especially in front of their friends - but deep down they know it's essential in the real world. And given the opportunities to learn it, theyβre ready, willing, and able to put in the hard work required to do so. Iβve seen it countless times.
The science surrounding pre-worked examples and the need for deliberate practice with instantly accessible feedback has been settled for decades now. Let's use it at long last to rescue the countless students like Christian who would fall through the cracks otherwise - by giving them the power to go back and rescue themselves.
