How I Helped My 6th Graders Ace Math... By Taking Them Back to Kindergarten! | Mastery Learning

Hey everyone, this is Jeremy Shifling at Khan Academy. I just want to thank you for taking time out of your super busy weeks to spend time on today's session, and I want to give a super special thanks to Tim Vandenberg, who's been gracious enough to share his amazing story with us.

Now, as you may know, Tim has been teaching for about 25 years, including the last 18 as a sixth-grade teacher in Hesperia, California. While he's definitely touched countless lives throughout his career, in the last few, he's really discovered an incredibly powerful way to help each and every one of the students succeed through mastery learning.

Uh, 80% of my students are minority students. All of them receive free breakfast and lunch due to the low-income socio-economic disadvantage of nearly all of my students. Ten of my students come to me at grade level each year from fifth grade to sixth grade, which obviously means 90% of them are below grade level, including uh about half of my class at the lowest level—what California might call level one—far below uh grade level on their previous year's state test. Nearly all of my students are reading two or more years below grade level.

So, um, if this sounds familiar to you, welcome to teaching, because that's what most of us struggle with here in America. We've got lots of challenges to work with, and some of us are blessed to have a little less challenges than that. But what I want you to know is that this worked in a classroom with real obstacles to overcome. These were not affluent non-minority students who have tons of support from home. These are struggling kids, so it worked for them, and so I believe it can work for you and your students too.

So, next slide, Jeremy.

So this is where my class came from. If you see that little dot on the left side, it says Vandenberg 1819. My students come to me—this is pretty typical—60 points below passing. That's pretty far; that's way far. The most recent scores I had at the time for California is 42 points below in fifth grade a passing score. Last year they're actually a little bit better; I got the recent scores after I made this chart.

And then the county and district are also low. So here's the point: everybody's leaving fifth grade on average in California—not everybody, but on average—pretty low. You can see California, it was two years ago, is my data; they went up, they brought their kids one 1.2 points closer to passing. The county brought up their students two years ago 3.6 points closer to passing, and the district that I teach in brought their students up 3.6 points more closer to passing. So there's improvement there. A flat line actually means that you achieved as a teacher a year's worth of growth because they took a harder test—the next grade level test—and if they stay flat, hey, you taught them a year. They didn't get any closer or farther, but you succeeded keeping them up to where they were.

But positive slopes, slopes that go up, that's really great because then you're bringing kids closer to their state standards. So, but you still see a huge gap there, and my class on the far left, way down there, far below.

So we're going to tell the story of what happened. So, next slide.

In September 2016, I watched this video from Sal Khan where he talked about let's teach for mastery and not for test scores. We're not going to show you the whole video, but we are going to show you about a minute and a half. Notice how Sal talks during this video, how he talks about the insanity of our current educational system—teaching students based on you have nine months, that's it. You learn what you learn, and you move on. Forget if you have a solid foundation in your math or reading or whatever you're teaching; just no matter what, you're moving on. Social promotion—that's just the name of the game in most schools in America. It's sad, but it's just the restrictions we're given.

So watch as Sal explains the insanity of this education model—that we don't wait until the foundations of learning are mastered before building on top of that. So go ahead, Jeremy, start that 90-second video.

And this will continue for months, and it'll continue for years. Always at some point I might be in an algebra class or trigonometry class and I hit a wall, and it's not because algebra is fundamentally difficult or because the student isn't bright; it's because I'm seeing an equation, and they're dealing with exponents, and that 30% that I didn't know is showing up. And then I start to disengage, and to appreciate how absurd that is.

Imagine if we did other things in our life that way, say home building. So we bring in the contractor, say told we have two weeks to build the foundation, do what you can. So they do what they can. Maybe it rains, maybe some of the supplies don't show up, and but two weeks later, the inspector comes, looks around, says okay, the concrete's still wet right over there, that part's not quite up to code. I'll give it an 80—say great, that's a C. Let's build the first floor; same thing—we have two weeks, do what you can. Inspector shows up in two weeks, it's a 75 percent—great, that's a D plus. Second floor, third floor, and all of a sudden, while you're building the third floor, that whole structure collapses.

And if your reaction to that is the reaction that you typically have in education, that a lot of folks have in education, you might say maybe we had a bad contractor, or maybe we needed better inspection or more frequent inspection. But what was really broken was the process; we were artificially constraining how long we had to do something, pretty much ensuring a variable outcome.

And we took the trouble of inspecting and identifying those gaps, but then we built right on top of it. So the idea of mastery learning is to do the exact opposite. Instead of artificially constraining when and how long fixing when and how long you work on something, pretty much ensuring that variable outcome—the A, B, C, D, F—and do it the other way around. What's variable is when and how long a student actually has to work on something, and what's fixed is that they actually master the material.

So as Sal was saying, why do we teach and have our education system based on this fixed time model? And why do we move kids along even though they're not ready for the next grade level or higher level of math skills? So, um, that's what he talks about—this mastery learning. Mastery learning means developing each skill to fluency and long-term retention.

And I thought, boy, I sure wish, and I'm sure every teacher in America wishes, that their students came to them with mastery learning of all of the skills that they should have learned in the previous grade levels. And we all think that what were they teaching the year before? You know, well, what were they teaching the year before that, all the way back to kindergarten? And what were they teaching before that? So how about instead we teach to mastery?

So, next slide, Jeremy.

I decided after I saw that video—that was my huge aha moment—I said I am done dangerously building on the unstable mathematical foundations. It's dangerous! Why am I doing this to kids?

Next. So from now on, I'm going to teach students with a solid number sense and skill mastery foundation. I'm going to make sure my students from now on have a solid foundation, even if I don't cover all the standards that I'm supposed to teach. I'm gonna make sure that their life is not ruined when they go to junior high and high school by actually having a solid foundation of math, and then maybe I can also teach them some of their standards for the year I'm supposed to teach.

So, Jeremy, Khan Academy was going to be my tool to make that happen.

So, next slide.

So in fall 2016, I decided my sixth-grade class is going to go back to kindergarten. That's right. We all know that the holes in a foundation begin all the way back with number sense. Research has shown that students’ number sense—those students who have a true grasp and mastery of number sense—are the ones who succeed well in junior high and high school math, the higher level of math: algebra, calculus, and so on. They're the ones who really get it.

Well, what if all of our students had solid number sense? So, using Khan Academy's menu of class options, I assign to my students every grade: kindergarten, first, second, third, fourth, fifth, sixth—because that's what I teach—the sixth. And on the left column, the top two—early math and arithmetic—those two kind of dovetail with K through three. Actually, arithmetic goes all the way to even up to a little bit of pre-algebra.

So I signed out to all my students and I paced out their learning for the whole year. We ended up having some students not even finish all of third grade, but at least they understood the meanings of numbers because they mastered K-12 for the rest of their life. For the first time in their life, every single student in my class mastered kindergarten, first, and second-grade math—truly.

So, next slide.

And so for the past three school years, doing this just like this, each of my sixth-grade classes have had this—the California state math test. I know it's different for every state, but that's the big high-stakes testing that our kids in California have to take—very rigorous, very thorough. Their growth looks like this: you see my little dot on the far side. Hey, I would be happy if they go up at the same slope of the county and the district. If they just go up like that, hey, we're performing as well as them; that would be great!

But let's see what happened. Jeremy, go ahead.

That is real cohort—same kids that came to me; that’s the same kids on the left that you see on the right. That is real growth. That’s 95 points of growth! That’s unheard of. I was speaking to a head data person for a nearby school district, and he's in charge of other state test data crunching, and he told me if he saw state test scores like that, he would assume the teacher was cheating. But this is real; this is kids truly mastering their standards.

And because they had a solid number sense foundation, the grade-level standards—the sixth-grade standards that they were supposed to learn—what they did cover, what we did teach, they mastered it. We don't just cover the standards in my class; we master the standards.

And I would far rather master half of the year's standards than just merely cover the entire school year of required standards but have my kids fail in their learning. So this is real.

So, let's get into a little bit of how to make this happen real quick. Oh, by the way, one of the results was Khan Academy recognized my homeroom students as one of seven national grand prize lunch store winners.

And that's them—those are real kids. I literally just ran into one of the boys in the front row, his mom at Walgreens yesterday, and she said oh my son is doing so great! He's now in honors math and junior high, and that's life change. I would have never guessed that he could have achieved that based on his fifth-grade state test scores. So, just amazing!

All right, next slide.

So what is this mastery learning thing again? I highly recommend all of you go in and watch these videos. It's a two-minute video of Sal Khan himself explaining what mastery learning is—highly recommended. And then also, what does this look like in a classroom setting? So Khan sent their video crew to my classroom, and they filmed for a couple of days, and you can see what it looks like—how to make this happen in a classroom setting. If you click on that second link that's on, all both of those are on YouTube.

So, okay, Jeremy, next slide.

So here's how I recommend making this happen. First of all, be honest and face the state test facts. Where are your students actually at? Quit pretending they're higher than they are. Do they even understand arithmetic? Do they understand the meaning of numbers? If you don't face that reality and stare the truth in the face, you will never be able to get your students to truly master the standards like they need to.

Second, acknowledge that math is cumulative. Prerequisite skills are exactly that—pre-required, not pre-suggested. Unfortunately, we don't have that option; they come to us whether they've mastered the prerequisites or not. But that's the way math is, and so because they have to have those prerequisite skills before I can even teach them how to add, subtract, multiply, divide fractions, they gotta know what a fraction is, they gotta know what whole numbers and fraction parts are, and so on.

So we go all the way back to kindergarten and use Khan Academy to remediate and fill in those foundational gaps. Then we teach to the common core standards to mastery. I do not cover the standards in my classroom; my students do not cover the standards. We master the standards. That is the expectation. You don't do your homework; you master your homework. You don't go to recess because you finished the assignment and failed in your learning of it; you go to recess because you mastered the assignment.

Okay, next slide.

Fifth, believe that every child can learn—a growth mindset. Check out the Khan Academy units on growth mindset—amazing lessons. Use that with your students, teach them to believe they can learn because they truly can. It happened with my students; most teachers would have never guessed they could. This is three years in a row that we've seen scores like that, so it's not just a random class that happened to; it's consistent; it's working; it's repeatable; it's real.

Sixth, teach, support, teach, support, teach, support. You teach; you're not just using Khan Academy as babysitting. You teach, but then you support those kids—struggle, encourage them to come to you for help, watch those videos as Sal and his crew provide online, and use those hints. Also, have your students help each other, elbow buddies—help them help each other.

Seventh, monitor progress regularly; intervene as soon as possible. Don't wait until December to discover your kids are way behind; intervene right away.

Eighth, set realistic long- and short-term learning targets. You'll see in the very last slide is a downloadable PDF of my class's weekly learning targets—how to keep up pace. Because I assigned to them to do every grade-level course every week, we don't just wait until you're done with kindergarten before you go to first grade. We don't wait until you're done with sixth grade before you go on to the higher stuff; you're working on every course simultaneously. The way the COD learning pro system works, it works best that way; they get more done faster.

Number nine, motivate, encourage, praise, reward, celebrate. When a student graduates and finishes an entire grade level to mastery, or if you're a high school teacher or junior high teacher, if they finish a lower course to mastery, we literally have a graduation ceremony. We give a certificate of mastery to the students, and Khan has some of those you can download; I'm sure Jeremy can provide them if you email them later. So that's what we do.

Next slide, so this is my class last year—that's 30 lives changed forever. I keep hearing from parents and those parents—there's these students. Oh, Mr. Vandenberg, I'm doing so great in junior high! Oh, Mr. Vandenberg, I was stuck in the low track for the rest of my life, but you intervened and now I'm in honors math! Believe it can be done; these kids can do it. Your kids can too.

So there you go, I think that's it. Last slide, Jeremy. There's your great links. Check out the cheat sheet on mastery learning that Jeremy provided. Also, you can email me questions, suggestions—reach out to me. I'm a Khan Academy ambassador; I'm not paid anything to help, but I want to help. And so as an ambassador, I want to support this program; this is changing lives all across America and the world. If it's used to mastery, learn what mastery learning is and check out that pacing guide; this is just a sample—you make it fit your situation.

But download that pacing guide and it'll be great for you and your kids. So, okay, um, Jeremy, I'll let you kind of take over; I'm going to delete my video here for a second; I'll be right back.

First of all, I want to give you a huge shout-out, Tim. You totally rocked our worlds here, even in the middle of allergy season, so thank you so much for doing that all after a long day of teaching. As well that being said, thanks for all the amazing questions coming in. We're going to go through them in the order they were received, so definitely stay tuned for lots of great answers from Tim.

Okay, so Tim, I want to start with this question that was asked by Vanessa Ridley, who said, "Okay, I totally get where you're coming from: taking your 6th graders back to kindergarten. What is starting with kindergarten realistic for a high school teacher?"

Okay, that is a great question. For high school, I would assign literally the early math. You will discover that your kids will struggle with the early math skills. They will come along and do great, and all of a sudden hit a standard in that course and realize wait, I never learned this, and that's the very standard that's keeping them from understanding the full foundation and to build all the way up to the high school level skills.

I would assign early math and arithmetic. In high school, they don't have time to do K through 9 lower grade stuff; instead, I would assign early math and arithmetic, and that covers quickly all of the skills that they need to be able to function in your high school classes. Or you may choose instead, maybe if you're teaching a higher-level math class, advanced students, or at least at grade level students, at least assign the course before the class that you're teaching so they can get those foundational skills. If you're an algebra teacher, assign the pre-algebra class; if you're a pre-algebra teacher, assign sixth grade.

But definitely the arithmetic class—you would be amazed how many mistakes your students will make on their calculus homework because they're not solid on their arithmetic.

Cool, great answer, Tim. And sort of a related question is coming to us from Barb Wick. She says, "Hey, if you're going to take students all the way back to kindergarten, how do we help them push through that material when they might lose interest or motivation, saying oh, I don't want to go back and do all that?"

You count it as part of their grade, and you give a reward. You have contests. You know, be the great motivational teacher that you are. You gotta be the coach—the teacher that changes their life—and you gotta sell them on this will change their life for math forever, all the way through college.

They have to have these foundational skills. You make your judgment call; what do they need? Find those skills and assign them in Khan Academy. But I've got to tell you, having them as a sixth-grade teacher, I used to teach the high math class the year before I started doing it this way. I had my high sixth-grade math class, the advanced students, go back to fourth grade and do the Khan Academy fourth-grade work—they could not do it! The gaps were so huge.

So I decided the next year, the first year this succeeded great, was just let's start it back at kindergarten, and you'll discover kindergarten goes quick. They're done in maybe a couple of hours. First grade, they might be done in a couple days, so don't think this takes a year to learn. Higher grade math students—the higher up they are, the quicker they get through it.

Um, and so, yeah, just play with it; make it work for you. But I guarantee you the issue that we math teachers have is their foundational skills, like Sal describes in that video—their foundational skills are still wet and unstable and unsafe to build on. And that's the reason why we're pulling our hair out as teachers to get them to learn the current grade level stuff that we want them to learn.

So you give them points for it; give them credit. I do! I count every single one in as each course as a grade, but the lower the grade is, the less value it's worth. Like kindergarten is worth like 1/6 of a point, whereas sixth grade is worth a full point.

Cool, lots of questions about the logistics of pulling this off. Sarah Glotzbach asks, "How did you ultimately pace it out? Was this during core math instruction, tiered intervention time? Where did you fit this in?"

By sixth grade, they have so much remediation. I got permission from my principal to allow—I'm a self-contained classroom, let's just be honest—we are teaching more than the usual 45-minute math block. So I had the flexibility of allowing remediation during class time. But upper-grade teachers who only teach 45 minutes to an hour, you can assign it for homework; they could do it, and they get excited. They're like wow, I'm doing this stuff finally for the first time in my life—these lower-grade skills that I never understood.

So yes, I did have time for remediation, but that means other things had to suffer. But their math and their reading are the two most important skills in all of life. I love history; I'm a history major in college, and I teach ancient history in sixth grade. I love that stuff, but we had to teach less of it. We still covered all the standards, but we had to just decrease our history time a little bit.

Maybe your high school teachers, your principals can have a math block just for remediation in addition to their core subject math class. A lot of classes do that. I know the junior high that my students graduate to have an extra math block for them to learn from.

Cool. Speaking of principals, a very common question is the one that was asked by Maria Quintanilla, which is did you get any pushback from your administration? If so, how did you handle that?

Absolutely! So the principal called me in that very first year I was doing this, 2016-2017—the very first year—and he said, "Hey Mr. Vandenberg, I'm getting some complaints from parents that the kids are on their Chromebooks a little too much. Are you teaching?"

And I said, "Of course, I'm definitely teaching! But instead of a textbook, instead of their answers being written down and for homework at home or in class, and not knowing if their answer is right or wrong until the next day when we go over the homework answers in class, instead they're instantly learning if their answer is correct or not right away on Khan Academy. It gives that little happy sound, and the kids love it. That's my textbook! But I'm still teaching."

But yes, they are on their Chromebooks more—please, Mr. Principal, I won't say his name to protect the innocent because he might listen to this later—please allow this one year and if the state test scores are not good, I won't ever use it again. But if they're great (a lot of schools use PLCs—professional learning communities—where you have to have common formative assessments periodically, once every month or so, a couple weeks or so), if your kids start rocking formal assessments and compared to their peers, then principals start to realize wow, maybe this thing works.

So when my students came back that first year, the state test scores blew every other classroom out of the water in terms of growth. Emphasize growth. Okay, not hey, you know, we beat the other class, but did we go up a lot? That's what matters as teachers.

If the scores are great, if the growth is great, principals get out of the way! My literally my principal just told me earlier this week, "Tim, I will never ask you to change what you're doing in your classroom because of your state test scores thanks to Khan Academy."

Cool! Well I know we're at the end here; I know everyone has to either rush off and pick up kids, make dinner, eat dinner. But I do want to thank everyone for making time out of their busy days to join today, and a special thank you to you, Tim, for sharing your expertise and making us all richer as a result and as a community.

That being said, I know we didn't even scratch the surface on all the questions, so maybe I will work with Tim, and especially if you can take some survey feedback right after this webinar ends to figure out if a follow-up session or some other resource will be useful for you and for your schools.

That being said, I want to wish you and your students tremendous success out there, and I want to thank everyone for joining. You will absolutely get a recording of the session as well as a copy of the slides in your email tomorrow, and hopefully, you've been as inspired by Tim's story as I have, and I hope it will carry you far.

So thanks everyone, and thank you so much Tim.

Okay, best of luck everyone! Thanks for joining us.