## Trying to find math inside everything else

### Making It Stick

After going to Anna Vance’s session on Make It Stick, I implemented some of the ideas she presented and thought I found reasonable success with them. However, as I hadn’t read the book, it was a little half-hearted and could be improved. When I was looking through my library’s education e-book collection and saw it there (amidst a sea of worthless looking books, save Other People’s Children, which I also checked out) I decided to pick it up.

A few things stuck out to me, some of which I tweeted, but the one that I keep thinking about is the Leitner System, which they describe thusly:

This struck me for a few reasons. First, I love the idea that the “flashcards” don’t have to be what we typically think of as flash cards, but rather representations of anything we need to practice. Second, it’s a system that is learner-led, so if I can get my young mathematicians onto the system, they can run it themselves. (And extend it to other parts of their lives.)

So my thought became thus: how can I weave this system into my classroom? Here’s my thoughts. I’d love some feedback.

1. Create a system of boxes (folders? tabs?) – I’m envisioning four in a set – for each student.
2. At the end of each lesson, have the class write on (an) index card(s) something from that lesson that they think they should know. (This practice of summarizing their learning is also mentioned in Make It Stick.) It could be a knowledge fact (the definition of a polygon), a skill (solving a linear equation), or something broader (what are some ways systems of linear inequalities are applied?). If it is a skill or broad question, it should not have a specific example. (So they shouldn’t have a card that has them solving 3x + 2 = 8 every time they see it.) Then put those cards in box 1.
3. Their standing HW is to practice whatever is in Box 1 every day. If it says something like “Solve an equation,” they need to generate their own equation, then solve it. (Generation is also mentioned by Make It Stick as a way to increase stickiness.) When they get it right, move it down a box. When box 2 is full, practice those the next session, and so on.
4. On Fridays, give some time in class for students to practice, especially their box 2 or 3, if they didn’t have the time to do that at home. Then give the usual quiz.
5. After taking a quiz, they should then reflect on what they did and didn’t know, and if there is something they didn’t know that isn’t on one of their cards, make a card for it right then and put it in box 1.
6. To qualify for a quiz retake, all the topics for a quiz need to be on cards in Box 3 or 4. Otherwise, they need to study more before they can retake. (This would mostly be an honor system, as nothing stops them from just putting the cards in there.)

Does that sound feasible? What needs improvement?

Two main things I wound up talking about at MfA Summer Think were talking in math class and grades. One thing we talked about in regards to grades is that students (and parents) often flip out when introduced to a new grading system that is different from what they are used to, even if by the end of the semester they come around and say that they are glad it was done that way.

I thought, then, instead of just springing my grading/SBG system on them, that we could reflect on what grading systems really mean and what they should do first, to prime the transition. So I created a grading Talking Points (with help from my Twitter mentions for some statements).

### A Boss Fight?

One of the things about arranging your grading system like a game, as well as being a math game aficionado, is that it is pretty easy to combine the two. While yes, students can take quizzes or write essays to gain levels, they can also beat me in a math game. Of course, I’m not easy to beat, so winning against me would really show some mastery. (I do, though, allow them to gang up on me when the game is more than 2 players.)

The only students that really challenge me are the ones that hang out in my room at lunch, even though I’ve offered the challenge to everyone. And it’s cute because when they do lose they get even more determined, often because they may lose by a very small margin. (This is occasionally by design.)

The only game I’ve lost so far is Blokus, where the two Kevins beat me (but my score was still above the 4th player). As a reward, I gave them a level in Visualizer, as I figured that was the most applicable skill to winning the game. Planning ahead and visualizing paths in your mind is a useful skill. That same skill is the reward if they beat me in Ricochet Robots. In that game a team of Jane and Kevin tied me, so I still gave them reward, but they didn’t win.

It’s interesting trying to match games with skills. For example, the reward for winning at 24 is Tinkerer (since you need to play with numbers and try different things to succeed). It’s easy for games I made myself: if they can win at the Factor Draft (an upcoming post, I swear), they are a master of factoring. I have considered giving some points, not quite mastery, if they win against their classmates or my co-teacher, but to be a master, you gotta beat the final boss.

I’d love to have a bigger collection of games that I can use as assessment of skills, not just algebraic skills but the Standards of Practice as well. Any suggestions?

### Rubrics for Standards

So my grading experiment has been going on for a month now, and so far I think it’s going well. But I was pretty stressed about getting it up and running, because a lot of the work was front-loaded. The thing I was particularly working to get done was my mega-rubric. I wanted to make a rubric that showed what exactly students needed to prove they understand to move up a level in a particular learning goal.

So here’s what I made (I call it the SPELS Book to go along with the students’ SPELS sheet):

I started by making the proficient categories, and for the first 8 (The Habits of Mind/Standards of Practice) it was pretty easy to scale them down to Novice, and then to add an additional high-level habit to become masters.

I was stuck, though, on the more Skill-Based Standards. I had all the things I wanted the students to show in each category, but how do I denote if they “sometimes” show me they can graph a linear equation? If I was doing quizzes all the time, like in the past, I could say something like “70% correct shows Apprentice levels.” But I wasn’t, and it seemed like a nightmare to keep track of across varying assignments.

So instead, my co-teacher had the idea that, if each topic had 4 sub-skills that I wanted them to know, we could rank them from easiest to hardest and just have that be the levels. So my system inadvertently became a binary SBG system, but still with the SBG and Level Up shell. Now if a student shows they understand a sub-skill, they level up. If they don’t, I write a comment on their assignment giving advice on what they should do in the future. What remains to be seen is how much they take me up on that advice. We’ll see.

Also, I’d LOVE any feedback you have on the rubric, and how I can improve it. Thanks!

SPELS Book (pdf)

Updated Student Character Sheet (pdf)

Updated Student Character Sheet (pages)

### Level Up! +1 to Exponents, +2 to Equations

###### Previously on The Roots of the Equation: You All Have “A”s, You All Have “0”s, and Grade Out of 10? This One Goes to 11.

I like games. All kinds of games: video, board, tabletop, role playing. And so I often think about how games and teaching align. One thing (good) games really do well is provide a sense of progress (especially role-playing games). You start off with not many skills, but as you advance you build them up, learn new things, and can conquer tougher tasks. By the time you reach the end of the game, those things that were hard from the beginning ain’t nothing to you now.

Games don’t usually score you on every little thing that you do. What they do is take a more holistic view and then, at some point, say that you’ve done enough to go up a level. And I say, why can’t I grade that way?

Many people have lamented that the best grading system would have no grades, just feedback that students respond to to improve their learning. But grades are required from external factors: school districts, colleges, parents, principals. But maybe there’s a way around that.

Last time, I said grades should just be a sum of the levels of the learning goals. So now I’m picturing students having a “character sheet” that looks something like this.

I maybe have created that name just so I could tell students to take out their SPELS sheet.

The N/A/J/P/M are my current grading system, Novice –> Apprentice –> Journeyman –> Proficient –> Master

At the beginning of the year we can do a pre-assessment to determine their “starting stats and skills.” Then as the year moves in, we do our work in class. But none of that worked is graded in the usual sense. We would write feedback on the assignment, giving areas for improvement, but the only time a grade is mentioned is when a standard improves. Even then, we don’t focus on what they are (“You now have a 3 in Exponent Rules”), but rather in how they’ve grown (“You gained one level in Exponent Rules!”). The former just highlights that they are not the best they could be. The latter highlights their constant growth and improving.

(Then, at the end, based on what I said in the last post, their grade is literally how many boxes are shaded on the sheet. Have 75 boxes shaded? That’s a 75.)

In order to do this effectively, what we really need to have are rubrics for each standard. That way we know what counts as evidence of a certain level in a standard across all assignments, so it doesn’t matter which assignment provides the evidence. The upside to this is that you do not need to then have a rubric for each assignment! You only need your standards rubrics, because that is all you are using. (The collection of these rubrics, then, in the hands of the students, are a road map to success.)

I’m pretty excited by this idea, and can’t wait to try it next year. This is my idea from the last two posts taken to the next level, with a clear focus on growth, and not deficit. We can’t get rid of grading, and I’m not 100% convinced that we should. But we can definitely minimize the damage that it does and use it to actually promote students’ learning. All we need to do is focus on how we always get better.

### You All Have “0”s

Last time, on The Roots of the Equation: You All Have “A”s.

To follow-up on my last post about grading, I wanted to talk about what I do in my class. What I do is applicable to all classrooms, whether they use SBG or not.

If a student gets that snapshot every day, then it is quite clearly going to fluctuate and lead to some distress. Since my school uses on online gradebook, students can, in fact, check it. But I wanted my promise of rising grades to go through. So, I had to make it actually happen.

On the first day of class, I tell all my students they currently have a 0. Instead of 100 and dropping, every single thing they do in my class that is assessed will improve their grade. Even if they do terribly on an assignment say, getting a 50, that still improves their grade, because 50 is higher than 0.

That actual implementation of this, however, is hard. It means that, at the start of every marking period, I need to think ahead about what things I’m going to be assessing for the whole 6 weeks, and then enter those into the gradebook with a grade of 0. That way, everything will start at 0 and go up when actually completed. (Students can still see how they’ve done on things completed so far, and can determine their own “snapshot average” if they like, but this gives the view of the whole marking period.)

On the left, averages and assignments we have already completed. On the right, U grades mean “Unrated,” usually for assignments we have not done yet. The student who got an A- last marking period currently leads the pack with a 60.

But…thinking ahead 6 weeks about what I’m assessing…shouldn’t we be doing this anyway? Isn’t that just unit planning? My current Algebra course has 7 units, so it does work out to be almost one unit per marking period. And the process isn’t that inflexible: if I delete an assignment because I decided not to do it, or add something in, that’s a small fluctuation compared to the overall experience.

By the end of the marking period (as you see in my picture), everything will match up to the number it would have been had I gone top-down. But the way we get there is important. It is always better to grow.

After being questioned by Andrew Stadel and Chris Robinson on Twitter, I have some more explanations.

Me: Parents felt it was unclear at first, until I input marks that differentiated between “not done or graded yet” and “missing.” Then they were more on board. Students were confused by it at first, but liked it in the end. Admin supports it.

Pros include feeling like we are always improving and, a big one, it makes grading so much more enjoyable for me, because no one goes down.

Cons are that it’s hard to gauge sometimes (in terms of “snapshots”), especially when you get a big rush of grades at the end of the marking period.

Chris Robinson: James, can your “grades” go down per individual standard/learning target through the term?

Me: I’ve seen it go both ways in SBG. For me, they can’t go down in content standards, but can in practice ones. I do continuously assess but I feel like once someone has shown some understanding, they keep it, and they just need a refresher. (But I think I got that from Dan Meyer’s original “How Math Must Assess” post.)

Stadel: Thanks for explaining. What percent of students adjusted to & welcomed it? I like the premise of zero understanding and working towards mastery.

Me: Adjusted to, I would say over 95%. Welcomed, in the 80%. (Super rough estimates.)

Stadel: Do you have any materials/handouts explaining the philosophy to parents & students?

Me: I…really should.