Examples of my 5 - 10 SBG rubric in practice.

•           Definitely check my prior post on my reasoning about how I grade. These are just some examples. 

•     The important thing is being consistent with yourself with students' tests and across retesting. We might disagree within .5 (that’s the smallest increment I give) but overall students will end up grade-wise being about where they should be A = full grasp of all/almost all content in the course B= strong grasp of content with some gaps/misunderstandings etc.        

•     I score honors harder and include more standards than a regular level class. These examples are all from a standard Math 1.

•  Sorry I don’t have an example for every level for every standard. These are some standards from tests I pulled in maybe 15 minutes of looking through some sample work. These aren't complete tests, usually those are approx. one page front and back.

Grading Examples: 

 I hope those examples make a little more sense! These aren't necessarily the best ones, but I only had a few minutes to choose some and these were the ones I could easily put my hands on. As always, be in touch if you have any thoughts or questions!

How I do Standards Based Grading (SBG) in a Traditional Setting

(And I pretty much should have written this after copresenting a session on SBG at #TMC15...sorry guys #betterlatethannever)

Some background real quick: I don't teach in a school/district that is full-blown SBG so I use what I call "SBG lite" that lets me operate in the traditional system but hold many of the ideals of SBG.

I teach high school, 90 minute block classes. Math 1 I see every day, others I see every other (A/B day), but have taught those on straight block as well. I usually test every 5 periods (when they see me on a Friday basically). Tests don't usually take all or even half of a period.

I will follow up once these stupid pictures load with another post including pictures of how I scored certain sections of some math 1 standards so you can get an idea of how the 5-10 works in practice with examples.

Here it goes...

I score on a 5-10 for ease of translating to a “traditional” grade (easier to communicate than the traditional 1-4 rubric for students, parents, and admin)

I like this ninja poster (just search ninja SBG to see lots of versions online) to roughly explain how I think (blue) when looking at the work and how a student feels (black text) when doing the work at each level. 

In general here is I define the levels:

10 – perfect, no errors including notation if applicable

9. 5 – Very minor arithmetic mistake

9 – Arithmetic mistakes or mistake that doesn’t generally show a *conceptual* misunderstanding

8 – conceptual misunderstanding (has gist of it but is still missing a puzzle piece)

Easier to come from the bottom now:

5 – nothing or just…wrong. If everything is blank (or not a real effort) I will give a 0.

6 – Can get started or understands one piece of the problem but gets very stuck

7 – A step above 6. Usually a combo of conceptual misunderstandings and arithmetic mistakes

FAQs:

How do you do retesting?

-         For Math 1 – 3, I embed retesting in the next assessment and it is mandatory for all students. I do this for many reasons, not the least of which is I want all students (even those with an initial 10) to show they’ve retained the material. Search for research on “retrieval practice” and the “testing effect” to see why this is crucial for transfer to long-term memory for all students.

•  Doesn’t this make the test long? No, it is similar in length to when I did a traditional test (about 1 page front and back, sometimes longer). But I’m much better about writing questions now. Don’t ask 3 of the same question if one will suffice. It’s not about *points* (ie more questions = less points per question) but about the type of mistakes.
•  Example of setup. Say it’s our second test. The first part will be retesting on the first test (A) (similar questions) plus the new material (B). The next week B will be the review material and whatever was taught the next week (C) will be new material. If there are certain standards they are still struggling with, those individual topics might get looped to another week after the initial retest.
•       Students see topics again in a quarter test that is cumulative. For YL courses the next         quarters will have sections for review on prior units. For instance, my 8 standards for unit 1 (Math 2) might collapse down to 1A Operations on Polynomials and 1B Factoring. By end of the year it will just be unit 1 and will be the most challenging questions only.
• Jury is still out on exactly how I will implement retesting in Precalc this year as the material is just so much longer. I'm thinking retesting IS on them to request out of class and will require HW to be complete and a remedial practice set on the standard in DeltaMath to be completed. They will still have the cumulative aspect of the units carrying through the course to hold them accountable in the future. 

How many standards do you have?

•          I have between 5-8 standards per unit depending on the length of the unit
•          If you feel like something is a “power standard” then you can adjust the weight in your gradebook (like in my honors Math 2 I make trig word problems weighted 2 times because I feel that application is crucial)

How many questions per standard?

• It depends on how long the problems take, I'd say the median is probably 4-5. Just enough to test the different levels of a topic. For instance with difference of squares I'm going to have 4: one normal, one that is "backwards" (constant first), one with two variables, and one with both terms being something besides one (like 9x^-25). In math 2 one of those will also have fractions. It can be as low as 2 or 3 (normal for quadratic formula for me) or higher if we are IDing transformations
• Choose the lowest possible number of questions you need to accurately see their level of understanding. This has made me think more critically about the questions I ask. No reason to ask something of the same level 3 times if 1 will suffice. Make sure there is a more "basic" question to see if they have some grasp of the concept. 

What is response from stakeholders?

•           After one explanation of my grading to a parent, I have not had a *single* issue about my grading in the 4 years I have used it. In fact, I get consistent feedback from students, parents, and guidance counselors that they appreciate this method because:

o   It lowers test anxiety and helps students see a test as just a data point about where they are in the journey of their learning (not the end)

o   Students retain information better because of being held accountable for it over time

o   Everyone is on the same page instead of not knowing what a 73 on a test means. Now everyone knows the student needs to work on 2.3, 2.5, and 3.1

If you are only entering grades for tests, how do you get students to do anything?

•           Grading is not the only way to hold students accountable. You can still be recording classwork/homework in some way to have discussions with students, parents, and guidance and even put this in your gradebook without that having to calculate in the actual grade.
•           Consider: are you grading compliance or content? I’d argue I want my grade to accurately represent what they know about the course. That doesn’t mean there isn’t communication etc about work ethic and such things or consequences for not doing certain things, but those are taken out of the grading equation.
•          Once you take out any grading of formatives, the nature of your class will switch because students don’t ask “will this be graded?” because they know it won’t and instead will do the work you are asking them to do because it is how they are going to learn it to do well on what is graded (assessments).
•           Incorporate activities and structures in your class that make not participating a kind of non-option (speed dating, #vnps (whiteboards), other games where everyone has to do work)

Aren’t we not preparing students for the real world?

•          First, I’d argue that a lot of things in the real world require constant revision in the search for doing things better (think about teaching!).
•           Second, my main goal is to have students learn as much of my content as possible. What will prepare them for the future in math class isn’t some arbitrary responsibility taught through 0s (how many students have changed habits from receiving a 0 from you?) but instead knowing the foundational math concepts in my class.
•          If (for instance) these gaps of understanding in my Math 1 class aren’t filled, they aren’t going to be closed in Math 2 and these students will fall farther behind. It is my goal to have students learn and master as much of my material as possible so that they can be successful later in their math career. Close the knowledge gaps now.

What do you do with the different scores on a standard?

•          Over the past 8 semesters of doing this, I’ve done pretty much everything. Average, average two most recent, just most recent. I’ve been doing most recent since what I care about is where we are ending up. In the RARE case they go down on a quarter test significantly, I look at what their consistent score.
•          I did like one semester where they got a 9.5 the first time it was perfect, and the next time it was perfect it changed to a 10. But at the end of quarter this took SO long to deal with after the quarter test it wasn’t worth it, in my opinion.

Random Advice:

•           Embed reteaching on these standards in class and/or homework (cue Math Maintenance!!!) so that students have an opportunity to receive corrective feedback and improve through practice before the next test.
• Have a way for students to record their progress so they can see it is working!

Whew! That was long. This is what works for me and one of the keys, as in anything with teaching, is finding the right combination for you. I've found this method keeps everyone on the same page and is pretty easy for students and parents to quickly grasp. 

Daily Structure

If you know me at all, you know I love structure. Actually, that is one of the reasons I love mathematics so much is all the structures you can find. So it probably isn't surprising that I like to think about how I structure different things in my classroom from the big picture. I'm finding this especially important since I teach a 90 minute block and last year switched to an A-day/B-day block for some of my classes.

First, I'm not saying this is what we will do every day, some days will be more heavily weighted for one section and sometimes say with early release I might scrap a section but overall I've tried to come up with a plan that serves several purposes:
1) Give better more timely feedback
2) Do a spaced review on topics we've done the week before and about a month before
3) Take up less paper 
4) Stagger the lesson and its practice to be on separate days to allow for the brain to forget and consolidate information when we return to it the next day.

Of course I came up with a color diagram that shows it better than I can explain it. 
Same color = same topic. 

Ideally I'd like to start playing with this with the actual topics before school starts, but I might be being optimistic. 
Quiz - I'm going to do peer "grading" by that I just mean trade and mark correct/incorrect, it's not going to go in the gradebook but I will glance at them to ensure accuracy but I want students to be getting immediate feedback here. I'm going to be making a big deal about the shift towards learning and the importance of "testing" oneself (retrieval) for learning versus a focus on the grade. 
Practice from the Day before -  Usually this will be some sort of activity (showdown, speed dating, #vnps which I'm hoping to get them moving during because...90 minutes) This also gives me a chance to reteach students who were absent!
Investigation/New lesson - Putting this right after practice I think will really help show the connections between what they learned previously - since they just practiced it! I don't do investigations every lesson, but it can be something as simple as a notice/wonder, WODB, or connecting representations prompt. Followed by any notes/direct instruction for the topic.  
Math Maintenance/Ticket Out - Since I'm getting laptops I'm going to try something new. I'm going to try to use Edulastic to give formative assessments on that. Occasionally I'll mix it up and do something "fun" but that will be our go to. I'm also going to try to focus on *one* topic for each math maintenance versus the mix it usually was. This will make it easier for me to a) reteach b) use assessments already in Edulastic (also it has really cool tech enhanced options) and c) gradually scale up the difficulty of questions when they see it again (about a month later) in math maintenance. I'll also include a couple questions from the current day's new lessons as my formative assessment from the day. I want to focus on an item that shows me any misconceptions they have an one summarizing/synthesis question. Combined these mostly for ease of giving feedback. Edulastic is like Google forms on steroids and I particularly like a) it automatically grades b) I can see just students who missed a particular question and then give them specific feedback c) I can give feedback to a student as a whole. It also integrates with Google Classroom as I can a) import rosters and b)they can just click a link and not have to sign in to something separately/remember even more usernames/passwords.  

Homework - I am going to give out homework but not focus on collecting/grading it. Those will be my normal lagging (spaced and interleaved) homework ala Henry Picciotto that is approximately 2 from that day, 4 review, 2 much earlier type questions. I'm going to post the solutions in Google Classroom so they can check their work and bring in any questions. I'm planning on dedicating the last chunk of pages in their NB to that so then if they aren't doing well on tests I can say "show me your homework section"...oh it's blank? There might be our problem. 

#somanygoodthings

This year I've tried as much as possible to contribute to #onegoodthing as I find it helps me reflect on the positive and remember the little things! But over the past few weeks I have had a lot of awesome good things happen that it's too much to fit in a tweet!

It's crazy for me to think about how things have changed in the past month. I had written down some longer term professional goals and been looking for more ways to grow/be in leadership and literally can't believe all of the things that have come my way pretty much over the past 2 weeks.

- I'm (fingers always crossed) going to be teaching Pre-Calc next year for the first time (since student teaching). I am so crazy excited about this. First, I love the content and had fun with it in student-teaching and can't wait to actually get into it as a teacher, now with more experience! And I have an AWESOME colleague teaching the other sections of the class who I totally mesh with. We are already bouncing around ideas about the course, planning, and overall structure. She does interactive notebooks (not yet for Precalc) and is on board with SBG. (Btw I'm hoping to get her on twitter soon ;-) ).

- The rest of my schedule is great and what I asked for. I'll have the Precalc all year every other day, along with one Math 2 honors every other day. I've actually thoroughly enjoyed Math 2 now that NC has changed the standards and some of the content - it has been much more coherent and I'm excited to be at the refining stages of that course now. The rest of my classes will be semester block Math 1. Along with my Math 2 honors, that means I have mostly freshmen which I actually love =). (All these schedule things could shift slightly, but I'm moving in the right direction and very happy!). I'm also happy that I'm looking at 3 preps (not 4) and only one of those being new!!!

Now for my bigger and more surprising opportunities :
- I will be heading up the Math Academic Team for the school ("train" and go to competitions against other schools). I'm really excited to spend time with students who are kind of like me in high school and get to do lots of math together!
- I'm going to be cosponsor of Mu Alpha Theta (Math Honor Society) next year. I've really missed being involved this year, but with being at a new school it was just a little too much to add to my plate this year. I'm hoping to bring some of what I did at my former school over and overall just have a great time!
- I'm going to be leading our Math 1 PLT (Professional Learning Team), basically just those of us teaching Math 1 trying to improve, share ideas, and reflect on what we are doing.
- Our district is doing a "Personalized Learning Cohort". I just found out today I was accepted as part of the first 20 teachers to work through this and develop model classrooms. It really is combining things I've already implemented like SBG and mastery learning, plus my videos and I'm excited to see how this pans out in the classroom and helping more of my students achieve mastery. Here's the graphic they are using to describe it:


I can't wait to get started (we will have a conference at the end of the school year for it) and think about how to take what I'm already doing to the next level and really hope this means I have more of an opportunity to try a more authentic SBG system - but we will see!


Thanks for reading =). I just wanted to share all my exciting news with y'all!

Systems of Equations

Not saying this is a ground breaking unit or anything, but I do love my new INB pages so thought I'd share <3

Intro and Solving by Graphing

Solving by Substitution

Solving by Elimination (aka I <3 flowcharts and being goofy)

Links to the docs (see, I CAN write a short blogpost!)

Math 1 (or 2 or 3) Factoring Unit =)

Hey guys.
Instead of going in order of my units, I decided to start with some of my faves first. I love factoring and I love how I progress through factoring. Hopefully eventually I'll do a vlog (never done one)/video talking you through how I build coherence through multiplying, factoring, and dividing - but until then, here's how I initially progress through factoring. I use the box/area/partial products method for factoring, so students are already used to using that framework.

My order:
Finding a GCF
Factoring out a GCF ("skinny box" AND intro factoring GCF from a 2x2 box)
Difference of Squares (this could also go at the end after trinomials)
Factoring trinomials where a = 1 ("X factor", aka just sum/product puzzles if you know those)
Factoring trinomials where a isn't 1 ("X Box" originally inspired by Julie at ispeakmath.)
Factoring completely


First thing is we need to establish what a GCF is and how to find it, which is part of a class period. The rest of the day we talk about factoring out a GCF from a polynomial by putting each term into a compartment of the hence forth "skinny box".

The same day and the beginning of the next we talk about factoring out of a 2x2 box. I think this is one of the key elements that helps my students be so successful later when we do trinomials. Hint: I used to teach this part as finding the GCF of each row/column but now just have them find the GCF of the first row and then go around saying what times (GCF) gives me whats in the box? Works SO much better now and works seamlessly with the intuition for dividing polynomials with the box in Math 3 (coherence!!!)

The next day we move onto Difference of Squares - next semester I might move this to the end. Stole the note form from Sarah Carter at mathequalslove. My twist with this is my "Difference of Squares" rap. While I haven't video taped it. I guess someone in my class recorded this and entitled it "When Math Teachers Try to Make Class Fun" <3 . Before direct instruction I have them multiply out several difference of squares to notice/wonder about the pattern.

Me doing it (slower than I usually do so they can see the steps)

Brave student then doing it for the class (LOVE HER!)

It's ridiculously cheesy but one of the best feelings later when the students learn it and you have a whole class getting into it with you. =)

Next up is trinomials where a is one which I affectionately call the "X Factor"...because you use an X, and you are factoring...and I love puns, especially if they are terrible. 

I give students a sum/product puzzle where at first all the numbers are given and I ask them to find a pattern that works for all the Xs. (Love introing things as a puzzle, because isn't that really all factoring is?! and you get more interest/buy in from students when you present it this way). We then talk about how to use this method to factor. Once we move onto where a isn't 1 we talk about why it always starts with (x    ) (x      ) if your a is 1. 

Then we move onto X Box. To start this off, I give them a filled in box and have them find the GCF and all the sides like we did Day 1. How was that? "Easy" then I have them do an X Factor problem. How was that? "Easy" I then write up the original polynomial we started with and ask them to notice/wonder about where the different numbers and terms are coming from in the original polynomial so that they practically discover the process for themselves. Thanks to Elissa @misscalcul8 for typing up my notes!

By the way, throughout all of this I'm constantly emphasizing that factoring is just rewriting a problem as multiplication. 

Last, we factor completely. For that I made a handy dandy flow chart because, let's face it, I <3 flow charts. 

Here's the link to my documents that I've actually created. I will add others to the same link as I get around to typing them up! Sorry for the awful handwritten copies for now, but hey - something is better than nothing! 

Here are my old youtube videos explaining it if you are still curious. Notes: I was still doing the GCF for all rows/column method in the X Box Video =/

GCF:

Difference of Squares:

X Factor

X Box:

SIDE NOTE: I actually am changing things up a bit by introducing solving by factoring/zero product property first and then practicing with every new method. I found this semester that it really helped students distinguish between what "factor" and "solve" meant!