Author: MaryAnn Moore

Last weekend was the annual UCTM Conference. I had a great experience and left feeling pumped! Steve Leinwand was amazing! At the beginning of his presentation, my friend turned to me and said, "I feel like this man is a math education evangelist. Like someone should be shouting out 'Amen' and 'Halelujah'." Well, I may not have shouted them, but I did give a few Amen's and Halelujah's during his presentation. I'm very excited to try his 2-4-2 homework strategy (2 problems covering new content, 4 problems of mixed review, and 2 problems which require students to explain their reasoning).

For me, another highlight of the conference was getting the opportunity to present. I actually presented twice - first a 5 minute Ignite talk on the Math Twitter Blogosphere (#MTBoS) and the power of community, and second a 50 minute presentation on Standards Based Grading. My co-presenter, Desirae Calkins, and I were both surprised at the level of interest and enthusiasm regarding our presentation on Standards Based Grading. Of course, I guess we shouldn't have been too surprised given that we both love it so much and could talk about it all day long. In case you missed it, or in case you came and are looking for the resources that I promised to share, I'm writing this blog post to describe how we do Standards Based Grading. What we do might not be quite right for you or your setting but we encourage you to take the general principle and adapt it to fit your needs.

​The Problem with Traditional Grading Methods;

The purpose of grading is to give students and parents feedback that helps them to identify their individual strengths and weaknesses. Imagine that you are teaching a course about aviation. One of the important standards in aviation is packing a parachute. You teach your students how to pack the parachute and then give them an assessment on this skill. Student A and B nail it right off the bat. Student C really struggles. As the course continues and you other topics in aviation, you continue to occasionally assess your students on their parachute-packing skills. Using traditional grading methods, each of these assessments would be averaged together, resulting in a final grade of 60%, or a D for all three students. However, if you look closer, the data seems to tell a different story. Student A struggles to retain this skill and seems to be progressively getting worse. Student B is very hit-and-miss. In contrast, Student C, who really struggled at the beginning, is showing consistent improvement and by the end of the course seems to have mastered the skill of packing the parachute. So the question is, who do you want to pack your parachute?

​How Standards Based Grading Helps

Here's a quick overview of how the assessment/grading cycle works in my classroom.

1. Identify content standards
2. Teach the standards (using informal assessments to guide instructional decisions)
3. Formal assessment (quizzes/tests)
4. Grade the student - giving a separate score for each standard assessed
5. Provide feedback that moves the learner forward

Any given test or quiz may cover four or five different learning objectives. In the past, after correcting a test or a quiz, I gave students one overall score at the top of the paper.  The problem with this system is that it fails to identify in which area(s) each student needs to improve. Two students who received the same score may have completely different areas of strength and weakness. 

In order to give improved feedback to students, I now use Standards Based Grading.  The content I teach and even the quizzes and tests I give students are essentially the same as in the past.  What is different is that after taking a quiz, students receive multiple scores - one for each learning goal (standard). Students receive a score based on a 0-10 scale.

Students must score two 9's in a row on a particular learning goal to earn a 10. I do this in order to make sure every student is continuing to pursue learning and to make sure that the concept is retained in long-term memory. The first time the student is assessed, the standard is entered into the online grade book as a score out of 9. The second time the student is assessed, it is changed to a score out of 10. Each time a student is assessed on a standard, the new score replaces the previous score.
Update: I found that changing two 9's into a 10 became a lot of work for me to keep track of in my gradebook. My coworker, Mrs. Calkins, still follows this same plan. However, I have just started giving students a 10 for a proficient score. Since each standard is assessed multiple times and the new score replaces the old, I don't feel like this does basically the same thing with less work and record keeping on my end. 

Re-Quizzing

If you are going to use Standards Based Grading, you need to have a way for students to show growth. Each standard ought to be assessed in class at least twice. I usually will give one quiz each week. Sometimes the quizzes are very short and sometimes they take a whole class period. Occasionally I will give students a grade print-out and I will let them vote on which standards they would like to be on that week's quiz. Of course, I get to make the final call, but I love it when arguments break out in my class over whether the quiz should contain problems on 'Solving Systems by Graphing' or problems on 'Placing Rational and Irrational Numbers on a Number Line.' Once the quiz topics have been decided upon, I plan my classes for the week so that I spend a few minutes during class each day that week reviewing those topics.  

Additionally, I allow students to come after school to re-quiz on any standard. If a student isn't able to demonstrate mastery on the standard when they re-quiz, I spend some time explaining the concept to them and give them some extra practice until it seems that the student understands. Then I ask them to come in on another day to re-quiz again. I do not allow students to get help from me and re-quiz on the standard on the same day because I want to make sure they can retain the learning.

Catching the Mistakes that Traditionally Get Swept Under the Carpet

As teachers, we all have our pet peeves. My middle school students aren't yet advanced enough to commit the mathematical sins that inspired the Dead Puppy Theorem and its corollaries, but fear not! They are quite capable of committing other mistakes that are just as annoying - the most obnoxious of which is their tendency to  use an unequally spaced scale on graphs. This grievous error gets under my skin so much that it inspired me to create this poster and write this blog post. In the past, I when I saw this happen on a quiz, I would dock them a few points from their total score, get really annoyed, and then move on. And the problem was never fixed!! The same kids kept making the same mistake all year long. However, when I switched to Standards Based Grading, I created a standard called "Create a Graph with an Appropriate and Evenly Spaced Scale and Label the Axes". When they started getting 0's and 5's on their graph score, my students quickly stopped making that mistake. Victory! I don't grade them on this all year long, but as soon as I start seeing the mistakes pop up, I add it to my standards again.  Sometimes I don't weight it as much as I do the other standards, but just having it in there helps the students with the low score identify this as an area that needs improvement.

Grading vs Giving Feedback

I think it is important to recognize what grades do and what they don't do. Grading is evaluating student work and putting a number on it. It tells the student where they are. Grading is not the same as giving feedback. Feedback is giving students information that helps move them forward from that point. This could be another blog post in and of itself, but I just wanted to put that out there. If you are expecting students to make improvements, just giving them a grade is not going to be enough no matter what kind of fancy-schmancy grading system you use. You are going to need to find a way to remediate and re-teach, all of which takes time. I have found ways to do this during class time, during the flex period that my school uses, and after school. How you give feedback, how you remediate will look different for you depending on your style and your setting. Standards Based grading will help you identify which students need help, but you've got to figure out how to give them the help that they need to move forward or nothing will really change in the end. 

Time
I could go on and on about the reasons why I love standards based grading (more productive collaboration, more effective parent-teacher conferences, more student buy-in into learning, greater integrity of grades, etc), but I think it's worth mentioning the greatest enemy to Standards Based Grading - time. Time is the enemy of all teachers. We don't have enough prep time, we don't have enough instruction time. You can't change that. I spent several years thinking about Standards Based Grading and reading all about it and the thing that kept me from implementing it was the amount of time it would take. And then I had an 'Aha!'.

I realized that I was grading my students 20% on their practice and 80% on their tests, but I was spending 80% of my precious prep time grading their homework (entering homework daily, entering late work, absent work, etc). Somehow I needed this to stop. I still wanted them to do all of the practice and be held accountable for it, but I needed to simplify this process if I wanted to start using standards based grading. Here is the system I came up with: 

Students get a sheet like this every week. At the beginning of each class, I look for a student who has completed the practice and showed their thinking. I stamp their homework and I stamp the record sheet using a date stamper that I picked up from Office Depot. I then hand the date stamper over to that student and he or she stamps the rest of the students in the class who have the assignment completed. If a student completed the assignment and showed an appropriate amount of thinking, they get full credit. Once everyone's papers are stamped, we go over the assignment. As I answer questions, I encourage them to correct any mistakes (this is practice after all). If students have late or absent work, these require a teacher signature for credit. At the end of the week, students turn in the record sheet and I enter one score for the entire week of practice. I keep the record sheets in a file cabinet until the end of the term just in case there is any confusion later in the term about who completed which practice tasks. I love that it's called a Practice Record! It makes it feel like band or orchestra - which it should be. Do students cheat on their math practice? Probably. They were probably cheating before, too. That's just the nature of the game. But just like in a band or orchestra class, once assessment time rolls around, it doesn't take a lot of detective work to figure out who has been doing the practice and who hasn't.

Practice is a means to an end. I've heard a lot of English teachers talk about how for students to be making significant improvements in writing, they should be writing so much that it would be humanly impossible for one teacher to read every single word of it. So they get creative about ways to get students to self-evaluate their work, peer review each other's work, etc. I think the same principle should hold true for math. We ought to be able to come up with creative ways to motivate students to practice and hold them accountable without grading every single problem they attempt as though it were a test question. If you have other good ideas on how to do this, please let me know.

Just Do It!

I worry you are starting to feel overwhelmed as you read through all the details of how I've made Standards Based Grading work for me. Here's the key though: I didn't start out with anything organized. I just knew I wanted to do it so I started. It was messy. I changed a lot even within one school year, but it didn't take long for me to feel comfortable and start seeing the benefits. The logistics of how my classroom works didn't come together overnight. You've got to try something and be willing to make mistakes before you will find the solutions that work best for you. We expect our students to make mistakes. It's part of the learning process. As teachers, I hope that we are professional enough to allow ourselves the same grace that we give so freely to our students.

You Don't Have to Take My Word For It

There are a lot of different ideas about Standards Based Grading and I studied a lot of them before I tried it out on my own. If you are wanting to read more, here are a few good places to start:

Global Math Department: This site offers free weekly webinar PDs - another great collaborative product of the Math Twitter Blogosphere (#MTBoS). On July 8, 2014, Jessica Bogie and Matt Owen presented on Global Math Department about Standards Based Grading. You can view the recording here.
Dylan Kane: Dylan's blog is one of my favorites. It is incredibly insightful and introspective and is usually right on the money with what current research says. He has recently written several great posts about assessment in general (here, here, and here) and a couple specifically about Standards Based Grading (here and here).
Dan Meyer: This post and this post had a huge impact on how I think about grading 
Dane Ehlert: This page of Dane's blog, When Math Happens, gives a great overview of how he uses SBG and is loaded with lots of links to more resources on standards based grading
Robert J. Marzano: His book Formative Assesment and Standards Based Grading is research based and the seminal work about Standards Based Grading
​Dylan Wiliam: One of my heroes. Though not directly tied to Standards Based Grading, no discussion of assessment would be complete without mentioning Wiliam's book Embedded Formative Assessment.

When I first learned about math teacher blogs, Dan Meyer's blog was one of the first that I stumbled onto.  I spent about half the day reading his posts, watching videos on his blog, and browsing through his 3-Act Tasks. I was hooked. In one afternoon, I'd gotten more good quality professional development from Dan Meyer than I'd gotten from years of state and district sponsored classes. And it was completely free!  I'm still learning from him and still working on implementing some of the great ideas I've gleaned from him. Recently, Dan Meyer posted a video of a presentation he gave at the 2014 NCTM annual conference. It's about an hour long but entertaining, thought-provoking, and well worth the time.

Here's what Dan Meyer has to say about this presentation: 

"Students generally prefer video games to our math classes and I wanted to know why. So I played a lot of video games and read a bit about video games and drew some conclusions. I also asked my in-laws to play two video games in front of a camera so we could watch their learning process and draw comparisons to our students.
These are the six lessons I learned:

1. Video games get to the point.
2. The real world is overrated.
3. Video games have an open middle.
4. The middle grows more challenging and more interesting at the same time.
5. Instruction is visual, embedded in practice, and only as needed.
6. Video games lower the cost of failure."

About the author: MaryAnn Moore (@missnarymm) teaches 8th grade math in Davis School District.  She coordinates the UCTM teacher blog and is also a regular contributor to the UCTM teacher blog. Please email MaryAnn at mmoore@dsdmail.net if you are interested in contributing to the UCTM blog.

Have you ever found a great resource on the web that you would like to use to teach your students but ended up spending hours turning it into something you could use because the file was in PDF or some other non-adjustable format?  Are you the type of teacher who likes sharing lesson content ideas with other professionals?  Would you like to have easy access to lesson materials in their original file format so that you can customize them to your teaching style in the format that you have chosen?  Then the Weber School District (WSD) Math-3 (honors) Professional Learning Community (PLC) file sharing site is for you.  

I created the WSD Math3H PLC file sharing site as my Math for America (MfA) Master Teacher project. My vision for the file sharing site is an outgrowth of the The Weber School District file sharing site called "Weber Tube" which allows Weber School District teachers to upload their teaching files that they can then embed into their blogs.  Unfortunately, the files on WeberTube all end up being PDF and are not customizable.  

The WeberTube file sharing site gets quite a bit of traffic.  In fact, my files have been viewed over 197,000 times!

I wanted access to original content and felt that sharing my own materials was an "even trade."  I have created my own file sharing site for uploading files in their original file format as a means of bringing together member lesson ideas so that everyone can benefit.  The link to my site is:  http://math3h.pbworks.com/ which takes you to the FrontPage.

The file organization format follows a schedule of topics that was developed based upon the Weber School District Math-3 Scope and Sequence Document (a suggested order of topics created by a team of Weber School District teachers).  Each PLC member takes the lead responsibility for a given week on an alternating basis.  The lead person selects in advance the lesson they are responsible for and other members provide inputs to that lesson.   Lesson inputs can be used by the lead lesson preparer but are not required to be used.  The goal is having original content available.  For the first iteration of this process, one finalized lesson per week is the goal. 

Members upload files and put them into the folder corresponding to the week that topic is listed on the schedule.

If you do not teach Math-3 (honors), I envision the project expanding to include Math-2 and Math-1.  If you would like to be involved in the project by uploading content for your own use and sharing your own materials, go to the file sharing site: math3h.pbworks.com and click on the link requesting to join.  If that does not work, please send a request to jelong@wsd.net (subject: math3h.pbworks.com).  

We can all benefit from a file sharing site like this.  Please consider joining. 

About the author: Jeff Long teaches math at Roy High School in the Weber School District. He coordinates the Weber School District Math-3 (honors) Professional learning community whose file sharing site is math3h.pbworks.com.  His school bog is at http://blog.wsd.net/jelong/ .

Last weekend I attended the Math for America Utah Fall Conference.  The topic of the conference was Mathematical Modeling and the presenter was Kara Imm, Co-Director of Math in the City.  My mind is still spinning a little from some of the ideas I received, but I wanted to share one or two in particular that have already had an impact on my teaching practice.

Less is More

Dan Meyer has been talking recently about how "You can always add. You can't subtract."  Usually a mediocre math task or even a good math task can be made much better by removing some of the information.  For example, in this task called Styrofoam Cups by Andrew Stadel, rather than presenting students will all of the information they need to solve the problem (how many cups will stack to reach the height of the door), Andrew Stadel asks students "What information would be useful to know here and how would you get it?"  Since we're not in Andrew's classroom and can't actually measure the height of the door and the height of the cup, he provides us with links to pictures of that information which can be given to students when they request it.  By leaving that information off to begin with, students are given the opportunity to think about the problem and why that information would be useful.  

I find that sometimes when students are given a problem that gives them every piece of information they need, they have a hard time then knowing how to process the information.  In contrast, when I allow students to think about and request information, they have a much better idea of what to do with it because they've thought about why the information would be important and how it relates to the situation.


Processing the Information

As students ask me for information, I ask them "Why do you think that would be important to know?" After that student gives their reasoning, I like to ask a few other students if there is any other reason they would want to know that information.  I don't tell them how to use the information they request.  They tell me! 

Choosing the Model

Each of these ideas about mathematical modeling (Collecting and Selecting Information, Processing the Information, and Selecting the Model) can be represented along continuum.  Some tasks are high in one area and low in another. Sometimes all a task needs is a small tweak to make it fall a little higher on the modeling continuum.

A Final Thought

In the four classes that have done the Styrofoam Cups task, my students were able to determine the information that they needed rather quickly.  However, all of those classes were honors classes.  This has me wondering if I perhaps ought to make some changes before I run this with my regular ed classes next week.  One thing that really got me thinking was this blog post by Joe Schwartz from Exit10A.  Joe talks about working on his own to solve this swingwraps task, also written by Andrew Stadel.  What fascinated me most about Joe's thinking was this image that he shared:

To help him think about how many times a swing would wrap around a pole, he grabbed a poster tube and a chain, and wrapped the chain around the tube.  What a beautifully simple model!  I would have never thought of doing that!