Archive for the 'Assessment' Category

Our Grading System

Standards Based Instruction

We decided a few years ago that the sequence of our texts don’t really work for us.  As a result, we began teaching one standard at a time. We have taken our state standards set up a sequence and pace  in a way that makes sense to us.  Some of the standards we have broken down into specific skills and these skills are what make up our gradebook.

Common Formative Assessment

Once we have done our initial classroom instruction, we give a common multiple choice assessment.  This assessment is graded on a 1-4 rubric.  A students next step is based on how well they do on the assessment which is a pretty fair cross-section of the different problems a student may be expect to do on the given standard.  We determine the initial score based on the percentage of problems they get correct.  85-100% = 4, 70-84% = 3, 55-69% = 2 and below 55% = 1. 

Less Than Proficient

The level of understand a student demonstrates determines what happens next.  If a student scores a 1 or 2, he will do a series of activities that may include defining basic terms and demonstrating pre-requisite skills.  Once finished with these activities, the student will then take the problems that were missed on the CFA and not only correct them, but explain what went wrong (verbally or in writing) and how to work the problem correctly.  Students who score a 3 on the initial assessment are just required to make the necessary corrections with explanation.  Once the corrections have been made, the student is then given a re-assessment and the new score replaces the old score in the gradebook. 


Although  students may get 100% of the problems correct on the initial assessment, we still give them a 4.  Our reasoning is that the multiple choice test doesn’t allow our students to demonstrate understanding that goes beyond classroom instruction, but it does allow them to show proficient understanding.  Students who demonstrate proficient understanding on the assessment are given the opportunity to turn the 4 into a 5 by choosing from two categories of activities.  Examples of activities may be creating a mini lesson, peer tutoring or some other project agreed upon by teacher and student.  The second activity is some sort of writing assignment that may require the student to explain the process or describe what skills a student may need in order to be successful with this standard.  Once a student has completed these activities and has shown the ability to explain his work the score in the gradebook will be turned into a 5. 


At this point, I can say that the strengths of this system are:

  • Students grade is based on what they understand and not a mere accumulation of points.
  • Students are allowed to re-assess and new understanding replaces old understanding in the gradebook.
  • Students seem to understand where they are having trouble and what skills they need to remediate.
  • Learning has become a conversation between teacher and student because in order to re-assess, student needs to articulate previous misunderstanding and current understanding.
  • Students have a choice on when to re-assess.  They can work at their own pace.
  • Students also have some choice on which activities to do in order to demonstrate understanding.
  • The dross has burned off the grade.  Students’ grades are based on what they understand rather than things like effort,  homework or extra credit.


  • Students have to take more ownership of their learning which means they have to un-learn some bad habits.  Not sure that it is a weakness in our system specifically or an indictment of the educational system in general.
  • Teachers are having to re-think classroom management when students are working on different activities.
  • We are having to decide if some of our standards actually lend themselves to “advanced” work or if later standards are the advanced version of some previous standards.
  • Need to develop more advanced activities for students to do while working towards a 5. We allow for students to create their own activity as long as it has been agreed upon by the teacher, however many students don’t know what to do with that kind of freedom. 


  • What’s the best way to take a series of 1’s, 2’s, 3’s, 4’s and 5’s that are based on levels of understanding and turn them into a letter grade? Do you use mean, median or mode? 
  • If we go with some sort of average from 1-5, what percentage do you use for an A, B, C, D or F? Currently we are going with average where > 4.5 = A, > 4.0 = B, > 3.0 = C, > 2.0 = D and <2.0 = F.

Adaptation for the Advanced Class

Because my classes are advanced, I have to adapt this system to suit my students’ needs.  Basically, I am using the standards as the “basic skills” for my class.  I have a posted a series of mathcasts and study guides on each standard and the students are expected to view the online examples and do the problems in the study guide prior to taking the pretest.  If a student scores above 90% on the initial assessment, there is no other work to be done on the standard–they receive a 5.  Students who score below  90%, need to correct their errors, explain to me that they understand why they made their mistakes and how to fix them.  Once I am convinced that they have truly corrected their errors, I give them a second assessment and the new score replaces the old one. 

My reason for allowing students to earn a 5 right off the bat is that 90% of our classwork is problem solving that uses the standards as the jumping off point.  Students in my 8th grade class receive two grades.  They are all enrolled in an algebra class as well as a geometry class.  We treat the algebra class as the “grade level” basic skills class and the geometry class is the “advanced” class.  The geometry we are doing is analytical so students are having to use the algebra at a much higher level…so I’m ok with not making them jump through hoops in the algebra class. 

Note: My department is awesome.  I truly loved my math department at my previous school and it was really tough to leave them.  However, I couldn’t imagine working with a group of teachers more willing to try new things.  We have pretty good discussions in our department meetings and there is plenty push back.  But at the end of the day, we are all trying to find the best way to educate our students.

Who Gets It?

Here’s the problem:

An airplane is flying at 36,000 feet directly above Lincoln, Nebraska.  A little later the plane is flying at 28,000 feet directly above Des Moines, Iowa, which is 160 miles from Lincoln.  Assuming a constant rate of descent, predict how far from Des Moines the airplane will be when it lands. [1]

Question: Which student demonstrates better understanding? Why?

Student A


Student B


Student C


Student D



[1] Problem courtesy of Phillips Exeter Academy.  Hat Tip: Alison Blank

What’s in a Grade?

“How many pages does it have to be?”

“Is this going to count?”

“How many points is it worth?”

“What can I do to bring my grade up?”

“Can I do extra credit?”

You’ve all heard these before, right?  I have said for a long time that the worst part of teaching is grading.  It’s a tough situation because somehow we have to put a number on it.  If we don’t grade, then “kids won’t do it.”  But because of grades, we often get students who are looking for the least amount of work for the maximum grade. I hate that about this job.  I want to ask questions that lead them to ask questions and have class end up with a giant group hug where we all walk away realizing that we may not know the answers, but man, we sure questioned the heck out of it. 

We have done a lot of work on our campus to try to get kids to go beyond the curriculum.  We just became the first middle school in our county to reach 800 in API.  Yeah, hold the applause.  It’s based on a standardized test which we all know don’t mean nuthin’ when it comes to having kids actually think.  But truth be known, this means that principals from our area will come calling asking, “what are you guys doing?”  They may be disappointed when they come to see the dog and pony show but end up seeing a staff that is doing their darndest to get kids to question and speak/write complete thoughts.  You see, these principals are asking the wrong question.  It isn’t about what we are doing.  It’s about what the kids are doing. 

Apparently our students are doing something right, though.  They are developing a reputation in high school for being “Sequoia kids” who sit in the front row, ask questions and, at times, challenge an occasional teacher to step up their game.  Fantastic!  But how do you grade that?  How do you grade a kid who has learned how to learn?  Last I checked, that isn’t in my state framework.  There’s no standard for that.  Which brings me back to grades.

How do you quantify learning? Why is 90% average the accepted norm for a kid who really gets it?  90% of what? Is this student truly advanced, or did she take a bunch of tests full of a bunch of basic questions and get 90% of them correct? 

So tell me, what does a kid have to do to earn an A in your class? What are you doing to ensure that the grade actually means something and isn’t just verification that a student jumped through all the right hoops?

Monologue to Dialogue

“When you add a positive integer with a negative integer, how do you know if your answer is positive or negative?”

 “Well if the negative number is bigger, then the answer is going to negative.  If the positive number is bigger, then the answer is positive.”

“Aren’t all positive numbers bigger than negative numbers?”

“Well, yeah.  But if you take the sign off the negative and it’s bigger than the positive, then the answer will be negative.”

“Why are  you taking the sign off the negative number?  What rule allows you to do that?”


“I know that I can give you 20 addition problems and you will probably get all 20 right, but I want you to explain to me why this works the way it does.  Come talk to me when you think you have an answer.”

*10 minutes goes by*

“Alright, I think I’ve got it.  If the negative number is farther down the number line than the positive number, then the answer is going to be negative.”

“Farther down the number line?”

“Yeah, it’s more negative than the positive number is positive.”

“How do you know that?”

“It’s farther from zero?”

“Oh, what do we call that when a number is farther from zero than another number?”


*5 minutes later*

“ABSOLUTE VALUE!.  If  the negative number has a greater absolute value, then the answer is negative.  If the positive number has the greater absolute value, then the answer is positive.”

“That is correct young grasshopper.  You have done well.  You may now enter into the realm of proficiency.”

I have had this conversation about 10 times over the last few days.  Our current system has students take a common formative assessment (CFA)which is very closely aligned to our state’s standards.  It’s a multiple choice test that has questions that look an awful lot like the same questions they’ll be seeing in April when we take the CST test.  Based on their score, they have a set of activities to do before they can re-assess.  Re-assessment may look like the conversation above.  I think I am really going to like this system because it allows for dialogue between teacher and student.  I have the opportunity to ask them about the why and actually tie it to their grade.  The benefit to this is that students have choice in how they demonstrate their proficiency the second time.  The first time, it’s a multiple choice test.  However, the second time may be written, oral or heck, they may even draw a picture. One of the best things about this is that the students are taking more ownership of their learning because they have to direct some of the activities.  They actually have choice.  And that’s empowering.  They aren’t waiting for me to give them another hoop to jump through. 

The parents are coming along slowly.  Many of them didn’t understand how their student could score 100% on the CFA and yet the score in the grade book shows up as 80%.  Last night was Back to School Night and I got the chance to explain that each standards’ assessment is two parts.  The first part is multiple choice and the second part depends on the student.  Once they realized that their child’s grade quits improving when they quit trying, I think they got it. 

It’d be nice if we could focus less on the grade and more on learning, but…

…baby steps.

The Easter Egg Hunt

Every nine weeks my district gives benchmark exams covering approximately one-third of the standards that have been deemed “essential.”  Many teachers feel the need to do a bunch of last minute cramming and do intensive review.  For the most part, I see the benchmark as a speedbump; one of those things that I have to do.  I mean, I we already have department CFAs (common formative assessments) that we use to re-direct our instruction, so I pretty much already know where my kids stand.  So for the last benchmark of the year, I decided to change up the review.

I made up a practice test covering the standards that would be assessed, uploaded it to voicethread and had students sign up to create a mathcast for specific problems.  However, this time they were looking for a fastball up and in and I gave them a change away. I asked a few students to do the problems incorrectly (of course, first they had to demonstrate to me that they could do the problem right.) Once everyone had added their comments to the Voicethread, I assigned the Easter Egg Hunt–Which ones are wrong and why? I think I really like this activity. Students not only have to work out each problem themselves, but they have to view another’s work critically. I would love to hear what you think.