Documents for CwiC Sessions at Anja Greer MST Conference 2016

Instead of passing out photocopies, I tried to think of a way that participants could access the “hand-outs” virtually while attending a session.  What I’ve done in the past a conferences is have them just access them on their tablet devices.  You can also go and access copies on the Conference Server if you do not have a device with you (you should be able to use your phone too).

These link to This is an Adobe Acrobat Documentpdf documents that I will refer to in the presentation about “Assessment in PBL”

Information on Spring Term Project and Spring Term Project Varignon 2015 (this document includes rubric)
Keeping a Journal for Math Class
Revised Problem Set Grading Rubric new
Rubric for Sliceform project and Sliceforms Information Packet

Page at my website with Rubrics and other guides for Assessment

Someday I’ll get this assessment thing right… (Part 2 of giving feedback before grades)

So, all assessments are back to the students, tears have been dried and we are now onto our next problem set (what we are calling these assessments).  What we’ve learned is that the rubric allowed us to easily see when a student had good conceptual understanding but perhaps lower skill levels (what we are used to calling “careless mistakes” or worse). We could also quickly see which problems many students had issue with once we compared the rubrics because, for example, problem number 6 was showing up quite often in the 1 row of the conceptual column.  This information was really valuable to us.  However, one thing we didn’t do was take pictures of all of this information to see if we could have a record of the student growth over the whole year. Perhaps an electronic method of grading – a shared google sheet for each student or something to that effect  might be helpful in the future – but not this day (as Aragorn says) – way too much going on right now.

We also changed the rubric a bit for a few reasons.  First, we found that when students completed the problem to our expectations on the initial attempt we felt that they should just receive 3’s for the other two categories automatically.  We considered not scoring them in this category but numerically felt that it was actually putting students who correctly completed a problem at a disadvantage (giving them fewer overall points in the end). Second, we also changed the idea that if you did not write anything on the revisions you earned 0 points for the revisions columns.  Many students told me afterwards that they felt like they just ran out of time on the revisions and actually had read the feedback.  This was unfortunate to me since we had spent so long writing up the feedback in the hope that the learning experience would continue while doing revisions.

Here is the new version of the rubric: Revised Problem Set Grading Rubric new

What we decided to do was to try the revisions this time without the “explanation” part of writing.  I think it will keep the students focused on reading the comments and attempting a new solution.  I was frankly surprised at how many students stuck to the honor pledge and really did not talk to each other (as they still got the problem wrong the second time around – with feedback).  Truly impressive self-control from the students in my classes and how they were sincerely trying to use the experience as a learning opportunity.

I do think the second assessment will go more smoothly as I am better at doing the feedback and the rubric grading.  The students are now familiar with what we are looking for and how we will count the revisions and their work during that time.  Overall, I am excited about the response we’ve received from the kids and hope that this second time is a little less time-consuming.  If not, maybe I’ll just pull my hair out but I’ll probably keep doing this!




Why Teachers Don’t Give Feedback instead of Grades, and Why We Should

First in a series of posts about my experiences with “Feedback Before Grades”

Holy Mackerel is all I have to say – Ok, well, no I have plenty more to say – but after about a week and a half of holing myself up with my colleague, Kristen McVaugh, (big shout-out to Ms McVaugh who is not only teaching PBL for the first time but was willing to dive into this amazing journey of alternative assessment with me this year too), I am totally exhausted, almost blind as a bat, partially jaded and crazy – but mostly ready for a drink.  This little looped video of Nathaniel Rateliff and the Night Sweats pretty much sums it up…

So here was our well-intentioned plan:  we wanted to start the year off with a different type of assessment.  I put out my feelers on twitter and asked around if anyone had a rubric for grading assessments where the teacher first gave only feedback and then allowed students to do revisions and then once the revisions were done the students received a grade. Kristen and I knew a few things:

  1. we wanted to make sure the revisions were done in class
  2. we wanted to make sure the revisions were the students’ own work (tough one)
  3. we wanted to give students feedback that they needed to interpret as helpful so that we weren’t giving them the answer – so that it was still assessing their knowledge the second time around
  4. we wanted to make sure that students were actually learning during the assessment
  5. we wanted students to view the assessment as a learning experience
  6. we wanted students to be rewarded for both conceptual knowledge and their skills in the problem solving too

So we created this rubric Initial Draft of Rubric for Grading.  It allowed us to look at the initial conceptual understanding the student came to the problem set with and also the initial skill level. Kristen and I spent hours and hours writing feedback on the students’ papers regarding their errors, good work and what revisions needed to be done in a back-handed sort of way.

Here are some examples:

Student 1 Initial Work

Student 2s initial work

Student 3 initial work


Some kids’ work warranted more writing and some warranted less.  Of course if it was wonderful we just wrote something like, excellent work and perhaps wrote and extension question.  The hard part was filling out the rubric.  So for example, I’ll take Student 3’s work on problem 6 which is the last one above. Here is the rubric filled out for him:

Student 3’s Rubric

You will notice that I put problem 6 as a 1 for conceptual understanding and a 2 for skill level (in purple). In this problem students were asked to find a non-square quadrilateral with side lengths of sqrt(17).  Student 3 was definitely able to find vertices of a quadrilateral, but he was unable to use the PT to find common lengths of sides.  I gave him feedback that looking at sqrt(17) as a hypotenuse of a right triangle (as we had done in class) would help a bit and even wrote the PT with 17 as the hypotenuse in the hope of stimulating his memory when he did the revisions.

The day of the revisions Student 3 was only capable of producing this:

Student 3 revisions

He followed my direction and used 4 and 1 (which are two integers that give a hypotenuse of 17, but did not complete the problem by getting all side lengths the same. In fact, conceptually he kind of missed the boat on the fact that the sqrt(17) was supposed to be the side of the quadrilateral altogether.


One success story was Student 2.  She also did this problem incorrectly at first by realizing that you could use 4 and 1 as the sides of a right triangle with sqrt(17) as the hypotenuse but never found the coordinates of the vertices for me. I gave her feedback saying there might be an easier way to do this because she needed vertices.  However, she was able to produce this:

Student 2s revision

Student 2s revision

Although she did not give me integer-valued coordinates (which was not required) and she approximated which officially would not really give sqrt(17) lengths it came pretty darn close! I was impressed with the ingenuity and risk-taking that she used and the conceptual knowledge plus the skill-level. Yes, most other kids just used some combination of 1’s and 4’s all the way around but she followed her own thought pattern and did it this way.  Kudos to student 2 in my book.

Next time I will talk about some of the lessons we learned, other artifacts from the kids’ work and what we are changing for next time! Oh yeah and some great martini recipes!

Buyer Beware…when using rubrics for critical thinking skills

One of my goals in my work is often to help classroom mathematics teachers to be more deliberate in the ways in which they assess problem solving.  Although many people can be cynical about rubrics, I think that students can find them at least helpful to know what a teacher expects of them.  I have some students who told me that they pull out my rubric for grading journal writing almost every time they go to write a journal entry this fall.

However, a rubric that is vague and ambiguous about expectations can cause more harm than good.  Just throwing a rubric around that students can look at, or one that you can post on your website that you can show an administrator and say, “See, I have a rubric for that” isn’t necessarily a good thing.  Especially for problem solving.  Problem solving as a process is a very difficult thing to nail down for students especially in terms of the levels of how they can improve in their work.

I recently ran across this rubric that posted on a website under the title “Awesome Problem Solving Rubric for Teachers.”

Is this an “Awesome Rubric” for teachers?

As I read through this, at first glance the categories look pretty good – Identify the problem, identify relevant information, analyze the problem, use strategies and reflect on the process.  Sounds like a pretty standard problem solving process –very similar in many ways to Polya’s process or the steps that Jo Boaler discussed in her online course How to Learn Math this summer.

The graded level descriptors of how a student might be able to see where their work “fits” in the rubric seems to only put the behaviors on a “continuum” of Always- sometimes- never instead of trying to describe actions that the student could do that describe a mediocre way of using a strategy.    For example, analyzing a problem can be so much more descriptive than just “I think carefully” about the problem before a student starts.

They could:

1. listen deliberately to others’ ideas and reflect on them in writing or verbally

2. question the given information of a problem – does it make sense in a realistic way?

3. think about the representations they can come up with for the problem – does a graphical approach make the most sense?  Why?  Would making a geometric representation be better, if so why?

4.  In comparing a new problem to ones I’ve already done, can I list the similarities and differences?  What is this question asking that others I’ve done not asked?

How many students can really ascertain what “thinking carefully” about a problem is?  I have found that more and more we need to erase as much ambiguity as possible to help students learn to be critical thinkers.  As we feel the need to teach critical thinking, reasoning skills and sense making, it is even more imperative to have rubrics that are as precise as possible.

Now, I don’t claim that mine are perfect, but my rubrics and student feedback forms have gotten some pretty good reviews from teachers and successful feedback from students.  I work on them every summer and am continually editing in order to be more deliberate about the feedback I give my students.

I also highly recommend the rubrics from the Buck Institute Website under their “tools” category.  I also adapted one of their critical thinking rubrics that was aligned to the Common Core and changed it directly for my PBL curriculum – more for presentation of problems and novel problem solving.  I’m still working on it because I have to think about exemplars for what would be above standards, but let me know if you have any feedback.

Critical Thinking rubric for PBL

So, I would just warn anyone to beware of “awesome rubrics” for teachers that they find on the internet because something that might seem awesome at first glance might end up doing more harm than good.