Monday, November 30, 2015

Approaches to Assessment

I thought to myself over this 5-day weekend that I'm really glad I'm the kind of person that wants to keep learning and growing as a teacher. Those are the people I am surrounded with each day. I love getting links to interesting articles (keep sending them, Miriam!) and trying new strategies in class. For that reason, we (Miriam and I in our Geometry Honors class) decided to attempt a different way of grading our most recent assessment.

We read Carmel Schettino's blog about Why Teachers Don't give Feedback instead of Grades, and Why we Should. If you haven't read it yet, I suggest starting there -- though I will also warn you of getting lost down the rabbit hole of amazing math teacher blogs. It still happens to me all the time...so, no shame in that! In short, Carmel wanted to give feedback without a grade after students took a major assessment - and then give students the opportunity (in class) to USE that feedback and make corrections on their work.

Is this how you generally feel when grading?


The process of grading was definitely time consuming. And we "screwed up" right from the start. My class was a few days ahead of Miriam's class, so my students took the Problem Set (what we're calling our assessments...more on this later) before hers. Generally, I have no problem with this. However, we should have given them on the same day so that we could grade together. Especially as our first time using the rubric, I see the importance of this now. It would have been great to be sitting together and helping one another with the feedback to give and whether or not something fell in the "3" or "2" category.

But I agree with Carmel -- students don't look at the feedback if there is a grade attached. Without the grades, they read my comments and used them to try and improve or correct where they went wrong the first time. Students knew we were going to do this the next day in class. I also started class by opening up and projecting the rubric and talking them through it.

Another problem for us is that we don't technically do Standards-Based Grading. When we wrote the assessment, we didn't make each part out of 3 points....so scoring them at the end was tough. Some were worth 6, others 9. So it wasn't HARD, just time consuming. We know better for next time now. If we give larger problems, we will simply make parts of them each worth 3 points to fit into the rubric.

I also think I will read the entire rubric with students again before the next assessment. I want to have a larger conversation about what a "3" means, etc.

Something that was really awesome: Since the rubric separates conceptual understanding and the mechanical skills needed to solve the problems, it was so evident when a student fully understood all the Geometry concepts, but didn't have the Algebra skills to finish solving a problem. One student hasn't been earning the grades he wanted all year and I was able to see that it really was his mechanics that were holding him back. It's awesome to look at it from that lens and see very clearly where he needed to focus his attention.

To sum it up...the rubric did several things that Carmel originally wanted (and that Miriam and I also wanted)

  • Revisions were done in class 
  • Revisions were the students own work (we did tell them that they would be doing these revisions the next day in class and that their only homework was essentially to look-up/study anything they wanted, but to not talk to other students about the problems)
  • Instead of immediately being a summative assessment, it became a sort of formative assessment and allowed for learning to take place DURING the assessment
Changes/Improvements/Other thoughts
  • Miriam and I need to grade TOGETHER next time! 
  • We found that students might not have thought they actually got a problem wrong after taking the assessment the first day -- so they didn't look up anything about that problem. I think we find a way to encourage students to revisit all problems that might be helpful...
  • All problems (or parts of problems) must be worth 3 points to make for an easier time totaling a score at the end


I have some other thoughts on ways to change assessments for next semester....and was inspired by the posts over at Experience First Mathematics (Blake School)  -- but that will have to be another blog post...this one is already too long! 



Tuesday, November 24, 2015

Unknown Unknowns Project

Quick blog to share info on this project: 

I called it the "Unknown Unknowns" project, since there are many things my students don't know that they don't know....not sure if it's a perfect name...but it made sense to me! 

Here is the info I provided on a handout: 

UNKNOWN UNKNOWNS PROJECT

Get ready mathletes!  It's time to learn some exciting mathematics! This project will require some hard work on your part, but I'm certain you will find the process rewarding.  I have come up with a list of possible topics. From those, we will sign up (I would like no two pairs to have the same topic!) for our topics.

Penrose Tiles
Fractals
Tessellations
Pascal’s Triangle
Golden Ratio
Cryptology
Bridges of Konigsburg
Knot Theory
Mobius Strip
Game Theory
Math & Music
Voting Theory
Fibonacci Numbers
Zero
History of the Abacus
Tangrams
Four-color Theorem
Monty Hall Problem
Pythagoras
Math & Modern Art
Zeno’s Paradoxes
Ada Lovelace
Parabolic Ski Design
Math NOT in base 10

The end result of the project will be a ten-minute presentation to our class (such as a Prezi or video).  Your presentation must be done on a computer.  Within the presentation, you must include some kind of activity for your audience to participate in. This could be a handout, quiz, activity, etc. I would also like a formal write-up of at least 300 words with citations. Through the course of the next couple weeks we will have some class time to work. So, be prepared to use that time wisely!

You must have at least three sources (non-wikipedia), and those sources must be cited (APA in text citations and References page). Each project must contain a historical component and images that make sense for your topic.

Timeline of Project Completion:

Monday, April 13 (Period 1)
Tuesday, April 14 (Period 7)
·            Project introduction
·            Topic Selection
Friday, April 17 (Period 1)
Monday, April 20 (Period 7)
·            Research time with Ms. Imhoff in our classroom
Friday, April 24
·            Progress Check (10 points)
·            Must be able to show some research completed at this point
Monday, May 4
·            Projects Due!
o   Turn in written portion and planned student activity
o   Upon request, be willing to show Ms. Reycer   your Prezi
Monday, May 11
·            Presentations Begin!
·            Ms. Reycer will email a schedule of presentations!


This was the timeline I used last year -- will probably try something similar in the Spring again -- but would love thoughts, suggestions, additions, etc! 

Saturday, November 21, 2015

Transitioning to PBL

I have been lucky enough this year to collaborate closely with a teacher new to our school, Miriam (@msinger216). She brings a wealth of knowledge from teaching at Deerfield with Carmel Schettino (@SchettinoPBL). We decided at the beginning of the year to "throw out" the old, traditional textbook and adopt the curriculum that Deerfield has been using (a collaboration between Deerfield Academy, Emma Willard School, and Phillips Exeter Academy).

Whoa has it been a whirlwind!

I have learned (and I'm still learning) SO MUCH.

I plan to post another blog VERY soon about a new way of grading assessments that Carmel developed and that Miriam and I used recently. But right now, I need to just word vomit my thoughts on what we've done so far this year.


  • Fully taking on a Problem-Based Curriculum is HARD. I think it truly takes a master teacher to have it be effective. There are so many small conversations that come out of just ONE problem. And sometimes I feel like I even miss things, though I am doing the problems before the students are doing them. I know that next year, it will be a little easier. 
  • Working ahead is essential. Too often, I find myself scrambling to do problems to know what length to make the next assignment. I know I need to get several pages ahead, and making time for that should be a priority. 
  • Having the FULL support of your administration is so important. There has been some push-back from parents this year. I get that they don't understand what we're doing. In a perfect world, they would try to understand it instead of attacking it because it's not the way they learned math (or their older kids learned it at the same school). If that is an argument against what we're doing, it's not a good one. Students of today are not the same as students of years past. We need them to be nimble problem solvers and critical thinkers that can decide which tool to grab out of their toolbox. 
  • I need to figure out when I think it's important to do something by hand versus doing it in Desmos or Geogebra. There are many problems that are made much simpler by solving them with technology. But, I also value being able to solve equations algebraically. Sometimes I want an EXACT answer versus approximate. But how often is it important? (I really would love feedback on this...will probably tweet about it too.) 
  • Going through these problems myself really helps me to better understand geometry. I have AHA moments in the classroom just like the kids do. And this is just pure FUN!
That might be all for now. Hopefully over Thanksgiving break, I'll blog about using Carmel's rubric and how it went in my classes. And what I learned from it, how to change it, etc.

Do you have thoughts, ideas, suggestions, comments? Please leave them below! You want to collaborate or chat? I'm up for that too!