Mile wide and an inch there a sliver of value in this approach?

Warning: unpolished thoughts (a.k.a. rambling) follow...

A colleague recently sent an article describing the age-old problem of math topic coverage being a mile wide and in inch deep.  A few excerpts from the article are enough to illustrate the main points math curriculum crisis transpiring in the state of Florida right now:

"The problem with the old standards, educators say, is that many topics were covered lightly and then repeated year after year."
"Because the state's annual test measured performance on the 89 standards, Kuches and other teachers had no choice but to race through them in the hope that students would learn. The results were not always good, especially for slower learners."
I used to think that this problem could be quickly fixed...just teach fewer topics and explore them from many different angles so that ALL students can understand them.  After a dozen or so semesters teaching, Geometry, I still think this is a good idea in theory, but I have also realized that some young minds just aren't mature enough to comprehend certain math topics.  Think about Bloom's Taxonomy (or a more specific math example, van Hiele levels of geometric reasoning) and how some students struggle with the knowledge or comprehension level of many topics in school.  In Geometry, our curriculum (i.e. proofs, inductive and deductive reasoning) implies students should be synthesizing and evaluating geometric ideas.  From my experience, that's just not cognitively possible for some students as fifteen or sixteen year-olds.  It might not be possible until they are seventeen or eighteen.  If the topics don't repeat themselves, at least a little bit, students will be missing out on the opportunity to be exposed to these ideas later on in their "math career." 

I do like the approach of only teaching several big ideas each year during middle school math, but I'm just not sure if its reproducible at the high school level.  Some spiraling of topics seems to make sense, but how much is too much given what we know about adolescents' cognitive abilities?  I am by no means an expert in adolescent psychology, so I'm hoping y'all are able to chime in with your thoughts and experiences.

ICTM 2010: How do you know if they know?

Presentation given at the Iowa Council of Teachers of Mathematics Conference, February 19, 2010.

How do you know if they know? Re-examining assessment through the lens of learning

Brief description:
This session will highlight “assessment for learning” techniques from a secondary math classroom teacher's perspective.  Come to get your beliefs about assessment and reporting learning challenged and refined as they relate this Iowa Core Curriculum characteristic of effective instruction.

Additional resources are available here.

Slidecast (slides and audio recording) from the conference presentation:

What do pre-service education departments need to know?

In April, I will begin serving a two-year term on the advisory committee for the education department at a small liberal arts college here in Iowa.  The commitment is two one-hour meetings per year.  Members include the general public, two students majoring in education, teachers (that's me) and administrators who work in schools that the college places their student teachers. 

"The role of the council is to advise the department on issues related to curriculum, pre-service methods classes, student teaching, and other matters related to the field of education."  
Aside from David Cox's suggestion of bringing up standards-based grading (don't worry, I will!), what else do pre-service education departments need to know from classroom practitioners?  Leave your thoughts in the comments below.  I'll do my best to represent YOU, my faithful blog readers. :)

Making sense of standards-based grading with parents

Do you think your grading system confuses students and parents?  An email I received this morning confirms it:

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This is yet another repercussion of grading pollution - parents want to help their children, but they aren't sure what the source of the low grade is...effort or understanding!

My guess was that the parent had not talked with her son, because she did not know that I report out learning target understanding rather than single assessment scores (i.e. Test 1: 95%).  Either way, here was my response:

Good morning, _______,
The grades you see in PowerSchool report both _____'s work ethic and his understanding of Geometry.  You will not see any "test" scores in PowerSchool.  Instead, you will see the concepts from each chapter listed and how well _____ understands each concept.  Take a look at the screenshot of ______'s Geometry grades in PowerSchool:

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If you click on "Ch. 1 L2" you will see the concept that _____ was tested on.

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_______ is currently at a "2" level (out of 4) when it comes to understanding basic terms of Geometry.  The scale for each learning target is:

Each Learning Target is scored using a 4-point scale:
4 – demonstrates thorough understanding
3.5 – high level of understanding, but with small errors
3 – demonstrates understanding, but with significant gaps
2 – shows some understanding, but insufficient for a passing grade
1 – Attempts the problem

This means that he does not understand this particular concept very well at all.  Does that make sense? 
You will also see scores that report out ______'s work ethic.  I enter in how many assignments _____ has turned in each week.  For example:

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Last week, ______ did not turn in several assignments.  If you click on the "Weekly assignments and warm-up: 2/8 - 2/12" you can read more information about the week's assignments that were turned in.  The actual practice homework assignments are listed daily on my website.....


Two thoughts that came to mind from this email conversation:
  1. Reporting out homework completion to parents may be a good data point, even though it doesn't make sense for it significantly impact a student's final grade. 
  2. Contrary to lesson #1, would it have been easier if I didn't report out weekly homework completion, so that my response would have merely been, "I only report student understanding of learning targets.  It is safe to assume that if your child is not doing well, it is because he/she doesn't understand the big ideas."  
On a side note, perhaps the teacher next door and I are starting a revolution in grading practices in our building.... and all this communication about grades will be unnecessary in a few years?!

Other teachers grade that way, too?

(Note: This post has been updated here)

Some of my students are absolutely in love with standards-based grading.  Others aren't.

They are all amazed when I tell them other teachers around the state of Iowa (and the country) are implementing this system, too.

Here's my best attempt at aggregating those teachers' blogs.  I'm sure that I've forgotten a few, so please leave your name and URL in the comments.  I'll update this post as the list grows.
  • Eric Townsley is an aspiring administrator, teaches high school math and blogs at Assessment for Instruction about his grading practices.  Full disclosure: Eric is my brother  :)
  • David Cox teaches middle school math and blogs at Questions? about all of the great things he's trying out in his classroom.   A description of his grading system is found here.  (Note: David's blog URL changed recently, so you may see links to two different sites)
  • Dan Meyer works for Google and teaches high school math part-time now.  A few years ago, he wrote extensively about his standards-based grading system.
  • Jason Buell has a catchy blog title, Always Formative.  With so many posts worth reading, it's hard to highlight just a few.  Advantages and disadvantages of standards-based grading are two that come to mind. 
  • Chad Sansing's blog, is focused on authentic engagement, but he has also taken some time to write about standards-based reporting, too. 
  • Becky Goerend is my sister!  She teaches middle school math and reading as well as blogs about standards-based grading and the use of digital tools in her classroom. 
  • Becky's husband, Russ, has given standards-based journaling a try in his middle school language arts class.  It seems to have lots of potential not only for more effectively communicating learning with stakeholders, but also simultaneously integrating digital tools along the way.
  • Riley Lark teaches high school math and laid it all out in a post back in November, 2009.  We teach a few hours away from each other, but sadly have never met face-to-face.
  • Shawn Cornally is the newest addition to my RSS aggregator.  He teaches physics, calculus and computer programming next door to me and I'm really thrilled that he's decided to start blogging.  His series outlining standards-based grading implementation in specific disciplines is here.
  • Kelly Nelsen teaches junior high and seems to have an interest in standards-based grading.  I'm looking forward to her future writing from a non-math teacher's perspective.
  • Kate Nowak aspires to be a lot like Dan Meyer (or at least the MathEdBlogging crew often teases her about it :) and her assessment scheme is closely related to Dan's, too.   Kate does not let her students off lightly during re-assessment attempts. 
  • Steve Phelps has taken formative assessment to the extreme.  Steve shares some Geogebra applets and math teaching ideas over at his blog, too.  It's worth a look.  
  • Update: Thanks to a comment left below, "What it's like on the Inside" has some in-depth commentary on standards-based grading here
  • Dan Greene teaches high school math at a charter school.  In addition to the worksheets, slides and lesson ideas he shares on his blog, I'm told that he is also an advocate for standards-based grading. 
A quick list of standards-based reporting folks on twitter has been started here

I hesitated to write this post for fear that I've left someone out.  Consider this a "formative assessment" in need of correction. 

Email me or leave a comment with your name and I'll update the post ASAP.

Grading pollution

In How to Grade for Learning, Ken O'Connor writes,

"Lowering grades simply because of poor attendance, misbehavior, or lateness distorts achievement; grades then do not have clear meaning.  Bobby's C may reflect his consistent achievement at that level, whereas Ann's C, although she consistently achieves at an A level, results from her absences, frequent lateness, and misbehavior." (89)
Ask any secondary teacher about emails from parents or conversations at parent/teacher conferences.  My guess is that the majority of them revolve not around what a student understands or does not understand, but rather the "soft skills" of being a student such as turning in work on time or participating in class.  These skills aren't unimportant, they're just misleading when we report our grades.  We (educators) say that our grades reflect a student's level of understanding or mastery of course content, but the way we report our grades is flawed.  Ann, as referenced in O'Connor's quote above, has a grade that suffers from grading pollution.  Discipline and responsibility issues should be taken care of via other mediums, not including the grade book.  We've been tricked into thinking that by lowering a student's grade because he/she doesn't turn in a project on time, that he/she will magically learn a lesson and magically become better prepared for the working world.  All the while, parents and students are confused when Johnny receives a B:

  1. Johnny knows everything, but didn't turn in a few assignments on time. He needs some help with meeting deadlines.
  2. Johnny knows quite a lot, but did not turn in the final project by the required deadline.  He needs very little help meeting deadlines or made an untimely mistake.
  3. Johnny knows everything, but does not participate in class conversations.  He needs some encouragement to share his ideas with others in classroom discourse.
  4. Johnny knows and can do nearly all of the course objectives, but has a very poor understanding on one big idea.  He might need additional time and assistance to better understand a difficult or challenging learning goal.
Johnny's parents are unable to decipher which scenario describes their son by looking in the grade book.  It is a complete mystery to them, because grading practices from classroom to classroom vary widely - our grades are often polluted.

What does a B represent in your classroom?  Are your grades polluted?

(My solution to grade pollution?  See commentary on Standards-based reporting)

Teaching is easy, right?

Read the curriculum guide and follow the standards.  Come up with some engaging problem-based learning ideas.  Differentiate.  Use some computers and cool web 2.0 tools so that your classroom doesn't become dangerously irrelevant.  Assess students in authentic ways.  Talk about collaboration and critical thinking.  Easy stuff, right?

A day in the life of Mr. Smith:

2nd period ends in frustration.  The computer cart checked out in Mr. Smith's name for the class period was not where it was supposed to be.  In fact, Cart A ended up being in Mr. Craig's room, even though he hadn't checked out the cart for the past three days.  Go figure.  Two senior boys enjoyed their time walking the school hallways looking for it though.  It took an announcement over the PA to find Cart A.  So much for giving students time in class to write about their data collection and analysis project ideas and submit them via Moodle.  If only every student had a computer of their own, this wouldn't be a problem.

Betsy walks in shortly before the 3rd period bell.  She's been out for the past week due to surgery and came back yesterday, but Mr. Smith didn't have time to catch up with her one-on-one.  Today is the chapter test and Betsy still has several unanswered questions even though she completed most of her homework assignments before she left.  In mid-sentence, Mr. Smith is interrupted by Jenny who informs him that she will be gone to Hawaii next week for vacation and needs her make-up work tomorrow.

The bell rings. 

Students begin their warm-up problem and check their answers to last night's homework.  Five different students have five different questions about the review assignment.  The rest of the class yawns or dozes off while Mr. Smith takes time to go over these five problems before the test.  Mr. Smith applauds the six unnamed students who took the time to come in before school to get help on the review assignment and encourages ALL students to follow suit in the future.

It's time for the test to begin.  Mr. Smith tells the students to get out their formula sheet (also known to students as their "toilet paper"...don't ask why) and clear their desks.  Thanks to a last minute print job, Mr. Smith informs the students about a typo on page three of the test.

Finally, students begin the test.

Mr. Smith circles the room for a few minutes and then checks his email.  Mr. Lair, the principal, has sent out a friendly reminder about Mr. Smith's role in the next day's staff meeting.  Great.  Something else to work on tonight in addition to checking the tests.  Mr. Smith fires an email back, "sounds great.  I'll make it happen!"  A few minutes later, the office secretary calls - James needs to leave right now.  His mom is ready to take him to his doctor's appointment and needs to leave within two minutes.  A quick discussion about finishing the test takes place between James and Mr. Smith.  Suzie walks up to Mr. Smith, "What am I supposed to do with the test when I'm done?"  Mr. Smith rolls his eyes and points to the red basket.

Five minutes later, Lance raises his hand and whispers, "Do I have this problem setup right?"
Mr. Smith responds, "If I answered that question, I'd have to put MY name on your test.  I can't tell you the answer to that question." 

The bell rings. 

Mr. Smith's day has just begun.  He thinks to himself, "I thought teaching was supposed to be easy."

Name that misconception!

I am looking forward to going over this quiz question with my Geometry students:


I recently added "part a" to this assessment, "How is XT related to XZ?" before asking students to actually solve the problem for this very reason:  I want to know what specific misconception, if any, the student has about the learning target, not just if they're able to setup and solve the linear equation. 

If Suzy realizes that XT is half of XZ (part a), then how could 2x + 11 = 5x + 8 (part b)? 

Name that misconception (and how to help students overcome it)!