No point(s) needed.

Once in college I was docked a point on a math test because I did not use the variable the problem told me to use. What a rebel.  My work was otherwise fine, mind you, just had the “wrong” variable.

I tell you this because early this morning, maybe a tad too early, I read Fawn Nguyen ’s recent post  “Scoring an Ordered List” ; at first I took what she was saying seriously because to me, everything she writes is solid gold. (You should probably read it to get where I’m going with this.) I gushed about her in my last post, for heaven’s sake.  Why is the great Fawn obsessing with points?  I started feeling some panic.  WHY WHY WHY is she obsessing with points?  I was flummoxed.

Then the caffeine kicked in and it dawned on me. She’s just messing with us. Having some fun with obsessing with points, and inviting us to join in, math-geeky.

Or maybe she’s making a point about points, in which case she has gone platinum.

Awarding and denying points is what many teachers do, across all content areas, even if other aspects of their pedagogy employ Best, or at least Better, Practices. Somewhere between arbitrary and intentional, they determine points per problem, points per quiz, per essay, per whatever. Preferably the points add up to something that can easily be turned into a percentage so letter grade convertions are a snap.

Why?  Because it’s what what they know, what they believe they are supposed to do, its what everyone expects. It’s another one of those pesky, unexamined “givens” in the dystopian Game of School. I don’t know if that’s the right use of dystopian here, but I like it so its staying.

Determine total points possible, deduct points for wrong-ness, calculate a score, assign a grade.  So math-y.


You can find scores of graphics like these online, which supports my statement about the Game.   I find the emojis particularly unsettling horrifying.

This poster is hanging in a school I frequent: ‘Grades are not given, they are earned.’

Bull. Shit.

I digress. Returning to Fawn’s scenario, suppose a teacher decides that the problem was worth X points, and to receive said points, every number has to be in the correct location. Black and white, not even one shade of grey. That is certainly the way a computer program would determine whether so-called feedback should be “Awesome! You Rock!” or “Incorrect.” Of course this means that if Kat writes the numbers greatest to least, she would be told she is ONE-HUN-DRED-PER-CENT-WRR-ONG, striking yet another blow to her growth mindset.

An alternative (that I am sure Fawn and many other awesome teachers use) would be to skip the points, look at work holistically, and ask Kat a question or two. The goal is to understand her thinking, to gauge what she understands and where her misconceptions may lie. Kat either needs a reminder to read and follow directions with greater care or a conversation around the words least and greatest. Easy peasy.

Just for kicks and giggles, here’s another example: Suppose I’m checking to see if my students can correctly follow order of operations to simplify expressions. Dougie clearly demonstrates mastery of this skill— nothing out of order in his work— yet it contains a minor calculation faux pas or two. (Been there, done that. Lost points.) I am NOT going to deduct points or even determine he is not meeting expectations. I am going to PASS Dougie on that particular skill, period.

There’s a significant difference between 1) using student work to inform both the teacher and learner so meaningful feedback can happen and learning can continue, and 2) using student work in order to pass judgement. Which should be valued, empowering all students to think critically, creatively, to make sense of (insert content area here), or rewarding some students for “correct” imitation and memorization? The first requires, if I may, a balanced, healthy, and inclusive teacher-student learning relationship; the second also involves the student, but is unhealthy and detrimental to learning because it also involves power.


Half-baked is better than nothing.

Like you, I have a zillion half-baked thoughts and ideas going on in my head.  Stuff that I’m reflecting on, stuff that I find interesting, perplexing, important, and would love to talk about.

One of the things that keeps my thoughts from showing up here is a silly yet persistent notion that whatever I post needs to be Complete and Polished.  Insightful.  Worthy.  Intelligent.  Helpful.  Because that’s how Everybody Else’s blogs look to me.

But if I believe (as I do) that the primary purpose of this blog is for my learning and growth, then it stands to reason that it is completely acceptable for me to share thoughts that are still rough, still in need of additional reflection, and definitely in need of feedback (hint hint).  Writing helps me focus and gain some clarity, and lack of some imagined perfection or level of “doneness” should not prevent me from posting.  Right?

With that said, here’s a taste of what’s rattling around in my mind of late:

Calculating is not mathematics.
Spelling is not writing.
Decoding is not reading.
Memorizing is not learning.

So what is?


Noticing, wondering, questioning, exploring, making sense of, using, testing, revising, expressing, connecting, analyzing, creating….

When a classroom or school or societal culture values performance and test scores, then teaching and learning evolve around that which that can be easily tested and graded.  Facts and rehearsed processes.  Right and Wrong answers.  Sort to accelerate and remediate.  Rewards and punishments, smart and…below grade level.

The development and questioning of ideas is messier, less quantifiable, harder to teach, harder to nail down.  It’s much more difficult to describe a students growth over time than it is to rank them.  More challenging (and rewarding!) to work with a student’s competencies and current understanding than to fault them for their deficits and errors.  A great shift in values needs to take place; teachers and students will spend their time and efforts differently.  What does this look like?  What’s my role?  How much time will this take? Yikes, what about the risks?!

Teaching is complex.  Learning is complex.  Learning about teaching is complexly complex.  Formal and informal professional development tends to focus on examining, questioning, and improving what teachers and students do and say in the classroom.  Planning and launching lessons, selecting worthwhile tasks and activities, anticipating student responses, questioning strategies, orchestrating discussions, making connections, closing the lesson….perplexity, curiousity, intellectual need, genuine engagement….active learning culture, growth mindsets, metacognition…. ALL REALLY REALLY GREAT and REALLY REALLY IMPORTANT and REALLY REALLY NECESSARY.

Yet the Student Learning Experience encompasses more than “The Lesson”.  What about homework?  What about assessment?  Grades?  What about __________? Without examining and questioning and improving ALL components, without implementing changes simultaneously, progressive efforts become at best undermined and at worst derailed and rejected. What’s the point (asks a student) to make sense of these ideas or persevere on this task, if they only thing I will be tested on for a grade (the only thing that matters) will be whether or not I can calculate the right answer?  Why should I be curious?  Why bother making connections?  Explain my reasoning? Transfer ideas?  Develop relational understanding?  Just tell me the trick/hack/rule.  That’s all I need to survive.

That’s what my dad did.  That’s what my grandma did.  That’s all math is.

Mad to Glad

IMG_2520I’m attempting to help a teacher friend of mine (Jackie) make over some lessons in her district’s new online curriculum. It’s a frustrating challenge; every lesson simply tells information and shows processes without any exploration or sense-making opportunities for the students. Very Old School, very passive (aka confused) students, very much perpetuating the myth that math is a jumbled bunch of random rules to memorize.


The topic in an upcoming lesson is irrational square roots. For Cathy Yenca’s very helpful online class Seeking Students Who Hide , I made a Socrative  “quiz” to generate discussion about the relationship between the area and side lengths of squares, the rational roots of perfect squares, and some perplexity about the root of a “not-perfect” square. If you already have a Socrative account, the import number to share my quiz with you is SOC-30095225*.  If you don’t have an account, get one now, I’ll wait. It’s FREE and fairly self-explanatory. Even I am figuring it out, and that’s something.


What’s important to note is that Cathy is showing us how this tech tool can be used for giving every student a voice, even an anonymous one.  Anonymous is safe.  No one gets to hide or opt out or dominate a discussion. So it’s not a quiz, its an equity tool, a real-time formative assessment tool.  I chose to have my “quiz” (what should this be called instead?) be teacher-controlled and anonymous so questioning, discussion, exploration, and justification can happen in between each prompt, depending on what students say, ask, and need. I’m picturing having them draw perfect squares on graph paper (low floor), introducing them to the square root symbol, using area models to make sense of the length/area relationship, and challenging them to make whole number “not-perfect” squares (high ceiling).

The final multiple choice question about an area of 20 square units is meant to be the zinger. Four of the five choices can be justified, IMO, so I purposefully marked every answer “correct” when creating it so that the data we’d see as a class would be IMG_2521about the percent of students who chose each answer, NOT NOT NOT about which answer (or who) is “right”. I actually hope for quite a mixed bag, which is the perfect place to start an exploration into irrational roots of “not-perfect” squares.

*I’d love feedback from anyone who even just looks at this quiz. This is new territory for me and I am not sure I’m going to get to implement it. If you use it, even modified, let me know what happened!  Here’s the bare-bones version; keep in mind something should be happening in between each question.

1. What are square numbers?
2.  How do you find the area of a square?
3.  Describe the relationship between the area of a square and the length of its sides.
4.  T/F. √ 49 = 7        5. T/F √18 = 9
6-8 Solve each of these: a + √36 = –5, √121 – x = 7 , –14 = n – √64
9. If y2 = 25, what’s y? Explain.
10. If a square has an area of 20 square units, how long is each side?

UPDATE:  Jackie and I have decided to go for the gusto and implement this Socrative lesson tomorrow!  What excites me the most?  Finding out what students say!

Aha! Aha! Aha?

During my time reflecting on teaching and learning these past 15 months or so,  I have arrived at some significant insights.  Significant for me, at least.  These insights came from reading as well as my journaling.   Sometimes I got there on my own and then stumbled on a post or two that echoed my very thoughts, usually with greather elequence.  Better yet, backed with reasearch.  Other times, what I read got me revisiting and questioning my beliefs and pushed me to grow.  I should and may blog about each insight, but for now, I want to just summarize the biggies.

Aha #1.  Grading, no matter how you slice it, is horribly detrimental to learning.  Some systems more so than others, but they all boil down to judgement handed down by someone who is not the learner, someone in a position of power.  Even when a system is intended to communicate learning, it is received as judgement.  Grades (points, percentages, levels, etc)  do not inspire or motivate, at least not instricially.  They teach compliance, which is not the same as responsibility.  They generate status in classrooms, schools, and communities.  They develop fixed mindsets and negative beliefs about self and learning and school.  They open doors of opportunity for some and close them for others.  I can’t even say they do more harm than good, because there simply is no good.

I say this understanding that most teachers are genuinely interesting in being fair, in doing what is right.  They find or create or use a system that makes sense to them and look for ways to make it efficient and meaningful.   I say this understanding that grading is deeply, so very deeply entrenched in the Institution of School that it is rarely questioned, rarely examined honestly and openly, and incredibly resistant to change.

Yet change is desperately needed.  We need to reject grading and adopt practices that support and foster learning.    I say this with very little to offer of what to do instead, because this is largely uncharted waters.  (Hence my aha with a question mark.) Yet I also say this with absolute conviction.  Grading is broken (always has been), and we need admit that and throw it out, not try to fix it.  Changing how we assess student learning (NOT the students themselves!) requires us to ask why we need to so do in the first place. I think the conversation needs to start there. For me, everything we (teachers, admin, parents) do including assessment should promote learning. Inspire learning. Deepen learning. Celebrate learning. For. Every. Student.

I believe the solution lies with involving students.   The Art of Learning, if you want to call it that, includes metacognition and self-reflection.  Anybody, any age, any where, knows whether or not they are learning, whether or not they understand, where their strengths are and where growth can happen. Frequent student led conferences with teachers and peers, written and verbal reflections, peer and teacher feedback, formative assessments, opportunities to revisit and revise,  and portfolios are all potential components, I think.  I’m certain there’s more.

Its going to require a stronger role from the learner and a more supportive role from the teacher.  It’s going to take effort and patience and flexibility.   Change is always difficult, but the difficulty of the task (and this one is really complex) should not be a deterrent and  is certainly is not a valid reason to maintain “tradition”.  After all, we are talking about the education of our youth, the adults of tomorrow.  Perseverance is mandatory; they’re worth it.

This turned out to be a longer post than I anticipated;  I guess I’m more passionate about this than I realized.   So I’ll close with a quote from David Wees’  latest post:

The goal of teaching though is not to generate specific student performances. The goal of teaching is to produce long-term changes in what students know and can do. While we study performances in classes and use these to make short-term decisions about what to with our students, we should also systematically compare these short-term performances with the long-term changes in student performances that then correspond to their learning.


I’m just going to be blunt.


(such as points, number right/wrong, percent,

proficiency level, letter grade, score, etc etc etc)

on student work

other than actionable feedback

STOPS learning

dead in its tracks.



Although I’ve come to the above realization, I have no idea how to make feedback a reality.  How to make it both effective and manageable.  So I’m starting a virtual file on the topic.

ASCD: 7 Keys to Effective Feedback

Mark Chubb: How do you give feedback?