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.

IMG_2524

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!

Advertisements

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.

Writing ANYTHING

(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.

 

Update:

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?