10%

We teachers learn early on that exams should reflect what students have learned. They should attempt to measure what was taught, to capture student understanding in a way that helps drive future instruction.

But lately, I’ve been asking myself, what if I included material on exams that students haven’t explicitly learned? What if I expected them to stretch what they did learn to apply it in a new way?

Specifically, I’m thinking that 10% of each exam would be stuff that students have never seen in class or homework. It would be unknown to the kids before they saw it on an exam. This 10% would push students to expand and enrich what they did learn. It would allow me to bridge pre- and post-exam content and possibly preassess things to come. It would trigger meaningful reflection afterward which, I hope, would cause students to genuinely learn something new. It would also help me measure how far their understanding of the mathematics will take them into uncharted territory — which is probably worth it in and of itself. And besides, the oh-so-high-stakes Regents exam in June is filled with problems that neither they nor I could have predicted…so why not prepare them for this all throughout the year?

All that sounds great. But what scares me is the unethical nature of it all. This is where my preservice days haunt me. How could I possibly hold my kids accountable for material they’ve never interacted with? Is that fair? This unpredictability for the students is making me second guess myself.

Although, I am only thinking about what’s expected now — which is that exams will follow suit with the problems they’ve already done. But what if this unknown 10% was a norm that was baked into our classroom culture from jump? What if it was something students understood and acknowledged going into every exam, an inherent challenge I placed on them to demonstrate their mathematical abilities to new ways?

 

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Checkpoints and homework, circa 2016

Here’s my current structure for exams checkpoints and homework. Everything is a work in progress.

Checkpoints

  • First off, terminology. Formally known as exams, I now call these summative assessments ‘checkpoints’ to further establish a low-stakes classroom culture. It feels much less formal, but I still reference them as ‘exams’ when in a rush. Plus, my frustration with the Regents exams is at an all-time high, so distancing myself and my students from any term that references them is a good thing.
  • I really liked how I lagged things last year, so I’m going to continue with this routine. This means that each checkpoint will only assess learning from a previous unit. In most instances this will be the previous unit, but once a month there will be a checkpoint that only assesses learning from material learned at least two units back. With my standards-based grading, students can lose proficiency on a standard at any time during the course of the year. The hope is to interweave what has been learned with what is currently being learned to help improve retention.
  • Speaking of SBG, I’m reinstituting mastery level achievement in 2016-17. I have yet to work out the kinks regarding how this will impact report card grades.
  • I will not review before any checkpoint, which is what I started last year. Instead, that time will be spent afterwards to reflect and relearn.
  • I make these assessments relatively short, they take students roughly 25-30 minutes to complete…but my class period is 45 minutes. I’m still trying to figure out how to best use that first 15 minutes. Last year I didn’t have this problem because my checkpoints always fell on a shortened, 35-minute period. Right now I’m debating over some sort of reflection or peer review time.
  • I have begun requiring advanced reservation for every after school tutoring or retake session. I learned very quickly at my new school that if I don’t limit the attendance, it is far too hectic to give thoughtful attention to attendees. Right now, I’m capping attendance at 15 students per day with priority given to those who need the most help.

Homework

  • Disclaimer: developing a respectable system for homework is a goal of mine this year.
  • Homework assignments are two-fold. First, students will have daily assignments from our unit packet that are checked for completion the next day. Second, they will have a DeltaMath assignment that is due at the end of the unit, again, checked for completion.
  • Homework is never accepted late.
  • Homework is not collected.
  • To check the daily homework, I walk around with my clipboard during the bell ringer. While checking, I attempt to address individual questions students may have. This serves as a formative assessment for me gauge where they are on the homework. After the bell ringer, but before any new material, I hope to have student-led discussion around representative problems, depending on the homework that day (I haven’t gotten here yet). The goal is to have students write on the board the numbers of the problems that gave them a headache…so we know which ones to discuss.
  • I’m going to do everything I can check it this year. It sounds simple, but over time things can slip away from any teacher.
  • I’m posting worked out homework solutions on our class website. I used to include the solutions in the back of the unit packet. This is an improvement on that, but also requires students take an extra step. Students must check their thinking, assess themselves against the solutions, and indicate next to each problem whether or not they arrived at the solution.

 

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A teacher’s dilemma: taking risks beyond the elimination answer choice C

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We ask teachers to embrace change, and the pressure on teachers is not to take risks but to march whatever children they can, lockstep, toward higher standardized test scores. – Robert P Moses, Radical Equations (p. 126)

Thanks to a recent conversation, once again I’m confronted with the heavy hand of high-stakes exams.

How can a teacher, like myself, establish and maintain a classroom centered on inquiry, contemplation, and sense making within a system that rises and fails on the scaled scores of New York State Regents exams? How can a teacher move a classroom of students beyond a no. 2 pencil and bubbles containing A, B, C, and D?

I guess this is nothing new. I’m simply reiterating a concern that most teachers have.

I find myself more entrenched in this battle than ever before. The more I teach, the more I realize how oppressive these exams are. I am forced to get kids “through” by whatever means necessary. Schools get recognized and accolades given out for producing students that are “college ready,” which is a reflection of students’ performance on Regents exams. This sort of verbiage gets everyone on the same page. The result is an unspoken, politically correct pressure placed on me and my students to conform to these narrow measures of mathematical fluency. This pressure results in anxiety and dramatically affects the quality of my instruction.

As someone in the classroom everyday doing this work, I’m so wrapped up in these damn exams that I don’t even have time to prepare my students to be “college ready.” Maybe I’m doing something wrong.

I’m essentially a Regents-driven machine whose sole job is to produce other machines who can generate positive results on these exams. Please, forget about the genuine, messy learning of mathematics that I desire.

Furthermore, in a society obsessed with test scores, obtaining a 65 (or 95) can indeed be the ticket to success. Students are only as good as the score they produce. They themselves know this, so their motivations often rise and fall on these exams as well. This is the cherry on top.

Despite this downward spiral, there is hope.

Patrick Honner’s Regents Recaps help me keep things in perspective. His reflections are thoughtful, full of mathematical insight, and shed light just how much of a joke these exams are. Without knowing it, he compels me to teach beautiful mathematics far beyond the expectations of a Regents exam.

And then there are educators like Jose Luis Vilson, Christopher EmdinRobert P. Moses, and Monique W. Morris. Through their writing, they’ve cautioned me that earning a 65 on a Regents exam for many of my students is the least of their worries, despite what school and New York State may tell them. They motivate me to bring often-ignored social issues to the fore.

There are many others who I have met either in person or online who have provided similar inspirations. There are far too many to name.

This leaves me torn.

On one hand, I’m fortunate enough to have a fairly high level of autonomy in my classroom. What my students and I accomplish in the 45 minutes we’re allotted each day is up to us. There’s relatively low oversight. Despite the immense pressures to bubble our lives away, I aim to spend time asking big questions, sharing the joy of mathematical discovery and learning, and enjoying the ride. This is empowering. Hell, I don’t even call my class exams “exams” anymore.

On the other, I am confused. And worried. The fear of a low passing rate has left me paralyzed in the midst of students who desperately need me to be fully aligned with their needs. But if I cannot afford to take meaningful risks in my classroom that go beyond eliminating answer choice C, if I can’t be bold in the face of oppression and conformity, what does this mean for my teaching? More importantly, what does this mean for my students?

 

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The day after

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I don’t like review days before exams. I’d much rather spend that day after an exam analyzing mistakes and relearning. I find this to be crucial in promoting a growth mindset in my students. My struggle has been how to structure these post-exam days. Here’s a formative assessment idea that I’ve used a few times this year.

The day after an exam, I set up the room in 3-5 stations. Each serves as a place to study a particular concept that was on the exam.

My bell ringer asks students to check their exam performance on the bulletin board in the back of the room. It lets them know for which concepts they earned proficiency. I also email the kids their performance immediately after assessing the exams, but many don’t check.

I hand back the exams and they move to a concept that they need help with based on their performance. If they have earned credit for every concept on the exam then I ask them to float and help others. At each station they use notes, each other, and the feedback I provided on the exam to analyze and learn from their mistakes. I also have practice problems at each station so they can make sure they understand the concept. I float around the room and help. Of course, the SBG data allows me to sit with students who need me most.

After a student feels they have successfully relearned a concept, and I usually check in to confirm, they can retake that concept. The retakes are in folders in the corner – students grab one and do it anywhere in the room. They submit it and begin working on another concept, if necessary. It doesn’t matter how many concepts a student retakes during the period, but it usually works out to be 1-2.

Before I did this activity I was concerned that since the stations would be full of students that struggled on a concept that they would all sit together and get no where. This hasn’t been the case. The kids are diligent to relearn. This may be because they like retaking exams and earning proficiency during class time, as I usually make them come after school to do this. It helps that the relearning is targeted and individualized to each student. Plus, it’s all formative. They go wherever they feel they need to. They assess themselves, but use one another in the process.

It can look and feel chaotic. But that’s the point. Improvement is messy. It’s also amazing – especially when it happens amongst your students.
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Internalizing feedback without seeing it

Feedback on exam in spanish

I’ve found that students all too often overlook, or simply ignore, the feedback I give them on assessments. For whatever reason they just don’t use it. This is a problem.

I value reassessment and see feedback as crucial in that process. If a student struggles on an exam, I need them to learn from their misconceptions. My feedback reflects this. I’ve always provided fairly detailed feedback, but this year I’ve stepped it up significantly. In fact, all I do now is give feedback. I provide no scores or grades on exams. This helps, but I still need to find ways for students to grow from the feedback they receive.

I have experimented with kids relearning concepts the day after an exam without seeing their actual exam. The day after the exam, I give a copy of the SBG results to each group. Each student uses the data to identify the specific concepts that they need to relearn or review. The groups are a mix of proficiency levels (based on the exam results) so if a student needs help with a particular standard, there’s someone in their group that understands it and can help them. I also give them blank copies of the exam to work on and discuss.

After about 15-20 minutes of peer tutoring, I give them their exams back. Based on their newfound understanding, at least some of their misconceptions should be alleviated. They now spend 15-20 minutes correcting their mistakes on a separate sheet of paper while directly responding to the feedback I’ve given them on the exam.

Ideally, this means that they are using feedback from their peers to understand and respond to the feedback I’ve given them. It serves as relearning/remediation before they retake the exam. What I’m missing, though, is a reflection piece that ties into the feedback as well.

A colleague conjured up a different spin on this. After an exam, he informs students which standards they didn’t earn proficiency on. (He doesn’t hand back their actual exam either.) He allows one week (more or less) of relearning/remediation on those standards – either on their own, or with you. He actually uses an online resource for this. Then, when they feel ready to retake, he returns their exam and asks them to self-assess and correct their original mistakes. If they can, he allows them to retake. If not, they continue relearning. It may not focus on feedback, but I like this.

Closing thoughts: what if I do get my students to internalize my feedback? Are they just going to be doing it to satisfy the requirements that I ask of them? When they leave my classroom, will they view feedback as a necessary component of success? Will my feedback really make a difference? How else could I get them to value it?

 

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