MeTA musings

Note: This is the fifth post in a series based on the book Never Work Harder Than Your Students & Other Principles of Great Teaching by Robyn Jackson.

One of the hardest parts of being a high school math teacher from my perspective is not falling into what Robyn Jackson calls the "Curse of Knowledge" trap.

"Once we know something, it is hard to understand what it is like to not know it. Our knowledge makes it almost impossible for us to imagine what it is like to lack that knowledge." (p. 104)

Perhaps someone in your building is always ragging on students because they just don't "get it." Isn't that our job...to help students go from "not getting it" to "getting it."?! If students came to me knowing everything there is to know about math, then...

1. I would have a pretty boring job, and
   
2. I would not have a job for very long.

When I begin teaching Geometry this August, I need to once again "recalibrate" my brain and think back to what it was like to know very little about naming angles, rays and line segments. I cannot assume that students know about Pythagorean's Theorem, let alone when (and when not to) use it. In my experiences, the difference between being merely a content expert and a master educator is the ability to comprehend and understand what it is like to "think like the students do."

The content expert says, "I know this and so should you."

The master teacher thinks, "What barriers exist between where my students probably are and where I would like them to be."

The realists in my readership are thinking right now, "How do go about doing this?" Robyn Jackson's fourth chapter and principle, "Support your students" suggests a few practical ways of getting past the curse of knowledge.

• Use pre-assessments to identify common misconceptions ahead of time. In our current era of high-stakes testing and accountability, pre-tests have been given a bad rap. Through pre- and post-tests, teachers are quickly able to "show" they are doing their job. While that may be true, a well-designed pre-test can quickly tap the brains of a classroom of students and in turn reveal commonly held misconceptions which can be used to guide future instructional planning. A pre-assessment of this type does not have to be scored or entered into the gradebook. It can merely be used as a narrative or snapshot or where students currently stand in their understanding of upcoming concepts.
• Focus on error analysis. What are your students currently struggling to understand and why are they doing so? Might I suggest my previously documented thoughts on debugging as a place to start your reading?
• Show bad examples and common errors/misconceptions. Once you have identified the errors and misconceptions, use them as future teaching moments. Some of my most meaningful group and individual remediation has not revolved around a new lesson plan script, but rather pulling examples of incorrect student work and asking students questions about it. Questions such as "What were you thinking here?" or "What do you think Johnny did wrong at this step?" These types of prompts also model self-assessment, a skill I believe is necessary for truly developing "life long learners" as so many of our school mission statements propose.

In what ways have you found success in helping your education-minded colleagues get past the "curse of knowledge"? What types of tools/strategies do you use in your classroom to identify misconceptions? Feel free to leave a comment below.

Today, my Statistics students were charged with applying their newly acquired hypothesis testing skills in a "real life situation." I typically roll out a new project like this one by outlining my expectations and through showing off several sample of previous students' work. A rubric accompanies each project so that students know how it will be "graded." A new layer I've added this year is requiring students to self-assess their work before they turn it in. So far, students have responded fairly well to the idea and seem to understand that the rubric is as much for "them" as it is for me. We've had several meaningful conversations focused on project-based learning and how a rubric should take the "mystery" out of the grade and expectations.

Below, you can read a more detailed description of this particular project.


The self-assessment piece typically happens the day students are asked to turn in or present their work. I decided to add a new component today by requiring my current students to look at a small sample of previous students' projects (before even beginning the planning process of their own project) and compare them to the rubric. Students were asked to choose the two sample projects they felt were done the best.

Here was the "student's choice." Neatness, readability, and ability to communicate the hypothesis test process were reasons given for its popularity.
It seemed like a nice "twist" to the culture of self-assessment I'm attempting to foster in my classroom. By allowing students to critically analyze others' work, I'm hoping it will carry over into their own work as well. This quasi-peer assessment exercise on the front end will hopefully help them see what "quality work" looks like in this context. I wanted to share this as a working example in my quest towards modeling self-assessment.

(This post is the second in a series based on metacognition as a way of improving classroom assessment and instruction)

In response to How Students Learn, a second book was written addressing discipline-specific strategies. How Students Learn: History, Mathematics and Science in the Classroom is an outstanding resource for those who want to dig deeper in to Bransford's key principles. The emphasis on metacognition continues as well:

"Ultimately, students need to develop metacognitive abilities - the habits of mind necessary to assess their own progress - rather than relying solely on external indicators" (Donovan & Bransford, 2005, p. 17)

The application of this idea seems to be natural from a theoretical point of view - learners must be able to tell themselves whether or not they are understanding a given concept. From a practitioners perspective, I am unsure how well this idea is accepted and applied in a typical mathematics classroom. Based on my experience and observations, a secondary math class looks something like this three day cycle:

DAY #1
8:20 - Teacher reads answers aloud; students check with a red pen
8:25 - Teacher asks if there are any questions; One student raises hand to ask what answer to #6 was as s/he was too busy writing the correct answer to problems 1-5 to hear the answer to #6
8:27 - Students hand in papers to teacher to be recorded in grade book
8:30 - Lesson ABC begins; students take notes
9:00 - Students work on homework, wondering if they have the "right answers"
9:15 - Bell rings; students leave not knowing if they understand lesson ABC

DAY #2: Students come back and cycle repeats itself. Students turn in homework for lesson ABC and are assigned homework for lesson XYZ
DAY #3: Students come back and receive "graded" lesson ABC homework that they started at 9:00 two days ago.

Two questions come to mind:

1. What opportunities are we providing for our students to go back and learn from their mistakes when their mistakes are sitting in a folder on our desk "waiting to be recorded"?
2. Even if we write detailed, diagnostic feedback on each students' assignment and give it back to them the next day, how many will take the time to go back and fix their mistakes?

I believe we're amusing ourselves if we think students will take the necessary time to learn from their mistakes after 48 hours have elapsed since they first started the assignment.

"Metacognitive functioning is also facilitated by shifting from a focus on answers to just right or wrong to a more detailed focus on 'debugging' a wrong answer, that is finding out where the error is, why it is an error, and correcting it." (Donovan & Bransford, 2005, p. 239)

The teacher-as-answer-holder system as we know it seems to be missing a valuable aspect of formative assessment - providing students with an opportunity to revise and improve their thinking. In my search for literature related to metacognition and assessment during the past few days, I stumbled across an ERIC article on student self-assessment. From the article:

"...students who assessed their own work were remarkably willing to revise it."

Sounds good to me. Perhaps we've never given our students enough opportunities to assess and revise their own work!

Possible Solution: Students must be trained how to assess and revise their own work.
Notice the key characteristics...trained....assess...revise.
I started out the semester working hard to train students to "check answers with a pen as I read the answers aloud and to not copy odd answers from the back of the book." I'm finding that this is a hard habit to break. For the past three weeks, I have not read the answers aloud, but instead encouraged students to check their answers against the key both during their work time as well as the next day when they come back to class. In general, students are simply not accustomed to the idea of checking their own work - they must be re-trained. There are the few who take full advantage of this new system and check their answers regularly. Others will check their work, but are unwilling to ask questions of their peers and/or me to overcome their misconceptions. The revision never takes place. I'm looking forward to the weeks to come as I develop strategies to break this habit that's been created by me and so many others in the "teacher-as-answer-holder system."

Just as we model positive group work behavior, passing in papers and appropriate use of technology modeling self assessment must be at the core of our daily practice. The image to the left is a sketch I wrote on the board for a student today as I was attempting to help him see the value of self-assessment.

The homework checking scheme I am currently piloting clearly encourages students to become "self-assessors" by eliminating the "teacher-as-answer-holder system," but I am unsure if it lives up to the revise key characteristic made above. Language arts instructors seem to have this characteristic down through the use of multiple drafts of an essay or research paper, but this seems like a relative weakness in the math education realm.

Looking towards the final post in this series, what strategies have you found to be useful in helping students revise their work through the lens of self-assessment?