MeTA musings

"Can you tell me how to do it?"

(or worse yet, "What formula should I use?")

"Can you help me figure out what I did wrong?"

Students ask these two questions of each other and of me on a daily basis. They are two totally different questions. As we reviewed for tomorrow's Geometry test, I had an opportunity to explain the difference to my students. A brief synopsis follows.

A student that asks, "Can you tell me how to do it?" most likely...

• has not thought it through first for his/herself, and/or
  
• more concerned about the "answer" than the concept/algorithm

A student that asks, "Can you help me figure out what I did wrong?" most likely...

• has already given some original thought to the problem, and/or
• has struggled through multiple ways of approaching the problem

The latter question is obviously the one I emphasized as students reviewed together.

From the Iowa Core Curriculum on "Teaching for Understanding":

"Teachers assist students in making connections between prior and new knowledge to develop deep conceptual and procedural knowledge"

When a student asks "Can you tell me how to do it?" or "What formula should I use?," I am not able to determine his/her prior knowledge. Perhaps this is why I struggle with answering whole group questions on the previous day's assignment at the beginning of class. When I spit out the solution to p. 697 #34, I am inevitably answering the question "Can you tell me how to do it?" for my students! Ideally, each student would be able to figure out their own misconceptions (a la metacognition), right?! On a more realistic note, it would involve me looking at what the student did and did not do on that particular problem to help him/her overcome the misconception.

In the future, I'm looking forward to more opportunities to model to my students the better question of the two, "Can you help me figure out what I did wrong?" To me, this is what formative assessment is all about.

One small change in my classroom this year has yielded incredible results. In an earlier post, I mentioned a quote from a book by Lorna Earl entitled, Assessment as Learning: Using Classroom Assessment to Maximize Student Learning.

"...changing classroom assessment is the beginning of a revolution - a revolution in classroom practices of all kinds...Getting classroom assessment right is not a simplistic, either-or situation. It is a complex mix of challenging personal beliefs, rethinking instruction and learning new ways to assess for different purposes." (Earl, 2003, pp. 15-16)

The revolution began by implementing standards-based reporting - the "how" behind my assessment.
Lesson learned: Clear learning targets coupled with examples of strong and weak work help students better analyze their own strengths and weaknesses. The "old points system" was flawed. Two students could both earn 16/20 on a quiz. Student A made four computation errors. Student B understood four of the big ideas and bombed the fifth. Both students (and their parents) were "tricked" by the system in to thinking they have the same level of understanding. As a math teacher, I did not like this numbers game at all.

Once I started focusing on the learning targets associated with standards-based reporting, it became evident to me how important it was to give meaningful feedback. I had been missing the boat thinking that I was the only person capable of giving students quality feedback. Students were being underutilized in this context. I declared everyday to be "formative assessment day" through an increased emphasis on linking assessment with instruction - the "why" behind my assessment.
Lesson learned: I saw the value of using ongoing assessment to guide my instruction. Formative assessment does not just involve more quizzes or exercises, but rather using the results from these carefully designed appraisals to continually guide forthcoming instruction. Linking "assessment and instruction" as the educational cliche grew in importance and applicability. The best definition for formative assessment I have seen is:

"Formative assessment is a process used by teachers and students as part of instruction that provides feedback to adjust ongoing teaching and learning to improve students’ achievement of core content" (source).

By re-examining the "how" and "why" behind my assessment practice, I see learning through a much different lens. Look for more posts next year describing these changes in detail.

What "one small change" have you made this academic year and how has it changed your philosophy of education?

Most of the learning in life is caught, not taught.

I don't remember where I heard this quote, but it seems to "make sense" in so many contexts.

• Social scientists often argue that behaviors and attitudes are manipulated and changed by hours of observation. Dialects are a perfect example. A person who spends an extended amount of time in a region of the world often comes back speaking a bit more like those he or she was surrounded by.
  
• In the 1975 book Schoolteacher, Dan Lortie's idea of the "apprenticeship of observation" rings true in describing how educators teach in ways similar to the way they were taught as students.
• Parents learn gestures and vocabulary from their parents.
  
• Young basketball players enjoy mimicking the shots and moves of Kobe Bryant.
  

If learning is so easily caught, the next logical step is to ask ourselves:

Is what we're doing in our classrooms worth catching?

Several related questions come to mind:

1. Are we modeling to our students that "learning" only involves memorizing facts and formulas, taking notes and studying for tests?
2. If metacognition and self-assessment are worthy ideals, what are we doing to help this practice rub off on our students?
3. Is the content we're teaching worth learning or is the textbook driving our instruction?
4. Do our facial expressions, tone of voice and attitudes towards teaching indicate to our students that the content is interesting or dull and boring?
   
5. What are we doing to make each day meaningful and memorable for our students?
   

A district administrator challenged a group of educators to recall several pop music and American history related questions. Few could answer them all correctly. The same administrator asked the group of educators who their first grade, fifth grade, junior high math and high school science teachers were. Almost everyone answered them correctly. A positive buzz surrounded the room as many lamented on their favorite memories of school and what they learned from each teacher.

Maybe it is worth asking my students a simple question at the end of the semester and see how they respond. What did you learn in this class?

I wrote quite a bit about metacognition last month. After thinking about it, if students were truly able to "think about their thinking" daily and without my intervention, I might find myself without a job! Part of any educator's job description should be to guide students in their thinking about the day's concepts and ideas. Fisher and Frey in the book Checking for Understanding discuss a common talking point in any teachers' lounge:

"...students aren't always self-regulated learners. They may not be aware of what they do or do not understand." (2007, p. 1)

It's too easy to complain and rant about students who just don't "get it" but think they do. I often refer to this type of student as possessing a "high confidence, low competence" personality. This is where formative assessment comes in to play. In my experience, this is a tough pill to swallow:

"...checking for understanding provides students with a model of good study skills. When their teachers regularly check for understanding, students become increasingly aware of how to monitor their own understanding" (Fisher and Frey, 2007, p. 3)

Checking for understanding doesn't just involve assigning more problems or worksheets. On p. 16, Fisher and Frey (2007) quote Schmoker (2006) in what I consider to be the "wRong Rx" of education:

"...an enormous proportion of daily assessments are simply never assessed - formally or informally. For the majority of lessons, no evidence exists by which a teacher could gauge or report on how well students are learning essential standards."

Too often, we aggregate homework, quizzes and tests in to some sort of group that exists to accomplish the same purpose. When this happens, what evidence can we point to that our teaching is producing positive results? I believe we (educators) must practice some metacognition as well and ask ourselves, "What is the purpose of this assignment/assessment?" Once again, Fisher and Frey outline this nicely:

"Even more importantly, we need to help our students understand the purposes of testing...while we cannot change the testing climiate overnight, we can create classrooms where testing is understood and appreciated by teachers and students for what it can accomplish...We must understand what different tests do and share that information with our students...We must develop a classroom climate that empowers students in their quest to check their own understanding" (2007, p. 99)

I wonder what my students would say is the "purpose" of homework, quizzes and tests? Before I ask them, here is what I hope they would say...

• Homework: practice and a time to ask any and all question
• Quizzes: an opportunity to find out how well we're doing with detailed feedback from the teacher
• Tests: the "big show" where knowledge is demonstrated and recorded
  

If students think otherwise, I have a great deal of "culture changing" to do before the end of the year!

What are you doing in your classroom to change the climate that empowers students to take responsibility for their own learning? What would your students say is the "assessment prescription" in your class?

I feel like I had a great pre-service education at Wartburg College. My recent graduate training in curriculum and instructional technology at Iowa State University was outstanding, too. The education department faculty that mentored me at both institutions were truly dedicated to the profession and often did an excellent job "walking the walk" in addition to "talking the talk."

Today, I came across a video of a professor at Iowa State who really seems to value the importace of metacognition which I also blogged about several weeks ago. While I never had Dr. Mike Clough as an instructor, his work has piqued my interest. It is well worth eight minutes of your time to watch the video linked on this page as he models metacognition and wait time for a small group of future science educators.

Reflecting upon my own practice, I'm most likely too impatient when it comes to soliciting students' thoughts in a large group setting. Seeing it through the lens of metacognition and the quest towards better understaning students misconceptions shed a new light on its importance. A simple tweak to this aspect of instruction seems like it has the potential to pay big dividends.

How would you rate your regular use of wait time?

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

Debugging concepts vs. procedures

"Outstanding teaching requires teachers to have a deep understanding of the subject matter and its structure, as well as an equally through understanding of the kinds of teaching activities that help students understand the subject matter in order to be capable of asking probing questions." (Bransford, 2000, p. 188)

When educators are focused on conceptual understanding, debugging can become an effective means of incorporating metacognition in the classroom. With a shallow level of content and pedagogical knowledge in my earlier years of teaching, I found debugging to only happen from a procedural perspective. I was more inclined to point out a step that a student missed in his/her computation and/or algebra rather then stepping back and analyzing where the misunderstanding might be that leads to the "bigger picture" causing students' misconceptions. With these thoughts in mind, I embarked several days ago on changing the way I handle students revise their formative assessments.

Debugging Opportunities
In my quest towards standards-based grading, I have been conducting formal formative assessments every few days (and without much resistance from my students either, I might add!) and reporting progress by standard:One of the many reasons I believe in standards-based grading is that it gives feedback to students on the specific standards ("learning targets") they "get" as well as the learning targets that they may still need more work on. Students took the quiz one day and the following day I paired up students according to their relative strengths and weaknesses on the learning targets and set them loose for about five minutes to ask questions of each other. I'm starting to make this a regular part of my formative assessments. Compare this with my previous practice of marking them up heavily with red ink and verbally regurgitating the preferred solution to commonly missed problems - an exercise that not only bored the students, but never seemed to produce positive results either. Several minutes into this diagnostic session, a really neat conversation was initiated. Two groups were eager to get my attention with similar inquiries:

"Mr. T...we don't understand how to do this problem - we did the same thing! Can you help us?"

This is the type of question that gets a math teacher chomping at the bit! Two typical responses come to mind...
Scenario #1: That's a great question. Let me show you how to get the right answer...
This scenario is what I call a return to the teacher-as-answer-holder system. In my previous post, I laid out several problems with this approach. It takes the responsibility of "thinking" away from the student and places it in the hands of the teacher. Hopes for metacognition and student-initiated debugging are quickly squashed.

Scenario #2: Wow. I'm so glad you asked. (Insert probing question)
This scenario is the one we should be aiming for, but as Bransford suggests this process requires a deep understanding of the subject matter in order to ask questions that will help students overcome their misconceptions - a practice I admit improves daily with practice. This is when the debugging begins on the student's part! Colleagues lament that this is ideal of behavior we wish all of our students would exhibit, but seldom do. I believe the keys to this practice of encouraging students' debugging are wrapped up in connecting collaboration with explicit opportunities for revision. We must teach and value revision through a debugging process. Not only must students be exposed to and practice debugging, the educator must also have a general idea of the common misconceptions students will face for any given standard/lesson.

"Expert teachers know the kinds of difficulties that students are likely to face, they know how to tap into students' existing knowledge in order to make new information meaningful, and the know how to assess their students' progress." (Bransford, 2000, p. 45)

Just as parents remind their children not to touch a hot oven, they must also be taught how to properly use a hot pad when navigating the same steamy temperatures. The quote above reminds me the importance of modeling to students "how not to do" something as well so that they are better able to debug their own academic work. I will never forget my fifth grade teacher who would often purposefully write sentences with mistakes on the board or solve math problems in an incorrect way and wait for a student in the class to notice. He modeled (and expected) debugging in his classroom! This was a one-of-a-kind ordeal during my K-12 years. I only hope that I can provide this same memorable (and academically stimulating) experience for my students.

A virtual colleage of mine deserves credit with a recent post in which he asked students two thought-provoking questions:

1. What do you want to be able to do a week from today that you can't do now?
2. What can I do to help you get there?

Kudos to Mr. G over at TAGmirror for putting metacognition into practice! Perhaps some debugging with follow as the students come back with their plans that potentially need revision.

Is "debugging" a natural part of your classroom practice? What type of debugging events are you planning for the remainder of the year?

(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?

I still have my Psychology 101 textbook sitting on my shelf. It's not because I particularly enjoyed the course and expected the material to someday become immediately relevant to my career as an educator though. I have to admit it's because the textbook publisher came out with a new edition and the bookstore wouldn't buy it back. Sound familiar? One of the ideas I actually remember from this undergraduate course was the concept of "metacognition." The definition is pretty easy to remember and maybe that's why it's stuck with me so long:

metacognition - thinking about thinking.

This absolutely makes my head spin around in circles:

Me: "If I'm thinking about my thinking...then am I not also thinking about my thoughts about my thinking? If that's true, and I'm thinking about what I'm thinking about when I'm really thinking about my thinking, then... "

You get the point. It's cyclical and only mathematicians and computer scientists get into that type of stuff. I digress...

John Bransford mentions metacognition in my favorite education-related book (yet another shameless plug!) How People Learn. I decided to keep this book from my graduate education due to its profound influence on my philsophy of education. If you haven't read the book, it is an outstanding synthesis of the science of learning. Bransford's writing centers around three key findings from research on teaching and learning. They aren't particularly earth shattering themselves to some, but I was particularly impressed by the way Bransford was able to piece together so much of what I've learned in other educational training in an often more disjointed way. His three key findings were:

1. "Students come to the classroom with preconceptions about how the world works. If their initial understanding is not engaged, they may fail to grasp the new concepts and information that are taught, or they may learn them for purposes of a test, but revert to their preconceptions oustide the classroom
   
   
2. To develop competence in an area of inquiry, students must:
   (a) have a deep foundation of factual knowledge,
   (b) understand facts and ideas in the context of a conceptual framework, and
   (c) organize knowledge in ways that facilitate retrieval and application.
   
   
3. A 'metacognitive' approach to instruction can help students learn to take control of their own learning by defining learning goals and monitoring their progress in achieving them." (Bransford, 2000, pp. 14-18)
   

He then goes on to suggest an implication for each key idea as it relates to teaching. The third implication for teaching is the one I'm most interested in.

"The teaching of metacognitive skills should be integrated into the curriculum in a variety of subject areas." (Bransford, 2000, p. 21)

When is the last time you sat in on a metacognition across the curriculum professional development session? Granted I've only been in education for five years, but I'm still waiting for one.

Most educators I meet agree that they'd like students to assume more of the responsibility when it comes to their learning. This is an impossible task when students have never been formally taught how to assess their own learning and understanding. On p. 19, Bransford talks about a model in which, "...students are able to prompt themselves and monitor their own comprehension without teacher support." Wow, talk about working our way out of a job! Is this theory from an extreme point of view pretty idealistic? Without a doubt, yes. On the flipside, don't we, as working adults, continually prompt ourselves and monitor our own comprehension without others support the majority of the time? My car hasn't learned to fix itself yet, but I have learned the art of calling a knowledgeable friend and/or a mechanic to get it back in working condition. It's a soft skill that is directly related to assessment. Homework, tests, projects and quizzes are all ways students are "bringing their car in to the shop." The difference between my broken car and the student's assessments is that I know when to call the mechanic and many of my students do not.

With these thoughts in mind, I would like to kick-off a series entitled, "Towards better metacognition." In this series of posts, I will be addressing several assessment-related ideas and strategies I've read about (and implemented) that I believe are helping students begin this quest towards metacognition.

Before the series kicks off, I'm interested in doing a "virtual literature review" through you! What strategies have you found to be useful in helping students develop their metacognitive skills?