Towards better metacognition - 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
- 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?

Towards better metacognition - Introduction

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?

Why assessment?

"What's your beef with assessment, Matt? Everyone does it a different way. Why can't you find a model that works for you and start writing about something more relevant?"
Great question. I read a great book a few weeks ago by Lorna Earl entitled, Assessment as Learning: Using Classroom Assessment to Maximize Student Learning and the author states a very succinct rationale for the personal "assessment craziness" that continues to push me to become a better educator.

"...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)
How we view assessment impacts everything we do in the classroom as I've attempted to illustrate below
Earlier in the book, it "hit me" how important it is to not simply "test" or "quiz" a time or two per week or chapter. What is the purpose of these assessments?

"It is not possible to use one assessment process for the many purposes we want it to fulfill. Different purposes require vastly different approaches, and mixing the purposes is likely to ensure that none of them will be well served" (Earl, 2003, pp. 12-13)
A few thoughts resonated with me after reading about this ineffective "mix" of assessment:

  1. What is the purpose for my chapter tests and weekly quizzes? I think often times my answer might be, "because I've always done it that way" or "because the book suggests doing it that way." Are my homework problems treated/graded like a daily test? What do I do with the results of my quizzes? Do students see a difference between quizzes and tests? Should they?

  2. Are standardized-tests used for AYP designed to "drive instruction" or report student growth/achievement? From the Iowa Testing website, "From its beginning in 1935 with the Iowa Every Pupil Tests, the emphasis in the program has been on the use of ITBS results for instructional purposes." With all of the attention to testing, it seems like addressing the purpose of the most widely administered tests is the first place to start.

The answer to the above-mentioned questions may be fairly simplistic, but the motivation to change as a result of thinking about assessment continues to be a driving force for me.
"Teachers who are working with a new view of assessment as part of learning are finding that it isn't possible to change assessment and leave everything else the same. When assessment changes, so does teaching, so does classroom organization, and so does interaction w/students and parents." (Earl, 2003, p. 45)
Maybe the key to "change" in schools isn't necessarily more/less/better technology, but instead re-thinking our view of assessment. It has the potential to be the medium in which lasting reform can be begin.

Look for more posts related to assessment in the near future.

Practice with feedback still matters

Practice with feedback matters, according to a 2007 study (pdf) published in the British Journal of Educational Technology. I've been hooked on this idea ever since I read Bransford's How People Learn two years ago. It's on my "highly recommend" list for other educators.

"The use of frequent formative assessment helps make students' thinking visible to themselves, their peers, and their teacher." (Bransford et al., 2000, p. 19)

As I mentioned in a previous post, I'm intrigued by the intersection between standards-based assessment and 21st century learning. In fact, I'm on a continual search for ways in which math education, assessment and technology might work best together. Where does "practice with feedback" fit in then? Without a doubt, formative assessment is a pretty hot topic right now at the Iowa Department of Education. In fact, I was at a district meeting of sorts last night and the "instructional decision making" model came up time and time again in conversation. IDM is the idea that instruction driven by data can help all students improve. K-6 teachers seem to "get it" through their use of DIBELS, BRI and DRA screening probes whereas us secondary folk are...well, assigning homework and giving out quizzes a few times a week! I believe that standards-based assessment/reporting has the potential to enhance my formative assessment practices, because it will better enable me to focus on what I'm teaching and how it should best be assessed. When I bring up connecting standards with assessment, the response I typically get is something like "Well, our text book matches our standards and we use the textbook tests and quizzes, so it must match up." I'm not convinced.

On the flip side, when I hear elementary teachers talk about setting up supplemental groups and choosing several different novels for their students to read based on ability, I admit that I get a bit jealous. It seems to me like the secondary folk are missing the boat somewhere. Math teachers are seldom accused of not giving our students enough practice, but I would like to propose that we are too often lacking in the area of meaningful feedback. The IDM probes referenced above are one way of enabling educators to provide appropriate instruction and in turn, meaningful feedback to those who need it, when they need it, and at a level that is appropriate for them.

Then there's the typical high school math classroom: Giving students a score out of five on a daily basis based on the neatness and accuracy of their answers, ability to show their work, and the responsibility of bringing a checking pen to class doesn't seem like meaningful feedback to me - especially when it takes 24 hours to collect papers, record scores and hand them back. A student said to me a few months ago, "I like knowing if I'm doing it right or!" What is the "answer" to this problem? Several technology-related answers come to mind:
  • Eliminate homework and make the move to more problem-based learning using appropriate technology tools
  • Create some sort of electronic means (Moodle?) of providing meaningful feedback on a daily basis
  • Who cares about homework?! Use student-response systems as daily probes to assess students' understanding
I have already decided to make the answers available to students ahead of time in order to help them get immediate feedback. I'm hoping to create a system that truly does make the students' thinking visible to both them and me. Reporting it out in a standards-based way seem like part of the picture, too. What am I missing in order to make practice with feedback a more visible part of my daily routine?

Giving up A's and B's for Apples and PCs?

In light of a recent article in the New York Times, I've been conversing via Twitter and Classroom 2.0 with several colleagues on the topic of "standards-based report-cards." If you're not familiar with standards-based assessment, grading and/or report-cards, I won't bore you with the details, but rather refer you to a nice resource on the benefits of this idea from the ASCD Inservice blog. In the midst of rolling out a "quasi-standards-based grading system" in my own classroom, I've wondered what it might look like in a semi-constructivist 21st century learning secondary math environment. By focusing so much on standards, are students losing out on opportunities to creatively express themselves and make connections among the various "real life" situations 21st century learning champions?
Should one be sacrificed for the other? Can we embrace technology appropriately while being explicit in the learning outcomes we'd like our students to address AND at the same time report this information out to stakeholders in a meaningful way?

PLN dieting

David Warlick is commonly credited for coining the phrase "personal learning network," now shortened to PLN. I've been an avid reader of several edu-bloggers for years, but most recently have soldered my "literature pot" together by aggregating it all via an RSS reader - thanks to a virtual colleague's suggestion. This, of course, is not uncommon in today's Web 2.0 world of Twitter, Plurk, Second Life, blogs, wikis, virtual conferences and other social media. Eating isn't uncommon either, at least for those of us fortunate enough to have jobs that put food on the table. As I sat down today to eat my usual brown bag cuisine of a cold meat sandwich, pretzels, dessert and fruit, I began to wonder what sort of diet might best best illustrate my PLN. Here a quick mental list of what differentiates various diets:

  • Frequency - number of times a person devours a snack or meal in a given period
  • Time - minutes/seconds/hours a person desires (or requires!) to go from "napkin on lap" to "brushing off the crumbs"
  • Choice - dietary or personal preference restrictions on the food to be consumed
I've never been one to "diet" other than one calendar year when I did not drink a carbonated beverage, so I don't consider myself an expert in this area at all. Here are some diets that came to mind and their corresponding PLN behaviors:

South Beach Diet: From wikipedia, "The South Beach Diet is relatively simple in principle. It replaces "bad carbs" and "bad fats" with "good carbs" and "good fats." This type of PLN is constantly changing. Mediocre tweeters and bloggers are purged daily in favor of fresh ones. Simplicity is the backbone for a solid diet of reading each day. Certain types of commentary are repeated while others are avoided like the plague.

Weight Watchers: This a very goal-oriented PLN. Weight Watchers have a specific weight in mind and are then put on a maintenance timeline in order to keep the excess weight off. Once a PLN has enough "good stuff" rolling in each day, the owner is happy to continue reading on a daily basis. Points are given in the form of sharing with others. Until then, it's a fight to reach that magic number of PLN happiness.

Fast Food: This isn't really a diet, but more of a state of mind. Fast food eaters are in a hurry to get their food and eat it as quickly as possible. This type of PLN has tons of options, but was created in a hurry and probably is scanned through quickly on a daily basis in order to best utilize a busy schedule. Healthy eating is not a priority, but good prices and free drinks are essential. Quick information and links to future reading is plentiful.

Applebee's: Your "neighborhood bar and grill" serves up favorites to all who walk through the doors. This type of PLN has the usual "big time" bloggers, tweets and feeds. The menu is pretty standard and you can usually find something good to read every time you pull up a chair.

Home cookin': Mom always made the best food from scratch, right? This type of PLN features one or two favorites and the rest is pretty open. Whatever Mom is-a-cookin' will surely taste good. A few local favorites are featured weekly as well.

What does your PLN look like and how much time do you spend tweaking it?

What's your "PLN diet?" Did I miss yours?

Better practice?

One of the most thought-provoking phrases related to education and technology that's ever crossed my RSS feed is

At a conference last week, Mark Weston from Dell computing stated that asking the question, "Does technology improve student learning?" is the wrong question....

The question should be, "Does technology support the practices that improve student learning?"

-Doug Johnson on Blue Skunk Blog
Since I started my graduate work, I've been on a rollercoaster ride of thinking about the use of techology in my classroom - both the pros and the cons. In a somewhat ironic outcome, I've started to wonder if technology itself can actually hinder learning at times rather then help. I'll come back to this thought.

Any educator whose gone through a pre-service program in the past ten years has surely heard the phrases constructivism, student-centered learning, and best practices - sometimes in the same sentence! I am no exception to this rule. As a seasoned math educator, I can attest to the fact that some learning goals are more suited for this style of learning while others are simply...not. For example, teaching Geometry students that the sum of the interior angles of any n-sided polygon is (n-2)*180 lends itself very well to a student-centered approach. On the flipside, instructing students how to solve multi-step linear equations or how to use the quadratic formula does not lend itself to a constructivist teaching style. James Cangelosi's book Teaching Mathematics in Secondary and Middle School speaks of the need to differentiate between construct-a-concept, discover-a-relationship, and algebraic skills, and developing knowledge objectives. The content/objective should determine the type of pedagogy used to teach the idea.

The same analogy applies to the use of technology in our classrooms. Are using blogs, Moodle, Google Docs, or Twitter the "best practice" for every discipline and for every standard in our curriculum? I've long been an advocate for Mishra and Koehler's TPACK framework.

(image from

With all of the talk in the education (technology) blogosphere about "best practices," I would like to propose that "better practices" is a much better term. There really is no "best" technology tool or teaching style to push unless it meets up with the corresponding content to be taught in the middle of the TPACK Venn diagram above. Wikis, for example, might have different uses in a British literature classsroom than they would in a ceramics class. At the same time, wikis may have no place in a particular P.E. unit. When we push things like "iPods" and "cooperative learning" blindly, its no wonder the masses see them as "add-ons."

Venn diagrams are hard to sell our colleagues...but so are "best practices." Are you ready for the era of "better" practices?

Why blog?

After holding out for quite some time, I've decided to give blogging a try. I outlined my rationale for starting this blog. Countless presentations and edu-bloggers have focused on the topic of "blogging in the classroom," but what's your personal motivation to write for a presumably public audience?

A few thoughts that come to mind...

  • Does it relate to expanding your David Warlick-inspired personal learning network?
  • Do you do it because you expect your students to blog as well?
What would you say in response to your colleagues who are anti-blogging as highlighted in this Edutopia article?