Two totally different questions

"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.

How is your classroom culture?


"Why do I give you time during class to work on your math problems?"
"It is busy work? You want us to do something during class?"
"You're a nice teacher? You want us to have less to do outside of class?"

Wrong! Neither was the the answer I was looking for today. The point I was trying to make with my students as we end the school year is the value of collaboration. While students are in class, they have access to....
  • answers posted on the board - that's right, all homework answers are "free" in this classroom
  • other students who are generally working on the same assignment - an invaluable resource as group work is highly encouraged on a daily basis
  • me, the instructor as I wander around the room and peek over their shoulders looking for common misconceptions and answering as many questions as possible in the allotted time.
Can I really blame my students for answering the "why class time?" question? Next year, I plan on focusing more on classroom culture. Emphasizing the importance of what we do and why we do it on a frequent basis is a first step in this direction. Here's a start at a few frequently asked questions and the responses I'd like my students to ideally answer after a semester in my classroom.
  1. Why am I assigned homework problems each and every day?
    Homework is practice. I need it to figure out what I "know" and what I "don't know" so that I can ask questions when I don't understand something. Not doing homework is like not trying on a pair of pants in the dressing room before purchasing them - a risk!

  2. Why do you get time during class to work on homework problems?
    During class, I have access to answers, friends and my teacher! At home, these resources are not readily available. It's like looking for food at the grocery store - all around me!

  3. Why do we take quizzes in this class?
    Quizzes are a way to find out "what I know" and "what I don't know" in a more structured format. It's a great opportunity to get detailed feedback and learn from my mistakes.

This list is just the beginning as I continue to think about changing the culture of my math classroom. Looking ahead to next year, what questions (and ideal responses) are important to you as you think about the classroom culture?

One small change

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?

Giving students real choices

"We don't tell kids to use one tool or another-- PowerPoint or iWork or iMovie; part of the assignment is to pick an appropriate tool." - Mike Arsenault, Maine middle school principal (source)
When learning supersedes the technology tools, students win. As I've lobbied for previously, an educator's job is to connect the content, pedagogy and technology in a way that has the best chance of engaging students with diverse learning styles to help them build upon their previous knowledge.

Conference breakouts and professional development sessions devoted to specific technology tools are typically self-serving and eventually undermine students' true ability to choose their own tools.

Here is the typical "show, learn, require" cycle seen in today's educational systems.
1. Educators are shown new tools from colleagues or outside consultants.
2. Time is taken to learn the new tools and develop new lesson plans.
3. Students are required to use the new tool because the educator is comfortable using it, thus killing student's ability to choose tools they might be comfortable with.

I realize that not all educators consider themselves to be tech-savvy, but should this be an "excuse" for limiting the tools our students use in the classroom? Let's give our students the choices they deserve!

Caught not taught: Part 2

A quote from a book I skimmed several years ago came to mind today. It directly relates to yesterday's post on "Caught not taught."

"The single most important factor in an individuals education is his teachers. All of us remember particular individuals who influenced and inspired us and gave direction to our lives. Not buildings, programs, curricula, philosophies of education, but men and women who by virtue of their personalities and their love of some discipline, some book, some kind of learning, opened the world to us, and showed us things we had not seen before, gave life a meaning it had not had before. What we need if we are to touch the minds of children, rescue the public school system and the democracy it should nourish, are inspiring teachers. They are precisely what the present system (i.e. colleges of education as currently constituted) militates against. Although they exist here and there, they do what they do in spite of the present system of preparation and in spite of all the odds against them which the system presents. Isn't it time we changed it?"

Rita Kramer, Ed School Follies: The Miseducation of America's Teachers, Free Press/Macmillan, New York, 1991; p.222
Technology doesn't matter? Student-centered pedagogy is worthless? The emphasis seems to be on the educator (human) rather than the books, blogs and blackboards.

What role does this eighteen year-old quote play in today's literature filled with buzz words such as 21st century skills, constructivism and accountability?

Caught not taught

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?

Effective homework - parents' role?

I am thinking about asking my students how they would describe "effective homework." My guess is that some will think the phrase is an oxymoron!!

Over at the ASCD Inservice blog, Diana Strasser posted some interesting commentary related to this topic. She quotes Robert Marzano's book, The Art & Science of Teaching in suggesting the following guidelines for effective homework:

  • Homework needs to be completed in order to produce the highest achievement gains. Design it with ease of completion in mind.
  • A large amount of homework does not result in better learning.
  • Homework should be academically purposeful, not a punishment or a symbol of the seriousness of study.
  • Homework should be explicitly tied to the current learning goals of the class.
  • Homework should be able to be completed without adult assistance.
  • Parents or guardians should not be expected to act as content experts.
  • Parents should, however, be provided with clear homework guidelines.
  • Assignments that involve using the parents' expertise or personal experiences (such as interviews) are often successful.
I am in full agreement with the first two points. Ease of completion and assigning "just enough" make sense. I have never been a fan of assigning homework as punishment. Apparently someone in today's educational system has used it as punishment, because my students sure do see it that way! Changing the "culture of homework" is a topic I hope to address in a later post.

I struggle with the suggestions that "Homework should be able to be completed without adult assistance" and "Parents or guardians should not be expected to act as content experts." These two seem to work against the final suggestion that "Assignments that involve using the parents' expertise or personal experiences...are often successful." As a math teacher, it is not uncommon to hear one of three comments at parent/teacher conferences:
  1. "I didn't understand/like math in high school either so I can't help my child at home."
  2. "I really use a lot of math at my __________ job. I always try to help my child with his/her math homework."
  3. "I used to be able to help out with math homework, but this high school math is over my head."
If parental assistance is available at home, then why shouldn't I expect those students to take advantage of the extra help? During class time, I highly encourage my students to ask questions of each other and of me. Parents are simply another available resource. Furthermore, parents may be able to explain a concept or idea from a different perspective based on their previous education and current working experience that might "click" with a student in a way that I am unable to communicate to them.

I am not ready to give up "extending learning" outside the walls of my classroom if it can be done in a way that benefits students. I admit that my experience teaching in a district with a predominantly middle-class demographic skews my perspective on this subject.

I am wondering if I am missing the boat here. Why wouldn't we want ("requiring" may be a source of disagreement, I admit) our students to take advantage of the expertise found in their own homes?

PLNs, People and Progress

A colleague emailed me today:

"My PLN is my new favorite coffee! I am just as addicted to it as I am my morning cup of joe. It has led me to reflect greatly on what I am doing in the classroom. Honestly, previous inservice time has rarely given me anything that makes me "think" about my teaching practices. I don't always agree with what I read, but what I am reading through my PLN has made me question the way I teach, the way I assess, the way I use technology...from A to Z, I have been reflecting and questioning why I do what I do. I have regained a sense of passion for learning...and learning about topics that I had never given any thought to. Assessing students' learning, for example. I believe a lot of what I do in that area is from the way I was assessed, both in secondary and post-secondary school, and the way I know others in my curriculum area assess. My PLN is changing the way I think. I am so happy that summer break is almost here. There are quite a few changes I want to make to my classes and to my teaching.

It's amazing how quickly my "network" has grown. I started with just a couple of feeds you had recommended and it has ballooned from there. I am still a "lurker." I have not made any comments...yet!

I cannot praise the PLN idea enough! The only downside, and this is just me personally, is learning how to manage all this information. I have so many interests and sometimes feel like I need to know it all. My reader often sits at 1000+ items because I have subscribed to so many different feeds. I need to learn that I don't have to subscribe to everyone's feeds that are related to my areas of interest, but find those that really hit home with me, really make me think, question, and reflect."
The email's energy and enthusiasm is the fuel keeping this project alive and well. Once month ago yesterday, I described a vision of rolling out personal learning networks as a differentiated professional development pilot in my building. Several educators from across the globe chimed in with their thoughts, experiences and related plans. I had hoped to elevate our building's awareness of PLNs at our scheduled half day in-service time tomorrow, but unfortunately other items were already on the agenda. Here is a proposal that I presented to the leadership staff for their consideration:

While I had hoped to be farther along with the first action plan step beginning tomorrow, I am still optimistic about the future. My building principal asked me to help him setup his own PLN tomorrow, so that is a step forward in itself. Other staff members have responded positively about their PLN experience so far. With permission, here are her thoughts so far:
"I have really enjoyed Reader and the information I get daily. It ranges from Chef Jamie Oliver's blogs in London, recipes, dance and education. I have taken articles and shared them with my students and it has enriched my lessons. The down side is remembering to check my google account. I get so busy during the day that I may not think about it until after school....I can't wait until summer when I have time to really search for new sites to subscribe to."
When thinking back over the past month's progress, I am nothing short of ecstatic. How are personal learning networks making a positive impact on the people in your area of influence?

the wRong Rx

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:
" 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?