Building Thinking Classrooms
This page explains what you will see in our classroom. Our 5-12 math department is doing a book study with a book called Building Thinking Classrooms. These are the essential elements of a Thinking Classroom from the book.
Visibly Random Groups
Almost all teachers use groups from time to time and some classes use them regularly. The research shows that when the goal of the teacher-arranged grouping method and the student goals are not aligned, it means some students will be unhappy and will disengage. It also shows that assigning roles is counter-productive because students comfortably settle into their one role, decreasing the thinking that happens in the group. It is much easier to be a follower than a thinker and pre-assigned roles encourage this.
The Solution - Visibly Random Groups (we do this almost daily)
Visibly random groups come to the rescue here. Students must trust there is no hidden motive in the grouping, and the groups must change regularly, sometimes as often as every class period. Cards or some other method of publicly randomizing is essential for students to trust this system. The benefit of this system is that by learning to work in random groups, students grow their ability to work with all people. Groupings are fully random, and not intentionally repeated when we use the random method. There may be times we have intentional groupings.
In our classroom, we'll have assigned seats to start the period but we'll move into our random groupings on most days.
Any materials that are not math materials will be stored in lockers or cubbies in our room. This practice allows us to move freely around the room during a class period.
*Source for more reading: Chapter 2 in Building Thinking Classrooms in Mathematics
Vertical Non-Permanent Surfaces
This is probably the topic in the book that has me most coveting corporate America. My husband works for a company that has gorgeous offices with vertical glass whiteboards that are all over the building. They write on these slightly opaque glass surfaces for everything! I want them. The research is clear that students (and adults I'd think) think better when standing and writing on something that has a non-permanent feel. I experience this all the time in collaborative settings; that fear of writing on paper or large Post-it because it feels so permanent!
An aside - something I almost always did before reading this book is to have a classroom arranged in groups. The book advocates groups of 3 (or 2), something I'd heard last year from a High School colleague as well. I'd always opted for 4, but the rationale is strong here especially when you pair this with randomly assigned groups. Additionally, it suggests "de-fronting" the classroom. That is SO liberating. When coupled with shifting away from taking notes (more in the meaningful notes section below), it opens up space in a classroom because you aren't committing to every student being able to see the board at all times from their seat.
The Solution - Vertical Non-Permanent Surfaces (aka whiteboards). We do this almost daily.
Our visibly random groups will all have a space to write. It may be our large whiteboard in class, or it could be a window surface. It may also be one of the 30 individual double-sided clipboard whiteboards that I just bought for our classes. It may not be quite as lovely as my husband's office environment, but it is a pretty nice setup!
*Source for more reading: Chapter 3 in Building Thinking Classrooms in Mathematics
Thinking Questions
This is the meat and potatoes of the math here. I am not going to try to list out everything, instead opting for a few bullet points that will help you get the gist.
Teachers answer too many of our own questions in a way that encourages students to stop thinking.
Teachers answer far too many proximity questions. These may be questions a student asks just because the teacher is there and they can look engaged that way.
The Solution - Answer only "Thinking Questions" - I'm working on modeling this.
Answer only thinking questions for students while validating that you have heard a student when they ask a "stop thinking" question. Stop-thinking questions are simply questions designed to let students stop thinking because we start to give them more information than we should.
*Source for more reading: Chapter 5 in Building Thinking Classrooms in Mathematics
Check your Understanding
Homework is a constantly debated topic in all education, especially in mathematics. We've all heard, "practice makes perfect" and "perfect practice makes perfect" along with so many other phrases. As the mom of two musicians, I've always seen homework through the lens of musical practice - you just can't get better without practice. But, the truth is that in a school musical group, a classroom or on an athletic field, our motivation to be there varies widely. Some are headed to the top of their field and are passionate about sucking up every bit of learning they can, others are genuinely not interested in the subject or overextended, and the vast majority are in the middle. This mix creates a true challenge in the classroom.
The research says that when you give homework, some won't do it, some will cheat, some will get help and a few will have success trying it on their own. Grading homework increases the number of students that do it, but it also increases cheating and getting help. It also increases stress for students. Most homework ends up being a regurgitation of sorts, with students reluctant to try something they don't already know how to do. Again, I apply a metaphorical mom hat here as well as my own learning style. When practicing music, you are typically practicing something you already learned in class, with sight reading making up a small portion of your practice, if any. As such, I'm not very bothered if the practice is drill and skill. I am concerned about cheating and stress as a result of scoring, as well as taking time from class to score something that creates these behaviors.
The Solution
Check your Understanding questions. This is not simply a rename of the word homework, but an entire shift in thinking.
These questions can not be scored or even checked. No overt teacher action may be taken in the form of praise or punishment. This keeps the questions safe for the student.
Answers need to be provided at the same time questions are given. Note that this doesn't mean fully worked-out solutions. Those may be provided, but not right away.
Will all students do these problems? No. Research shows that 15-50% of students will not do them. But, the key difference is that the students who are doing them are doing them for the right reasons. We also do not have to only offer these for at home time - they can be a mix of in and out of class.
*Source for more reading: Chapter 7 in Building Thinking Classrooms in Mathematics
Meaningful Notes
I have long struggled with the concept of notes that have blanks for kids to fill in (guided notes), vs students taking their own notes fully, or just not taking notes at all. Some bullet points from the book:
Once a student gets behind in notes, they just copy complete or "dead" notes instead of living notes where they understand what is happening in that moment.
Taking notes is not really a thinking activity but instead gets in the way of thinking. When you are copying things down frantically, you are not available to think.
Guided notes are the worst kind of all - students actively look for the things to fill in the blanks, and many stop listening at all but instead, opt to copy what their neighbor puts in the blanks.
The solution
We'll use a mix of graphic organizers for note-taking to help give direction - just having a constrained box approach helps students prioritize, and a process whereby students write notes after the lesson ends - often with a partner or group member.
*Source for more reading: Chapter 11 in Building Thinking Classrooms in Mathematics
Evaluate what is Valued
I've found myself in this situation a lot in a classroom. I say I'm looking for students to take risks or collaborate, but I don't have any system that helps support student growth in this area. If I want students to demonstrate these skills, I need to evaluate them. This I know already. The book comforted me because it helped me realize that all teachers struggle with this AND they offer a solution.
Their solution also addressed a common conundrum. Spoiler alert: The solution is rubrics. However, the rubric has an inherent problem. The numbers. When there are numbers, students ignore the feedback. What does it really matter anyway if it is all about the overall number and ultimately the average? I've had long conversations with colleagues about this over the years as they test out feedback approaches. I have seen it with my children and their reaction to numbers and comments. I see it with students and I also see it with myself. If there are numbers attached, I look at the number first. I skim the feedback and look for ways that it reinforces the number. If I don't like the number but have good feedback I get confused. If the number is great but I have constructive criticism, I also get confused. So what do we do?
The Solution
The solution is more elegant and simple. The rubric is simply 3 columns instead of 4 with items in the two exterior columns and nothing in the middle. It is fairly easy to write what it looks like when you are not succeeding in a task and likewise, if you are succeeding. The middle is where it gets murky. So the solution has a continuum where a teacher can mark where on the continuum the student is.
The solution also acknowledges you can't be evaluating all groups all the time! It would be impossible to teach and learn if you are always evaluating.
*Source for more reading: Chapter 12 in Building Thinking Classrooms in Mathematics
Grade based on Data
As Trumansburg moves toward full standards-based grading, this advice is a perfect fit. We're essentially making sure that we use actual data to discern what a student knows how to do and what they are still working on learning how to do. Mastery-based grading lends itself to a physical model. I'll use myself as an example. If I'm running track and I run the mile and I have a mile time of 7 minutes, 9 minutes, 10 minutes, and another couple of miles in the 9-10 minute range, could I really say, "Coach I have a 7 minute mile time. I got this" when they need a 7-minute mile to happen reliably? No. We can't do that using an average or using a growth model because I've only achieved the 7-minute mile once. Likewise, taking the average isn't going to be terribly useful depending on the data.
In the classroom setting, we often give a test or quiz that is filled with items from different standards, and maybe one standard props a student up because there are so many questions from that standard. Another could pull them down, and then the overall grade is all they see. It doesn't really tell the student anything. Worse, it can mask problems because the standards that a student understands, and those that they don't understand are all muddled together. Or, another common scenario; the student CAN complete the standard but with support from a group, just not yet on their own.
The Solution
The solution is complex. It is something I'll aspire to, but it will take time for me and for students to adjust to the model. It involves having a tracking system for individual standards for individual students. It involves having a basic level an intermediate level sometimes, and often an advanced. These correspond to those 1-4 numbers for mastery. Since it will be by standard, and observed during the course of a unit of study, tests may not be the same as in the past. I may have hit all the standards before a test, or only need to demonstrate mastery on 1 or 2 of them.
I urge you to be open to this way of thinking as we try it out in our classroom this year. I'm sure there will be hiccups, but also growth for the students and for me.