Tag Archives: Thinking Classroom

Leveraging Vertical Whiteboards for Effective Formative Assessment

First of all, my 6th grade students love working at boards (Vertical Non Permanent Surfaces). They ask me if we are working at boards EVERY SINGLE DAY. That alone is a powerful win in my math class. They would rather work collaboratively to solve problems than listen to boring notes from me. This is 100% in line with my core philosophy: whoever is doing is learning; students thinking rather than listening. Although this post is written from the perspective of the math classroom, boards can be used for formative assessment in any classroom and content area.

One of the exciting things that I have learned is how helpful board work is for me to formatively assess students’ understanding and misunderstandings in real time.

The Numbers

The first advantage of boards for formative assessment is that there are less numbers of places for me to check on. With a class of 30 students, there is not enough time to individually check on each student in an hour long class and provide adequate support. At best it takes me most of the work time to check in with each student, leaving some kids without coaching until the end of period when I finally get to them.

With partner work, there are still too many groups to check on quickly with up to 15 pairs. I can easily get bogged down with a couple of pairs and neglect others. Using groups of 3 at vertical boards, I have a maximum of 10 groups to check. This is more manageable for a single teacher. With boards I assess the entire class by making one lap around the room glancing at each group’s progress before talking to any students. This allows me to quickly assess which groups are on the right track and which may need my support in less than two minutes.

The Visibility

Secondly, quiet students don’t slip through the cracks with board work. When students work alone or even in pairs on practice problems at their tables, I am mostly dependent on them to ask for help when they need it. I always provide answer keys so that students can self-assess and admonish them to seek help when needed, but there are always a segment of students who will quietly struggle without seeking assistance. Whether because of shyness, apathy, or fear of “looking dumb” these students will rarely ask for help.

With seat work, I walk around the room and peek over shoulders to verify that students are on the right path, but this proves time-consuming and often difficult to see student work without interrupting their flow. I often need them to move their hands or stop working so that I can view their work. Some of my students write very small and I cannot read it without taking their paper from them.

But with board work, all student work is clearly visible with my quick stroll around the perimeter of the class. No student can hide from me, not even the shy ones. Students naturally write larger on the boards than on paper so my old eyes can clearly see their work. There is also a quiet buzz around the room so a shy student does not feel singled out when I question them.

I have found boards to be the single most effective formative assessment in my math classroom.

The Work

What am I assessing when I look at student board work? I am looking for common misunderstandings and creative solutions. I don’t just check right or wrong answers, but analyze student thinking and their problem-solving approaches.

  • Do they have a different way of approaching the problem than I would?
  • Are there conceptional errors?
  • Have they forgotten about past math ideas that would help them now?
  • How can I link previous knowledge to current problems?
  • Are they checking each other’s work?
  • Can they explain their thinking?
  • Can they apply their method to a new problem or situation?

The Support

After my quick assessment stroll, how do I address what I observe? When I see a common mistake among many groups, I use a call and response to stop and address the whole class immediately. I “teach” from wherever I am in the room. If it is something minor, students stay at their stations and just listen.

Sometimes I gather the class all around one group’s work to see a unique solution. Other times I might challenge them to find the error in a group’s thinking. Since we have a culture of sharing our attempts at problem solving, there is no embarrassment at looking at partial solutions or imperfect thinking.

Another approach I use is to stop and ask a group to explain their thinking. We can have a conversation about their work and I can push back on misconceptions or give hints as needed to connect their thinking to new or old concepts. I try to use questioning to guide them to figure out their mistakes in computations or challenge their thinking.

Another strategy is to teach a mini-lesson (5 minute lecture) to a specific group or multiple groups during board work. The rest of the class is busy working and I have the undivided attention of the 2-3 students in the group. I have found this to a thousand times more helpful than whole class instruction. The small group is actually listening and you are addressing their specific ideas based on their current work.

However you choose to use board work, I have found it to be the fastest and clearest window into student thinking. How do you assess student board work? What support strategies do you use?

Note: this post is a reflection on my implementation of the Thinking Classroom book by Peter Liljedahl. I have not fully implemented all of his ideas but are playing with the philosophy in my room.

Learn with me!

Board work is just one of the strategies that I use in my classroom. If you are interested in how to implement PBL and SEL to build self sufficient learners, I would love to have a conversation on how I can help. I am now scheduling workshops and book studies for spring and summer. Check out my workshop page or drop me an email at mikejkaechele@gmail.com. I would love to chat and co-plan meaningful PD for the educators at your school.

Pulse of PBL

Grammar of Math

I am getting into a regular routine of using VNPS (Vertical Non Porous Surfaces or working at “boards” as I call it with students) and am noticing a couple of things. The philosophy states that students should either be doing open ended problems or “thin slicing”–doing progressively difficult problems that challenge students to discover ways to solve math based on their existing background knowledge and number sense.

Much of what I teach in 6th grade is an introduction to basic concepts that are the foundations of algebra: order of operations, distributive property, exponents, and one step equations. Some of these things cannot be “discovered” through inquiry by students but must be taught as definitions. I call them the “grammar” of math. Rules for the order of operations are a good example. One can demonstrate the need for them with different solutions, but the agreed upon rules must be explicitly taught.

Recently I used whiteboards for progressively harder problems writing and solving exponents. I noticed is two things that break the “rules” of thinking routines. First students needed me to tell them if it was correct or keep working. They have no way to double check their work to prove if they are correct other than comparing to other groups who may also be wrong. Second, I made laps around my room either telling students to retry or giving them a new problem. As we progressed, I could not keep up. Students started getting bored and off task a bit. Nothing major, but playing with markers or erasers and conversing with other groups.

I don’t see this behavior when I give an open ended task because students are more invested and stick with it. What I now would say is that my exponents was not really thin-slicing at all but practice problems (the book calls them Check Your Understanding or CYU) done in a group at the boards.

Sometimes we have to explicitly teach a specific skill or mathematical technique. For example my curriculum requires students to use factor trees for prime factorization. Now factor trees are not really a new technique, but one they learned in previous years. What is new is writing the prime factorization at the end–which again is a grammar thing as it has to be written a certain way.

Variety of Approaches

So here is the approach that I am developing about when to use or not use whiteboards. I will use the introduction of exponents as an example.

  • Day 1 Introduce Concept: Students work on an open ended problem at the whiteboards without vocabulary. We used the tax collector for exponents and followed it up the next day by reading One Grain of Rice together.
  • Day 2 Introduce Vocabulary and Group CYU: I explicitly teach vocabulary and techniques based off from previous day’s experience and then students practice at their boards (group CYU). I taught them the vocabulary for exponents and showed them how to write and solve them. Then students solved progressively more difficult exponents at the boards.
  • Day 3 Individual CYU and Assessment: Students practice problems from the book at their seats. Answer keys are posted so they can freely check their answers at any time. They work with a neighbor as needed, and I roam the room helping. We finish with a quick assessment so I know who has understanding or needs reteaching.

The days are not rigid as I sometimes mix several of these things in the same day. But what I am realizing is that my Day 2 is not really in line with the Thinking Classroom, but it is needed. It is a form of “we do” but without much help from me. I think my students benefit greatly from group practice.

In reading some posts and comments in the Building Classrooms Facebook group, I am not alone in seeing that the thinking classroom approach is not necessarily all or nothing. My Day 2 actually does require the whiteboards at all but could be a game (traditional or online like Gimkit), stations, card sort, partner work, or any other kind of hands on practice. I have been using whiteboards primarily because my 6th graders like them and I don’t have time to create hands on activities every day. As a goal I will develop one strategy such as stations per unit and slowly build things over time.

Learn with me!

If you are interested in how your school can use a PBL framework to teach SEL skills. I would love to have a conversation on how I can help. I have limited availability for PBL & SEL workshops during the school year so contact me early. Check out my workshop page or drop me an email at mikejkaechele@gmail.com. I would love to chat and co-plan meaningful PD for the educators at your school.

Pulse of PBL