On perseverance…

On Tuesday I took the afternoon off to finish my Japanese Encephalitis immunizations. Yes, it took the whole afternoon  – more a lesson in patience than perseverance as I waded through the Taiwanese medical system. But, this post is not about my experience. It is about what happened in my classroom while I was gone.

I’ve been going through some Park City Mathematics Institute materials and came across a Painted Cube problem. I left it for my 6th grade students.

We’ve been looking at patterns and representations through sketches, words, tables and graphs. I set the room up so that each pair of students had the problem, a large whiteboard and lots of whiteboard marker colors. The teacher who supervised my students let me know that he was impressed at how the students worked. They talked, they drew, they problem solved and they kept at it! For an hour.

At the beginning of the year, they would have put 10 minutes max into a challenging problem and called it quits. This week, they did it for 60 minutes. I told them that they are awesome!


Student Thoughts

I recently asked students to provide some input on their processing, communication and thinking about a problem. A few responses dealing with group work:

Did you give space to others to allow them to share their ideas?

  • Yes, because maybe others have better ideas.
  • I think I could hear others’ advice more but I did try this time.
  • Not the most but some. I feel like some members liked to wait and listen to the talkative ones to make decisions. I think they should stand up and speak more.
  • Yes because I asked other students their thoughts. No, because I spoke Chinese and made it hard for another student to fit in.
  • Maybe not enough, seeing that I was the one who probably talked the most.

Did you have a voice and feel comfortable sharing your ideas?

  • I usually don’t because if I tell them something wrong I would lead them astray. 
  • I think I did have a voice and felt comfortable sharing ideas because they would be accepted or at least evaluated if they are valid or not.
  • I think I would if I have some ideas.
  • Yes, I feel like I can talk to group mates and tell them what we can do.

Interactions between students are important to me. Whiteboards are great in providing a meeting place for work. However, as students work many interactions pass by without my hearing. Are they being respectful to each other? Are the voices of various students being heard? Student reflections provide a snapshot of these interactions. Over the course of the year, several of the more talkative students have begun to slow down and ask for the thoughts of quieter group members. Would they be doing this if I didn’t explicitly ask them to think about giving space?

I’m still puzzling over how to help out and provide more access to those students who are scared of leading partners “astray”. I also think I need more pointed (and well written) reflection questions. 

Follow-Up: Whiteboarding and the student

Earlier this week, I posted up a lesson where students worked in groups to design a method and collect data. The project started through a company request to test a scaled-down version of a zip line. (I forgot to mention that the majority of students in the class experienced a zip line on a class trip.) My goal was to find individual thoughts among the group processing. Students finished data collection and emailed me images of their whiteboards which I have printed out. These will form the basis of an assessment.

Students will have time to meet and verify the printed images and review what happened during the planning and data collection phases. They will then be asked to individually write a report to the company (“Zippy Fun”). Here is the memo outline that students will complete. There are two portions – processing data and a self-reflection.


Whiteboarding and the student

Whiteboarding has been a great change in my classroom. Students fully adopted working on the whiteboards and I often find them independently gravitating towards their use. However, I am still a whiteboarding newbie. Discussions have increased and I’ve peered into the toolkit by trying out the Mistake Game but I’m struggling a little with finding the individual student. While students work, I roam around the class. Sometimes I simply listen, other times I ask for explanations or give pointed questions.

Yesterday, a zip-line company – Zippy Fun – requested their input on a proposed course. Their scaled down version ran 6 m with a vertical drop of 0.4 m. Groups were asked to report back to Zippy Fun with the velocity and acceleration at meter intervals over the course. The class buzzed as zip lines were strung across the room. My goal was to find the voices of the silent student. Each group of four typically had two students who often sit back and let others do the talking. I therefore specified the students who could explain the group’s process and answer questions regarding their actions. If those students could not, I left to return later after the group discussed the topic.

It was challenging for many students. The talkative ones squirmed to avoid blurting out. Some students had difficulty explaining and we worked through language. Other students really did not know what their group was doing. Requiring them to be the spokes-people caused conversations that might not have happened. Were more students engaged? I think so. Did more students walk away understanding the what their group was doing as data was collected? I hope so.

As with any class, time expired and students were left with a lot of work on their whiteboard. At least one member of each group possessed a phone to take photos and email me the whiteboards.


What now? I want to find out what each student can do with the data collected during the group phase. I want to find out which students are unsure these ideas.

So, here’s what I’m trying and any feedback is greatly appreciated. I have images of each whiteboard. I plan to print out an image for each person in the group and give them some time to check for legibility. Then, students will individually process the data by writing up what the group did, creating position vs time and velocity vs time graphs, etc. Students left class knowing that they would be expected to do this next class.


How are those whiteboards coming?

The first quarter of the school year is in the books. Some things are going well but there are a few items that I need to process through. In general, whiteboarding added a strong dimension to class discussions. Particularly for my math students, whiteboarding moved group problem solving and whole group discussions to a new level. Student inhibitions to write something down or to share seem to diminish when equipped with a marker and an erasable slate. I can quickly assess where a group of students are on an idea as I circulate around the room. I’m loving it.

But…In my physical science class, I haven’t found a good recipe for whiteboard use. A goal of mine is to place more of an emphasis on discussion of data and what students observe during experimentation. I’ve tried to use whiteboards as an experiment command center with limited success. I feel that class is getting bogged down during experiments and and students are left with data on the whiteboard, unable to continue work. I believe that part of the problem lies in the amount of time that it takes this group of students to accomplish tasks. Compared to previous years, we are moving much slower that I have in the past. (Unfortunately, this rate is not accompanied by amazing class discussions that magically make time disappear.) Speed bumps:

  • This bunch of students is quite chatty and transitions take a long time.
  • Lack of outside work. I generally avoid much work outside of the class but at times ask students to prep for an upcoming class. This could mean creating data tables for the upcoming experiment. Many students come to class empty-handed.
  • Off-task behavior + a general slowness- Even when groups appear to be working on the task at hand, items are completed at a snail’s pace.

Looking forward, what am I going to do? Math class success with whiteboards stems partially from the fact that problem are relatively short, especially if compared to a lab. Students process a video, image or text on the whiteboard and then develop solutions. Conversations are focused to the problem at hand. Lab experiences involve much more – students need to create a procedure, decide how to collect data, run the experiment, record data and then process. With the second quarter, my whiteboard focus will be limited to processing of data when the activity is finished. Using the Claim-Evidence-Reasoning framework, students should have a focus (similar to the success in math) and adequate space to provide a claim and include supporting evidence. Round table discussions can then be used to flush out each group’s reasoning. It’s a continuous process, right?

Less than one, equal to one, greater than one

Courtesy of Dan Meyer’s 3-Act Math resource, students began today’s class in detective mode. A brief, 30 second video clip captured their attention as two CSI investigators pulled out a sawed-off limb. The portion of the video where the percent of the mass of the lower leg to the body mass was bleeped out. Students were up and on their way asking questions about the scenario. I love questions from 6th graders and we spent some time wondering how the leg portion could have shown up on the screen before returning to the math.

I asked for an estimate that students thought would be too high and another they thought to be too low (sometimes I inadvertently let this step slip by but it is oh so revealing). The range began at 1% to 500% and after a bit of discussion was narrowed down to a range of 10-50%.

A group’s thoughts in process… We’ve been discussing ratios and are moving to percents so I was happy that groups began looking for comparisons and writing them as ratios. Today’s surprise came as I rotated through groups. A group wound up with a ratio of \frac{42}{147} and wanted to turn in into a percent but was not sure how. (A benefit of spending large amounts of time on a single problem is that opportunities for quick mini-lessons to groups of students always pops up.)

I asked the students if they believe the fraction to be less than one, equal to one or greater than one. Jumping that hurdle seems to help students position their thoughts and gives me a good idea of what they are thinking. Two of the three members in this group believed the fraction to be greater than one. Their reasoning was that 147 is greater than 100 so the fraction must be greater than one. They were convinced. Pulling a value out of a hat, I asked if \frac{13}{14} would be a smaller or larger amount. The two students indicated that the 147 would be larger though neither had a explanation as to why. Soon, they were busy breaking equal sized rectangles into portions to represent the two fractions. The student in charge of 147 pieces quickly became frustrated at having to make so many small pieces and the group had a good discussion about part to whole relationships.

Looking back, I wonder what was the foundation of the students’ original thoughts and at the moment lean towards a developing concept of the relationships between fractions, decimals and percents. They appeared to understand that a percent greater than 100% is greater than one whole. Did they transfer the thought to fractions and think that the value must be bigger than 100%? I’m working on some follow-up activities to bring out these relationships but additional ideas would be appreciated.

Whiteboards – dipping my toe in

Last school year, I followed many great physics blogs (oh so unlike my high school physics class or the ones in college. Seriously, it was believed that a person without physics could come in and be successful due to the multiple guess format. Just buy the previous course packs and you’re set). Ok, enough digression. Physics teachers seem to be getting it dialed in through modeling instruction and the use of whiteboards. I ordered a pile of whiteboards for this school year and am working out ways to use them.

The whiteboards are roughly 2′ x 2.5′ and offer plenty of space for a few students to gather around and work together. I’ve used them with my sixth graders for a few problems during the first week. Student conversations about math are higher than when each student is busy scribbling in his or her notebook. They ache to yank the cap off of the pen and write on the board. Even quieter students seem to be more comfortable sharing with the pen.

I am fortunate to have extra space in my room so students move out of their seats to get to table clusters containing the whiteboards. At this point, they choose to carry their chair along or work standing. A few bring a chair though most stand, pace or shift around as they problem solve. A nice dynamic is created as the students sit or stand as desired and think in the way that suits them best.

Organization and display are issues. A majority of the students are “well-trained” to solely focus on an answer. The process seems secondary. My task is to slow them down. Bring the thinking out and have group members articulate their thoughts through words, graphics and mathematical expressions.

What about class notes? If a class revolves around in-depth thinking of a problem worked out on a whiteboard, what will the students look back on later? Well, I’m not sure how many sixth graders truly review their notes but the focus is on the process of mathematical thought. I can provide key elements to students for their notebooks and will offer time for them to capture the day’s ideas and/or work. It’s a start…The next step is to begin work on student presentations using their work. I’m hoping that this focus increases the need for thinking to be made explicit.

For good resources check out Frank Noschese and Kelly O’Shea