Daylight and Moon Phase

Just this week, a student came to me and said that he recently went outside one night to look at the moon. Woohoo! Day after day I get the nagging feeling of a growing disconnect between my students and the natural world and I’m hoping to devote class time to reconnect their lives to the world around them. Friday, we looked at the data students posted during the past two months.

Students predicted the next new moon and many began counting and looking for patterns. A few were dead on while others did not really know what was meant by a “new moon”.

I also asked them to note any trends that they see in the sunrise and sunset data.

Students picked up that we’re losing day light but were surprised when I asked whether light is being equally lost from the morning and night or if more is being lost in one or the other.  The prediction was to note when students thought the shortest day of the year would fall. It was now my turn to be surprised at the range of data. All sorts of days were proposed from mid-October to December 31.Students are going to hold onto their predictions for a while to wait and see. As I write this, I’m considering placing a poll beside the data (located outside of my classroom) to get students voting on the shortest day.

Students typically seem to need a lot of work reading and interacting with graphical representation of data. Good questions were generated as students looked over the data and I hope an important outcome is more students take a gander outside to check on the moon before going to bed.

I’ve fallen into the e-grade trap

The fall has been quick.  We’ve been required to use GradeQuick as a grading program but this is the first year that information opened up to parents and students. In the past, progress reports, printed by teachers, went home regularly and the physical act of handing reports to students nudged me to do more. The act was twofold: I handed out the progress report and students then logged progress on standards into a tracking sheet.

My tracking sheets now languish on the sidelines as I’ve fallen into the trap that students have access to the information online so it is easy for them to stay up-to-date. Whoa! Stop right there and remember the students in years’ past that quickly filed away progress reports without a second glance. The tracking sheets made them look at current levels and set goals. Now there is no accountability. The students who barely looked at reports in class are likely not hopping online to check each time reports are updated.

I feel that instead of getting students more involved in progress, the lack of accountability lets most ignore what is happening. A key element of a standards-based system is that students must be part of the conversation about their learning. I need to bring the active tracking back to my classroom. At the moment, I think I have to go back to regularly printing out updates but look forward to finding new solutions.

PD #1: Hands-On Learning

I’ve recently begun an online course (gotta get some hours in before OR changes its license requirements again), which requires written submissions. I’m going to work through the prompts here and see if any comments spur further thought.

As a middle school teacher, I find that the majority of my students require a constant dose of kinesthetic learning in their daily schedule. These students are figuring out their bodies, can have short attention spans and crave interactions with each other. I have taught math classes containing only boys and mixed classes of 6-7-8th graders and consistently find added engagement when students begin moving. Sometimes an activity requires students to vote with their bodies. For example, stand up if you think tonight’s moon phase is full, jump up and sit back down if it is a half or sit on the floor if you believe a new moon is the current phase. The action takes just a moment but students receive a quick break from body positions and those not involved in the discussion are drawn back in. Other times, activities span a lesson of movement. Predator-prey relationships unfold naturally in games of tag. Extended activities require deliberate debriefs where students’ attention is drawn back to the purpose of the game. The processing part of the lesson is essential to move the lesson past a fun activity and to a learning environment.

Kinesthetic specific activities comprise a portion of my class time though hands-on learning is constantly employed. I teach a 90-minute block class and eschew lecture to allow students time to be scientists or mathematicians. They need to be in positions where they are comfortable interacting with each other and I often need to get out of the way and let them work. Many classes center around a problem. In math courses, the problem may unfold through a video (i.e. Dan Meyer’s 3-Acts) or scenario. In science, a design issue or question asks students to decide how to collect evidence to support, or refute, a position. These activities go well when the problem is accessible to students. I believe that accessible means a student is capable of understanding the task (though this may take some work) and can advance on the problem. Ideally, the student eventually gets to a place that does not make sense and, hooked by the situation, wants to work out outstanding issues. A few guided questions hopefully nudge them forward.

My current focus of improvement revolves around explicit discussion of process and understanding. I believe that I’ve done my fair share of hands-on activities where students exit class without connecting their experience with a content area. Maybe I didn’t keep good tabs on the clock and the clean-up genie appeared too late. Scrambling to beat the bell, students race over the class and manage to finish last minute data collection and get cleaned up just in time. Two or four days later, when the class finally meets again, key points are distant memories. So, what am I doing to improve? First, I’ve begun using whiteboards (posting by Kelly O’Shea containing great ideas) a lot. I expect students to process ideas as they go. Whiteboards provide a platform that students enjoy writing on and are big enough to gather around. Typically, I am able to quickly check a group’s progress.

Another shift I’ve made is to a Claim-Evidence-Reasoning structure (described by Jason Buell). I want my students thinking that they are collecting evidence and building a case for their ideas. I want them to be eager in wanting to describe the finds made by their group. I want them to see a purpose in a hands-on activity instead of leaving happy that the could do a lab during class. These are works in progress but I’m enjoying the case for being more deliberate.

Camel break –

SBG explained in “a few paragraphs”

The SBG bus stop in central Taiwan is yet to be established. At least it hasn’t pulled up at my school and it seems as if I’m constantly trying to break new ground without much support. I’ve been asked to write up a couple of paragraphs about my grading policy to show that there is school support behind the idea and that I’m not being a renegade. So, here goes my first attempt – any suggestions would be greatly appreciated. I see a potential audience being the weekly school newsletter – a random email that I wrote earlier in the year somehow found its way to the newsletter so I’m a bit more guarded now.

As a teacher, I am sometimes asked what guides the units and design of my class. Our school adopted a set of standards that drive curricular goals. Units are created by deciding what are the basic skills of the material (what I consider to be a Level 3) and what are the main concepts and ideas (Level 4). I then build lessons to provide students with experiences to construct their understanding of the topic.

For me, assessments are a form of communication between teachers, students and parents. I believe that my assessment system should be one of multiple ways that we can talk about a student’s understanding of concepts. Therefore, my feedback needs to be directly related to a student’s progress on the topics. In the same way that I divide standards into basic skills and concepts, my grading system is designed to provide information on how a student is doing on each skill and concept. Feedback lets students know if they have shown understanding on Level 3 and Level 4 concepts. Level 1 indicates that the student has not provided any work on a skill or concept while Level 2 indicates that the student is progressing but needs some work to explain an idea. On the other end, a Level 5 indicates that a student has moved beyond what we are directly discussing in class and can apply his or her understanding to more challenging scenarios.

Is homework a necessary part of a student’s performance? Homework can be beneficial to student improvement though it does not factor into the grade of the student. It is time to practice, to put thoughts together and to develop questions. It is not part of a grade.

That’s it in a few paragraphs. What have I missed?

Math Blogger Initiative

Just over a month ago, Sam Shah proposed a math blogging initiative for those of us out there on the sidelines of blogging. The initiation process involved at least one blog posting a week for four weeks. A series of prompts were sent out to help people get going and then a host of established bloggers (JulieFawnAnneMeganBowmanSamLisaJohnShelliTinaKateSue) linked new posts from their blogs. It’s been a good experience. Unfortunately, the time to write more appears to be lacking at the moment but I’ve managed to at least get one posted a week. So, a big thanks to Sam for setting this up and I’m trying to commit to maintaining a post a week throughout the school year.

Was the rant necessary?

When was the last time a company’s idea of packaging and your needs matched up? (My whole concept of packaging has been turned on end by living in Taiwan. Wow! Individual packaging galore.) It has been a long time since I watched Father of the Bride but last year I came across this clip from the movie. George Banks, played by Steve Martin, is having a rough day and heads to the supermarket to buy hot dogs and buns. I used the clip as a jumping off point of unit rate.

This year, as I looked at the clip again. Before watching I asked students to think about the following questions:

• What did George want to do?
• What would the cashier done if George received the outcome he desired?

I was pretty happy that students quickly brought up unit rates after a few good laughs. I then asked if George’s actions were necessary? Some student replies:

• He can buy three bags of hot dogs and two bags of bread and it can make 24 hot dog buns.
• He didn’t need to take 3 packs of buns. He only needed 2 packs.
• He could have bought 3 hot dog packages and 2 bun packages, cause 8*3=24 and 12*2=24 so they are even.

As it turns out, George took four buns out of each bag of 12. He then bought three bags. I didn’t pick up on this the first time through and wonder if the movie producers even thought about the fact that the packaging actually agreed with his purchase (contrary to his rant). A few of my students picked it up on the first “blind” watching.

Did the packaging actually agree in number with the amount George put into his cart? After working out what the cashier would have done if George did not end up in the slammer, I posed the question to my students…

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.