blog reboot and getting outside

I'm trying a reboot of my blog. My goal is to keep posts short, update what is going on with what I'm doing as a teacher and to make up for the years of blog posts that I spewed disgusting technology and data focused ideas...

This year I've made it a goal to get students out of the classroom on a weekly basis to see the math that we are learning appearing in the world around us. 

We walked the perimeter of the school grounds which I learned (after being here for 14 school years) is actually about a mile. Our shoes got wet but we now have a good memory to connect with perimeter!

We went into the cafeteria to find the area and that looked like counting floor tiles and subtracting areas of the room that had closets or protruding sections of wall. 

We went outside to look for right triangles and determine if objects being measured represented right angles.

I'm finding the students are enjoying getting out to be active and the more often we do this I'm able to see the students' creativity in finding ideas present I wouldn't have thought of. 

#codemath: Student created code on simplifying square root expressions

Today as an extension activity for students that have already mastered simplifying square root expressions, I offered students a chance to complete a symbolic example using my #codemaths structure.

Here was the minimal prompt given to students in a unit google document:

Fill in the gaps in the worked out solution in this #codemaths project

I gave a short explanation of how the variable "a" is randomly generated and when they type [a] it will output that value instead of the letter "a". (I recently switched from <a> to [a] to allow for simple html formatting to be used in code output. <b></b> for bold, etc.)
Students only needed to "fill in the gap" of the potential worked out solution from their perspective on how they would solve it--filling in enough detail that would help a fictional struggling student viewing it as a potential worked out solution.

The existing code in the worked out section looks like this:

And will print out:

For the sake of not giving away the solution to the problem, I will just share screenshots of the student output from the #codemaths worked out solutions they wrote and emailed to me:

"Remember to give credit to the makers!!!"--Melissa and Katelyn

"Here mr. schwen this is my super awesome code"--Ken

Pretty fun application for the kids and little time is spent explaining writing code because of the simplified process and kids are thinking more deeply about the mathematics embedded in an activity like this at a pretty highly symbolic level.
One student, wide-eyed and excited, said to me after getting his to work that "This is really fun!" I like too that there is a trial and error aspect to this as they refine and revise what they think will output and what actually does show up when they test it out.
In all honesty, not all my students are doing this but for the kids that are ready for it, it turned out to be a great discussion and application of where we had been in our mathematics and a good preview as to how math can be used in an increasingly more coded world.

Breaking my silence: Where I am today

The title probably makes it sound like I'm going to talk about some controversial topic that I've just been holding back on for beyond my limits. Maybe it would have been a good title to boost my statistics had I actually be making any money on these posts. Where it is actually coming from is, for the past year I've spent a lot of my time keeping closer with the students in my classroom, my family and in collaborating with the teachers in my building. I became a little turned off from the self-promotion and "making a name for myself" attitude that I was seeing more of in the edu sphere and creeping up in myself as well.
I had a chance to catch up with a good friend last night on the phone that also happens to be in education. Talking with him some about this he reminded me that it is still important to share our experiences with other teachers for the sake of the kids and improving our schools for them. So that being said, even after 12 years of teaching, I still feel like I don't know what I'm doing but will share a new post on where I am today and the journey that I hope is ahead for my classroom.
I'd like to believe that my classroom is centered more this year and last on conversations between students 70% of the time each day. That as often as I can I'm providing activities that first help them to explore and build their understanding that at some point tip toward developing efficient and meaningful math skills development and solid mathematical thinking. I am thankful for the continual improvement of resources like Desmos' Function Carnival in having some engaging ways of doing that in a way that is fun for kids. I also like the idea that it isn't just the typical edtech garbage--that there are good math people I know under the hood developing it in a thoughtful way.
This year in my professional reflection process I'm desiring to make a better connection to activities like this and what we are learning rather than just having isolated fun, engaging things that don't really move my students to a better understanding of the other class stuff we do.
Today we are unpacking what we did yesterday through function carnival and my hope in this activity was to lead kids to develop the skills necessary for future success based on what they explored yesterday.  This lesson started with students thinking individually, sharing with their partner and then having a large class discussion for the first 10 minutes of class and then partners moving forward at their own pace, discussing and writing their responses. I was free to talk with groups as the need came up and pulled us together as a group as it seemed necessary.
I think this is an area that we need to get better at as teachers--myself included. Yes, still trying to incorporate explorations and investigations but then getting better at connecting those activities to learning and use of those skills learned in future learning opportunities. Maybe in sites like Function Carnival there could be a teacher lesson pool that we could start sharing ways of getting to that with students?

#codemaths: Student outlining his approach to coding an algebra solution.

We are up and running in class today. This morning I caught a glitch that caused any use of commas to break the code but that is fixed. I had students working in class on this that were already proficient in solving equations with variables on both sides and understanding the causes for no solutions and infinite solutions.

The task for the group working in #codemaths was this:

Code an equation w/variables on both sides. Try to avoid no solutions and ∞ solutions. https://t.co/irksPBOASt

Before you watch the video keep in mind that these students have had little or no experience up to today in writing computer code.

Unpacking a student example of dividing by a fraction

Today in class students were choosing different practice activities for review for our test tomorrow. One pair of students was working on a worksheet that involved dividing an integer by a fraction. This is a topic we have not reviewed yet but that students have learned in past years. As I looked at his work I knew that I wanted him to explain his process to me. As I listened I knew this was something that I wanted to share. While some of his explanation is now based on procedures I really get the feeling that he has a deeper understanding than a student that is just taught to 'flip and multiply'.

In preparation for looking at it in a future lesson I tried to look at what is happening with the mathematics behind his explanation and what to do when a problem addressed is a little messier.

Comments, suggestions and additional strategies are welcome!

Here is the student's work from when he showed the class:

This is my take on what is happening as the student is moving forward with his procedure:

Class agenda for today

Three levels of activity today

For each lesson that I've been preparing this year I have been trying to have practice, review and extension options for each learning target. This unit I actually have the extensions ready to go ahead of time (probably having to do with us just having 10 days off). 

Our progression

We started the lesson a few days back with a large group investigation, following the golden ratio idea. Yesterday we did some more formal practice. Students that were rating themselves at an understanding or mastery level began to work individually on their practice material instead of staying with the large group. I used a couple clicker questions to help students identify how well they were understanding the material.

Student choice

We started in a similar fashion today and added a tier of activity for students that completed the practice yesterday in class--beginning work on extension activities for this learning target from a menu of choices (example). 

Throughout class I had students moving about the room, helping each other, asking me questions and digging deeper into the concepts. I love my job. 

Making adjustments and seeing benefits

I have always wrestled in my classroom with doing what is best for kids and learning. Opinion or experimenting sometimes win my favor but in the back of my mind I'm always thinking about what research says is best. That being said I've made some changes in my classroom lately that I think (both by opinion and research) are benefitting my students.

Begin with inquiry where students construct or discover much of what they are learning

In the (recent) past the videos were used to introduce new material and the idea was that we'd go beyond that material when students came to class. The trouble came with when students either didn't watch the videos or worse yet didn't understand them. By introducing the material through video I was also bypassing the opportunity for students to construct their own understanding through inquiry and make meaningful connections.

As a geometry teacher I want my students to understand the hinge theorem because they construct some triangles on paper rather than because they wrote something down what I said in a video--that won't make sense to them and they won't be able to apply it in new situations if they don't understand it.
I'm not throwing out videos, I'm changing the role they play in the learning cycle based on Ramsey Musallam's Explore-Flip-Apply method. Students first explore the concept in our classroom community, after our explore activities are complete they then view video (flip) later on to anchor what they are developing in understanding based on the investigation and then students apply the learned ideas to new situations. This has helped in focusing our class time and giving more meaning for us to scaffold our learning on.

Also during our class time I either begin with a question (often review but not always) or a new seating chart. I take attendance either by missing seats or by who didn't respond to the question. I base the seating chart off of data although the kids don't always know that. Our current seating arrangement places kids who scored better on our last assessment next to those that scored lower.

The intent is to raise the level of conversation for all students as we are doing these community based activities. Students will usually just choose their friends (which they still can on some days) but I want to make sure great math is happening at all groups. 

In some cooperative learning staff development I had years ago we were told never to place the highest achiever next to the lowest achiever (neither would be able to understand each other). With that in consideration, I created a seating chart that relies on recent High, Medium High, Medium Low and Low scores. I have students with highest scores seated next to students with the medium low scores and students with lowest scores positioned next to the medium high scorers and some of each at each table group. I also know which table groups are hot-spots in the room so I make sure to get to those more often as I anticipate they'll have more questions. I generate a chart for each class on a selected assessment and then throw screenshots into a Google presentation so I can access them quickly to either print or use at the start of a class.

For those that use my assessment system you can actually add the seating chart template to your current dashboard by searching and installing my seating chart script that is now available in the script library. It is also included for new users automatically.

My instruction needs to be more focused on learning targets.

I was concerned that by focusing on separate learning targets and objectives students would see the learning as separate modules and not make connections but instead I've been finding the opposite to be true. Because we've been more focused, students have more readily made the connections themselves.

As we begin new ideas, they are grasping them quicker and making connections across ideas that I haven't seen with past years. 

Students begin each unit by looking at a self-assessment rubric written for each specific learning target. They continue to look at the rubric as they are in the learning cycle and write down new dates as they see themselves moving to the next level. Students are taking more ownership in their learning by seeing what it will take to get to a mastery understanding of each learning target.
As a teacher I can anticipate the levels of understanding a student will show as they move through the cycle. This helps them identify their own level using specific indicators in the rubric can help them see where they are in the learning process.

Past practice for me was to just give them the "I can" statement but they didn't really know if they could or couldn't or to what extent. 

In anticipation of some students arriving at mastery sooner than others I'm trying to include a link for many learning targets to an activity that is an extension of the learning. Here's an example of a rubric for an upcoming unit.

No more homework quizzes

I've done away with submitting work answers online for class work that is formative in nature (not for grade). I found students were bypassing learning and just trying to come up with answers. I've been able to attend some staff development by Tim Kanold where he said to give students the solutions to homework for them to work toward in place of students not knowing the answers ahead of time. I have put together class work problems where the expectation focuses more on explaining their understanding and applying of skills from the current learning target and integrated review of targets from the past. 

Solutions are posted online (worked out by me) and also in a printed binder in the classroom and students are encouraged to check these both when they get stuck or when they finish. I said last week: 

"Don't assume that you are awesome and got them all right. You might be awesome, but just double check your solutions before you think that." 

By giving students the solutions they are able to check for their own understanding and I am not spending my time recording more data in my grade book or checking individual homework assignments. I can spend my time as a teacher preparing meaningful activities for what we do while we are together.

Always reflecting on what we do

I believe that I will probably be doing something totally different a year from now or maybe even next month as far as class goes. I will always be looking for methods that will help my students learn math (and life) in more meaningful ways. I believe this is what makes us as teachers better is that constant struggle for how we can be better for our students. If you think there is a better way or I am totally off-base with this approach, please feel free to guide me in the right direction in the comments below. If you just criticize without offering solutions that helps no one.