Meaningful University Partnerships

This spring semester lead to a great opportunity to work with a UNC-Charlotte Math Ed Professor Allison McCulloch (Twitter: @awmcculloch) and her Math Ed Technology students. The coursework focuses on the use of free technology such as Desmos and Geogebra to make lessons. Allison's idea was for her students to develop one lesson within the spectrum of our standards using appropriate technology. Once the students had a solid lesson, I would teach it and they would observe and reflect on the process. She provided a lot of support and feedback in the intial creation of the lessons, then a draft was sent to me. I then had the opportunity to provide feedback and the students made edits. Once they addressed all the edits I reviewed it one more time and a date was set for instruction where I taught the lesson. Now that everything is done I'd like to share my thoughts on how the process and lesson went as well as some of the work that came out of it. 

Positive

The first note I want to make is that the reason this process worked so well is because McCulloch made the effort to seek us out with a genuine interest to better the University's program and our own. I often get propositioned by faculty and professors at the University to "do" something with my students. The problem is that these individuals do not let me know what they can do or provide in a partnership. Most of the time I find that they want the benefit of access to our kids for their benefit with no real focus on how the partnership is supporting the teachers and students (future teachers) in our program. The constant question I generally get is "What do you need from us?" or "How can we help?" when I don't often understand the services they could provide or how they intend to get involved at all. I also find that when people have offered these partnerships they do not have a reasonable idea of the work and effort teachers can put in with other things going on. So the reason this partnership worked so well is because McCulloch had a vision of how the process would work, executed it and kept us in the loop when certain stages of the work was being completed. There was a justifiable amount of work for me to get involved and have buy-in to the idea. She had an understandable objective of creating meaningful coursework for her students and providing me with a cohesive lesson within my content standards. 

The second note I want to make is about the quality of the work that came to me. Although I left a ton of feedback. (Just my M.O.) The original draft of the lesson was a quality lesson, that if I had written as an undergrad, I would be really proud of. The final lesson was done on a Geogebra workbook with a set of inquiry based questions written in a google doc. The lesson went over four major discoveries: proportional relationships between chords intersecting in a circle, congruent arcs and chords, equidistant chords and congruency, bisected chords and right angles. Of course there are always after thoughts and things you want to polish, but it was a well written and integrated seamlessly into the way I teach my class. It was so well written that it rivaled a PAID product I use all the time: Gizmos. My kids literally operated it the same way and drew the same conclusion they would have in the Chords and Arcs demo. My students could discuss the work and draw conclusions and summaries from this investigation as well as they could a Gizmo. In fact I've stuck to Geogebra workbooks for my circles to write my inquiries. You can access the Geogebra Workbook here. 

Professionally (and personally) this was incredibly fulfilling. Since I work at Teaching Early College, my main focus is churning out excited and exposed future teachers. I got to do this in my classroom and hopefully contributed to some of that with the undergraduates by participating in a rich and valid practice. There is also potential to try and inspire other teachers to make these partnerships happen in their own professional learning communities. 

Polish

There were a few things that I put into the lesson that I know my kids are used to doing with our inquiries. So one thing I added to lesson was an investigation summary. You can read more about them and see what those normally look like here. So this was a change I made this a day before without discussing the changes, but I knew my kids needed to summarize their findings based on the investigations. I also put together a simple 5 question homework where students looked at some circle problems, solved them and explained how they decided to set up the problem by referencing the investigation that supported their claims. Besides that change I would clarify some of the instructions on the investigation and possibly re-ordered it to help the flow of things. 

There are a few things that I would change about the investigation questions and the way I ran it in class. Since I've been pushed to start my final unit so early, I really think I needed another half a class period to finalize thoughts on new vocabulary, and relationships with inscribed and central angles. I would have also like to revisit content from the earlier semester in Math 2 with similarity and congruence in triangles and angles. It could have gone a long way in making the deep connections my students were struggling to make. 

The last thing I've considered is my delivery. I like that we did the first two questions and discussed our findings to give students the confidence to keep working. I think next time I would set a timer and do check-ins after each inquiry rather than let students work in their partners through it. I feel as though I rushed through a bit of the findings and might have made it less clear. But when I collected my 5 question homework check the next day almost all of my students got the 5/5 with a few exceptions getting 4/5, meaning they could apply the theorems discussed. 

Questions

Finally I want to think about some questions I still have about the partnership and that I'm still thinking about to continue having these genuinely positive experiences. 

1. What else can we do next time? McCulloch offered some other involvements in the semester that excited me, but I didn't do a great job following up on them. One thing that was mentioned was recording a modeling lesson or a three-act-task in my classroom to use for undergraduates. Also, there was some mention of students volunteering to participate in after school opportunities to interact with developing technologies in math that I want to be sure I offer my students next year. 

2. How can I communicate, to other interested university parties, what a successful partnership looks like to me? How can I encourage rich experiences for all parties? It might be sad that the main question I keep asking myself in reference to this question is : "What is in it for me?" But when teachers put in their extra time into these partnerships there needs to be some payoff. I've got to find a friendlier way to word this in order to convey my message clearer to other interested people. 

3. Do I tell my students that the lesson wasn't mine and get feedback on it to pass on? Obviously the feedback from other teachers is totally valuable, but sometimes a fourteen year old has a perspective we haven't visited. I may want to do this tomorrow that way its as fresh as possible. It may just be a follow up blog post. 

April 20, 2018

There are some days where we struggle so much as teachers to find the light. When the nation devalues your craft, when the world is riddled with difficulties that you try to overcome in your classroom, or when you lose faith in yourself because of ineffective lesson, or when the people who you work for/with can not find a supportive way to hear/give feedback. That was NOT today.

TODAY WAS A DAY THAT CONFIRMED THE IMPACT I AM MAKING AS A TEACHER FOR FUTURE TEACHERS. TODAY WAS A DAY THAT I CAN REFLECT AND GAIN STRENGTH ON FOREVER.

Let me explain how April 20, 2018 was a day that I will forever mark. Today we also changed the schedule for National Walkout Day to protest Gun Violence. Student Council brought it to me a month ago that they wanted to participate. We made a plan and they decided an open dialogue about gun violence would be a good use of the time. They wrote questions and lead the discussion with the 30 or so (out of 46) that participated. All students listened and opened up about their thoughts and feelings on the issues. Myself and a coworker also contributed and before long kids were asking questions to each other about things they felt and offer advice and suggestions of how to ensure we make CTEC a safe space. At the end I thanked them and they all clapped for each other's candidness and maturity. I got emotional right near the end and just offered our willingness to continue to hear their concerns. 

Strange thing happened as we exited the building and entered the building at UNC-Charlotte. I caught a glimpse of a guy etching names on the monument. I realized a previous coworker Patti Norris was supposed to be on there soon after passing with a long battle with cancer a year prior. Sure enough her name was being put in as I was there. I sent it to previous coworkers at Central Cabarrus in hopes that they would see the impact they made in her memory. They sent it out to the school and made sure it brought some grieving teachers joy. I explained to some of my students who she was and why I was stopping to take a picture and they really empathized with the gravity of it.

In third period a college professor and two future math teachers came to watch me carry out an amazing lesson that they wrote. I got to put into action an inquiry based technology lesson after several levels of feedback from myself and the professor. I plan on writing an entire blog post later on this experience so look for more details about that. I don't want to give away too many details yet. 

As I mentioned our schedule was altered. The other reason why is because we generally take kids to lunch on campus and get them outside to play for part of their PE fitness logs. At lunch I talked to three boys about their families, their life, and their plans to become teachers. It was amazing just connecting and talking to them. For PE time I usually play soccer with a specific group of kids, but today we played capture the flag with the few cones I have. It was spectacular fun. Running around and playing with these kids. All the teachers played this time and more of the students joined in than ever before. 

After exhausting myself I came home to a wonderful message on remind: "I wanted to send you the pictures because you look so beautiful in them sooo here you go I hope they send !!" (You know this is a real text because of the run on sentence and lack of punctuation.) Then attached was a picture of me with five of our kids on the steps of the Union. My heart melted and I thanked the student. 

The last random thing I saw that made me realize the fun I bring and impact I have was a picture and video in my time hop from my Calculus class two years ago. I took them to Calculus the Musical after school one day (on UNCC's campus of course!) and we had the best time. There is a hilarious video when EJ goes on stage with the performers and I laugh every time I watch it. I took a picture of the kids after the show as well. I remember the names and personalities and great people they are as well as the great people they will grow into. 

The last thing I want to say is that today was in no way perfect. I had to scold students for stealing out of lunches and forced them to replace items out of their own money. I had to punish a student for forging signatures on progress reports by having her call home. I had to tell two boys over and over not to slide down rails and one almost severely hurt himself. But these are still wins in character and safety. And although they were exhausting efforts and negative in nature, they don't take away from the whole purpose of the day. 

The maturity, the empathy, the care, the effort, the heart of these kids is working hard on me today. The joy of teaching is beaming out of me with every moment. My passion is ignited by these kids.

Gizmo's Investigation Summaries

So, let me first start off by saying that I am lucky enough to have a subscription to Gizmo's (www.explorelearning.com) paid for by my school. (#notsponsored) I split a single subscription log in with 2 other teachers so that it stretches more. If you haven't ever tried it, I highly recommend creating a free 30 day account and seeing what its about. Its simply a way for students to experiemnt with specific math and science topics while making conjectures about patterns and things. Some people make incredibly similar things on Desmos and Geogebra with the same success, but the ease and depth of the content available really lends itself to the Math 1, 2, and 3 that I teach. I'm a big fan and think that if you have multiple teachers willing to share an account its hard not to justify the cost. The content is already built in with lots of great features like: vocabulary sheets, exploration sheets, keys, and quick assessments. All that can be edited to best suit your kids. 

With that being said, sometimes my students are mindlessly filling in the Gizmo exploration sheets without connecting the big ideas and coming up with take-aways that I really want from them. So I started making "Investigation Summary" sheets to partner with pre-made exploration sheets. My students complete a specific activity, then they summarize their findings within that activity. These investigation summary sheets essentially become my kids notes and/or the take-aways I really want them to hone in on. I have really seen major growth in what my kiddos take away from the Gizmo's and the connections seem deeper. 

Here are some examples of ones that I've used thus far and some links to the content on Gizmo that I partner it with. Be aware that a free account gives you much more ability to really peruse this and see the connections between the documents. I will continue to drop my Investigation Summary sidekicks in this folder. Feel free to use and explore, or just have them as lesson summaries for your students. 

Polynomial Optimization Problem

Polynomial Optimization Problems... Okay, its just the box problem that we've been trying to get the kids to understand every year of every math class EVER!!! I've always done a hands on approach and a project. I feel like I'm finally connecting all the dots to what can happen with the optimization problems. I've had obvious influences from Fawn Nguyen's blog and really buy into the process of constructing the boxes. But my kiddos struggled visualizing the formula from the box so I wanted to introduce tables, graphs, sketches and expressions into my process.

The Exploration- I designed a Desmos Activity . First part of the Desmos activity explores the common problem of maximizing area given a restriction on perimeter. The second question is the open box with the four corners cut. Students are still participating in hands on construction with the influence of recording their data in many different ways.

The Project- Students design and market a popcorn container for Rohan Oza in the Shark Tank. Students explore and/or come up with viable nets that work to create a box with a lid. They write expressions for volume, length, width, and height. Once they've explored at least two possibilities, they decide on a box construction and come up with a reason why. Hopefully, it has something to do with volume. (fingers crossed). There are some other 21st century skills embedded through designing the actual product, marketing it, and coming up with a pitch for Rohan Oza in "The Tank".

Here is my project planning document. Maximizing Volume Package Design Project Above are a couple of screenshots of the detailed project info and rubric.

Re-Thinking Warm-Ups

We've been told for so long that students need a bell-ringer, warm-up, do now as soon as they walk in the classroom. For math, generally that content falls into one of three arenas:

• 3-4 problems that review content from the day before
• A pre-requisite knowledge probe to see what students already know on some content
• A problem or two of review from previous content in the semester

I have definitely leaned hard on these for sometime now as my "GO TO" when starting a lesson. (I have also used my warm-up as the hook in a 3 act task, but that kind of falls in category two anyways.) What is my newest favorite way to design a warm-up? Take a look here!

So a couple things worth noting about this warm-up. Its the warm-up I do after students complete factoring with algebra tile lessons, but before learning the formal patterns (rules) for factoring GCF, basic trinomials, and difference of squares, and factoring by grouping (All with the box, I'll state my case for that in another post soon!).

As far as the benefits I've gotten from a warm-up like this:

• My students are reviewing content, but beyond that they are anchoring tasks from my classroom teaching and previous skills and tasks to the subject at hand all the way back from elementary school. They are explicitly seeing vertical alignment.
• My students are seeing the whole picture of factoring and defining the term themselves based off all the tasks in the warm-up. This is much more powerful than having them recall from memory.
• One of my favorite parts of this warm-up was the way it played out in the classroom. Some of my strongest students were struggling to do the review portion and some of my weakest were finding lots of success in the skills they had tucked away from elementary and middle school. Students were trading solutions and collaborating in a very strong way in the completion of this work. 
• All of my kids had to reflect on their learning in the final question. They all executed skills, but how were they different/similar.

Simply put, this has been the answer I've been searching for. The only down-side is that sometimes I spend 15-20 minutes on a warm-up in a 90 minute class. By the time we finish and I see the power in this design, I never stress because that time lost is actually well used and critical to success in my class.

Here are a couple others I've done recently with my reworked method. The second has a really great way of pushing the kids to understand past skills and creates that exchange.

Homework

We all try to come up with effective ways of taming this beast. Some of us just ditch it all together because its been inconclusive about the gains that homework has. I have even considered this tactic as well because of the pain of grading and the influence it has. Since I'm at an Early College, I think the reality of doing homework for understanding is important for students in my courses. But if my students are not gaining an introspective look at their understanding of the concept, what is the point? In my class student homework grades are based on what they try (by that I mean a reasonable effort). When the students come in they either get a Homework Check Slip or a QR Code for Missing/Incomplete HW. They usually only get 10-15 questions that shouldn't occupy more than 30 minutes of their night.

Students that get the QR Code fill the google form linked and plan for turning in their homework while the rest of the class pairs up and checks homework.

First they switch papers an write their names on the Checked By, Fill in the title, and calculate the number of questions on the homework and the amount attempted by each student. These are all I use to calculate the grade, but the other part is much more telling and important to me gathering information. After they "grade" correct vs. incorrect, they switch papers and homework and note their missed questions. Then they finish the statements "I understand..." and "I struggled with..." What I gather from this process is the most valuable. Here are some student samples and what I've gained from them. Note this is the first hw check of the semester, so we haven't practiced much with the statements. 

So this student did well on the homework, but if you read the two responses, they actually mean the same thing to me as a mathematician. I struggle really knowing what they do or don't understand, but the number correct leads me to believe they understood the content for the most part, but struggle in articulating their abilities. 

This student just realizes that she didn't have any success at home and she "got it" when we did it in class. Likelihood is that she didn't really get the lesson and needs some deep remediation. This is also a student that does not volunteer in class, so putting her in the center of the class conversations may help. Since she focuses on environment rather than content, I know she also struggles with articulating her own learning. 

This student could specifically tell me that multiplying functions and evaluating functions are strengths, while subtracting is a weakness. She also has the skills to articulate this clear to me and explain what causes her weakness in subtraction. 

So while this student got majority correct, the details about their learning are a little hard for me to uncover exactly what the difficulties were. They get the "function notation thing"and what I infer is subtraction operations gave them trouble because "switching signs is confusing."

I also have done a version of this where I ask them to list the questions they get wrong. This allows me to do a quick item analysis of the homework and use those questions in lessons at a later date. 

Rube Goldberg Project

THE IDEA 

As a teacher that has been in the STEM and Engineering mindset for the last few years, I've been awkwardly obsessed with Rube Goldberg Projects. But lets be honest, doing a project for fun (the project's sake) is totally against my teaching philosophy at this point in my career. I will say that the process of building a Rube Goldberg machine would have students connect to the CCS 8 Mathematical Practices. So I did my research and found a couple very helpful videos that made me start thinking about this as a cross-curricular project. Eventually I tied this to my probability standards as well as a ridiculous amount of science standards from earth/environmental. So the new task for students was to build a Rube Goldberg Machine that represented a cycle/process in science. And the results were amazing! Here's how I did it.

PLANNING

First my brain storming about what I wanted from students (in google sheets of course).

Then I came up with a run down of how I wanted the week to go. 

And finally I called a friend that's a Earth/Environmental Science teacher. She teaches AP as well as freshmen at a high school in the system. She brainstormed a couple options for process/cycles we could use for the game. From there my science teacher from the previous year gathered a video and image resource for each one. We purposely eliminated the student's own research because the other project we gave them for english/history was very research heavy.  

MONDAY - INTRODUCTION

So I introduced the concept of a Rube Goldberg Machine on Monday. The presentation involved first introducing them to Rube and some interesting facts about his life. Then I had them look at three drawings and do a classic notice and wonder protocol. 

Students wrote their answers to these questions on chart paper with a group and any other information they gathered by looking at the comics.  I loved hearing their answers. My favorite question from a group was: "Is this supposed to be easy or complicated?" In the end I took a screen shot of urban dictionary's definition of extra and compared that with Webster's definition of Rube. Then we watched some examples of machines in action. Of course OK GO's music video was shown as an example. So this lead to me clipping down their TED Talk into an Edpuzzle video. Students completed with a partner. Within this video they went over some probability of systems of machines working. So I asked a few questions about how changing the likelihood of a machine working increases the likelihood of the whole machine. So I had students applying independent probability to Rube Goldberg on Day 1. Crazy! 

TUESDAY - EXPECTATIONS, RESEARCH & "PLAYING IN THE SANDBOX OF IDEAS"

I followed up the previous day by having some students recap the first day, particularly because some students were not there the first day. I went over the expectations for the project. Then I filled out a brainstorming document while the students threw out ideas. I did my example on the four seasons. It looked a little like this:

Then the students accessed the research document and recreated this document for their own processes or cycles that they were assigned. Once they felt confident on understanding their process and had brainstormed, they were given free-range to a number of materials (mostly recycling we stole out of bins) and a few ping-pong balls. We told them to "play in the sandbox of ideas," much like OK GO suggested for their TED Talk. Ultimately they want a plan can work with certainty, so they have to test ideas and see how reliable they are. Some students already had a great start to the project at that point.

REST OF THE WEEK

Wednesday and Thursday were build days. Not a ton of structure happening like previous days, but a lot of coaching, facilitating, and refining ideas. What impressed me the most about the work and working was that it was intentional. Every design, no matter how simple or complex had legitimate reason backing it from the research they did. On Friday we did presentations, reflections, and evaluations. During the presentations they were asked to address the following:

• What is your topic?
• Explain your cycle/process?
• How does your machine illustrate your process/cycle?
• Demonstrate your machine (3 tries max)
• What is a problem you had in your machine, and how did you fix it?

Presentations went great. Most of them were 2 min or less in length. I thought it was good practice to help them focus these to the main ideas of what this project was truly designed to do.

Something different about this project was the way we  decided to grade this first week. Our message to the kids through our grading this week said a lot. We really wanted the students to focus on mastering a minimal amount of content in this project and focus on growth mindset, perseverance, grit, and meaningful contributions to their teams. So after we had a lunch break students came back and did a self/peer evaluation and demonstration of knowledge. They completed this google form that focused on the the criteria above.

MY REFLECTION

In all reality, I want to give you a link to ALL my responses from students about the project to let you in on the depth of thinking that went on for some of these kids. Of course not all are impressive, but I'm seriously having a hard time choosing. Since I don't know them academically well (yet!), I'm not sure how hard they pushed themselves. Also, ignore the writing and spelling. We'll be working on that. Below are some of the highlights of what I want to share with you from our students.

I know that this is probably a lot of responses, but I could have kept going. Look at the power these students gained in evaluating themselves and their peers. I definitely should have forewarned about complete sentences and spelling. I just really felt like these things were what I was going for and achieved better than I thought. I tried to remain super flexible in this project and have the kids do the same. I feel as though this is my best executed Project Based Learning to date. As a first week project it was very whirlwind. If I were to grade this on a 4-point rubric, I would have had many interventions with feedback. I would definitely integrate a peer and teacher feedback component during the design process to help students refine thoughts in the future.