2017-10-23 3 Lessons to Creating Student Authors of Mathematics

Diving into a connected series of lessons this week, I am trying my first rep at creating students who are authors of their learning in mathematics. The lesson series is the culminating process of three areas of mathematics innovation I have learned from Brian Stockus’ (@bstockus) Numberless Word Problems, Chris Shore’s (@MathProjects) Clothesline Math, Annie Fetter’s (@MFAnnie) #NoticeWonder, and mathematical literacy. Similar to app smashing, putting these pieces together made sense to me, so last school year, I created this series of lessons around 3.OA.4, a problem our girls were having a hard time with at the time this series was created. Through this process, our girls formalized their thinking, and became masters of their understanding here.

As with most learning experiences, I wanted to start the girls with a #NoticeWonder experience, but I needed a problem to build this around. The right problem makes a big difference in getting exhausted students with negative mathematics experiences to begin the journey anew. The Frameworks for California Mathematics for third grade provided an excellent pseudo context to build the problem around, when I found this example, I knew I was on to something.

Two things that made this problem stand out:

1. The problem has a feminine hero, powerful for learners to identify themselves in the role of the main hero.

2. The problem has monkeys, who does not love monkeys, so interest factor immediately built in.

Although I had the problem in hand, the problem was too manufactured, it lead straight to the problem, and students could access, or they cannot. About this time, I had discovered Brian Stockus’ Numberless Word Problems, I loved, loved, loved this approach to inviting students into the learning, and this seemed like a natural fit. Stripping the problem down to build up to an open ended prompt, the natural fit for this process was a #NoticeWonder approach. I went one step further, using a strategy similar to my use of the Fraser model, called a Diamond Paper that Dr. Boaler introduced to our learning cohort of improvement specialists. The one sided paper is now two sided, with the problem solution on one and the #NoticeWonder problem on the back.

For each passage, students write a #NoticeWonder statement, then share with their partner, then share out whole class. This slow process grows in complexity each time. And with a couple of reps under my belt now, I am not surprised that students will proudly proclaim the answer to the Frameworks problem usually around the third time we #NoticeWonder, which provides immediate satisfaction, but isn’t the center stage of learning.

The 4 statements I created for this problem are:

Once students are through this process, they create a question from their #NoticeWonder statements. The range of questions if usually interesting, but this is their first rep at doing this process. Next, the students share their created questions with their partners, and then their group. I then have them flip their sheet over, and they must synthesize their questions together, or create a new question that the whole group is going to answer. After a few moments, the group shares out their questions, I project them and write them down by group, and this is their second and third reps. Finally, we, as a class, synthesize these questions down into one more question, we all write down in our diamond on the flipped side.

Once students have their question, the students go about solving our problem. Having usually done this in pieces, this week I got a chance to attempt this part and it took a whole two hours for students to get through these pieces, including the solutions. I will note that the students were with me the entire time, and we did do a couple of brain breaks (a stretching routine and a couple of GoNoodle sing and stretches). The great thing was one student stopped me and said, “This is so great, I wish we could do it everyday.” I asked her what about the process she liked and she said it was the writing…I know, these students liked to write about the mathematics. Another good note, the teacher said after she returned from taking the students to the bus that several of the students told her that their brains hurt, and they knew that that meant they were learning – we are a growth mindset district and that’s the power of harnessing the work that Dr. Jo Boaler and others are doing.

The next day is our short day, the second lesson is a kinestetic activity for students, and to test if the learning from the previous day actually stuck. A bonus from the previous day, I lucked out that one of the students started solving the class problem with a number line and that made for a natural opener. So I started with a picture of this students work and I ask the students to #NoticeWonder again (I loved when the student recognized his work was being highlighted). Moving into modeling what the students are going to do, the teacher, a student, and myself all worked together to model it. We had less that 30 minutes to launch this problem, with almost five minutes before the students left for the day, the students were launched on their task. It was an amazing flurry of using jump ropes and paper tents to sequence the numbers. There were three blank tents that students were asked to write the number they identify from the pattern. This uncovered some great misconceptions, as most students nailed the pattern, but made mistakes on writing the blank numbers. One group wrote had 0, 4, 8, 12, 16, 18, 24 and another group sequenced 0, 4, 5, 10, 12, 16, 24, do you see the misconceptions? Both mistakes are easily understandable in the context of the day, and both groups told me the pattern was counting by 4s.

Now the moment I was dying to know, I asked each group, “How might the pattern they sequenced be related to the problem we did yesterday?”

EVERY STUDENT could tell me that the number sequence represented the number of bananas and the number of cards represented the number of monkeys. Apparently the process and the sense making from the problem really, really stuck. And one student summed up this experience for everyone, “This is the funnest math thing yet!” I couldn’t help but think, “Wait until tomorrow my friends.”

The next day launched the newest addition to this family of lessons, I want the students to write an ebook about their own problem related to this problem sequence. We will start with a traditional paper style book, but I’d like to push this beyond to the point that students are creating a powerful learning experience for other students. The students were introduced to the book “written” by our girls when they were in third grade last year. I handed a copy of the book to each student and we read through it whole class. Many students noticed that the bulk of the book was the scaffolding sequence of sentences we #NoticeWonder about on the first day. As time was again limited on this process, I wanted to make sure we got exposure to the book idea and build the students excitement to diving into the writing process in another class meeting.

I am excited to dive into having students formally dive into writing their two books and how I might sequence out those pieces in detail. I do want students to write one book that is around the same content, and I’d like them to write another that is open to their hearts desire. I am not sure how to sequence all these pieces out yet, that is some careful thinking and sequencing I will need to do today to get ready for next week. Once students products are available, I will gladly share them here, and I’ll look forward to your responses.

2017-10-16 What a Week

Returning from Northern California this past weekend, I was thinking about all the challenges that we had to accomplish this week with a mixture of dread and excitement.

Monday

The week began with the implementation of my newest game created around the 4.MD.3 standard. The game also involves six other standards interlaced within the clues students must solve to unlock the locks. I planned the game for 30 minutes for the fourth graders. The two 4th grade classes that would attempt the game were new to this learning experience. Normally I don’t like to give the first rep of a game to include grade level content, but this was a challenge I had to meet. The energy in the room from the two reps taught me a lot about the quality of the game, and some interesting facilitation pieces that make the game a lot more accessible for all learners.

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The students did a great job of working together, though not fully to the point of genuine collaboration, which is wonderful since students pointed that fact out in the debrief. The biggest change idea we implemented from class to class was students working in groups from the start of the game. While this isn’t new for me, it was new for doing it for the first time at this grade level. I usually like to let students go without too many structures for a first rep and let the chaos become a need for roles. Starting out with groups forces them to slow down, and focuses them on solving the problems, not playing with the locks…something that I hadn’t predicted…I am more a believer in structured learning from this point forward.

Tuesday

Although we introduced the lesson last week in this amazing special education class, I wanted to remind the students of the work we had done to get to this point. Starting with my approach to Numberless Word Problems, students went through a sequence of four NoticeWonder questions as the story grew in complexity showcasing the learning goal. The students would then write a question from their wonderings, and then come to a consensus on the question they were going to ask for the whole class. In our case, we helped facilitate this part, to give the language of the task we were attempting to solve. Background information about this group of students: The students love, love, love Youtube. So our lesson was built around trying to figure out the best deal if Youtube were to offer you two choices for a contract to make films for their channel.

Each group was given a different representation, that is each group had a different contract offering. The students had to sequence both the amount of views and the value per views, with some of the numbers not filled out. Since every tent was not filled out, students would have to make sense of the pattern and fill in the missing pieces, i.e. the part of the standard students were meant to cover. Each student had a job

  1. Two students hold the two ropes (turned into just one rope for us)
  2. One student sorts and sequences the money tents
  3. One student sorts and sequences the view tents
  4. All students contribute to sequencing through discussing their NoticeWonder pieces

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The end result is to get the groups to come back together and decide which is the better deal and why. The use of the Numberless Word Problem approach to introduce the context gave the students a powerful intuition to come up with a question (which is guided by careful questions), and then using clothesline math to explore the learning made for two powerful hits. I will be following this approach in third grade next week (on Wednesday and next week), as we go through a sequence to solve 3.OA.4 through 3.OA.7, and students will create a book afterwords.

We also launched a dream of mine that has been in the making for the past five years, and really come into focus the past two years. We started a Breakout EDU Academy with eight teachers covering third grade through sophomores in high school. This initial group will become Jedi masters by December. Once January comes, they will adopt a padawon, and together, they will create a training from our district offerings and turn it into a game. The padawons become masters in May, and will adopt a new class for Fall, the Jedi Masters will become the Jedi council and oversee the operation from this point.

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Wednesday

I had the opportunity to introduce the 3rd graders to the NoticeWonder component of the Numberless Word Problem that starts our journey on becoming mathematics authors. The students had a variety of great observations, but the 30 minutes was not enough time to have the students go beyond.

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Another big task on Wednesday was a collaboration for the next day’s training. Our team of secondary math teachers are fostering student grit through a football theme. One of the learnings is focused on an article titled, “17 Reasons Football is Better Than HS.” We are utilizing the PDSA cycles to implement changes and looking if we can find a change idea(s) that will help our students gather grit.

Thursday

Our plan was to have two repetitions of collecting data around the strategy we had implemented in this classroom as the students tried the performance task. Using the data we would see what adjustments we could make for future implementations.

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Our day took a few turns and the students were amazing in their flexibility of tackling the task and answering questions. We tried a new change idea in the second observation as we were more pointed and went about a little bit of teaching the students how to take a performance task, like breaking it down using the strategies the teacher had taught them, and sequencing through the performance task.

The day was really interesting and quite surprising in many ways, one of which I will share here. The teachers were asked to provide me with feedback on how the day went. I am always looking to improve, and these are some of those results. For your information, the scale is 1= unacceptable 2= poor 3= satisfactory 4= good 5=very good. 

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I am curious what your take aways are from this, I am still processing the thinking. That being said, their comments were illuminating on a variety of pieces to make this both more meaningful and impactful for them and their students.

Friday

The week ended with an all day event for many fourth graders in our district (and neighboring districts) as they learn about life in the time of the pioneers (California history). The entire Zalud Park in Porterville is taken over as 1,200 fourth graders go through a series of stations, each with a learning experience about the times.

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The students get to find out what life was like through first hand experiences of that time and get to be outdoors and share friendships with school mates. Just an aside, at lunch watching students laughing, rolling down hills, and just being happy kids while at school is what makes being in education worthwhile. Days like this day are a great reminder we are in the people business, not the test getting, show me the best score you can get business, but I digress.

Saturday

In mountains near Yosemite National Park, a group of different math teachers met to listen to Dr. Timothy Kanold, author of Heart!. The surprise was complete when I see several of my old teaching colleagues are seated at the back table, so I asked if I could join them. Immediately I was seeing a lot of fantastic familiar faces, which going up solo and not knowing what to expect this was a huge surprise.

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The most incredible thing happened when I ran into an #eduhero, Duane Habecker, who was also in attendance. We have established a learning connection, we will be able to meet up face-to-face soon to get better together. And the learning from the day was phenomenal. I am enacting these five things moving forward, and I do not doubt it will make our learning better and impact students directly. My five learnings are:

  1. Creating an agreed upon VISION for the group is fundamental
  2. Every decision (or action) needs to be research based
  3. Every decision (or action) needs to move the VISION forward
  4. Always celebrate the small wins excessively, and push for the long term goal
  5. Always start with an Essential Question tied to your VISION

So, all that to say, I was righteously anxious driving home last weekend, but I am always so glad for so many wonderful learning opportunities and how impactful those things are.

PS I didn’t link the lessons I am referring to in this entry. If you’d like me to share, please leave a comment, or otherwise connect with me, and I’ll gladly do so. I would love to hear your feedback, I am a little nervous publishing my feedback, but I need to be transparent and grow. I am wishing you all the best in your learning journey and hope we can grow better together.

2017-10-02 Improvement Science & Mathematics

The past two weeks have been an intense dive into the work we started over a year ago, and the feeling that we’re finally digging into something will set in.

We will find a process by which we can triple the scores on the state standardized testing in mathematics at the fifth-grade level. If we are successful, or not, we are learning a lot about our system, and we will be sharing that out at the termination of our process.

To determine if we are successful, we have utilized the power of Improvement Science. Although I have been learning the process of Improvement Science for 1.5 years, I feel comfortable discussing all of what I don’t know when it comes to this complex set of machinery.

I am working on putting all Improvement Science into a visual, comprehensible approach and it gave me the opportunity to work on my creative graphic designs. The series of several images and video are a result of that time and learning.

Students learning, students engaged in the growth mindset, and all this great stuff is just so exhilarating to be apart of this unfolding story. As the journey continues, I’m excited about the learning that will continue to grow from this process. One simple example is the productive analysis of learning when teachers from different sites come together to plan, watch, listen, and grow better together.

Here is my first repetition of making Improvement Science a visual learning experience.

Or you make click below at the PDF as well.

Improvement Science

2017-09-25 Visual Multiplication of Fractions with Reducing

Recently, I was on a Sunday run when I received a compelling question I couldn’t wait to dive into. The question asked how would I teach the multiplication of fractions with reducing.

The teacher provided some background information to frame the situation. The students had been instructed on how multiply fractions and reduce. When the lessons were over, the students all showed they were competent in both skills on their formative assessments; however, when this teacher gave them a summative assessment, the shock of students’ performances afforded me this opportunity.

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To get started, I didn’t quite know if I understood what the teacher had tried to explain. Luckily the teacher shared images of the student work to shed some light on the situation. Being curious about the student work, without making any inferences was my first order of business.

Next, I thought if this was my student, what would I try with them, given where they are at?

The student’s work made me think a visual model might illuminate the concept, inferring from the student work might be one of the missing concepts.

If I’m going to a visual model, how might I represent this such as the student will tell me their #NoticeWonder statements?

The #NoticeWonder strategy is my go to when trying any learning experience with students. My mentor once said, “Never tell a student something they can tell you….” and creating opportunities for your students to tell you something about their learning is very powerful. I also created a video explanation of the visual strategy and an animation of the visual strategy that the students #NoticeWonder about.

Using the progressions for mathematics and comparing to the California frameworks, I wanted a visual representation that is both flexible and powerful that goes across multiple grade levels. Although, the use of the area model is a strategy students should be familiar with by the time they are done with second grade, the full power of this model may not be fully understood until much later. Utilizing it for how to decompose and multiply fractions seems a natural fit to build upon.

I am always curious when creating a lesson how it will go over with actual students, not just the idealized math lovers we all have hidden inside us. Presenting this lesson with some enthusiasm and, as Dave Burgess says, some sort of hook. I have a steak here that can be prepared so well, but when it’s cooked it gets ruined, so I’m thinking about how to hit that sweet spot of a juicy medium rare in terms of proper delivery. 

What are your thoughts? Would you try it with your students and let me know what changes you made to make it better?

Thanks for helping us all get better together.

2017-09-18 Published 1st Article

Near the end of July, I received a random email message from someone associated with Edutopia….I thought to myself that either this is one of my friends playing a practical joke on me or this email was sent to me by accident. The email asked if I would be willing to write an article on Visible Mathematics for the educational resource, and it wasn’t a hoax.

My reaction was skeptical at first, I had a hard time believing that the amazing resource of Edutopia would want something from me. You have to understand three major problems with this: 1) I am a physics, math, and technology nerd….writing is a huge challenge for me and I don’t think I write very well; 2) Like Dave Burgess says, being creative is hard work (it’s like being good at anything, it requires a lot of hard work); and 3) The article is going to be very public!

The challenge to overcome these huge obstacles was almost enough for me to choose not to pursue writing an article about mathematics. I have a fixed mindset regarding my writing, but I am working on it, so I tried to write the article.

In my first attempt, I wrote a narrative, with myself removed from center stage. Recreating a time when visuals in mathematics made an impact on students learning. I spent a week of writing, revising, and seeking feedback, before, I sent it to the kind folks at Edutopia. Their response was gentle, kind, but let me know that was not what quite the idea they wanted to capture. Although this type of feedback normally shuts me down, I am working on a growth mindset in my writing and I wanted to persevere.

In my second attempt, I focused on a personal story. In my story, I learned something so powerful I will never forget it and use it instructionally whenever I can. I won’t spoil your read of the article, but the learning was powerful and changed me as an educator. The second story flowed out and I was happy with it, so I tried one more time sending it back to the great folks at Edutopia.

Eureka! They were almost there, the tough job for them was on. The editors had to figure out how to display it, clean up my horrible grammar, and get it ready for publication. With ease the process seemed seamless as the folks at Edutopia put it all together.

The night before it was to be published, I felt like a kid on Christmas Eve, the anticipation was killing me.

When I woke up the next morning, I saw it was published, and I let out a squeal. I awoke my wife by jumping on the bed, singing, “Do you know what today is…” Well she didn’t appreciate that at all! After the morning fog wore off, she was very happy for me, and I learned my excitement could at least wait until the sun had risen.

I also find it amazing that writing is a process that shows us how unorganized our thinking is, and it always feels so good when a well written piece is produced. I am so so grateful for the experience and for the great folks at Edutopia for working with me, despite the number of revisions. As I continue my growth journey in my writing, this was a story that I am excited to tell. Happy Monday and have a week worth writing about!

2017-09-11 Coding a Newsletter Template

A journey from last year that I really enjoyed doing was creating a monthly newsletter that indicated the successes we were having as a district mathematically speaking. While I enjoyed creating the newsletter, I was never happy with the design, and always thinking about how I could make it better. Well I went from using pages to Google slide decks (because I love, love, love slides) and still ran into a similar issue…actually I think the Pages version was way better which makes it worse….well new journey this week, I am excited to be working with a teacher and their coding and design clubs, as I am going to pose as a customer to order a new newsletter and they are going to design it for me. I am going to “hire” them and they will design it for me.

I will give them a list of specs and a “budget” to work from, they are posing as a small startup company and this is one of their first jobs. I am super excited to see how this will go and I hope I get a sweet newsletter out of it too!

2017-09-04 Numberless Word Problems

There are two things that I learned about toward the end of last school year that got me so excited I couldn’t wait to try them, Numberless Word Problems was one of them. One of my #eduheroes, Brian Bushart (@bstockus on Twitter), created this idea some time ago, and I was just learning about them. So, I wanted to get a couple reps in ASAP, and I was able to get a couple of reps in before the end of the year, and it confirmed my initial excitement.

With this school underway, I want to jump in early and often to get everyone on board with this idea, exposing all students to this opportunity and making it an ever growing area of powerful learning. On this journey last year, I was able to modify this into a sequence of learning events, where we start with a #NoticeWonder activity that builds the Numberless Word Problem the students create. Since students create the word problem, whether or not there are numbers is there choice, and it is so interesting what they come up with. The students smash their questions together to make a new question, and then they answer their question (or switch with another group and answer theirs) four ways.

Once the students have shared their answers and we’re all on board with the questions and answers, we compare our information to the state standards example(s). Students are always surprised that their questions are much harder than the state examples and think the state question is easy. Compared to previous times when given the state question, they typically shut down because it’s “too hard,” I’d say this is an amazing outcome.

Anyway, it’s still a work in progress and I’m super excited about it. Thanks Brian for sharing and making us all a little better.

2017-08-28 PDs

This week was the week of Professional Developments (PDs) with my creation and delivery of Interactive Math That’s Meaningful (Horrible Title, I know) and 3 Powerful Math Routines. Each one has some amazing pieces to it that I am very proud of, and both have some areas I do not feel meet my goals. Time and reps will let me know if my feelings are accurate, and it will reveal where other holes are and where great stuff is as well. It’s pretty hectic this week, so this is just short note to remind me to breath.

2017-08-16 ReNew Learning and RTR

I love when I come to a new understanding about something that I had previously known, which happened this week. We had the blessing of having a consultant come to our campuses from the county office of education to help us with some work we are doing. Part of the work is to implement Rich Task Routines (RTR) in mathematics to help our students become stronger math students.

What is a RTR you may be wondering?

An RTR is an activity designed to help us (teachers) be purposeful in our delivery of content to give students access to deeper and more challenging learning targets. The idea flows from the 5 Practices made famous by NCTM book by the same name. The work and intentionality of what we put into, seeing the whole cycle with students, and reflecting on the process made for a great day of learning. I can’t wait to continue this journey.