I ended the trip with a visit to a well-known private school, Nueva High School. They recently built a new campus, and it is GORGEOUS. Not exactly a budget-priced facility, but there were lots of ideas that could still apply to any school from their space design. I spent most of the day visiting two Olin alums, Steve and George, who teach together at the school in their design labs. They, and other teachers at the school, are awesome.

The physical space is intimate and flexible. The shop / design area consistent of four classrooms all connected together by interior doors and sliding whiteboard walls. The sound-proofing between rooms was great while one end held a discussion and the other ran the CNC router. The folding walls made it possible for a teacher to be in one space while supervising students in another.

I liked the projects they selected for students -- one group was studying bike repair, going out and finding abandoned bikes around the city and working with their teacher to scrap out parts and create a few working bikes. This weekend, at the school's STEM Fair, students would be repairing bikes for visitors at no charge. Service learning was a common piece of the learning experience.

Another project had students building a physical clock, a cool integration of mechanical design, electronics, machining, and art. They started with open-ended brainstorming to think broadly about ways of telling time, then narrowed quickly into something they could build in 10 class periods. It was interesting watching Steve work with one student who had a bit of a crazy idea -- a clock that would strike a battery and cause it to explode. Rather than say "that is unsafe and just stupid", which was my initial thought, he was able to engage in a productive discussion that left the student feel validated in his idea yet understand that he could not explode batteries in class. Steve praised the artistic vision of ticking down to an explosion event, explained why exploding batteries posed safety and environmental hazards unless you had a lot of setup time and expertise with battery acid, and then clearly stated that it would not be possible to carry it out in the 10 build days of school, leaving the possibility of making that final step happen outside of the class if done safely at home. This is a mindset I have seen at other private schools as well and want to do my best to bring that open-minded attitude with parameters into my own classroom.

One interesting class that I joined was reflecting on a documentary they watched about food waste. After watching the film the day before, they worked in groups of three to draw a system diagram of where waste was being produced, discussed what the underlying causes were at each step, and then talked about ways they could create projects based on the topic. Only a few students decided in the end to pursue a project with this topic, but others preferred some of the prior topics they studied. The intent of the video and discussion was exposure to one more thing students could be passionate about.

To end the day, I hung out with the Nueva FIRST Robotics team, 4904, one year newer than our team (4859). It was neat to see how their team operated -- they were incredibly student-driven, a shift from some of the strong programs I visited earlier in the week who had much more mentor direction. Given my ongoing tension between encouraging students to work in ambiguity and the power of providing students with very strong hands-on skills, I can't decide which approach is "better". But they are definitely different. I hung out mostly with the programming team, doing my best to learn about how they handled vision-tracking, something our team is yet to master, but something that is really important if we want to have a strong team in the future. Students showed me a prototype on an arduino that talked to their RIO, then a better prototype on a RasberryPi, and finally their plans to have more efficient tracking from a new RasPi 3. I won't pretend to understand it, but it was fun watching them teach me and at least give me footholds into asking the right questions when we start learning.

## Sunday, March 13, 2016

### Creativity and Design (Part 3 -- d.tech)

On Friday, I started the day at a new public charter school, d.tech, which aims to be the high school version of Stanford's d.school. The school started last year with a group of 9th graders and plans to add a new class each year until they reach capacity. They are also building a gorgeous new facility on Oracle's campus that the company helped fund. In the meantime, they are acting like designers and creatively making the most of a neat, mostly open space they have now with make-shift classrooms separated by whiteboards, and building on the theme of the d.school, making sure everything had wheels.

It was fun to see how the teaching staff started every morning -- coming together for a standing meeting (scrum), putting all hands in, and yelling a new cheer to kick-off the day. From there, teachers went to their spaces where they were joined by the students. Fridays have an unusual schedule because every Friday afternoon is set aside for staff development and the morning is focused on design-lab time. Students take short (about 6 weeks long) courses of their choice ranging from "building social seating" (groups were each making wooden benches of various designs) to techniques to understand empathy (a classroom-based course where students discussed empathy, watched videos, and did small activities). Since all students are working on design labs at the same time, all staff (including the curriculum director) teach a lab. Many teachers do it with a co-teacher. (Below: a 3D model of the bench, followed by the workshop where teams were building indoors thanks to the rain that took away their outdoor space.)

Another common theme from these awesome schools that d.tech also echoed was integrated social-emotional instruction. The entire school watched a documentary on male gender-related stereotypes and challenges last week and watched one on female challenges this week. Afterwards, they discussed the videos and what they learned in smaller groups. Some of Dan Pink's books emphasize the importance for designers to be both empathetic (traditionally seen as a woman's role) and willing to start building solutions (traditionally seen as a man's role). Through the videos and discussion, they hoped to both address the cultural dangers of a macho man or 'perfect'-bodied woman, but also reinforce the positive view of how to be better designers. (Below: the empathy lab classroom followed by the open center-space where they watched the documentary.)

Before I left, I had a great conversation with Matt, one of the two math teachers, about how he approaches the subject in such a non-traditional school. It was awesome to see that his thoughts are not too different from mine, and very much in line with many of the group-concensus ideas from the #MTBoS (despite not participating directly on Twitter). His initial curriculum is a hybrid of video lectures (based on concept development, not example problems) and digital practice problems through MathXL. He sees the same issues that I do from these tools (students not always engaging in videos and digital curriculum presenting a chopped-up view of mathematics), but also takes the designer perspective that it is much better than a traditional, one-pace lecture course and he continues to ask big questions and redesign with his team as he goes.

We also talked through my Grand Challenge Design course for next year. Given all that I wanted to embed in the course (more than 4 years of college), he highly recommended that I scope it DOWN. One thing he liked from their design labs was modularity and choice -- there were labs on real-world building (like the benches), design mindsets (like the empathy class), and there was an incubator program for students who wanted to take an idea to market (something an Olin friend was volunteering with that day). He recommended that, if at all possible, I didn't work alone, opting instead to team teach. Given cost constraints, I may need to get creative here (community volunteers, recent graduates who want to TA, or student teachers all come to mind).

Matt also acknoledged the challenges I would face in teaching design, the largest being student apathy during open-ended activities and a fear of opening up while interviewing or doing empathy-building activities. From what I know of students' reaction to similar things I have done in the past, it will be a big hurdle. To help, he suggested lots of improv games as daily class starters to get students more comfortable being silly and taking social risks. He also recommended lots of hands-on quick-build activities (such as the popsicle stick house that has to survive a "windstorm") to get students to practice the "bias towards action" that designers always talk about.

It was fun to see how the teaching staff started every morning -- coming together for a standing meeting (scrum), putting all hands in, and yelling a new cheer to kick-off the day. From there, teachers went to their spaces where they were joined by the students. Fridays have an unusual schedule because every Friday afternoon is set aside for staff development and the morning is focused on design-lab time. Students take short (about 6 weeks long) courses of their choice ranging from "building social seating" (groups were each making wooden benches of various designs) to techniques to understand empathy (a classroom-based course where students discussed empathy, watched videos, and did small activities). Since all students are working on design labs at the same time, all staff (including the curriculum director) teach a lab. Many teachers do it with a co-teacher. (Below: a 3D model of the bench, followed by the workshop where teams were building indoors thanks to the rain that took away their outdoor space.)

Another common theme from these awesome schools that d.tech also echoed was integrated social-emotional instruction. The entire school watched a documentary on male gender-related stereotypes and challenges last week and watched one on female challenges this week. Afterwards, they discussed the videos and what they learned in smaller groups. Some of Dan Pink's books emphasize the importance for designers to be both empathetic (traditionally seen as a woman's role) and willing to start building solutions (traditionally seen as a man's role). Through the videos and discussion, they hoped to both address the cultural dangers of a macho man or 'perfect'-bodied woman, but also reinforce the positive view of how to be better designers. (Below: the empathy lab classroom followed by the open center-space where they watched the documentary.)

Before I left, I had a great conversation with Matt, one of the two math teachers, about how he approaches the subject in such a non-traditional school. It was awesome to see that his thoughts are not too different from mine, and very much in line with many of the group-concensus ideas from the #MTBoS (despite not participating directly on Twitter). His initial curriculum is a hybrid of video lectures (based on concept development, not example problems) and digital practice problems through MathXL. He sees the same issues that I do from these tools (students not always engaging in videos and digital curriculum presenting a chopped-up view of mathematics), but also takes the designer perspective that it is much better than a traditional, one-pace lecture course and he continues to ask big questions and redesign with his team as he goes.

We also talked through my Grand Challenge Design course for next year. Given all that I wanted to embed in the course (more than 4 years of college), he highly recommended that I scope it DOWN. One thing he liked from their design labs was modularity and choice -- there were labs on real-world building (like the benches), design mindsets (like the empathy class), and there was an incubator program for students who wanted to take an idea to market (something an Olin friend was volunteering with that day). He recommended that, if at all possible, I didn't work alone, opting instead to team teach. Given cost constraints, I may need to get creative here (community volunteers, recent graduates who want to TA, or student teachers all come to mind).

Matt also acknoledged the challenges I would face in teaching design, the largest being student apathy during open-ended activities and a fear of opening up while interviewing or doing empathy-building activities. From what I know of students' reaction to similar things I have done in the past, it will be a big hurdle. To help, he suggested lots of improv games as daily class starters to get students more comfortable being silly and taking social risks. He also recommended lots of hands-on quick-build activities (such as the popsicle stick house that has to survive a "windstorm") to get students to practice the "bias towards action" that designers always talk about.

### Creativity and Design (Part 2 -- the d.school)

Later Thursday afternoon, I broke from high schools and visited Stanford's Design School, known as the d.school. I joined another Oliner, Andrea, who was the TA for an undergraduate 101 course that served as an introduction to design (a course that recently was approved to meet Stanford's creative expression requirement). The last day of class turned out to be a great time to jump in -- I saw final presentations, students' finished design notebooks, the professor's summarizing lecture that pulled everything together and reviewed what they learned over the quarter, and I ate some of their coffee and donuts.

The student presentations followed a simple format: introduce a persona character, state their problem, walk the audience through your idea generation / sketches, present your solution (slides and a physical prototype), and explain how the solution solves the character's problem. Most students did a great job keeping slides clean and highly visual. Many also used humor throughout their presentation to engage the audience. The prototypes were not particularly high quality, but that was not the intent -- they needed to work through multiple iterations of the design to make sure that they were really solving the user's problem. For this particular project, students worked alone and they were their own user, so this step was much simpler.

The summary at the end focused on the key attributes of the course. His goal was to increase students' fluidity and flexibility with idea generation using open-ended sketches and structured activities. He gave a few assignments specifically to improve students' ability to make realistic sketches. He talked through five key habits of designers: use radical collaboration (teams of people from very different backgrounds), reframe problems in new ways, use curiosity and wonder, be mindful of the design process, and always have a bias toward action (when in doubt, start making something). He also pointed students to resources they could (and I could) continue to use: the collaboration toolkit and the rules of brainstorming. Finally, he ended with a "pinning ceremony", where all students had to find someone near them and award them with a small black pin to signify that they are now designers. It was a neat way to end a course. Even I got pinned!

After class, Andrea took me on a tour through the spaces. For being so well known worldwide, it is actually pretty small -- about a building and a half of space. Everything, literally everything, was on wheels (nice ones too). They deeply believe in the importance of physical space and its layout, and thus the ability to quickly reconfigure the room as needs change. They don't have white walls, opting for color all over. Whiteboards are everywhere -- some hang on a hook so you can leave your sketches up over time (just move your board to the back of the hook), while others are large and roll on coat rack bases. There are small, quiet team spaces and large open areas (with the ability to sub-divide them into more intimate ones). Graduate students had a little cubby area where they could store projects in progress with open lab tables in the middle of the room to use while actively working.

I plan to borrow lots of these ideas as we build out our robotics lab / Grand Challenge Design classroom this summer. Most of the concepts are low-cost, but yield a number of great ways to setup a working and learning environment. I also have to embrace the idea that design is messy, all while figuring out strategies to keep our space clean enough to use for multiple purposes throughout the day.

The student presentations followed a simple format: introduce a persona character, state their problem, walk the audience through your idea generation / sketches, present your solution (slides and a physical prototype), and explain how the solution solves the character's problem. Most students did a great job keeping slides clean and highly visual. Many also used humor throughout their presentation to engage the audience. The prototypes were not particularly high quality, but that was not the intent -- they needed to work through multiple iterations of the design to make sure that they were really solving the user's problem. For this particular project, students worked alone and they were their own user, so this step was much simpler.

The summary at the end focused on the key attributes of the course. His goal was to increase students' fluidity and flexibility with idea generation using open-ended sketches and structured activities. He gave a few assignments specifically to improve students' ability to make realistic sketches. He talked through five key habits of designers: use radical collaboration (teams of people from very different backgrounds), reframe problems in new ways, use curiosity and wonder, be mindful of the design process, and always have a bias toward action (when in doubt, start making something). He also pointed students to resources they could (and I could) continue to use: the collaboration toolkit and the rules of brainstorming. Finally, he ended with a "pinning ceremony", where all students had to find someone near them and award them with a small black pin to signify that they are now designers. It was a neat way to end a course. Even I got pinned!

After class, Andrea took me on a tour through the spaces. For being so well known worldwide, it is actually pretty small -- about a building and a half of space. Everything, literally everything, was on wheels (nice ones too). They deeply believe in the importance of physical space and its layout, and thus the ability to quickly reconfigure the room as needs change. They don't have white walls, opting for color all over. Whiteboards are everywhere -- some hang on a hook so you can leave your sketches up over time (just move your board to the back of the hook), while others are large and roll on coat rack bases. There are small, quiet team spaces and large open areas (with the ability to sub-divide them into more intimate ones). Graduate students had a little cubby area where they could store projects in progress with open lab tables in the middle of the room to use while actively working.

I plan to borrow lots of these ideas as we build out our robotics lab / Grand Challenge Design classroom this summer. Most of the concepts are low-cost, but yield a number of great ways to setup a working and learning environment. I also have to embrace the idea that design is messy, all while figuring out strategies to keep our space clean enough to use for multiple purposes throughout the day.

### Creativity and Design (Part 1 -- Del Mar High)

The final days of my adventure were spent in the San Francisco Bay Area. This part of the trip involved a heavy dose of Oliners and design-centric education. Though unusual by traditional standards, it was what I was used to from my own undergrad years. The application to K-12 was really amazing to see first-hand.

My first stop Thursday was Del Mar High, home of the Dons (interesting mascot) and my Olin friend, Becca. She is at a traditional, high-poverty school teaching physics. The quotes around the walls scream growth mindset. After greeting each student at the door, she facilitated an open-ended water wheel design activity. Teams of 3 needed to use cardboard circles, dixie cups, straws, and skewers to make a wheel. When the team poured water on the wheel, it was supposed to turn with enough power to lift a cup on a string filled with metal. The tough part was that most of the students seemed to have no idea how to deal with a open-ended design-build challenge.

It was interesting to watch Becca return student requests for help and direction with questions that prompted them along in carrying out their own design. As I interacted with some of the groups, I found it interesting how many students felt very comfortable taking the cardboard circles, attaching them to each other, and putting them on a spinning axis, but had no idea how to approach the problem of capturing water in order to make it move. Like most people, they simply avoided the hard part, hoping a teammate would figure it out.

The morning reminds me of the challenges of open-ended learning when students have been trained for years on recipe/fact/algorithm-based direct instruction. As we move towards more of these experiences for students, this becomes less of a challenge, but until then we need to invest a lot of effort into teaching strategies to students that help them create their own structure in open activities. Sets of questions (sometimes called lenses), such as "what is the most important mechanism in this product that will make it work" or "what is the hardest component to design", are the kinds of questions I ask myself before jumping into a new construction activity that give me focus and direction amongst the ambiguity. Keeping this in mind as I plan for next year will be huge if I want to be fully hands-off by the end of the year.

It was also awesome to see her school's old, abandoned wood shop. There are a number of amazing machines (a laser cutter, multiple lathes, don't get me started) and a huge open space, but since the district made cuts in their career tech programs four years ago, it became a junkyard. Becca was recruited to the team of teachers who are planning to transform the space into a modern makerspace. She will be teaching the IB Design Technology course next year in the newly renovated space. Becca's planning will be much more constrained by the IB requirements than my own planning (purely open elective), but I hope to use some of the principles of this course to add structure to my own and create enough points of overlap in the curriculum that we can work together and help each other design amazing experiences for students in both schools.

My first stop Thursday was Del Mar High, home of the Dons (interesting mascot) and my Olin friend, Becca. She is at a traditional, high-poverty school teaching physics. The quotes around the walls scream growth mindset. After greeting each student at the door, she facilitated an open-ended water wheel design activity. Teams of 3 needed to use cardboard circles, dixie cups, straws, and skewers to make a wheel. When the team poured water on the wheel, it was supposed to turn with enough power to lift a cup on a string filled with metal. The tough part was that most of the students seemed to have no idea how to deal with a open-ended design-build challenge.

It was interesting to watch Becca return student requests for help and direction with questions that prompted them along in carrying out their own design. As I interacted with some of the groups, I found it interesting how many students felt very comfortable taking the cardboard circles, attaching them to each other, and putting them on a spinning axis, but had no idea how to approach the problem of capturing water in order to make it move. Like most people, they simply avoided the hard part, hoping a teammate would figure it out.

The morning reminds me of the challenges of open-ended learning when students have been trained for years on recipe/fact/algorithm-based direct instruction. As we move towards more of these experiences for students, this becomes less of a challenge, but until then we need to invest a lot of effort into teaching strategies to students that help them create their own structure in open activities. Sets of questions (sometimes called lenses), such as "what is the most important mechanism in this product that will make it work" or "what is the hardest component to design", are the kinds of questions I ask myself before jumping into a new construction activity that give me focus and direction amongst the ambiguity. Keeping this in mind as I plan for next year will be huge if I want to be fully hands-off by the end of the year.

It was also awesome to see her school's old, abandoned wood shop. There are a number of amazing machines (a laser cutter, multiple lathes, don't get me started) and a huge open space, but since the district made cuts in their career tech programs four years ago, it became a junkyard. Becca was recruited to the team of teachers who are planning to transform the space into a modern makerspace. She will be teaching the IB Design Technology course next year in the newly renovated space. Becca's planning will be much more constrained by the IB requirements than my own planning (purely open elective), but I hope to use some of the principles of this course to add structure to my own and create enough points of overlap in the curriculum that we can work together and help each other design amazing experiences for students in both schools.

## Thursday, March 10, 2016

### A lot of thoughts on the big picture of math instruction

The topic that has been eating away at me since the day I committed to becoming a math teacher is "why isn't there more project based learning (PBL) in math?". I had seen a handful of awesome schools, but most of them did PBL everywhere except in math, that unfortunate subject that just seemed to get in the way.

Over the past couple of years, I had been moving away from my belief that it wasn't done because nobody knew how, shifting towards a different view that math was in fact something different that needed a different form of instruction. To be clear, this different form does not resemble what we do in most math classrooms now, but it isn't PBL either. My visits to High Tech High and Summit, along with my discussion with Amir at DPEA, solidified this view. I will do my best to explain what I think math instruction should be striving for. <!--Begin opinion-->

At its core, math is the study of patterns. You can look at patterns of growth and decay in a function when you discover an underlying mechanism between steps such as add 1 each time (counting, leading to a y=x equation), add 3 each time (skip counting / adding, leading to a linear equation with a slope y=3x), or double each time (multiply by 2, leading to an exponential equation y=2^x). Inverses of these core functions include logarithmic, radical, and inverse functions. Other functions include absolute value, step functions, sine waves, and many other patterns to describe how one thing changes in relation to another.

Patterns are also prevalent in Geometry. Intersections of lines create congruent angles in the same places every time. Parallel lines produce a number of identical intersections in a predictable way. Closed shapes grow the sum of their angles in a predictable, drawable way. Similarity, which is calculated through proportions, really just comes back to linear functions and the patterns discussed above.

Patterns also show up in the way you evaluate expressions. For example, 1x + 2x is similar to 1√(2) + 2√(2) and 1x² + 2x². A key rule that we rarely discuss when teaching these skills (that you must first factor the common component out, then evaluate the numberic addition) would take longer to do, but would clarify why expressions like 1√(2) + 2√(5) or 1x + 2y cannot be further simplified.

Some of the best math teaching ideas, such as 3-act lessons (http://wmh3acts.weebly.com/3-act-math.html) started by Dan Meyer and visual patterns (http://www.visualpatterns.org/) started by Fawn Nguyen, start by giving students a chance to understand a concrete situation. However, they do not stop there, instead pushing students to figure out what happens next. This may start with wild guesses, but with practice, becomes a process of figuring out the underlying mechanism of change. From here, students can test their mechanism by building out the next few steps to see if it produces what they expect. Finally, students use the growth mechanism to write an equation (such as turning "it doubles each time" into "y=2^x"). This is where observations becomes what we traditionally recognize as math, and students are armed with a powerful tool to predict far beyond what they can model in front of them (how many pennies are needed to cover the earth? or how many boxes are in step 43?). Mathematicians and people in many fields use modeling to make similarly complex predictions that they cannot easily imagine or model.

One step from this towards PBL is teachers who ask students to estimate crazy-huge numbers such as "how long of a thread would be needed to roll up into a ball of yarn the size of the earth". In these kinds of problems, students figure out some base measure, such as taking known lengths of yarn and making a ball, and taking measurements. They also look at the growth rate, so in this example, the volume grows at a rate proportional to the cube of the length. Using the starting points and growth function, along with known reference numbers such as they radius of the earth (after using dimensional analysis to convert all units to be the same), they can make their prediction in a way that they could justify and explain to others.

Another branch in the high school math picture is logic. This shows up most clearly when working with proofs in Geometry, as it is one of the few places we ask students to use generalized rules in an explicit way to make a new generalized rule. Boolean logic, the use of AND, OR, and NOT, is another place where we ask students to apply general rules to determine an outcome. When connected with probability, we can calculate the chances of one or more events occurring. Even more mathemagic happens when you introduce randomness, study the patterns present in random events, and then apply it to data collection through statistical inference.

One piece of mathematics instruction is teaching the process used to do difficult mathematics, something embodied in the idea of "productive struggle". Students need enough background to get a start in the problem and enough confidence to play with a few ideas. This is also where groupwork is highly effective, as students can bounce ideas off of each other as they try new methods of moving forward. This is different than simply plowing into a new problem and discussing when they get stuck -- it is instead a collaborative planning and experimentation process.

In my visit to Summit, I saw that one group's presentation for math class focused on this kind of group scenario. The teacher asked the group to explain the problem to the class, explain how they approached it, and walk the class through the solution (the last part looking more like a demonstration speech). After that, the group had to present on why the problem was interesting and challenging, where they struggled and how they overcame it, and what they got out of working on that problem. The problem was heavily tied to the math content they were studying, but was an application problem that reached into physics.

More generally, if you want to see how math aught to be, just go to the expert: Jo Boaler. I liked her stuff since I first came across it, but I appreciate and understand it more every day. https://www.youcubed.org/

Projects come into play when math is being applied in a more open-ended way. Ideally, this happens outside of the math classroom (science, computer science, and engineering are great places). Why? Most of the math teachers I talked to, including me, find that their students are not getting enough practice and fluency in core math skills when they spend a disproportionate amount of time on projects, causing more harm than good.

Many of the better math projects that I remember from college and witnessed this week are rooted in science or social science contexts. For example, you could study a simulation of an owl population and try to find patterns to predict the next steps. You could model a billiards ball on a computer and program in the equations that govern the system. You could calculate torque requirements for a robot. There are a host of cool things you could do, but most of the interesting ones are either covered in the "pattern recognition / estimation" above (generally a small amount of class time to complete a problem) or belong embedded in content from another subject.

---

And then there is what I do now. It is a small percentage of what is above. Our curriculum is organized topically, such as by quadratics and radicals, since that seems like an appropriate way to lay out one class of problems at a time. Given the procedural instruction method (Madeline Hunter's I do, we do, you do), it makes sense. Video-based instruction is a nice improvement: the "I do" phase is now delivered at the time and pace the student needs. Mastery-based quizzing is a fantastic improvement for this system as well: the "you do" phase is checked and repeated until the student can actually do it, rather than moving on aimlessly when the teacher decides it is time. Students working on practice in groups or collaboratively on the whiteboard makes the "we do" phase something that a teacher can monitor but students can struggle with more effectively.

I'm not sure what the place is for efficient algorithms that can obscure deep understanding. For example, I can multiply any two digit number by 11 in my head by adding the digits and making in the middle number, so 72 * 11 = 7_(7+2)_2, or 792. There are reasons why this works, but when I use this trick, I don't think about them, I just execute the algorithm. We do this more commonly with students when we use the quadratic equation, factoring tricks, "combining" like terms, and strict rules (such as "never cross out terms through addition in a fraction"). All of this helps me do math faster, and when I take an ACT, I can burn through thanks to all the algorithms I was taught over the years. (For helpful examples, see Tina Cardone's Nix the Tricks).

The balance we play as math teachers is when to ask students to generalize and derive, and when to hand out the shortcut. If you go to my YouTube channel, you will find over 500 examples of me ruining a good learning opportunity for students as I provide them with a recipe on exactly what to do next. That said, I learned with examples and procedural instruction through all of my math career. I made lots of connections along the way on my own and have a very rich understanding of mathematics as a result. Without some procedural fluency from the drill-and-kill I received, I may have never been "good enough" at math to advance to interesting new challenges or become a math teacher.

---

Given all of this reflection, this is what I am imagining for 9th grade math:

The baseline is rooted in patterns. It would give all students a chance to play in the physical world, look for growth mechanisms (and distinguish the many different underlying functions), and then predict much larger numbers in a way they can explain. Tasks for students need to have context (as in nearly all word problems), and answers should be right with justification, not just black and white. 3-acts, Visualpatterns, estimation problems, and Desmos lessons would all fit very natually in this framework.

Building on patterns is language around functions. We describe graphs with terms like "intercept", "zeros", "concave down", "region of increase", "increases as x goes to infinity", "axis of symmetry", "vertex", and others. These terms can be introduced as relevant questions are asked ("find the peak height of the projectile, which is called a 'vertex'") and further generalized with more questions that use the term differently. They could also be taught through more traditional video lectures and students could memorize them as baseline knowledge.

Algebraic manipulation through explicit form change and student's justification would form the second pillar. Students need to be able to distribute and factor linearly with extreme comfort, as it forms the basis of all that we do in algebra. x^2 + 4x^2 + 3x can be rewritten as (1 + 4)x^2 + (3)x, making the grouping rules clear. We can do the same with fractions: 1/4 + 2/4 can be factored out as (1 + 2)(1/4), making the answer of 3/4 painfully obvious rather than something potentially tricky (trying to remember the "rule" of whether or not to add the denominators). Equation-based thinking about equivalence needs to be practiced in many different forms as well, and notation needs to adapt with it. When you "add to both sides", the new term should be on the far right of each side, not lined up with the "like term", or it can lead to the appearance of new rules. Subtraction and division should be banned, instead simplifying to make all operations negative addition or fractional multiplication. Practicing this with one variable, multiple variables, multiple powers of a variable, and radicals in the same unit enable connections to be formed and skills strengthened.

Some skills, such as trinomial factoring, offer little return on investment at a young age. As students work toward Algebra 2 and advanced math, more in-depth time can be spent playing with the relationship between factoring and binomial distribution to analyze how form change can lead to new insights about an expression. We don't inspire this kind of mathematical curiosity right now since most students have no interest. I think this is not worth fighting for a while. Quadratics can be solved graphically or with a computer with a focus on purpose rather than calculation.

Throughout the course, students would have smaller numbers of problems to work on with higher levels of rigor. Communication of understanding could come through group presentations, conferences with the teacher, or written justification of work. The course would need to also assess students individually in the applied use of vocab and math notation.

I would love to see clarifying questions and push-back with everything I am saying here. The path forward is still muddled in my mind, and though it keeps getting clearer, I need a lot of help from anyone who took the time to read all of this. Please keep poking holes so I can continue to grow. Thank you!

Over the past couple of years, I had been moving away from my belief that it wasn't done because nobody knew how, shifting towards a different view that math was in fact something different that needed a different form of instruction. To be clear, this different form does not resemble what we do in most math classrooms now, but it isn't PBL either. My visits to High Tech High and Summit, along with my discussion with Amir at DPEA, solidified this view. I will do my best to explain what I think math instruction should be striving for. <!--Begin opinion-->

At its core, math is the study of patterns. You can look at patterns of growth and decay in a function when you discover an underlying mechanism between steps such as add 1 each time (counting, leading to a y=x equation), add 3 each time (skip counting / adding, leading to a linear equation with a slope y=3x), or double each time (multiply by 2, leading to an exponential equation y=2^x). Inverses of these core functions include logarithmic, radical, and inverse functions. Other functions include absolute value, step functions, sine waves, and many other patterns to describe how one thing changes in relation to another.

Patterns are also prevalent in Geometry. Intersections of lines create congruent angles in the same places every time. Parallel lines produce a number of identical intersections in a predictable way. Closed shapes grow the sum of their angles in a predictable, drawable way. Similarity, which is calculated through proportions, really just comes back to linear functions and the patterns discussed above.

Patterns also show up in the way you evaluate expressions. For example, 1x + 2x is similar to 1√(2) + 2√(2) and 1x² + 2x². A key rule that we rarely discuss when teaching these skills (that you must first factor the common component out, then evaluate the numberic addition) would take longer to do, but would clarify why expressions like 1√(2) + 2√(5) or 1x + 2y cannot be further simplified.

Some of the best math teaching ideas, such as 3-act lessons (http://wmh3acts.weebly.com/3-act-math.html) started by Dan Meyer and visual patterns (http://www.visualpatterns.org/) started by Fawn Nguyen, start by giving students a chance to understand a concrete situation. However, they do not stop there, instead pushing students to figure out what happens next. This may start with wild guesses, but with practice, becomes a process of figuring out the underlying mechanism of change. From here, students can test their mechanism by building out the next few steps to see if it produces what they expect. Finally, students use the growth mechanism to write an equation (such as turning "it doubles each time" into "y=2^x"). This is where observations becomes what we traditionally recognize as math, and students are armed with a powerful tool to predict far beyond what they can model in front of them (how many pennies are needed to cover the earth? or how many boxes are in step 43?). Mathematicians and people in many fields use modeling to make similarly complex predictions that they cannot easily imagine or model.

One step from this towards PBL is teachers who ask students to estimate crazy-huge numbers such as "how long of a thread would be needed to roll up into a ball of yarn the size of the earth". In these kinds of problems, students figure out some base measure, such as taking known lengths of yarn and making a ball, and taking measurements. They also look at the growth rate, so in this example, the volume grows at a rate proportional to the cube of the length. Using the starting points and growth function, along with known reference numbers such as they radius of the earth (after using dimensional analysis to convert all units to be the same), they can make their prediction in a way that they could justify and explain to others.

Another branch in the high school math picture is logic. This shows up most clearly when working with proofs in Geometry, as it is one of the few places we ask students to use generalized rules in an explicit way to make a new generalized rule. Boolean logic, the use of AND, OR, and NOT, is another place where we ask students to apply general rules to determine an outcome. When connected with probability, we can calculate the chances of one or more events occurring. Even more mathemagic happens when you introduce randomness, study the patterns present in random events, and then apply it to data collection through statistical inference.

One piece of mathematics instruction is teaching the process used to do difficult mathematics, something embodied in the idea of "productive struggle". Students need enough background to get a start in the problem and enough confidence to play with a few ideas. This is also where groupwork is highly effective, as students can bounce ideas off of each other as they try new methods of moving forward. This is different than simply plowing into a new problem and discussing when they get stuck -- it is instead a collaborative planning and experimentation process.

In my visit to Summit, I saw that one group's presentation for math class focused on this kind of group scenario. The teacher asked the group to explain the problem to the class, explain how they approached it, and walk the class through the solution (the last part looking more like a demonstration speech). After that, the group had to present on why the problem was interesting and challenging, where they struggled and how they overcame it, and what they got out of working on that problem. The problem was heavily tied to the math content they were studying, but was an application problem that reached into physics.

More generally, if you want to see how math aught to be, just go to the expert: Jo Boaler. I liked her stuff since I first came across it, but I appreciate and understand it more every day. https://www.youcubed.org/

Projects come into play when math is being applied in a more open-ended way. Ideally, this happens outside of the math classroom (science, computer science, and engineering are great places). Why? Most of the math teachers I talked to, including me, find that their students are not getting enough practice and fluency in core math skills when they spend a disproportionate amount of time on projects, causing more harm than good.

Many of the better math projects that I remember from college and witnessed this week are rooted in science or social science contexts. For example, you could study a simulation of an owl population and try to find patterns to predict the next steps. You could model a billiards ball on a computer and program in the equations that govern the system. You could calculate torque requirements for a robot. There are a host of cool things you could do, but most of the interesting ones are either covered in the "pattern recognition / estimation" above (generally a small amount of class time to complete a problem) or belong embedded in content from another subject.

---

And then there is what I do now. It is a small percentage of what is above. Our curriculum is organized topically, such as by quadratics and radicals, since that seems like an appropriate way to lay out one class of problems at a time. Given the procedural instruction method (Madeline Hunter's I do, we do, you do), it makes sense. Video-based instruction is a nice improvement: the "I do" phase is now delivered at the time and pace the student needs. Mastery-based quizzing is a fantastic improvement for this system as well: the "you do" phase is checked and repeated until the student can actually do it, rather than moving on aimlessly when the teacher decides it is time. Students working on practice in groups or collaboratively on the whiteboard makes the "we do" phase something that a teacher can monitor but students can struggle with more effectively.

I'm not sure what the place is for efficient algorithms that can obscure deep understanding. For example, I can multiply any two digit number by 11 in my head by adding the digits and making in the middle number, so 72 * 11 = 7_(7+2)_2, or 792. There are reasons why this works, but when I use this trick, I don't think about them, I just execute the algorithm. We do this more commonly with students when we use the quadratic equation, factoring tricks, "combining" like terms, and strict rules (such as "never cross out terms through addition in a fraction"). All of this helps me do math faster, and when I take an ACT, I can burn through thanks to all the algorithms I was taught over the years. (For helpful examples, see Tina Cardone's Nix the Tricks).

The balance we play as math teachers is when to ask students to generalize and derive, and when to hand out the shortcut. If you go to my YouTube channel, you will find over 500 examples of me ruining a good learning opportunity for students as I provide them with a recipe on exactly what to do next. That said, I learned with examples and procedural instruction through all of my math career. I made lots of connections along the way on my own and have a very rich understanding of mathematics as a result. Without some procedural fluency from the drill-and-kill I received, I may have never been "good enough" at math to advance to interesting new challenges or become a math teacher.

---

Given all of this reflection, this is what I am imagining for 9th grade math:

The baseline is rooted in patterns. It would give all students a chance to play in the physical world, look for growth mechanisms (and distinguish the many different underlying functions), and then predict much larger numbers in a way they can explain. Tasks for students need to have context (as in nearly all word problems), and answers should be right with justification, not just black and white. 3-acts, Visualpatterns, estimation problems, and Desmos lessons would all fit very natually in this framework.

Building on patterns is language around functions. We describe graphs with terms like "intercept", "zeros", "concave down", "region of increase", "increases as x goes to infinity", "axis of symmetry", "vertex", and others. These terms can be introduced as relevant questions are asked ("find the peak height of the projectile, which is called a 'vertex'") and further generalized with more questions that use the term differently. They could also be taught through more traditional video lectures and students could memorize them as baseline knowledge.

Algebraic manipulation through explicit form change and student's justification would form the second pillar. Students need to be able to distribute and factor linearly with extreme comfort, as it forms the basis of all that we do in algebra. x^2 + 4x^2 + 3x can be rewritten as (1 + 4)x^2 + (3)x, making the grouping rules clear. We can do the same with fractions: 1/4 + 2/4 can be factored out as (1 + 2)(1/4), making the answer of 3/4 painfully obvious rather than something potentially tricky (trying to remember the "rule" of whether or not to add the denominators). Equation-based thinking about equivalence needs to be practiced in many different forms as well, and notation needs to adapt with it. When you "add to both sides", the new term should be on the far right of each side, not lined up with the "like term", or it can lead to the appearance of new rules. Subtraction and division should be banned, instead simplifying to make all operations negative addition or fractional multiplication. Practicing this with one variable, multiple variables, multiple powers of a variable, and radicals in the same unit enable connections to be formed and skills strengthened.

Some skills, such as trinomial factoring, offer little return on investment at a young age. As students work toward Algebra 2 and advanced math, more in-depth time can be spent playing with the relationship between factoring and binomial distribution to analyze how form change can lead to new insights about an expression. We don't inspire this kind of mathematical curiosity right now since most students have no interest. I think this is not worth fighting for a while. Quadratics can be solved graphically or with a computer with a focus on purpose rather than calculation.

Throughout the course, students would have smaller numbers of problems to work on with higher levels of rigor. Communication of understanding could come through group presentations, conferences with the teacher, or written justification of work. The course would need to also assess students individually in the applied use of vocab and math notation.

I would love to see clarifying questions and push-back with everything I am saying here. The path forward is still muddled in my mind, and though it keeps getting clearer, I need a lot of help from anyone who took the time to read all of this. Please keep poking holes so I can continue to grow. Thank you!

## Tuesday, March 8, 2016

### Dos Pueblos Engineering Academy

After a long late-night drive from San Diego to an hour north of Los Angeles, I jumped off my AirBnB air mattress, showered, shoved down a granola bar in the car, and just made it to my 9am meeting with Amir Shaeer, the guy who started Dos Pueblos Engineering Academy (DPEA). His program is an add-on to a traditional high school: students are only with him for one period each day from 9th-11th grade, and then spend 3 hours/day in the program as seniors. Structurally, the 9th-11th grade components are comparable to Project Lead the Way (PLTW) courses, but I think their curriculum is much more engaging and rigorous. The senior year component has the complexity of FIRST Robotics, but with a full-year time scale and complete mechatronic projects for every group.

I found DPEA from a the book "The New Cool" which shares the story of Amir's FIRST Robotics team (the same league I coach with), his seniors, his mentor team, and their robot. The book positions FIRST Robotics Competition (FRC) as the next varsity football, something that fully engages and challenges students at a high level. DPEA's FRC team, #1717, has been competing for many years at a high level.

As a FRC coach and a teacher, I wanted to see how Amir and team put school and FRC together. At first, I was a little surprised to find out that last season was their last year of FRC -- team 1717 no longer exists! However, with everything Amir explained to me about their program and all that I observed, I think it makes perfect sense for them to stop doing FIRST programs as part of the classroom experience. More about that and the new senior experience later.

---

DPEA gives up creativity for technical complexity, but then goes back to add in as much creativity as possible. For example, students build a glass-rod light sculpture. Every student uses an Arduino microcontroller, a set of LED lights, glass rods, and a block of plastic as a base. They use similar wiring and controls across all projects. This greatly simplifies the teacher time required to build the project resources and teach the entire class. It also allows students to more effectively help each other. This is necessary because the skills required to do this project are high: learning and using CAD software, milling out a block of plastic with precision, cutting and mounting the rods, learning the Arduino sketch language, learning how to wire LEDs, soldering and electronics layout, and creating the logic for the controls.

However, every sculpture has a different layout pattern of rods, different colors, and different timing patterns with the lights. Even for a single sculpture, students can create multiple different programs to run different patterns as you turn the knob on the side of the sculpture. Giving students this kind of freedom doesn't distract from the technical objectives above. However, this kind of infusion of art makes the project much more engaging and appealing than some of the PLTW projects.

One thing that is particularly impressive is the gender equity of the program, both in numbers and in practice. When I pushed more on this, he said that he used to teach "Physics" and it was 50% male / 50% female. Then, he created a new title for his course, "Engineering Physics", to better reflect what he was already doing. Only two girls were in the class. To fight this, he started inviting girls one at a time from his classes to join FRC, and from this core group, continued to advertise the program to more girls. As he developed the 9-12 program, he continued to lean on the girls he already had in the program to help tell the story so more young girls would sign up. He also made sure that projects deeply integrated the arts, something that is relevant to both boys and girls, but that tends to attract far more girls toward technical work. At this point, the program is self-sustaining. In a district with 1500 kids per year, there are 300 applications for the DPEA program with 100 accepted. The qualified applicant pool has a gender profile that matches the school. More than numbers, I see girls doing every task that boys do, and doing it at the same or high levels than boys. Though some groups are clumped by gender, girls and boys are not separated in their work as they tend to do on my robotics team. It is true, complete integration.

I enjoyed reflecting with Amir on some of the differences I saw between what he does and what other PBL programs seem to do. When he told me about the FRC robots, he talked about the precision of the parts they built and why it mattered. When he talks to students, he speaks in thousandths (of an inch), even to the point where he doesn't even say thousandths (instead just saying "650" or "give me 5 more") and students know exactly what he means. Yes, this is standard for machinists to use this as a unit of measurement, but he expects precise work from everyone around him. When things don't sound right, he slows kids down to debug and find the problem, looping back to the same group many times per hour to touch base. He moves fast, but he is always precise and exact, and his students and other teachers work the same way.

This culture extends into the way the program is designed: teacher and student minutes are better utilized here than any place I have ever seen people learning. While I was here, I saw no downtime -- classes rotate between the classroom spaces so that machines and computers are always fully utilized. Teams are further split down to pairs or individuals because there is too much work to be done to do it any other way. Students are always busy. They are not always speedy, as Amir and the others slow them down to make sure they do it right the first time, but they are efficient and they are constantly learning. The learning productivity here makes my classes look like a joke.

Back to the structure: the first three years have well-planned curriculum that all students work through. By the end of junior year, students are excellent at programming a microcontroller, wiring and soldering electronics, designing a part in CAD, and manufacturing nearly anything in metal or plastic. The kinetic art project below is an amazing example of the complexity of mechanical engineering they do, something comparable to my FRC students' dream to build "swerve drive" (module pictured as well -- both use similar mechanical principles). This provides the basis for the senior project.

For many years, Amir used FRC as the senior project. It gave students in-depth experience with many of the skills above in an exciting, high energy program. However, there were only ~10 students getting the most exciting, interesting part of the design process. In a cohort of 100 seniors, many were left machining spacers and lightening parts while most of their skills sat dormant. Last year, Amir moved to a senior project called the "Physics Carosel". The was much more effective at engaging all students by getting them to work in small teams with a very complex outcome. The final integration of the components at the end took more time than expected and left some students disengaged, but this year's new version of the project hopes to solve that. Having seen this thing run right in front of me today, you would be blown away by what an incredible piece of engineering and manufacturing this is.

One of the initially discouraging parts of DPEA is the money they seem to burn through. They have a $100,000 CNC monster router, a lab with 15 lathes and 15 mills (I would kill to take just one of each), a lab with a huge CNC mill and lathe, a laser cutter, 4 huge milling machines, two labs with 30 really intense CAD computers, a bunch of 3D printers, and other toys that make a nerd really jealous. Check out this facility:

I found DPEA from a the book "The New Cool" which shares the story of Amir's FIRST Robotics team (the same league I coach with), his seniors, his mentor team, and their robot. The book positions FIRST Robotics Competition (FRC) as the next varsity football, something that fully engages and challenges students at a high level. DPEA's FRC team, #1717, has been competing for many years at a high level.

As a FRC coach and a teacher, I wanted to see how Amir and team put school and FRC together. At first, I was a little surprised to find out that last season was their last year of FRC -- team 1717 no longer exists! However, with everything Amir explained to me about their program and all that I observed, I think it makes perfect sense for them to stop doing FIRST programs as part of the classroom experience. More about that and the new senior experience later.

---

DPEA gives up creativity for technical complexity, but then goes back to add in as much creativity as possible. For example, students build a glass-rod light sculpture. Every student uses an Arduino microcontroller, a set of LED lights, glass rods, and a block of plastic as a base. They use similar wiring and controls across all projects. This greatly simplifies the teacher time required to build the project resources and teach the entire class. It also allows students to more effectively help each other. This is necessary because the skills required to do this project are high: learning and using CAD software, milling out a block of plastic with precision, cutting and mounting the rods, learning the Arduino sketch language, learning how to wire LEDs, soldering and electronics layout, and creating the logic for the controls.

However, every sculpture has a different layout pattern of rods, different colors, and different timing patterns with the lights. Even for a single sculpture, students can create multiple different programs to run different patterns as you turn the knob on the side of the sculpture. Giving students this kind of freedom doesn't distract from the technical objectives above. However, this kind of infusion of art makes the project much more engaging and appealing than some of the PLTW projects.

One thing that is particularly impressive is the gender equity of the program, both in numbers and in practice. When I pushed more on this, he said that he used to teach "Physics" and it was 50% male / 50% female. Then, he created a new title for his course, "Engineering Physics", to better reflect what he was already doing. Only two girls were in the class. To fight this, he started inviting girls one at a time from his classes to join FRC, and from this core group, continued to advertise the program to more girls. As he developed the 9-12 program, he continued to lean on the girls he already had in the program to help tell the story so more young girls would sign up. He also made sure that projects deeply integrated the arts, something that is relevant to both boys and girls, but that tends to attract far more girls toward technical work. At this point, the program is self-sustaining. In a district with 1500 kids per year, there are 300 applications for the DPEA program with 100 accepted. The qualified applicant pool has a gender profile that matches the school. More than numbers, I see girls doing every task that boys do, and doing it at the same or high levels than boys. Though some groups are clumped by gender, girls and boys are not separated in their work as they tend to do on my robotics team. It is true, complete integration.

I enjoyed reflecting with Amir on some of the differences I saw between what he does and what other PBL programs seem to do. When he told me about the FRC robots, he talked about the precision of the parts they built and why it mattered. When he talks to students, he speaks in thousandths (of an inch), even to the point where he doesn't even say thousandths (instead just saying "650" or "give me 5 more") and students know exactly what he means. Yes, this is standard for machinists to use this as a unit of measurement, but he expects precise work from everyone around him. When things don't sound right, he slows kids down to debug and find the problem, looping back to the same group many times per hour to touch base. He moves fast, but he is always precise and exact, and his students and other teachers work the same way.

This culture extends into the way the program is designed: teacher and student minutes are better utilized here than any place I have ever seen people learning. While I was here, I saw no downtime -- classes rotate between the classroom spaces so that machines and computers are always fully utilized. Teams are further split down to pairs or individuals because there is too much work to be done to do it any other way. Students are always busy. They are not always speedy, as Amir and the others slow them down to make sure they do it right the first time, but they are efficient and they are constantly learning. The learning productivity here makes my classes look like a joke.

Back to the structure: the first three years have well-planned curriculum that all students work through. By the end of junior year, students are excellent at programming a microcontroller, wiring and soldering electronics, designing a part in CAD, and manufacturing nearly anything in metal or plastic. The kinetic art project below is an amazing example of the complexity of mechanical engineering they do, something comparable to my FRC students' dream to build "swerve drive" (module pictured as well -- both use similar mechanical principles). This provides the basis for the senior project.

For many years, Amir used FRC as the senior project. It gave students in-depth experience with many of the skills above in an exciting, high energy program. However, there were only ~10 students getting the most exciting, interesting part of the design process. In a cohort of 100 seniors, many were left machining spacers and lightening parts while most of their skills sat dormant. Last year, Amir moved to a senior project called the "Physics Carosel". The was much more effective at engaging all students by getting them to work in small teams with a very complex outcome. The final integration of the components at the end took more time than expected and left some students disengaged, but this year's new version of the project hopes to solve that. Having seen this thing run right in front of me today, you would be blown away by what an incredible piece of engineering and manufacturing this is.

One of the initially discouraging parts of DPEA is the money they seem to burn through. They have a $100,000 CNC monster router, a lab with 15 lathes and 15 mills (I would kill to take just one of each), a lab with a huge CNC mill and lathe, a laser cutter, 4 huge milling machines, two labs with 30 really intense CAD computers, a bunch of 3D printers, and other toys that make a nerd really jealous. Check out this facility:

The positive story is that it is not as expensive as it looks. The cheaper lathe is a little over $1000 plus hardware. The cheaper mill and digital readout are under $2500 (see Travers Tool). A lot of the other components would need major grants, but could come with time as a program develops and the need is more obvious.

Crunching the numbers further, Amir estimates the need for $1 million of operating expenses for his 400 kids beyond the districts' $8500 per-pupil-unit funding. This averages to an additional $2500 per student to cover all consumables and the extra staffing needed to make the program go. In total, with similar teacher salaries to Byron, this adds up to $11,000 per student per year to provide them with this experience, the same funding we already receive in Byron. However, like in most places, this money is pre-allocated to district administration, staff development, and teacher salaries, leaving little margin for program expansion. I would have to spend many more hours than I already have reading through all of our district finances and getting schooled by our business manager Jenn before I could pretend to understand it. The short of it is that this is very possible to pull off, and if it was achieved by pulling in some students from out-of-district via open enrollment (additional revenue with minimal new overhead), there might be cash freed up to make something like this work.

Final take-aways: DPEA is not a full school day program (yet), but they use the few hours they have with students at an incredibly high level, blowing away any school I have ever seen. The culture is focused on excellence, high performance, and precision. The students are incredibly engaged and act like professional engineers at an exciting job (so much so, that when discussing with Amir about internships that other schools do during the school year, I told him to just stick with summer internships because it would be a let-down for students to be away from here and at a job site). From a cost perspective, what they do is expensive, but not out of control. They spend about $1000 per student per class hour in the program for the school year, something that can be raised with grants + district support + private donors. With the money saved by abandoning FRC, this becomes slightly more feasible.

I think their next steps should be the construction of an "export" institute -- a team of two people who are grant-funded to take everything they are doing now and get it out into other schools. Amir wants to disrupt college since what they are doing is better than most colleges, but by making the resources available and getting training out there, high schools could also start adopting the model. It would take teams of very dedicated people at any given district to do this, but the vision of having so many students able to design incredibly complex machines at this age is amazing.

### High Tech High

Day one began at High Tech High in San Diego. A student tour guide spend 2 hours with me at the relatively new High Tech High International, allowing me to chat with a number of teachers and students, before I gave myself another 3 hour self-guided tour of the original school. The short of it: they are doing a lot of really cool stuff in class, but culture change is the even greater accomplishment. I will talk about culture and curriculum in general here, but write a separate post to discuss just math and its role in PBL schools based on the synthesis of my first two days on the road.

International is a new, separate school about 100 feet away from the main building, part of an effort to replicate the school, slightly diversify the approach, and keep buildings small. More than anything, the infusion of the arts blew me away. There was not a wall in this place that wasn't covered in paint or projects, giving everything a home-y feeling. There was a handful of music practice rooms and small music classrooms equipped with all kinds of instruments, digital and acoustic. The painting room was awesome.

As I walked through, I couldn't help but feel like things were not tremendously different from our best classes in Byron. My guide told me about one of his favorite teachers that happened to be a start-to-end intense lecturer with hard tests, but you stayed riveted the whole time. Another teacher did lots of role plays and debates. There were whole class and individual projects all happening. Though the physical spaces were different, the differences were more at the school level than classroom level.

Students are grouped in advisories with about 5 students per grade together. They do not just get together once/week as a rallying point before dispersing off to do homework -- they chat about life together, do college visits as a group, go camping together, take out of state trips together, and just become a very cohesive unit. They rely on each other and their adviser for advice and support for non-academic things as well.

More than anything, there is a huge attitude set that everyone is going to a 4-year college. They do not force this, but they connect student's dreams and goals to the education required as young as possible and talk about college a ton. There isn't a guidance counselor, but the college adviser's office is in the middle of the building with a ton of exposure. Don't get me wrong: I think it would be bad for our nation if all high school students wanted 4-year degrees. However, if a student has the drive and skills for a certain career, it is not our place as a school to stop them, just to present the facts about true costs and benefits of higher education.

There is also much less focus on the nit-picky rules, like snacks in class, that get teachers into battles. Everyone is 100x more chill than at most schools. I never saw anyone appear tense or ready to burst all day.

One unique structural component is the one month internship all students have during January of their junior year and the externship that all seniors have for two months before graduation. This is very powerful, even if it is a bad experience at the time, since it gives students a sense of whether or not they might want to work in a given field. It is a great reality check.

Another unique piece, something that reminds me of Olin and many other awesome schools, is the limiting of course choice. PBL schools maximize choice in the classroom, but you get no say in which classroom you go to. This greatly simplifies team teaching, student scheduling (also saving counseling time for college support), and planning, though it makes in-course differentiation and personalized approaches to teaching become completely essential rather than good ideas.

---

Over in the original building, I was greeted with more of what I expected from High Tech High: clear paired teaching at all levels, projects everywhere, chop saws in half of the classrooms, tons of windows, and students building all kinds of things. Like most PBL work, there was some inefficiency in student time, with a handful of kids blocked or waiting on things out of their control at the moment, but most had something to be working on.

Many of the teachers heavily leaned on their course websites. Students created pages on the teacher's site that tracked all of the project components and deadlines. Most projects were large, 2-4 month projects, and many were spread across two traditional periods of the day (the two subject teachers working together on the project). Teachers reused as many projects as they could year-to-year, but would also switch things up just to try new ideas or improve upon past challenges in the project flow or students learning and engagement.

Teachers and students all seemed to float across the building pretty easily. Given the San Diego weather, most rooms had external doors so students could work with more space outside, but students wandered to other rooms to get what they needed without hesitation. No passes or traditional nonsense. Teachers also roamed a bit to check in with students in different areas or touch base with their team teacher. It was clear that student teams and teacher teams communicated effectively and often. It was also clear that everyone was treated with respect and trust and they wandered around.

The biggest required subject where PBL was full force was always physics / physical science. Beyond that, other sciences, social studies, then English, and finally math. Electives were often paired with required courses to maximize project flexibility.

One thing I wondered about was Special Education services. The school still has paras and SpEd teachers working with students as most schools do. More than anything, they seemed to focus their efforts on helping students manage the social and management complexities of project based learning. As an example, one student I observed was frustrated about problems he had with his teammates and with an unexpected teacher deadline. The SpEd teacher coached him through the conversation he needed to have and then went with him to see it through since the boy's story didn't really make sense. My impromtu afternoon tour guide, a SpEd student himself, told me how they helped him transform from a "bad freshman" (he didn't do homework or care about school) to the senior he now was (he appeared to be more on-task than peers when I first ran into him and was very articulate about what he was doing and learning).

The specific projects I witnessed were pretty cool, but more than anything, I think that the way students viewed their own high school education and beyond was the key benchmark that made High Tech High so cool. Students were grounded in the reality of what they could do now, but believed they could learn and do anything with effort and practice. This is the same attitude that fueled me my entire life, and to see that in other young people cut across gender and racial lines is really awesome. The school uses PBL as an important tool, but it is NOT their "why". Instead, they focus on students' growth and future opportunities and provide all students equal access to an excellent education.

## Sunday, March 6, 2016

### The Journey Begins

This week, I'm coming off of an intense FIRST Robotics build season and Duluth Regional and making a tight transition to a trip that I had been dreaming about for the past 7 years -- visiting a number of the schools that I consider to be the most amazing in the country.

As I was designing and officially proposing a new 2 credit course, Grand Challenge Design, that I plan to teach next year, I found myself left with too many questions. The course is designed to give students immersive experiences working in a design team, partnered with a non-profit organization or individual who has a challenge to be solved. From there, teams will define the underlying problem they observe from their field work, invent new solutions, and iteratively test them with their clients until they successfully solve the problem.

I have a lot of experience to draw upon from my experiences with Olin College, Future Problem Solving, the Grand Challenge Scholars Program, and FIRST Robotics, but I also knew that there were passionate teachers all around the nation who already successfully adapted many of the ideas I was pursuing for the high school level. Sometimes I can be an inventor, but if it helps me make school awesome as quickly as possible, I would rather just be a thief. Thus, my dream to go see a number of awesome schools I had been collecting in my mind for years was rekindled.

After making my dream list, most of the schools I wanted to see were clustered in Southern California and the Northeast, leading my initial plan to consist of a two week trip that spanned both coasts. Knowing that our professional development budget was tight, I never considered asking for travel reimbursement, choosing instead to self-fund and just keep costs low. Despite this, the plan was shot down on the grounds that missing two weeks of block classes in the middle of the school year would be very harmful to students' learning. Though I didn't like this answer, it was fairly true. I scaled back the plan to the highest concentration area, a stretch from San Diego to the Bay Area, and received approval for a 5 day journey.

Once the plan was cleared, I started reaching out to my list to solidify visit dates. Rejection after rejection, I was not only annoyed but terrified that with all the approvals in place, I would have no where interesting to go. On a whim, I reached out on Facebook where my Olin College and other friends offered support in droves. Suddenly, I had an "in" everywhere with direct invites from close friends of teachers and school directors. Who knew that engineers could be so connected in education?

THE PLAN:

Monday 3/7: High Tech High (HTH) in San Diego.

HTH is a powerhouse in the project-based-learning (PBL) world, known widely for its highly interdiscinplinary approach to teaching and ability to get students working in teams beyond the classroom. I look to draw on my PBL experience at Olin and PBL training from the Buck Institute as I see how it all comes together and works at a public high school.

Tuesday 3/8: Dos Pueblos Engineering Academy (DPEA) in Goletta.

Monday night, I will rent a car and drive 5 hours north to Goletta, just past Los Angeles. Here, I will meet Amir Shaeer and his students at DPEA. The academy started as a few add-on classes for high school students that formed a hands-on sequence to spark a passion for engineering and provide students with the prerequisite skills to succeed in the field. The capstone project for seniors was designing a robot for the FIRST Robotics Competition, the same league I compete in with students in Byron. I am excited to see how Amir and team weave FIRST into an immersive and engaging curriculum for students during the school day.

Wednesday 3/9: (probably) Summit Public Schools, Facebook, and Alt School (Bay Area).

Tuesday night, I will get up near San Jose where I will begin to crash with a number of my Olin friends. Due to the very high concentration of amazing places between San Jose and San Francisco, I plan to double and even triple-up my meetings to squeeze all I can out of my time there. Unless I flip days with Nueva, I will start the morning visiting one of the Summit schools, a public high school that invests deeply in personalized learning. They partnered with Facebook to build out new software tools to manage this process of personalization. I hope to meet over lunch with some of these engineers to better understand the philosophy behind this tool. Finally, I'm planning to head up to Alt School, a private school founded on the idea of personalizing learning for all students in an open-ended, hands-on way. Operating more like a tech start-up than a school, they have a dedicated team of engineers whose full-time job is to build the systems that makes all of this work seamlessly. Finally, I plan to end the night visiting some Olin friends working on an early stage business incubator for education-focused start-ups. This will easily be my most exhausting day.

Thursday, 3/10: (probably) Nueva School and Singularity University (Bay Area)

One of the most amazing schools with a very strong reputation for excellence is the Nueva School. I am thankful that an Olin alum is managing their makerspace on campus. I am hoping to see how they mix traditional high-intensity academics with open-ended learning experiences in a well funded private-school setting. I know many things won't easily transfer to the Byron Public Schools budget, but the approaches and ideas surely will. In the afternoon, I am visiting an old friend who co-planned a sister cities youth conference with me back in high school. He is now working with an organization that tries to bring together some of the most talented minds to work on very challenging problems together. I am excited to see how advanced students are pushed and stretched in this new school.

Friday, 3/11: Design Tech (d.tech) and Stanford's d.School

On the last day of the trip, I am 100% focused on design. This will likely be my favorite day, as everything I know about d.tech makes me think that it is Olin College for the high school level, the goal I have been working on since deciding to become a teacher. I will round out the day with a visit to the real flagship of design education, the d.school at Stanford. Between the two, I hope to figure out a solid model to work from with my Grand Challenge Design course next year.

This week is going to be awesome. Though I have a grueling schedule and will still have fires to put out at home, I plan to stay disciplined by taking a crazy number of photos and blogging every day, maybe more, as I process and reflect in real time. I'm excited to also mix in reflection from an awesome robotics season, something I have had no chance to mentally process and reflect upon quite yet. Perhaps my long drives early in the week will give my brain a chance to put some of this to words as well.

There are a lot of details of the plan yet to be worked out, so it will be a true adventure with plenty of audibles along the way. I'm hoping and planning for wonderful conversations, crazy new ideas, and lots of excitement. Here it goes!

As I was designing and officially proposing a new 2 credit course, Grand Challenge Design, that I plan to teach next year, I found myself left with too many questions. The course is designed to give students immersive experiences working in a design team, partnered with a non-profit organization or individual who has a challenge to be solved. From there, teams will define the underlying problem they observe from their field work, invent new solutions, and iteratively test them with their clients until they successfully solve the problem.

I have a lot of experience to draw upon from my experiences with Olin College, Future Problem Solving, the Grand Challenge Scholars Program, and FIRST Robotics, but I also knew that there were passionate teachers all around the nation who already successfully adapted many of the ideas I was pursuing for the high school level. Sometimes I can be an inventor, but if it helps me make school awesome as quickly as possible, I would rather just be a thief. Thus, my dream to go see a number of awesome schools I had been collecting in my mind for years was rekindled.

After making my dream list, most of the schools I wanted to see were clustered in Southern California and the Northeast, leading my initial plan to consist of a two week trip that spanned both coasts. Knowing that our professional development budget was tight, I never considered asking for travel reimbursement, choosing instead to self-fund and just keep costs low. Despite this, the plan was shot down on the grounds that missing two weeks of block classes in the middle of the school year would be very harmful to students' learning. Though I didn't like this answer, it was fairly true. I scaled back the plan to the highest concentration area, a stretch from San Diego to the Bay Area, and received approval for a 5 day journey.

Once the plan was cleared, I started reaching out to my list to solidify visit dates. Rejection after rejection, I was not only annoyed but terrified that with all the approvals in place, I would have no where interesting to go. On a whim, I reached out on Facebook where my Olin College and other friends offered support in droves. Suddenly, I had an "in" everywhere with direct invites from close friends of teachers and school directors. Who knew that engineers could be so connected in education?

THE PLAN:

Monday 3/7: High Tech High (HTH) in San Diego.

HTH is a powerhouse in the project-based-learning (PBL) world, known widely for its highly interdiscinplinary approach to teaching and ability to get students working in teams beyond the classroom. I look to draw on my PBL experience at Olin and PBL training from the Buck Institute as I see how it all comes together and works at a public high school.

Tuesday 3/8: Dos Pueblos Engineering Academy (DPEA) in Goletta.

Monday night, I will rent a car and drive 5 hours north to Goletta, just past Los Angeles. Here, I will meet Amir Shaeer and his students at DPEA. The academy started as a few add-on classes for high school students that formed a hands-on sequence to spark a passion for engineering and provide students with the prerequisite skills to succeed in the field. The capstone project for seniors was designing a robot for the FIRST Robotics Competition, the same league I compete in with students in Byron. I am excited to see how Amir and team weave FIRST into an immersive and engaging curriculum for students during the school day.

Wednesday 3/9: (probably) Summit Public Schools, Facebook, and Alt School (Bay Area).

Tuesday night, I will get up near San Jose where I will begin to crash with a number of my Olin friends. Due to the very high concentration of amazing places between San Jose and San Francisco, I plan to double and even triple-up my meetings to squeeze all I can out of my time there. Unless I flip days with Nueva, I will start the morning visiting one of the Summit schools, a public high school that invests deeply in personalized learning. They partnered with Facebook to build out new software tools to manage this process of personalization. I hope to meet over lunch with some of these engineers to better understand the philosophy behind this tool. Finally, I'm planning to head up to Alt School, a private school founded on the idea of personalizing learning for all students in an open-ended, hands-on way. Operating more like a tech start-up than a school, they have a dedicated team of engineers whose full-time job is to build the systems that makes all of this work seamlessly. Finally, I plan to end the night visiting some Olin friends working on an early stage business incubator for education-focused start-ups. This will easily be my most exhausting day.

Thursday, 3/10: (probably) Nueva School and Singularity University (Bay Area)

One of the most amazing schools with a very strong reputation for excellence is the Nueva School. I am thankful that an Olin alum is managing their makerspace on campus. I am hoping to see how they mix traditional high-intensity academics with open-ended learning experiences in a well funded private-school setting. I know many things won't easily transfer to the Byron Public Schools budget, but the approaches and ideas surely will. In the afternoon, I am visiting an old friend who co-planned a sister cities youth conference with me back in high school. He is now working with an organization that tries to bring together some of the most talented minds to work on very challenging problems together. I am excited to see how advanced students are pushed and stretched in this new school.

Friday, 3/11: Design Tech (d.tech) and Stanford's d.School

On the last day of the trip, I am 100% focused on design. This will likely be my favorite day, as everything I know about d.tech makes me think that it is Olin College for the high school level, the goal I have been working on since deciding to become a teacher. I will round out the day with a visit to the real flagship of design education, the d.school at Stanford. Between the two, I hope to figure out a solid model to work from with my Grand Challenge Design course next year.

This week is going to be awesome. Though I have a grueling schedule and will still have fires to put out at home, I plan to stay disciplined by taking a crazy number of photos and blogging every day, maybe more, as I process and reflect in real time. I'm excited to also mix in reflection from an awesome robotics season, something I have had no chance to mentally process and reflect upon quite yet. Perhaps my long drives early in the week will give my brain a chance to put some of this to words as well.

There are a lot of details of the plan yet to be worked out, so it will be a true adventure with plenty of audibles along the way. I'm hoping and planning for wonderful conversations, crazy new ideas, and lots of excitement. Here it goes!

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