All models are wrong but some are useful

Rumination from MPX10 from the week of Aug 31
On the Values and challenge of models

As we explore and set our projects and experiences around the big theme of climate change this year in our 10th grade exploratory classes, I am continually designing into our experiences the important framework of modeling. It is no surprise to me that the latest versions of the Next Generation Science Standards (NGSS) and the Math framework in the common core (here) emphasize heavily the importance of the generation, exploration and elaboration of modeling, and more particularly mathematical modeling. When we ask learners to work with models, we push them to deepen, extend and anchor their understanding of relationships between variables: position and time, force and acceleration, parts per million of carbon and global average temperature, really any defined system of interest. 

In our class this week we have been working on the mathematics of linear expressions and the physics of Constant motion (broader target: developing the language and understanding an engineer needs for looking at transportation). As a means to deepen our understanding of the modeling of constant motion (broadly leaning of the work of the modeling pedagogy of ASU) we generated experimental data (position and time) of the motion of 2 battery powered cars that move at different speeds. From that data the students use a modeling tool (in our case the wonderful *free* Graphical Analysis App from vernier software http://www.vernier.com/products/software/ga-app/) to create a mathematical model for each car.

position time graphs for the two battery powered cars

position time graphs for the two battery powered cars


The culminating activity was a predictive model session. The students were given a scenario (the red car starts 7 seconds ahead of the green car) and needed to use their models and data to try and predict when the faster green car would catch the red car. The first pass at this activity generated a LOT of conversation, questions and difficulty for the students as they moved from superficial understanding to deeper meaning making.

Students brainstorming in teams

Students brainstorming in teams

This kind of learning in our class provides so many layers of learning. It challenges students to truly show they understand the models they have created. It gets to the heart of experimental  science in designing experiments that generate meaningful and reliable data. It requires students to be active – to analyze, explain, predict and defend their work. Importantly it starts to replace naive thinking of the real world with internally constructed models that real scientists use to observe and understand phenomena. Oh – and it is fun!
In the process of planning for our modeling I found a great quote from statistician George E. P. Box  “all models are wrong, but some are useful”.  In order to appreciate the power of this statement my goal is to nurture a real awareness and appreciation for modeling as well as its limitations. 

Putting together the puzzle

For Laura, my co-teacher, and I, we are working towards better laying the foundation for why we need to look at alternatives to lifestyle choices we take for granted in the context of climate change, and the even greater issue around sustainable lifestyles. Since much of our work will focus around energy and transportation, we thought a trip to the power plant at Waiau would give us an opportunity to have the students start grappling with energy and sustainable living. The students did preliminary readings and outdoor walks to look at the ways that electrical energy is both made and brought to our homes, schools and businesses. The trip then served as an opportunity to see both the marvelous engineering that goes into building something on that scale, as well as the inherent challenges given the way the world is heading. Some pictures from that trip here:

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when we came back, we ask them in teams to generate responses to a three, two, one bridge thinking routine – three thoughts, two questions, one analogy. This gave them a chance to both reflect and broaden their thinking about their experience today. More to come…

A counting we will go…

A counting we will go!

The school year has started off, and we are already a week into class. I spent some time trying to think of a kickoff activity that would both give students a chance to collaborate, problem solve, do some mathematical thinking, and do it in the context of an interesting problem. I ended up settling on the idea that there are more stars in the universe then there are grains of sand on all the beaches of Earth. The students started off by looking at this short video from Hubble of a slice of the Andromeda galaxy:

Then we launched into the activity – they were put into teams of three, given a 1 L jar of sand, and asked to come up with a method, measurements, and calculation to give their best estimate of how many grains of sand were in the jar. Some of the pictures from that activity here:

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Surprisingly (or maybe not much so) even though there were a wide range of methodolgies put into place, most student groups came up with a fairly consistent number in the range of one to one and a half million grains of sand. Of course, if we extrapolate that to how many stars are in our galaxy, it would take something on the order of 200,000 L of sand to approximate the number of stars in our galaxy. This is about the size of a small swimming pool. The final kicker is that there are as many galaxies as there are stars in our galaxy. So, you would need a swimming pool full of sand for each grain of sand in the swimming pool – certainly seems to be more sand than you could put on all the beaches of Earth.

All in all, the activity went well, and students were both challenged to think and explain about their mathematical calculations, as well as a deeper sense of appreciation of everything from the size of the galaxy, to the importance of scientific notation and exponentials.

We Have to Stop Pretending

In response to Scott McLeod’s Challenge to answer “When it comes to education, what are 5 things that we have to stop pretending?”

When it comes to education, we have to stop pretending…
– real learning cannot be fun and purposeful
– students only learn when an adult controls the experience
– it is impossible to integrate subject areas meaningfully
– time for faculty collaboration should be the last priority
– 21st Century (Deeper learning) competencies should be taught outside of specific content standards

#makeschooldifferent

Keep it Real – Reflections on Learning so Deep that it hurts…but in a good way

On the plane heading back from #deeperlearning 2015, ruminating on that experience, thinking about the Book “Show your work” by Austin Kleon (thanks Ramsay Barnes) and looking back over the last couple of weeks of my students’ work.

A few thoughts on the Deeper Learning 2015 experience. (This was my third year going so I was one of the few “threequel” attendees). So many good things here, but maybe the focal point could be Rob Riordan’s (High Tech High’s “emperor of rigor”) reminder to us of Rob’s Rules of Rigor:
There is no rigor without –
• engagement
• ownership
• exemplars
• audiences
• purpose
• dreams
• FUN!

The conference experience typified this, with a powerful, engaging keynote on Day 1 from Chris Emdin (@chrisemdin) who delivered a thoughtful, energetic and passionate exploration of “Reality Pedagogy”. He pushed us to stay true to ourselves and our motivations that brought us to education and made a passionate case for meeting our students where they are at – as bright, motivated learners. A few quotes from his talk:

“The Masters Tools will never destroy the Master’s House”

“Ground Zero for Changing the world is teachers…dig deep and dig out!”

“You just can’t wake up and deem yourself culturally relevant.”

“If you say that education is the civil rights issue of our time, then you better teach it in a civil rights manner in your classroom!”

Wednesday Night we watched a film “Most likely to succeed” which looked at the education system historically and made the case the school transformation in deeper learning practices is the best way to prepare students for their future. It both looked wide at cognitive science and the facts around educational succeed, but also followed a few students at High Tech High through school year, documenting their challenges and successes in a real Deeper learning experience. MUST. SEE.

Thursday I ran a 4 1/2 hour deep dive based on our year long project investigating sustainable transportation through understand, designing and building electric bikes (a little more about that work below). I had 12 eager, talented and diverse colleagues (teachers and students!) and we spent the day exploring riding and designing around the bike experience. Their artifact presentation at the end of the day was exciting because it showed the diverse ways they approached deepening their understanding of this work. I am still collecting pictures of the day, but I am posting them here: https://flic.kr/s/aHsk9Uk3JT. The webpage that holds the resources the dive are here: https://sites.google.com/a/hightechhigh.org/dl2015materials/deep-dives

The real power of this meeting of the minds was just that – meeting, laughing, talking, sharing with like minded passionate practitioners with deliberate intent to understand and support our work together.

The work over the past couple of weeks in my classes points towards these rules of rigor. In MPX two projects are reaching their conclusion: the Math and Art project has been in the holding phase as I have been working toward getting permission to exhibit the student work on the exterior walls of the Hartley complex. Back when we designed this three building complex, we had planned to place provocative, fun engaging art and exhibits through it, but these items were cut from the budget and never brought back. It has been in my planning for years to get exhibits posted into this space and this project is the perfect place to start. The students created art, created math models of their art and elaborated on their learning – three examples below:

Kendall"s Math and Art Poster

mahina's math and art poster

Brianne's Math and Art poster

At the same time, most of our bike groups now have operational electric bikes! This project which took two months longer than planned (hey, who said doing real work was easy or fit neatly into a box?) had students explore everything from torque and rotational mechanics, to forces and motion, to electricity and magnetism, to air pressure, to climate change. The ultimate goal will be an auction in May with the proceeds going to a charitable cause that supports our work. The class flickr site https://flic.kr/s/aHsk1yMvRc has photos through the whole process, but here are three slides from my presentation at Deeper learning that show different stages in development. They don’t show all the formative assessments and knowledge construction that were necessary to accomplish this project, but you can certainly see the active role of the students in their work and learning:

moving from idea to construction

moving from idea to construction

learning to repair bicycles

learning to repair bicycles

looking at circuit design

looking at circuit design

Last example of “Keep it Real” is the work from our Innovative Design Technology Class. Our latest project challenged the students to propose, design, develop and complete a project of their choosing. Students projects included
researching, designing and building an athletic shoe,
3-d scanning and 3-d printing a mounted owl for curation and designing as mascot gifts
programming and wiring a raspberry Pi and stepped motors to make a camera shoot rig.
storyboarding and designing a mobile app that would gamify trash collection to increase involvement in cleaning up the community.
Some slides on that below, but what was clear was that students more than not dove in deeply and generated something of value through their interests and passions.

koa's canvas design on motion and  dance

gian's show making process

gian's shoe finished

Erika's design sketches

Erika's Hiking Bag design

These projects and the resulting student learning are not perfect, but when I look at Rob’s Rules of Rigor, I see many of the elements he defines in this work and that encourages me to “Keep it Real”

Mastery learning and the role of formative and summative assessment (aka: Wait….What? How much do you charge for that?)

I was having a conversation with my fifth grade colleagues yesterday as they are preparing for their students to present their capstone projects. I have been working with a couple of boys as a mentor for their work in understanding atomic structure – both what happens with the electrons around atoms, as well as what’s going on at the nuclear level – their work is amazingly deep and meaningful. But I digress…

In thinking about what the final assessment for their capstone presentation should look like, we got into some deep conversation about their final presentations, how those could be assessed to judge learning, and the importance of the learning path that occurred and the artifacts that the students are collecting as they move towards this final assessment. One of the challenges we were conversing about was the importance of formative feedback, and the opportunity that these pieces allow for feedback and reflection as well as the final presentation which provides an opportunity for feedback as well.

As we were talking, it reminded me of the story from good friend Dr. Phil Bossert at the HAIS office. He was at a resort on the Big Island and during a special event, a well-known local artist created a landscape painting while chatting with guests over the course of an hour or so. At the end of the conversation, the painting was done and was really beautiful. When the guests asked how much he would charge for the art, he responded $6000. Some people were surprised and asked how he could charge that much if it had only taken him an hour to create it. He responded by explaining that had not taken him an hour to paint it, it had taken him a lifetime of honing his skills so that he could create it the way that they had seen.

In much the same way, we often look at final presentations of learning as the only evidence of what has occurred, often forgetting the amount of enormous effort that goes into drafting, research, feedback loops, trial and error and the myriad of other ways our learning takes us before we get to the final exhibition. These presentations are often high-stakes affairs in that a 10 to 20 minute presentation can be worth a considerable amount of student’s grade. As teachers, we have sat with and talked with the learners as they have walked through the whole process, and in my opinion, if we have done our job right we have assessed and expected students to maintain clear and meaningful artifacts along the journey so that the story of their knowledge building is more fully told. Let me give you an example:

One of the projects that my students have worked on has been to create artwork under the guidance of the visual arts teacher. They have researched a particular style – Cubism and after creating their art were challenged to re-create it using mathematical functions in a online mathematical modeling software called Desmos. We are just at the culmination of this work where the students are going to create a art opening that showcases their artwork, their mathematical representations, and a written narrative that explores this range of knowledge building. One example of this work is from Justin:

Justin's Math and Art Work - look at the functional representations he has used to create this!

Justin’s Math and Art Work – look at the functional representations he has used to create this!

We had a visitor from Greenwich High School in Connecticut, Brian Walach and Justin showed him this work. He was pretty impressed with what he saw, and inquired how much time Justin had put into a mathematical functions that represented his art. Justin replied that he’d spent over 80 hours – most of it of his own volition tweaking and massaging functions to make them work to produce a close replica of his lines and curves. When Brian asked him if he had been required to spend that much time, Justin explained that he had been driven to want to get it right – and had been willing to put in the time to took to understand the mathematics, and then create the final product. In much the same way that a driven artist or craftsman will work ceaselessly to hone their skill so that their work is their best representation of their abilities, when we’re designing great projects, we provide opportunities for students to dive in deeply and experience the pleasure, passion and yes, pain of working until it is right. As the adult who has been given the opportunity and challenge to assess learning, it is important to consider both the path and the product if we are to best determine the learning that has happened. Sometimes, the end product is just the tip of the iceberg and we do a disservice without thinking about the path the student has taken to get there. Malcolm Gladwell talks about the research that it takes 10,000 hours to become an expert in many fields. There is some debate about if this is an absolute requirement, but I think we can all agree that it takes dedicated time for anyone to become a true master craftsman in any field.

If we can create situations in our classrooms where students spend this time because they feel it is their urgent need, and less that they will be punished if they don’t, I know we would engender a more fully engaged, responsible and healthy learner.

Paint and Learn by Numbers (Flowers are Red, Young Man)

A car trip to the airport with my older “Hanai” son Jim today led to my ruminating about the joy, struggle, and emerging clarity about trying to design and implement real-world learning for mathematics and science in my MPX 10 classroom. In trying to explain the difference between traditional pedagogy and constructivist, learner centered environments, I was trying to come up with a metaphor for why so many students think they’re not mathematicians, when conversing with them makes it clear that they are clearly mathematical thinkers, but they don’t fit into traditional mathematical (or science for that matter) classrooms. As I was trying to come up with a way to differentiate this struggle I am having, it occurred to me that one analogy/metaphor that worked for me (your mileage may vary) was the difference between painting by numbers, and creating art.

Imagine a classroom where the goal of the classroom was to fill out increasingly more difficult paint by number drawings, each one very prescriptive in both how to do it, and what the outcome should look like. Cognitively, the student requires very little effort to accomplish the task, and at the and they have a piece of art that more than not looks like the learning target that was intended. The assessment wouldn’t be the quality of thinking that went into the artwork, but more a case of how well they match filling in the shapes neatly inaccurately according to the schematic in the plan. An example might look something like this:

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(from http://www.davidkhurst.com/wp-content/uploads/2013/09/FRS-Paint-By-Numbers_1.jpg)

Think about a classroom that would use this as a means to teach kids about art – everyone would be clear about what they were “learning”, assessment would be a process of conformity – no allowed color changes or going outside the lines and if you don’t cause trouble, you have to do very little real thinking. You might think yourself “why can’t I create these instead of do someone else’s”, but that’s not the goal of the class, is it? And ultimately, if you were to ask a student to paint an elephant or even more heretical she paints something of their own idea, they would not really know how to even begin to take into account color, shading, perspective, foreground and background, or any of the other things that are part of an artist’s repertoire of thinking, habits of mind, and tools. If a student were to become an artist, it would likely be in spite of their experience, not because of it.

I am struck by the sense that much of what we do in math and science education has a fairly direct corollary. The work we do in math and science classrooms, at least the ones that I attended when I was in school, and that I still still think are fairly prevalent in most students’ experiences is a paint by number approach. The unit of instruction starts with more than not a particular kind of problem or learning target (we are going to learn Newton’s Laws, we are going to learn how to find the slope of the line) and then the approach is a very linear sequential already mapped out method to get to the intended answer – the giraffe. This would be fine if the goal was to teach kids how to do math or science by numbers, but I’d venture to guess that it does little to create a sense of being a mathematician or scientist, and does not engender a sense of action, engagement, or application of any of the ideas, because they are not connected to anything but the painting with the numbers itself.
In our science department meeting in thinking about how we are going to implement next-generation science standards (NGSS) one of the ideas we agreed on was the importance to move from science facts – memorization and shallow learning to having students involved in more of the process of learning and bringing engineering into the work so they understand how what they’re learning can be applied. One of my colleagues mentioned that research shows that as students move from elementary to middle and high they begin to move away from their curiosity and the number of questions they can generate about phenomena and instead start to just become task oriented around lower-level work. Ken Robinson tells this wonderfully in his books “Out of Our Minds” and “The Element”. If our classrooms are paint by number classrooms, it’s hard to imagine that we would create any other condition than this.

If we want to create artists, we can’t do paint by number, we need to have students develop the eye, the mindset, the language and the work of real artists. In much the same way, in our math and science classrooms, we need to re-think and purpose our energies around creating classrooms in which we don’t give students work sheets or repetitive problem sets, which are the equivalent of paint by numbers, but instead design and challenge our students to investigate, create, reflect, collaborate and implement artifacts that show the work of a mathematician or scientist. If our classrooms already have a fixed outcome and there is no energy, creativity and even mystery around what we might end up with in the process of exploring our field of study, then we are doing no better than paint by numbers.

All of this thinking made me remember a marvelous song by Harry Chapin that I’ve known for over 30 years, but just came back into my thinking while I was ruminating about this issue in my classroom and everyone’s learning environment.
If you’re not familiar with it, I hope you find it is relevant, sad and insistent about re-thinking our classroom environments as he intended it to make us consider over 40 years ago.

Frameworks, models and structuring learning

It’s been a few weeks since the last post, – not an indication of little happening, but more a case of a flood of activity that’s been hard to sit down and organize and share.
Certainly the photo streams that I post on Flickr have been updated regularly:

For the design class here: https://www.flickr.com/photos/121697751@N02/sets/72157646692621755/
For the MPX stem class here: https://www.flickr.com/photos/121697751@N02/sets/72157646271766017/

It’s late on a Friday already, but it’s worth sending out a few ideas about what we’ve been working on – things have been exciting and reaching some interesting points in our work.

One of the things that is clear is that in both of the classes that I’ve been working with, the need for structure around the things we’re learning is clear and fits well within our understanding of how we learn science around us – if we can develop effective, simple and applicable models of the way things behave, then it makes them easier to apply an understanding novel situations.

STEM

The big activity we have been working towards has been building electric bikes – not a ready-made kit with easy to attach parts, but the nitty-gritty and get your fingernails dirty kind of building that involves identifying parts that put together would allow a cheap, effective and creative way to provide urban transportation. In order to get to this, a fundamental understanding of electricity and magnetism are necessary so that when we are connecting these industrial grade parts we have an appreciation of things like voltage, current limits, parallel and series and their role, why wires have different gauges… Etc.

In order to set the foundational knowledge for this, we needed to have a good working model for understanding electricity. Back in my modeling experiences from the 1990s, I was introduced to CASTLE (Capacitor-Aided System for Teaching and Learning Electricity) approach to learning electricity which was developed by Melvin Steinberg of Smith College and uses a compressible fluid approach to understanding how charge flows in circuits ( a brief description of the curriculum and its rationale here:http://www.pasco.com/prodCatalog/EM/EM-8624_castle-kit/ ). I really believe in this kind of structured but constructivist approach to building an understanding of circuits, charge flow, and a functional understanding of what’s going on with electrical devices, so we’ve been using this to build our foundational knowledge as we have been unpacking our kits.

This week we reach the culminating point where the students started hooking up the parts of their electric bike kit and needed to learn everything from the correct schematics to hook it up, to stripping wire and crimping connectors to make things fit together correctly – a lot of this was new to me working with the scale of items and it was both exciting and challenging to make sure the students were able to work on these ideas. By the end of class today, Friday, two of the five groups had connected the parts together and successfully got their motors working through the controller and the throttle – success! There are more pictures of the Flickr site, but here’s a few pictures below. Next week, we get to the really challenging work – how to put these parts on a bicycle so that it is powered and can be used to transport students across our campus.

Students working with their electric motor kits

Students working with their electric motor kits

click here for a movie of a groups working motor

Another group grapples with putting together their components

Another group grapples with putting together their components

All students were required to create a schematic diagram that showed the correct connections between the components for their electric bike

All students were required to create a schematic diagram that showed the correct connections between the components for their electric bike

Defense of understanding of circuits and charge

Defense of understanding of circuits and charge

Students defending their understanding of the circuits and charge flow

Students defending their understanding of the circuits and charge flow

Innovative Design Technology

We finished the first large project and shared designs a few weeks ago, and so we wanted to give the students a few smaller challenges to give a little more variety to the design work that they have been developing. As a result, we chose a roundtable activity where we let them determine categories where design might be interesting and applicable to address real-world problems. Eight different teams ended up choosing problems with either steering wheel redesign for cars, or looking at recycling as a opportunity to think about how design could improve people’s behaviors in the process. I have attached a couple of the slide presentations in PDF format, and one of the challenges continues to be to make sure that there is good science rigor underneath the work that they are doing – in the case of their work in this round, students investigated thermodynamics, heat transfer of different materials, ergonomics as they looked out the ways in position that people hold wheels, the different kinds of plastics that exist and the ways they are recycled, and how temperature can be measured by a variety of means.

As we use our design thinking to approach problems, it becomes a really useful framework for learners to consider both what they know, how to identify a problem that needs to be solved, and a process to get to the end. We have actually looked at a couple of different models for design process – including this week how the Wright brothers attacked building the first airplane, and how engineers approach building design. The design framework becomes a means to look at problems, to think about what we know it but we don’t know, and how to quickly generate possible solutions and test them. Some pictures below as well as the presentations from this last round of work:

PDF Presentation sam audreen erika

Steering Wheel Keynote_Koa, Marshall, Sam

Prototype creation

Prototype creation

Scaling ideasFrom computer-generated models to working size

Scaling ideasFrom computer-generated models to working size

Construction with cardboard for the prototypes

Construction with cardboard for the prototypes

Opening slide from another group talking about their chair process

Opening slide from another group talking about their chair process

Students defend their chair design to the class

Students defend their chair design to the class

So much to talk about, and so I’ll try to blog more frequently over the next few weeks as we reach some culminating points in our work…

A week of construction and reflection

Well, here we are eight weeks into the semester. What are we up to these days? And for that matter, what’s on my mind about our work?

Let’s start with interacting with text for meaning. We often in education asked students to read text to acquire new terms and concepts, to expose students to different opinions and to consider different perspectives and approaches. This week in the design class the students were reading some different articles on the importance of ergonomics as they go through the process of designing, prototyping and testing their chair designs.
As I was looking through their notes, there was a wide gap between some students and others. As I was thinking about the role that these notes played, I realized I was having the students take the notes to deepen their understanding of the field, but I wasn’t really having them interact with their own thinking enough. Below are a couple of pictures of work I considered exemplary because they show students not just taking down ideas, but organizing, reflecting and sketching to try and deepen their meaning.

Matt's Sketches on good ergonomics

Matt’s Sketches on good ergonomics

notice Samantha's interaction with her own text

notice Samantha’s interaction with her own text

some of samantha's notes

some of samantha’s notes

notice how matt organizes through color and offsetting text

notice how matt organizes through color and offsetting text

There are certainly many ways to go from this initial data mining activity to more meaning. I realized I wasn’t doing enough to have them consider their own work, so I asked them to go back through their notes and highlight three important concepts and two areas where they felt that they didn’t really understand the ideas fully and annotate those in a way so that we could talk about what they learned and what they still have questions about. I also debated whether having them do a think pair share activity would be helpful so they could talk about that – I plan to have them do that when they come back together with me next class period. All of this is tied to working towards creating a more reflective process in their learning. Their blogs are another element in doing this.

As a part of the design class we have been working on re-designing the student chair experience. They have created designs in sketch up make:

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They have been working on printing these in our 3-D printers, which added another layer of technology to this project. The last step is to create a full scale prototype out of cardboard. I realize that most of them have not made a full model out of cardboard before so to get them warmed up, we had them research ways to work with cardboard and then pick a small-scale project to build from the following website: http://www.ikatbag.com/2011/03/how-to-work-with-cardboard.html

Today they showcased their constructions which took about an hour and a half of class time:

mini top hat

mini top hat

hinged gift box

hinged gift box

sabers and swords

sabers and swords

top hat design - love the aesthetics

top hat design – love the aesthetics

mini top hat

mini top hat

dragon boat

dragon boat

alien space ship (the inside was detailed as well)

alien space ship (the inside was detailed as well)

top hat with examples of ways to adhere edges

top hat with examples of ways to adhere edges

so for them, the next step now is to build the chair out of cardboard – more to come on that activity…

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The 10th grade MPX students have still been exploring issues around transportation, but we’ve also been trying to understanding the kinematic equations of motion which are part of our physics content as well as a deeper conversation about motion in transportation. One of these sidebar projects I’ve had them working on is building a catapult by first converting the design into orthographic representations, building a one quarter scale model out of chopsticks with the ultimate goal of building the catapults, which we will start tomorrow. There’s many layers to this particular activity – working with the mathematics of scaling, attention to detail around design and construction, understanding how we move from concept to design to construction and central to the core content, the physics of projectiles… The pictures below show the scale models that the students completed which took a couple of hours of class time between creating the schematics which I showed in my last blog, and the final products you see below:

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careful measurements

careful measurements

finishing touches

finishing touches

attention to detail

attention to detail

competed 1/4 catapult scale models

competed 1/4 catapult scale models

construction of scale models

construction of scale models

Hopefully by the next time I create a blog post, we’ll see examples of their final product work. Tomorrow we pull out the power tools and let them have at the full construction! Speaking of which, our ninth graders just started working on their first construction which is building tables that they will be using to do their full scale aquaponics constructions on during the course of the year:

engineering: from design to construction

engineering: from design to construction

mpx 9 construction team

mpx 9 construction team

working in our make-shift lanai shop

working in our make-shift lanai shop

When we say we believe in constructivism, we really get our hands dirty!

Knowledge, Understanding and Application

The work over the last two weeks in our exploratory class has been really focused on three pieces that I am working to weave together for our students. In the common core standards for mathematics there is an emphasis on three domains of learning: procedural knowledge (I will refer to as knowing) application and understanding. In a sense, the work that we are trying to do in both mathematics and science is to build not just the knowledge of things like definitions or how to solve problems, but putting them into real-world context so that we can use this knowledge to solve problems, and to apply that information to novel situations.

So how does this play out over the last two weeks? In our mathematics work, we have been looking at solving algebraic expressions which is a foundational skill that will allow the mathematical models that we are developing on our science side to be more fully understood and accessible so we can solve for a wide range of problems. As a school, we are working with Dr. Milfreid Olson from the University of Hawaii Curriculum research development group (CRDG) to help us reflect, strengthen and deepen our approaches in mathematical work throughout campus.
In our class, that has meant doing some traditional math practice work with the equations and eventually inequalities as well as moving on to more complex functions like quadratic equations which will help us better express and understand motion that is both linear and constant as well as changing and accelerated.

As an example, we just did a investigation on Wednesday that had students rolling a golf ball down an inclined plane to try and better understand its motion through the mathematical model generated by looking at its position as a function of time. I’ve included an example of graphs and mathematical models that the students generated as a part of that study below.

investigating motion of golf ball

investigating motion of golf ball

golf ball rolling in action

golf ball rolling in action

analyzing video capture of motion

analyzing video capture of motion

Cami explains the math model in numeric, graphical and motion map forms

Cami explains the math model in numeric, graphical and motion map forms

What is notable here to me is in order to get to the kind of representation you see, it requires students to do all three phases: knowledge, application and understanding. We can deepen this more in the post investigation that will occur on Friday as we look at different inclines, try to use these models as predictive representations of the real world and try to come to a more complete understanding of what the unit analysis and the mathematical function tell us about the motion.

The ultimate goal is to make this real world applicable and we are in the midst of learning about the mechanics of bicycles as a part of our year-long investigation in transportation. This week we spent our double block on Tuesday taking apart cleaning up and reassembling the different bearing systems that allow a bicycle to translate force into motion by reducing friction.

using torque to take apart the crank shaft

using torque to take apart the crack shaft

taking apart the bottom bracket to expose the bearings

taking apart the bottom bracket to expose the bearings

galen explains the roll of bearings

galen explains the roll of bearings


All of these activities lend themselves to rich meaningful conversations around terms like friction, torque, force, procession, rotational mechanics, mechanical advantage, simple machines and much more. We will be using part of our time on Friday to unpack some of the terminology and physical understanding that was easily evidenced by their work on the bicycles.

There isn’t always a perfect fit between the work we are doing with our math, science and technology (STEM) but as much as we can, we are trying to draw meaning between these investigations so that we are weaving together these strands into a more tightly integrated and understood unit about our investigations of the physical world.