Week 2 Water Work

The wondrous and wasteful world of water…

This week started with the official launch of our mini project on water quality. For a bunch of reasons both strategic and educational, Lyssa and I both wanted to do a quick dive into projects both to help us look at how our students work together, and to give them some ideas of the assessments, supports and structure we would use over the course of a longer project. We gave them the challenge of identifying a community in the United States that is struggling with a water quality issue, understanding the place and the people, investigating the water issue including possible solutions, and to present that information on Friday to a mock panel of experts that we deemed to be a “community board”. Over the course of the week they had an opportunity to explore with some new research tools like Wolfram Alpha, work on their library skills with a session in our library with our most excellent staff David Wee and Nicole Goff, work with their team taking on roles within the community, work with our media arts teacher Erin Carnes to design a graphic that would support a call to action and prepare and deliver presentation. yes – all in one week. Our panel consisted of Joshua Noga, the conservation program coordinator for the Sierra Club, two of our parents who are involved with community action and business development and our visual arts teacher. We were so appreciative of them taking the time to sit in and both listen to and ask hard questions of our student presenters over the course of two hours.

This gave Lyssa and I an opportunity to tightly script a project that was mapped out in a series of steps with deliverables, have us work with the students on formative and summative assessment practices, observe and jump into some of the groups to shape the way students work and learn in our class and to set the tone for the year. The pictures below gives some visual aspects of the story – I tried to caption them for their context in the above storyline. We took about 30 minutes to debrief the activity with the students, to talk about was what worked and what didn’t, and to give them a chance to reflect on their learning over the course of this experience. We certainly were energized by what we saw and heard over the last five days!

Next week, we start our investigation on chemistry and conflict – the ways that society, science and the physical world intersect and sometimes create tension and challenges in society.

Group presentation on water quality in front of our mock community board

Group presentation on water quality in front of our mock community board

Presenting on water quality issues in San Diego

Presenting on water quality issues in San Diego

Thursday – time to practice our presentations for ironing out problems and feedback

Thursday – time to practice our presentations for ironing out problems and feedback

Practicing presentations for Friday within our groups

Practicing presentations for Friday within our groups

Learning about valid sources – the quote of the day was the Internet gives you what it thinks you want not what you need!

Learning about valid sources – the quote of the day was the Internet gives you what it thinks you want not what you need!

Considering what kinds of sources we consider valid – time with our librarians

Considering what kinds of sources we consider valid – time with our librarians

Working on our call for action artwork using a variety of tools

Working on our call for action artwork using a variety of tools

Designing graphics for a call to action

Designing graphics for a call to action

This graphic turned out marvelous – a firefighter shooting water hose to fill water for houses – metaphor for delivery of water two houses by firemen and police in impoverished communities

This graphic turned out marvelous – a firefighter shooting water hose to fill water for houses – metaphor for delivery of water two houses by firemen and police in impoverished communities

Three Kinds of Math?

Money, Philosophical and Artisanal Math

There was a wonderful piece on National Public Radio this week that told the story of Harvard researcher Houman Harouni (https://www.gse.harvard.edu/faculty/houman-harouni), who had done historical research on why we learn mathematics the way we do.

(His full dissertation is here: https://dash.harvard.edu/bitstream/handle/1/16461047/HAROUNI-DISSERTATION-2015.pdf?sequence=1)

In the dissertation, he gives a very specific example of how this kind of approach to mathematics can be viewed through three different approaches.

Money Math
He makes the case that all of western mathematics has ended up looking like problems of this type:

Susan has 12 oranges. Her mother gives her 15 more. How many oranges
does she have now?

or: 12+15 = ?

This kind of mathematics came out of the economics of the time – money counters and accountants, business people needed to know this kind of math in order to balance the books. He makes the compelling case that the economies drove the need for this kind of math to be necessary, and it became the predominant way of thinking of mathematics since the Renaissance.

Philosophical Math
He offers two other types of mathematical approaches. What if the problem was worded this way:

27 = ?

This approach is a more philosophical approach about the nature of the number, and the ways that it might come to be and what it represents.what could go into the right side of that equation? 9×3? Three cubed? Log base three of 27? It invites a very different kind of mathematical thinking and exploration.

Artisanal Math
Another approach would embed the math in the professional work during apprenticeships with craftsmen. This was very reminiscent of the work of Jean Lave (http://www.ischool.berkeley.edu/people/faculty/jeanlave) and her excellent work on situated learning. In studying the traditions of apprenticeship for Tailor’s in countries like Tunisia, it was clear that mathematical learning was built into the apprenticeship, but it is not anything like what we would call traditional teaching and learning of mathematics. Moreover, these tailors had a high functional ability to work with mathematics that were specific to their craft.

Tying it all together
Over the past six years in working in our MPX program I have been delighted and challenged to try and build all three kinds of mathematical approaches into the work we do with our projects. We have developed mathematical models in our scientific community to understand and categorize physical phenomena, we’ve looked at form and function in ways that they express themselves in artistic work in design and engineering, and we’ve practiced traditional math as a means to understand some of the ways that procedural knowledge in mathematics can help us unpack what we see behind certain expressions. I think the real challenge of the evolution of mathematics education needs to be in rethinking how do we approach these sometimes complementary but more often than not this connected or even underutilized approaches to building mathematical understanding in all of our students. In some ways, they fit the three legs of mathematical understanding that are part of common core: no (money math), do (artisan old math), understand (philosophical math).

Here is the NPR story that explains some of the research:

His best line: no one knows how long it will take anyone to learn anything. 

How does this play out in a student’s life? Let me give you the most egregious example in my professional life, which I hope will change. In most schools if a student fails a class like geometry they need to retake it. The grade (let’s say it was an F) goes on their transcript. If they get a B the second time, that goes on their transcript as well. The F however, stays. WHY? If the report if truly about what they learned, the only grade that should count is the B. I have known this to be true a long time, but it is still revelatory – it challenges and exposes some very ugly truths about what the grade really means on a typical report card. I could go on about this topic, but Rick shared a writing in response to push back on this idea that does a far better job then I here: 

https://www.adams12.org/files/learning_services/Wormeli_Response.pdf

On another topic, my session on “designing meaningless projects” Slide deck Here:

went very well – it was not surprising to hear the are lots of schools trying and struggling with implementing powerful appropriate deeper learning experiences (pbl being one common variant of this). Lots of people agree it is the right way to go, know what they are shooting for but lack the time and the resources and most importantly (in my opinion) the structure/framework to get there. Our work with Kupu Hou Academy  has helped us refine the language and support to move teachers along the process. I hope the teachers I met with at the conference find these resources helpful in their quest.
There was lots more of incredible conversations and topics at the conference that will leave a lasting impact on my work. But the last thing worth mentioning for this post is the beautifully crafted “in this we believe” document that. AMLE has developed to support their work towards a better middle level experience for all.

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Looking at the 16 characteristics, it is hard not to agree with what they say about what good learning environments (ok, let’s call it school) should be at EVERY level – not just middle. The real work is in implementing it. In much the same way that faithful go to their place of worship to strengthen their faith and reaffirm their beliefs, conferences like AMLE serve much the same purpose. The real challenge for a person of faith is living your faith every day. The real challenge for schools and their staff is much the same – we need to live these values and put them into place because they are the truest expression of what “we believe”.

A bicycle is an engineering marvel!

This week saw three important pieces of our fall work overlapping and developing together.

Bookshelves:

During one of our extended blocks, our learners worked closely with our building and engineering consultant Ross to start setting up their metal and wood for the bookshelves they’re designing. This mini engineering exploration is designed to give them the opportunity to work on scale drawings, design, feedback and iteration, and most importantly metalworking skills that they will need in order to do the larger project in transportation. The week before, they had moved their ideas from paper sketches to one quarter scale prototypes made out of foamcore, wood towels, and other appropriate materials. Now was their chance to learn how to work with the tools that allow metalwork to happen: reciprocal saws, grinders, welders, sanders to name a few. We unpackaged the new tools, and the students created guide sheets on the safety and proper operation of the tools that they shared and then posted in class.By the end of next week, all of their pieces should be cut and ready to be assembled into their design.
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Motion/kinematics:

In order to develop the proper terminology in transportation, we are working towards better understanding motion, and the mathematics of linear and nonlinear relations (for example, when that object changes its speed, what are the mathematical models that govern that kind of behavior?). We’ve already developed baseline terminology and understanding of motion through looking at constant velocity, and this week we added a new motion to understand, what happens when an object changes its velocity? Students conducted an experiment on an inclined plane, and are collecting data to build mathematical models but they can use to create predictive models for motion that is much more complex. It was exciting to see some students already derive their mathematical models, and one group did a predictive analysis of how far their car would’ve gone if it continued in its motion for 60 seconds – it showed a wonderful connection between the models they were creating and the real world result of them. Terminology like friction, acceleration and terminal velocity came up in our conversations which is exactly where this experience was designed to lead us towards. Of course, this will lend itself to quadratic’s which are a key component of our Algebra 2 curriculum.

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Transportation/bicycles:

The biggest event of the week was our first trip to KVIBE ( Kalihi Valley Instructional Bike Exchange). We spent over three hours at their Kalihi facility with students getting a broad overview of the community outreach work that KVIBE does, and then we dove into the mechanics of bicycles under the excellent tutelage of Marcos, Galen, and Lorenzo. We did some work with naming of parts, but the key experience for students was understanding how the wheel (hub, spokes, rim) works and to take apart and reassemble the wheel hub – cleaning bearings in understanding the ways that it is put together to create a nearly frictionless rotational center for the wheel. In the process of explaining the mechanics of the bicycle, a large number of significant physics terminology came into our language – tension, torque, peer pressure, friction, statics… As they were explaining their work, Lorenzo commented with great emphasis “the bicycle is truly a marvel of engineering!”. Students worked with their teams, and were both collaborative and diligent in tackling the task of disassembling and reassembling wheels to better understand how they work, and the physics concepts underlying them.

All in all, it was rewarding to see our students tying together these three strands looking towards the broader goal of designing and sharing ideas about their learning with the community. Students have already talked about sharing their knowledge with other schools about how to repair bicycles, putting up instructional webpages about the values (health, environment, social connection) and giving examples of how to live a more sustainable lifestyle. It was an exciting week!

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*** All of our photos for the year are kept on our Flickr page here: https://flic.kr/s/aHskiFvesE

Good Design, Good Projects

Good Design, Good Projects

I spent some time this weekend re-reading Dr David’s Merrill article “Pebble-in-the-Pond Model for Instructional Design” (http://www.ispi.org/archives/resources/Vol41_07_41.pdf). I count myself lucky to have been able to take a class from Dr. Merrill and consider him one of the great minds in instructional design. In the day-to-day lives of teachers, there is rarely the opportunity to do a complete instructional design process that is advocated by instructional designers, but the ideas he lays out in this wonderful summary are the same basic structures that we use when designing good projects.

One of my favorite parts of the article is the diagram that he uses to lay out the foundations of good whole problem design:

Phases of Effective Instruction

Phases of Effective Instruction

Dr. Merrill advocates for designers to first start with the whole problem – to both engage and immerse the learners in the “why we need to know”. In much the same way, when we design good projects, we need to back up and ask what’s the essential/driving question that will direct our focus, direct our learning explorations, and give us a reason for wanting to do this work. The next step is to “identify a progression of such problems of increasing difficulty or complexity such that if learners are able to do all of the whole tasks thus identified, they would have mastered the knowledge and skill to be taught.” In other words, we need to identify the scaffolded activities that will allow the learner to build the requisite knowledge and skills to understand how to solve the whole problem. Once we know that, we can provide activities and feedback to learners so they correctly learn and apply the skills and content knowledge they need in order to work towards the whole problem.

In our work in Mid-Pacific eXploratory (MPX) and the ways that we work with other teachers through Kupu Hou Academy (kupuhouacademy.com) our work mirrors much of that found in this good instructional design methodology and there is much to be continually learned in order to apply the best design of deeper learning practices around these essential “first principles of instruction”.

One of the things that this can lead to is moving away from teaching knowledge and skills as discrete items that we might use, and instead become necessary components that one must know in order to work on the whole problem. This year in our 10th grade class, we’ve been talking about ways that we can make a difference in the prevailing issue for this generation – climate change. In the areas of transportation and energy, there are things that we can do to have an impact. We started the year with visits to sustainable buildings and Hawaiian Electric, and are breaking down this big task into components that we need to understand in order to be knowledgeable and capable enough to propose possible solutions. That means understanding motion,energy and electricity, as well as understanding the mathematics of modeling and analysis. Those are the component skills that we are developing in order to propose and create solutions to help make a difference in the big issue of our generation. By anchoring our activities in the “need to know” we create a more powerful learning experience that will stay with learners far beyond the life of this course.

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.