Moving from Impossible to Trivial

In the front of my classroom, I have a quote that is attributed to Ernest Rutherford:

“All of physics is either impossible or trivial. It is impossible until you understand it, then it becomes trivial.”

Those who know me, know that I am a lover of great quotes – perhaps I interject them too much, but that’s another story. More than physics, I think that learning as an entire journey is moving from things that we think are impossible to understand or do to making them trivial because we have correctly understood them to the right depth, or practiced to the point of ease. In my work, I find it critical to hold to the mantra “know – do – understand – reflect”. I would argue most of us in our past educational experiences mostly spent most of our time memorizing and practicing lower order thinking algorithms, rarely getting the chance to do something with that information we learned, and even more rarely moving to understanding the core idea underlying the knowledge. To understand something means more than just know it at a different level, it means being able to put it in context of a simplified model, being able to view it from many perspectives, to be able to synthesize, articulate, apply and explain in powerful ways through our expert lens. It is my goal when we start investigating any kind of learning objectives that we want to move students to this kind of understanding and to be able to reflect on what that means and how it works for us.

So with that in mind, we begin this week with our quarter long project on “Chemistry and Conflict”. In order to create the need to know, I started the week with a few short demonstrations of phenomena that did not behave the way students expected. In science education we call these discrepant events. The value of the events is really multi-purpose. It elicits attention, as it creates excitement and questions around something that surprises us. It exposes our naïve understanding of some physical phenomena and hopefully asks us gently to consider what were missing from our understanding that would move us to a more expert view. And at some level, it guides our inquiry to try and look at what we can understand better about the natural world.

On Monday, I started with four discrepant events:
– putting ice cubes in two different beakers of liquid – where one floated and the other sank
– putting 50°C water into a container and watching it boil even though it was well below 100°C
– starting an instant ice pack, and watching the temperature dramatically fall
– setting a piece of metal on fire, and watching the result turn into a white powder
For each of these events, I had the students use the thinking routine See Think Wonder which comes from the marvelous resources on visible thinking http://www.visiblethinkingpz.org

In our next class, we investigated more deeply the phenomena of phase change. My colleague Gregg had designed a wonderful apparatus in which the students lower the temperature of water down to -5°C, then heat it up until it is boiling. We used our brand-new Lab Quest Streams ( another blog post I should explain the value of using real-time data collection tools to strengthen our scientific research), which enabled us to connect real-time data to our iPads wirelessly – powerful and easy technology. As the students took the data, it became clear that some things behave the way they expected, and then there were surprises in the data. Sometimes liquid water was found to exist under 0°C, sometimes temperature increased while we were cooling, sometimes temperature stayed the same while we were heating.

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After all this experimental work, we spent most of the next class period analyzing and unpacking what had happened. It gave our students a chance to be part of a scientific conversation – practicing the habits of mind scientists do when they look at data, draw inferences, and reach consensus. Over the next six weeks we will continue to investigate the properties of matter that are embedded in our standards: why does the periodic table the look way it does? In what ways does matter interact, combine together, and give off or consume energy? What are the structures of the atom that make it reactive or not? How do we know the model of the atom is an appropriate explanation of the way nature behaves?

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Lastly, as a part of our work over this project our art teacher Erin is having the students learn a variety of photographic techniques which has its own embedded chemistry in it. After some initial investigation, and talking about the physical, visual and social aspects of all art, our students started their exploration by creating a set of cyanotype photograms in class. In order to do this, we needed to turn our classroom into a dark room – not an easy task but as you can see from some of the photos below we succeeded! I’m excited to see where we go next with this in the upcoming weeks. I hope you follow along.

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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: