Tag: Pedagogy

Math Flowcharts

Flowchart in progress. Showing topics being covered in basic statistical graphing.
Flowchart in progress. Showing topics being covered in basic statistical graphing. The topics they are working on at the moment are highlighted in yellow. The worksheets attached to each topic are linked on the left side in the highlighted area.

To help students track their progress in math we’ve started requiring them to map what they’re doing on flowcharts. Right now, they’re doing it on paper, but we’re working on getting it to be all electronic.

Tracking with the charts helps them see how what they’ve done fits into the bigger picture. It allows them to be able to go back up the chart to previous topics if they need to review, and look forward to what comes next (and to work ahead if they would like).

The image above shows a sample what a student’s flow chart would look like while they are working on a subject (statistics in this case). The topics they are working on at the moment are highlighted in yellow. The worksheets attached to each topic are linked on the left side in the highlighted area. Links to references (Khan Academy for example) are linked on the right–there are only a few on right now (see the Mean topic on the upper right of the flowchart).

The topics on the flowchart can be expanded (using the green button on the top right of each topic) to show more detail.

Expanded window for the topic "Mean".
Expanded window for the topic “Mean”. Detail on the topics is a little sparse at the moment as we’re focusing on setting up all of the flowcharts first.

At the moment, I’m uploading the flowcharts that we’re currently using up on the website myself. Students can use the website to get worksheets and links to references, but if they mark what they’re doing on the webpage it’s not saved. We’re currently working on making it possible to create and edit flowcharts on the website itself. After that, we’ll be setting it up so students can log in with their school accounts and track their progress electronically. One ultimate goal is to map the entire upper school curriculum with these flow charts so a student might be able to track their work all the way from 7th to 12th grade.

Preparing Students for a Technological Future

I’m currently preparing a proposal to create a laboratory of digital fabrication machines–a CNC, a laser, and a vinyl cutter–and one of the questions I’m answering is about how the proposed project would prepare students for a technology-rich future. What you see below is my first response to this prompt. It’s a bit longer than I have space for in the proposal, and probably a bit too philosophical, but before I cut it down I wanted to post this draft because it does a reasonable job of encapsulating my philosophy when it comes to teaching technology:

Preparation for a technology rich future is less about preparing for specific technologies and more about getting students to have a growth mindset with respect to technology. We are living in a truly wonderful moment in history. Technological tools are rapidly expanding what we as individuals can accomplish. They are allowing us to see farther (think about remote sensing like lidar and tomography), collate more information (especially with more and more data becoming publicly available), and create things that push the limits of our imaginations. Indeed, to paraphrase a former student, we are already living in the future.

To prepare students to live and thrive in this ever-evolving present we need to demystify technology and give students the intellectual tools to deal with the rapid change. We can start by letting them peek into the black boxes that our technological devices are rapidly becoming.

We request electronics stations and tool kits not just to build things, but to be able to take them apart and look inside. Students greatly enjoy dissassembling and reassambling computers, for example, which provides younger students a good conceptual understanding of how most modern devices work. This foundation helps when they start building circuits of their own and realize what they really want to do is to control them–making lights blink and turning motors for example–and this is when they will start working with Raspberry Pi computers, Arduino microcontrollers and programming.

As students start to build (and even before really), they naturally start thinking about design. We all have an affinity for the aesthetic. If you’ve ever had the opportunity to see a laser in action, you’ll remember your sense of fascination the first time you saw someone’s design emerging from the raw material right before your eyes. Thus we get into graphic design, computer aided design (CAD) and computer aided manufacturing (CAM) and the digital fabrication machines we propose.

By the time they’re done with this curriculum, we intend that students will have developed an intimate familiarity with the technological world–including the ability to create and design their own, which prepares them for the technological future.

Cell Phone Shelf

Cell phone rack in use.
Cell phone rack in use.

Managing cell phone usage at school is a tricky topic. We have some teachers who’d like to ban them outright, but we also have a growing number of parents who are expecting to be able to communicate with their kids–to organize pickups and carpooling during the day for example. The phones can be great for data-collection and documentation in classes, and a lot of my upper level math students prefer the Desmos app to using their graphical calculators.

Our current compromise is that middle schoolers have to leave their phones in the front office, where they can check them at lunch time or check them out if a teacher wants them to use them.

The high schoolers are allowed to keep their phones with them, but have to put them in a basket at the front of the classroom. Since they don’t like piling them into the basket, I experimented with the CNC machine to cut some plywood into a cell-phone shelf.

The shelf can hold about 30 phones, and I can easily see how many phones are on there from across the room, so I’d say this one worked out pretty well.

Bloom’s Taxonomy

From Wikimedia: https://commons.wikimedia.org/wiki/File:BloomsCognitiveDomain.svg
From Wikimedia: https://commons.wikimedia.org/wiki/File:BloomsCognitiveDomain.svg

Bloom’s cognitive taxonomy offers a useful model for defining learning objectives. You start with the basic knowledge of the subject that requires some memorization: fundamental constants like the speed of light; fundamental concepts like conservation of mass and energy; and basic equations like Newton’s laws. On the second level, you use these basic facts and concepts to extrapolate and generalize with questions like: is the Earth an open or closed system with respect to mass and energy? And then we can start to apply our knowledge and understanding to problem solving: determine the average temperature of the Earth based on conservation of energy. Finally, at the highest level, we can analyse our models and evaluate their advantages and disadvantages.

Devices

I tend to let my students have a lot of freedom to use their myriad technological devices as they will. Just as long as they use them responsibly (i.e. for academics during class time). What’s most interesting these days is seeing how they combine the various electronics.

Working with pen, paper, tablet and laptop.
Working with pen, paper, tablet and laptop.

This Chemistry student is referring to her textbook on the iPad, while she creates a presentation on her laptop. Yet pen and paper are still integral parts of the process.

Human Jobs in the Robotic Future

After all the time I spent working with Raspberry Pi microcomputers and Arduino microcontrollers this summer, it was interesting to see Claire Cain Miller summary of a PEW report on “AI, Robotics, and the Future of Jobs“.

Miller provides some interesting quotes from the experts surveyed for the report. One quote stood out in terms of its perspective on education and pedagogy:

“Only the best-educated humans will compete with machines. And education systems in the U.S. and much of the rest of the world are still sitting students in rows and columns, teaching them to keep quiet and memorize what is told to them, preparing them for life in a 20th century factory.”

— Howard Rheingold, tech writer and analyst .

The Key Findings from the PEW report provides a good summary of their results:

Half of these experts (48%) envision a future in which robots and digital agents have displaced significant numbers of both blue- and white-collar workers—with many expressing concern that this will lead to vast increases in income inequality, masses of people who are effectively unemployable, and breakdowns in the social order.

The other half of the experts who responded to this survey (52%) expect that technology will not displace more jobs than it creates by 2025. To be sure, this group anticipates that many jobs currently performed by humans will be substantially taken over by robots or digital agents by 2025. But they have faith that human ingenuity will create new jobs, industries, and ways to make a living, just as it has been doing since the dawn of the Industrial Revolution.

These two groups also share certain hopes and concerns about the impact of technology on employment. For instance, many are concerned that our existing social structures—and especially our educational institutions—are not adequately preparing people for the skills that will be needed in the job market of the future. Conversely, others have hope that the coming changes will be an opportunity to reassess our society’s relationship to employment itself—by returning to a focus on small-scale or artisanal modes of production, or by giving people more time to spend on leisure, self-improvement, or time with loved ones.

— Smith and Anderson, 2014. AI, Robotics, and the Future of Jobs.

The full report is worth a read.

Mars Colonization Project

My high-school biology class is taking their exam on genetics and evolution. To make the test a little more interesting, and to point out that there may be some relevance for this knowledge in the future, I made the test a questionnaire for the new head of the Mars Colonization Project. It begins like this:

Friday, January 30th, 2054.

Dear Dr. ________________ (insert your name here):

We are excited that you have accepted our offer to head the Biomedical Division of the MCP. As we are engaged in the first ever effort to colonize another planet, we know that we will face many unique challenges. Your expertise in pluripotent stem cell research and oncology will be extremely valuable to us — even though some of us administrators still don’t know what pluripotent stem cells are.

Please fill out the questions in this document to help us with our planning for the colony and to help our Human Resources department assemble your research and medical team.

Because of the sensitivity of some of the personal information included in this document, please write out, and sign, the Honor Code below before turning the page.

Yours truly,

Board of Administrators,
Martian Colonization Project

Front page of the High Schooler's Biology exam.
Front page of the High Schooler’s Biology exam.

Then I pose all of the questions in this context. For example, to get their knowledge of vocabulary I ask them to define the scientific words and phrases (which they’ve used in their scientific publications many, many times), in terms that laymen — like the people on the board of administrators — could understand.

To get at more complex concepts, like the molecular process of gene expression and regulation, I phrased the question like this:

Medical Issues Related to Ongoing Colonization Planning

The trip to Mars will take five years, so we will be placing most of the colonists into cryogenic sleep for most of that time. We are still working out some of the bugs in the cryogenic technology, and we need your help.

To put people into cryogenic sleep, we need to stop their digestion of carbohydrates. Your predecessor, Dr. Malign, told us that we could do this using RNA interference, by injecting them with engineered microRNA that would block the production of the enzyme amalyse.

Could you draw a diagram of a cell showing how proteins are expressed from DNA, and how microRNA would interfere with protein production. Are there other methods for preventing protein expression?

We’ll see how the students do on the test, however at least one student glanced at the front page and said, “This is kinda cool,” (actually, she first asked if I’d stolen the idea from the internet somewhere), which is significant praise coming from a teenager.