Category: Education

As 3D printers come into homes and schools, you will be looking for tools that let you make your own designs.  Here are a few free titles that I think should be on your list:

Inkscape is primarily a drawing program for two-dimensional designs. It is an amazingly powerful tool that even automates the process of drawing complex objects like gears.  Drawings created in Inkscape can be saved in the SVG (scalable vector graphic) format so they look great at any magnification.  You can also export images in traditional graphics formats like PNG (portable network graphic) that looks great when used on websites, etc. But the real power of Inkscape as a 3D drawing tool comes when you install the support plug-in for 3D extrusion to an OpenSCAD file (described later)  that can be rendered and exported as an STL file for the printer to use.  The way this works is that you select the part of the drawing you want to extrude into a three-dimensional shape.  When you choose the extrusion option, you just indicate how many millimeters you want the extrusion to be, and a 3D file for OpenSCAD is generated automatically.  To get this shape to your printer, the next step is to open it in OpenSCAD, compile the image, and save it as an STL file.  STL (Stereolithography) files are the format your printer expects to see when it starts the process of getting your model ready to print. This sounds laborious, but it is easy to get the hang of it, and the whole process goes very quickly.

You may be wondering why I would mention a (primarily) two-dimensional drawing tool in the context of 3D printing.  The reason is that, while building 3D objects on the computer screen is likely a new task to students, they probably use two-dimensional art programs all the time.  Our goal is to build from this strength on the path to (later) creating designs with 3D drawing tools.

While I will largely use OpenSCAD as an extrusion tool for Inkscape, it is, in fact, a full 3D modeling program that builds models from text commands.  It has its own programming language that might be appropriate for high-schoolers to play with.  An advantage of building geometric models in OpenSCAD is that they can be “parameterized” – expressed in a way that lets one design make several related shapes by changing the values of a few variables.  For example, a propeller can be designed in OpenSCAD in a way that lets the end user change the number and size of the blades.  This is a real feature, and quite a few Thingiverse models include OpenSCAD files for just that reason.  Used in this way, students can tinker with existing models to create a custom part for their construction.  The final model is displayed on the screen to be sure it is what you want before saving it as an STL file.

Sketchup is a professional 3D modeling tool that is super for creating geometric structures from scratch (architectural designs, for example).  The free version (Sketchup Make) has all the features that students might need to build models of the parts they want to print.  If your model can be built from boxes, cylinders, and balls, it is a great tool.  It is not what I would choose for more organic shapes, though.  The Sketchup Extension Warehouse has a free plug-in that lets you export your finished part as an STL file directly.  My only caution about this tool is that it is not the best program for editing completed STL files.  They show up as a mass of dots and triangles, and I haven’t found a way to render the surfaces as nicely as you can from models made in Sketchup in the first place.  This is a shame, because older versions of Sketchup handled imported STL files much better.  The good news is that there are many other alternatives for you to use.

This program also lets you create projects from scratch using a library of geometric shapes.  My experience is that it is easier to align parts in 3DTin than it is in Tinkercad (another cloud-based design tool).  3DTin lets you download your drawing as an STL file ready to print!

Autodesk is one of the premiere publishers on computer-aided design software.  Their products are found in design firms and architects offices all over the world.

They decided to support the beginning 3D designer with a rich suite of tools that covers the gamut from parts designed from geometric pieces, to the more organic designs suitable for modeling living organisms.  In fact, Clark Barnett, a teacher in  the Conejo Valley Unified School District  in California does a project with his kids using one of the Autodesk applications on the iPad – 123D Creature.  With this tool, students design their own insects that could live in the ecosystem of their classroom.  Once printed, these “insects” are mounted in a display tray and students explain why their insect is likely to survive on its own in the classroom ecosystem.

While not geared specifically for “creature” creation, Autodesk has a wonderful free product called Meshmixer that is perfect for creating organic, rather than geometric shapes.

This tool lets you sculpt by hand as if you were working with clay.  Anyone who has worked with modeling clay will know how to use the tools in this program, and there is a great manual to show exactly how to get the most from this program.  Tools like this bring 3D printing into the life sciences classroom.

This amazing tool is a great next step for Meshmixer users.  It was designed for sculptors (and would-be sculptors), instead of a blank screen you are presented with a round ball of “clay” that can be shaped into just about anything you want.  While not geared toward the creation of geometric objects, it is a perfect tool for building models of various creatures – both real and imagined.  Finished projects are exported as OBJ files that can be easily converted to STL files by Meshlab (see below).  Once you start working with this tool, hours happily go by as you build amazing things, all of which can be built on your 3D printer.  This software comes with good documentation and links to some video tutorials I highly recommend for anyone interested in this tool.

This program lets you build mathematical knots of all kinds.  While created for math geeks, knots are pretty to look at, and students can use this program to explore this branch of mathematics – a worthwhile activity in itself.  One great feature of this program is that it lets you export your finished knot as an OBJ file if you want to tweak it in Meshlab (see below).  You can also export your image as an STL file directly and send it to your printer software with no further work required.  Finished knots can be sent out for metal plating in case you want to make your own jewelry. (You probably have some service providers in your area that will do this inexpensively.)

Other tools:

Sometimes (as with Sculptris) your 3D images will be exported as OBJ files that need to be converted to STL files so they can be printed.  Meshlab does this job beautifully and even lets you adjust the mesh from which the model is defined to optimize it for printing.  This optimization process lets you clean up your model so it will print perfectly.

This is the plug-in you need to allow Inkscape to create extrusions for OpenSCAD.  All the instructions are provided in the web link shown above.

And there are more good programs coming out all the time, so keep your eyes open and let us know what you find (!

The Trinity Fractal

The story behind this discovery dates back to the 1970’s when I used to volunteer as a math resource specialist at a small school near my office.  One day, a teacher introduced me to a 10 year-old girl (we will call her “Ann”) who was (in the teacher’s  words) “bad at math.”  I found that to be  strange announcement since, in my view, Ann had never been exposed to math, but only to arithmetic.  So one day I invited my class to do an experiment.  

I brought my own bucket of pattern blocks to school, in which I added some regular pentagons I had made.  Piles of the same shapes were put on several desks, and students were asked to tile the surface with just one shape – and I made sure Ann was at the table with the regular pentagons.  After a few minutes, all the students had succeeded – excepting those at the table with the pentagons.  No matter how hard they tried, there was always going to be a gap.

Ann said, “Well, we can do it, but we are going to need a lot of grout.”  And, after looking at the other tables, she said, “This is a strange kind of math – 3 works, 4 works, and 6 works, but 5 doesn’t work.  Why is that?”

I was delighted to hear that question because this is the kind of question mathematicians ask themselves often.  Ann told me she wanted to experiment more with the pentagons, and I gave her a bunch to take home so she could report her findings the next week when we met again.  At this point I didn’t know what to expect, but it sure wasn’t what she showed up with.

The next week, she started off with the following pattern:

Starting pattern

Ann pointed out that this shape, while not a tiling pattern, looked like a pentagon if you “squished” your eyes a little bit.  “So,” she said, “suppose we start with this pattern, shrink it in size and build a new pattern with the same shape.”

First generation pattern

Then, she said, just keep repeating this process.  You will always need some grout, but the picture should be very pretty.

The next two generations of patterns are shown below:

Second generation

Third generation

As you can see, Ann was quite right.  Yes, you still need grout, and, the resulting pattern is quite pretty.

Basically, what Ann had discovered (and accurately described) is a fractal – a shape with a non-integer dimension.  I’ve told Ann’s story many times, but never before constructed the fractal patterns to show people.  I decided to call this the Trinity fractal, named after the school where I volunteered (Trinity Parish School in Menlo Park, California.)

I lost touch with Ann, but talked with her on her first day of college at UC Berkeley, where she was majoring in mathematics.

I’m glad I may have played a small role in helping her see the beauty in this subject, and have no doubt that she has gone on to do great things.

I’m also happy to finally share her discovery with others in the hope that it encourages other teachers to move beyond arithmetic to see the beauty in real mathematics, as encouraged by the Common Core State Standards for mathematics.  Our workshops on CCSS Math can be scheduled by e-mailing me at  Also, our work with pentagon tiling has continued in a new way.  See to see what we’re doing in this area!

Before getting into the content of this blog, I want to ask the flame brigade to hold off until they get to the end of the message.  This blog is not anti-iOS, not anti-Android, not anti-tablet.  It is simply my view of how things seem to be turning out.  So here goes:

Schools around the world have diven into the deep end of the tablet pool, purchasing these devices by the thousands (or more) in the quest to bring powerful technology into the hands of students.  The reasoning behind tablets is that they are rugged, have amazing battery life, and provide access to various apps that may be of value in the classroom.

This last point has been a sticking issue for some.  I’ve argued for decades that the choice of a computer platform for kids needs to be driven by the software they will use, and this message has been lost on some districts who chose the platform first, and then tried to figure out how best to use it.  As with the Apple vs. Microsoft battles of the past, the fight quickly broke down into two camps – the iOS folks (iPads) and the Android enthusiasts.  While some have found ways to use these tools in remarkably powerful ways, the question arises: should we have been looking at tablets at all?

In a 2012 piece in THE Journal (, Therese Mageau argued that the race to buy iPads (for example) largely came without thinking about the deeper educational shifts implied by every child having his or her own connected device.  While she is correct, I’d like to take a different approach to the question – to ask if tablets were the right choice at all!

While the world was focused on iPads and the like, Google announced the Chromebook at their developer’s conference in May, 2011.  Like tablets, Chromebooks have long battery life (8 hours or more), virtually no boot time (8 seconds from a cold start), a low price (under $300) and the ability to run some applications (word processing, spreadsheet, presentation tools, watch videos, etc.) without Internet access – although this tool was designed to be used when you are online.

While some schools started to adopt Chromebooks, many did not, even though the Chromebook looks like a thin laptop with a full keyboard and high quality display.  But, once again, the question arises on the application front.

Google has done a wonderful job of helping developers create apps for the Chrome Web Store ( and amazingly powerful educational apps abound – a great many of which are free!  For example, you can get Geogebra, the Scratch programming language, even all fifty of our own Knights of Knowledge inquiry-starter videos that span grade levels and subject areas.  The list of educational apps is growing daily, along with the adoption of this tool as the one-to-one device of choice for many.

And this brings us back to tablets – or more particularly to the schools and districts who purchased so many of these devices for student use. Given what we now know, would different purchasing decisions be made?  As the pundits say, hindsight is always 20-20.

The fact is that the Chromebook emerged as a wild card in a field that never seems to stop and catch its breath.  Does this relegate tablets to the storage closets?  Of course not.  It merely suggests that we need to base our purchasing decisions on the best information we have at the time.  And, make no mistake about it, there will be something someday that eclipses the Chromebook.  This just reinforces the importance of ensuring that whatever purchase we make is based on the actually utility of the device to kids in support of their learning.  As long as we do that, we are on solid ground.

Earlier this month I got a Samsung Chromebook because many of the schools we work with have adopted them in their one-to-one programs.  I just admit that I had some misperceptions that kept me off the Chromebook wagon for over a year, but now I think I can use it as my primary road-tool for giving presentations, creating documents (such as this blog) and doing other things (but not all things) I used to use my laptop for.

My original thinking was that this could be a very cool device.  From a historical point, it all started in 1984 when Sun’s John Gage said: “The network is the computer.”  When he said this many computers (including the brand new Macintosh) came without a modem or ethernet port – so this was a very bold statement.  About a decade later, when the first graphical web browser (Mosaic) was released, I said: “The browser is the operating system” and, just two years ago the Chromebook hit the market.  This ultralight laptop replacement uses the Chrome browser interface for all applications.  The browser is built on a Linux base (just like iOS, MacOS, and Android) thus leaving Microsoft out in the cold.

Because of the browser interface, I assumed (incorrectly) that all applications needed to be used when you were online.  This is not true.  Once you register with your Gmail account, you are able to create documents (such as this one) along with slideshows even if you have no internet connection at the time.  Once you go online, all your new documents and edits get synchronized to the cloud automatically.  This a great for kids who may only have good internet access from school.  They can still work on projects at home even though they are disconnected.

The automatic update feature applies to more than documents.  Applications reside in the cloud (unless you are running local versions on the Chromebook) so upgrades are automatic.  The Chrome operating system is virus proof.  If you completely mess up your system (hard to do), you can do a fresh restart and everything you were doing gets automatically put back in place as soon as you log in.  This means that if your Chromebook gets run over by a truck, you can turn on a fresh one, log in, and keeps working as if nothing happened.  Start-time (from cold start) is about eight seconds.  If you have the Chromebook sleeping, it wakes up immediately.

There are a few changes that need to be made.  Some of the applications (e.g., Geogebra) do not have all the features of the laptop version, and there seems to be a bug in the current release of ChromeOS that makes it hard to rename files in GoogleDrive.

Of course GoogleDocs is the home for word processing and other traditional mainstream applications.  Finished documents can be exported to a wide range of formats (.docx, for example) so you can share your work with others in the format they prefer.

As I continue to use this new device, I will post more insights on this blog.  In the meantime, if you want a reliable device with long battery life (I get over 8 hours) for the bulk of what you do that is web-based (and local to your machine when it is nowhere near the Internet), this can be a very good $250 investment.


Well, this is my current attempt to distill some of the core ideas in the Next Generation Science Standards (NGSS) in the form of an infographic.  Let me know if you find it interesting or useful.

I used Inkscape to create the graphic over a period of a few weeks as we were preparing for one of our NGSS workshops.

ngss infographic

Over the years, I’ve gotten to know some Flash programmers who have mastered an arcane art:  How to use a tool so cumbersome that it provides full employment on projects that could be done in a fraction of the time in Hyperstudio and then exported to HTML5.

This all came home to me when I was asked to help edit some e-books using Adobe Flash Pro.  Those of you who remember Macromind Director, and the adage that a camel is a horse designed by a committee, can imagine what the interface looks like.  You have libraries of resources that you import to either frames or libraries (and be sure you never get them confused).  Animations made from still frames can be made in only five times the time it takes to do this in Quicktime.  But the real time sink comes when attaching everything together.  Heaven forbid you need to duplicate a frame without duplicating the frame’s inheritance since once you edit the “new” frame it will replace the contents of the one you copied it from as well.  Of course this is all fixable by a series of crafty maneuvers that only take a half-hour to learn.  Next comes the linking of sounds to images, but I’ve made my point.  Once you have your e-book project finished in a month or so you then need to compile it for every platform on which you want it to run.  “Voila!” (which is French for “my wrist hurts,”) you are done at last.  See, full employment for even the simplest of projects!

Hyperstudio, on the other hand, handles the same project this way.  First, create a background screen with the major navigation buttons and a text frame.  Make as many cards with this background as you need (this takes 20 minutes, if you include a 15 minute coffee break.)  Next, and this is the tricky part – drag and drop the images and text for each page onto each card.  If your images are movies, then drag and drop works just as well. Of course, if you are in a hurry, all you need to do is create the original template card with the navigation buttons and the text object marked as group objects, you can then do one “New Group Card” action (Edit menu) to start a group, and then just drag and drop the entire folder of images on to the HyperStudio icon in the dock.  This will instantly create as many additional group cards as you have images in this folder.  This skips the many steps of dragging and dropping each image individually on to each new group card as you make it.  What makes this step tricky is how you create the illusion that it takes days, not minutes, to assemble these pages.  Next, attach sounds as needed so that when (for example) you click on some text, the narration plays.  Finally, there is the matter of exporting to HTML5 which is done by choosing Export and HTML5 from the menu.  The result plays on virtually anything.  Put a fork in it, you are done.

Now how you explain the next 29 days of R&R is up to you.

Staff development

Now that the next generation science standards (NGSS) have been released, about half the states have adopted them.  The missing element seems to be staff development.  Because these new standards go way beyond content to address the very methodologies of education, it seems essential that all teachers have the support they need to implement the new standards.  According to a recent article in the journal Science  (vol. 340, p. 1391, 21 June, 2013), while 83% of science teachers think NGSS will improve learning, only 38% think they will get the training they need.

Now if the only thing that changed was the order of existing content, this wouldn’t be a problem.  But these standards go way beyond that.  For example, Engineering is now specified as a K-12 subject – a field that teachers in general need to know more about.

In general, the standards move us from nouns to verbs – to activities students explore to enhance their understanding of core concepts.  For example, the standards state, with reference to the application of math in science:  “Emphasis is on assessing students’ use of mathematical thinking and not on memorization and rote application of problem-solving techniques.”

Now at first glance, coming off a generation of NCLB-driven education, this shift is overwhelming.  In fact it is delightful – provided teachers get the support they need.  This support can take many forms, but our own approach is to engage educators in hands-on experiences that enhance learning and rekindle the joy that drove teachers into education in the first place.

Contact us for more information:

I was engaged in conversation last night with one of my best friends in the world, Roger Wagner – the inventor of Hyperstudio (  One of the things we talked about was the shift in educational technology use from computers as tools of creation to computers as tools of consumption.  Programs from technology in education conferences used to be filled with sessions on everything from Logo programming to how to help students create interactive multimedia.

Since the onset of NCLB, all that has changed.  Our knee-jerk reaction to high-stakes testing has stripped creativity and curiosity from the the curriculum, and replaced it with just enough of the right content to get students to pass tests.  Because it is not blindingly obvious how students knowing the intricacies of programming, or the ability to create multimedia projects, will improve test scores, these topics have fallen by the wayside, leaving the beautiful minds of our youth in tatters.

As for (currently) non-tested subjects (e.g., engineering,) classroom exploration is non-existent, providing no incentive for students to learn something about areas of study that can lead to very exciting careers!

Next week I speak at the International Space Development Conference (ISDC) and the International Space Society has just released the new roadmap for space exploration (  This is an amazingly bold document that anticipates a time when there might be more humans living in space than currently live on Earth.

Of course, without a large number of scientists and engineers, none of the proposed milestones will be reached.  It took 400,000 people working full time to make the Apollo missions a success – and that was just to allow short trips to the moon.  Any of the new space objectives will require even more than that – yet students entering college today have known nothing but NCLB’s test-driven mandates, and they arrive at college bereft of curiosity and creativity.

One of the handouts for my session at ISDC is an “incomplete” manual for an interplanetary spacecraft that has about 50 topics for students to explore in finishing the document.  (I will post the document online for all to have very soon.)  My purpose in creating this document is that it represents a standalone activity that can lead to an interest in students in topics ranging from life sciences, to physics and engineering.

We have a tremendous amount to do as we repair the damage of NCLB and prepare ourselves, and our students, for a delightful and exciting future.

Floors and ceilings

Education in the United States is about to undergo significant change with the adoption of the next generation science standards. Rather than focus on specific content associated with each grade level, these standards address three things:

  • How scientists and engineers think and solve problems
  • Disciplinary core ideas, and,
  • Crosscutting concepts that link science and engineering to other disciplines including those addressed by the Common Core standards.

This transformation is important in my view because of floors and ceilings.

For too many years, we have been limiting the development of student knowledge by teaching in ways that revealed the answers to the kids. Every time you tell the student a solution to a problem, you have put a ceiling on this knowledge, and students have no incentive to go further. On the other hand, when subjects are approached through inquiry, we provide a floor for their learning and they can move up from there.

This is the core idea behind our Knights of Knowledge project (

Of course, this transition is not easy to make.  Teachers who would never give a child a book of crossword puzzles with the answers filled in, still give students textbooks with the “answers” to all the content area explored in a course.  While directed instruction will always have its place, it is important to know when to stop sharing information with students, and when to send them off on learning adventures of their own.

Tragedy at Sandy Hook

Last week we all experienced a tremendous tragedy when a gunman took the lives of so many people in a gun attack at the Sandy Hook School in Newtown, Connecticut. I was enraged when I heard the news, but could not write a blog on the topic at the time. That has changed.

On the day of the incident, White House spokesman Jay Carney said “today is not the day to discuss gun control.”

That is pure bunk. Friday would have been a perfect day for the President to do more than offer condolences. He could (and should) have called for immediate legislation to regulate guns and the make sanctions against gun-produced crimes extremely severe.

I’ve heard all the arguments against gun control: “If guns are outlawed then only outlaws will have guns;” “Guns don’t kill people, people kill people.” These platitudes make nice sound bytes for the NRA, but they don’t sound so convincing when juxtaposed against a photograph of a six-year-old girl laying dead in a pool of her own blood.

Why our President is reluctant to take on the NRA is beyond me. He isn’t running for office again, and doesn’t need their support. If the issue is the Second Amendment, maybe he should read it again – in its entirety. “A well regulated militia being necessary to the security of a free state, the right of the people to keep and bear arms shall not be infringed.” Note the “well regulated militia part.” If you really want to shoot weapons at people, join the armed services and hope for war. Don’t spray classrooms full of bullets, killing many young people, destroying families, and bringing sadness to the entire country.

Yes, I”m aware that In 2008, the Supreme Court issued a landmark decision concerning the Second Amendment. In District of Columbia v. Heller, 554 U.S. 570 (2008), the Court ruled that the Second Amendment protects an individual’s right to possess a firearm, unconnected to service in a militia, and to use that firearm arm for traditionally lawful purposes. This ruling flies in the face of the Second Amendment as written, but what do I know – I only have a PhD and am able to read without moving my lips. Maybe an attorney can explain this too me. I’m sure the Supremes would argue that the mass murder of children was not a “traditionally lawful purpose,” and argue that their ruling was just (even though it conflicts with the very clear language of the second amendment.)

In the spirit of full disclosure, I used to shoot on a regular basis (and even have some marksmanship medals in a box somewhere). But my rules were clear – I either shot at paper targets or at dinner. I am not against game hunting – only against the ease with which your typical nutcake can get weapons and use them against innocents.

So, what would I do if I could?

First, I would make any fire-arm-related shooting of a person (by non-police or militia) a federal offense with a mandatory sentence of life without parole. Then, I would track down the place or manufacturer from whom the gun was purchased and impose a mandatory fine of one-million dollars per shooting event to be paid to the families of those who were maimed or killed as a result. Say the perpetrator had a mental breakdown, fine – then the incarceration starts in a mental hospital and moves to a prison later, with no chance of parole.

My guess is that, if this was the law of the land, we would see firearm-based attacks drop by a tremendous amount.

If it kept even one child alive, it would be worth it. Children don’t belong in caskets, and our President’s failure to speak out on this issue makes me sick. We have a right to expect more from him.


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