Optimal Engineering Constraints In Open-ended Learning Experiences

I became interested in the determination of optimal engineering constraints in open-ended learning experiences when adapting a spaghetti bridge project, that I had previously taught online to elementary teachers,  to middle and high school engineering students.

When I initially did not constrain the amount of pasta and glue, most students created very strong structures with large amounts of glue providing much of the structural support.  This was especially true of middle school students and not as much for high school students, with one exception. When I previously taught this project to teachers, teachers also build traditional bridges with spaghetti trusses and used glue only to connect the beams.  Let’s call this the minimal constraints case. See below for some middle school examples.

After I noticed that the bridges were basically indestructible and mostly made of glue, I decided to try and further constrain the problem to see if the results would be more in line with real bridges. When I constrained to 40 linguine and 2 glue sticks (and the addition of a rubric that included aesthetics and other considerations), the results were much more aesthetically pleasing and in line with actual bridges.  Let’s call this the fixed constraints case. See below for minimally constrained (top) and fixed constraint bridge (bottom) from the same middle school team. 

My next thought was to change from fixed constraints to a fixed cost where students could choose/buy materials based on what they had designed – so each piece of pasta has a value as well as each glue stick with the bridge required to support a certain amount of weight at the lowest cost.  This makes the problem even more realistic in terms of providing cost based engineering constraints. High school students built a second spaghetti bridges under this fixed cost, variable materials case. Students built realistic bridges and furthermore were more “spare” than the fixed constraints  middle school bridges, reflecting consideration of the cost constraint. See below for minimally constrained and fixed cost, variable materials bridges made by a high school student.

Here’s another example of a minimally constrained (bottom)  and fixed cost, variable materials (top) bridges made by the same high school student.  

Taking the fixed constraints case (but would also apply to fixed cost, variable materials case), we could theorize that as the constraints are made tighter, there would be a frustration point and the project would be too hard.  Likewise, if the constraints were too lax, it would turn into the minimal constraints case. So I got to thinking about whether there was some optimal constraint that exists for engineering problems given to students. This is reminiscent of the notion of trade-offs in engineering.  

I did a literature search of academic papers but could not find any previous research on this topic.  I also consulted with two leading academics in the field, who reported they were unaware of any research on this topic.  It would be interesting to try and set up some experiments to find the optimal constraints for different age students for this project.  The research questions might be:

  • What is the optimal constraints value in the fixed case that is not too strict (frustration) and not too lax (not realistic)?
  • Should this differ for different students or teams to differentiate the project?
  • At what age, should the most realistic fixed cost, variable materials case be used?
  • What learning does or does not take place in each case and how does it differ?

I did capture some artifacts in my first go around on the project.  The first was a question to high school students in their project documentation.  Three students did not answer the question. Students reported that the more constrained bridge was harder to design and construct.  

Question:  compare and contrast the minimally constrained and fixed cost bridges both  in terms of your engineering design process and the final result.  

Student 1 (HC)

The minimal constraints bridge I paid little attention to the amount of materials I was using. I just used as much as I wanted until I thought it was as sturdy I could make it in the time given for construction. I used the glue very liberally to make the connections as strong as possible. For the constrained bridge, I more thoroughly planned out my design for it to be as strong as possible using the least materials. Also I only used as much glue as I needed as to not run out of glue and have to buy another. 

Student 2 (LK)

Between my two bridges the first one was stronger and could support more. This is because we could use as many resources as we wanted and the second bridge we had a limited amount of resources so it was harder because we had to be cost efficient. 

Student 3 (ML)

Both followed a similar rectangle design. But, the unconstrained one used too much glue. The unconstrained one would easily succeed.

In summary, I found that minimally constrained bridges didons  not generally produce a realistic civil engineering experience.  Younger students seemed less constrained by traditional notions of bridges and produced very creative, strong, glue heavy bridges while adults and high school students were less likely to do so.  At this time, I am planning to use the fixed constraints case for middle school students and use the fixed cost, variable materials case for high school students. Further experiments are possible to further refine and answer the proposed research questions.  I have four rotations per year of middle school students, which provides opportunities for further research and refinements.  

High school student testing fixed cost, variable materials bridge. 


high school student carefully building his bridge according to his 1:1 scale plan.  

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Engineering Projects Help Add Common Sense to Math

In my Make Your Own Dragster unit, middle school students first calculate the velocity of a non-geared up robot car, in this case Riley Rover. They take three time measurements on a ten foot course. I observed that students do not have a common sense, deep understanding of the mathematics. My thesis is that this comes from years of largely doing calculations on worksheets removed from any real world context.

Example 1 – Average of 1.73, 1.73, 1.173

Students used calculator, made a mistake and got an answer that was not 1.73 and did not notice a problem. If students had an understanding of what average means, they would know that they did not need to calculate and the answer is 1.73.

Example 2 – Average of 2.78, 2.50. and 2.30

Students got an answer of 7.20 and did not notice a problem. Students with a conceptual understanding of average should have seen that their answer was not reasonable and the average should be 2 point something.

Example 3 – Students write answers like 2.434566 ft/sec and do not notice an issue.

Students should know that the measurement variation and errors make digits beyond one decimal point meaningless.

Of course, it was a great opportunity to discuss all these examples with the class.

Engineering really makes mathematics meaningful, useful, and ties it to the real world. The danger of years of mathematics education largely out of context is that students focus on getting the calculations right and not really understanding the concepts behind the calculations.

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ISTE Webinar on My Research Online


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Book Now Out on Kindle

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Interview From PBS Connecting Point

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Engineering Is Egg-citing Day

I can’t thank you enough for everything you did for Engineering Day. I have received incredibly positive feedback from students and teachers. One student said it was the biggest highlight of the year!

Kate Arsenault, Library/Media Specialist

Wow! Thank you, John! What an amazing day! One of the very best days that I have seen in any school. 100% engagement from all students!!! The pics are amazing! I can’t thank you enough!

Kristen Gordon, Principal

My 6thgrade son graduates from our small, rural elementary school in Western Massachusetts this year.  I had struggled  for many years to try to bring in some robotics-based engineering experiences to the school.   However, a new principal and new library/media specialist were very excited about the prospect so we worked together to create a PK to engineering day. I racked my brain for a while to try and come up with a cohesive theme.  I was finally inspired by the egg drop challenge the first-grade teacher does every year at the nearby elementary school where I teach.  We expanded on that idea to create engineering challenges based on eggs.  At the kick-off assembly, we did a skit where farmer Kate explained that she needed help with transporting eggs around the farm and we challenged each class to help her with a specific task.

  • PK students reported on progress of each class back to the principal
  • K and grade 1 students did a traditional egg drop challenge where the designed some kind of container to protect and egg from breaking when dropped off a fire truck at the end of the day assembly outside
  • Grade 2 students designed non-robotic LEGO egg vehicles that could drive down a ramp and not break the egg inside
  • Grade 3 students designed robotics egg mixers and optionally included craft materials
  • Grade 4 students designed robotic cars using LEGO WeDo 2 kits and Apple iPads
  • Grade 5 students designed devices that transported eggs horizontally with LEGO NXT robots and EV3 software
  • Grade 6 students designed egg lifter devices that transported an egg from the floor to a table

All classes had craft materials available and, in most cases, needed them to create some kind of egg holder. We mostly used hard boiled eggs but grade 1 students decided to use raw eggs for their final egg drop test.

While it was challenging at times to get around to multiple classes to check in and give help, it was very interesting and exciting to see kids K-6 all doing engineering challenges at the same time.  Kids (and teachers) were fully engaged and so proud to show me what they had created.  I also saw great collaboration and cooperation as most kids worked in teams to accomplish the task.  As I returned to classes, I was amazed at how designs had grown and changed during my absence.  I scaffolded as needed for students who were stuck or needed technical help.  We had minimal connection or technical issues with the various LEGO software we were using.  Students, especially fifth graders, made interesting physical connection with LEGO and non-LEGO materials.  Some of the most rewarding moments were when I saw students with various visual, emotional, or learning issues succeed alongside their peers and were literally be beaming about their work.  I got reports from parents and kids at our local swimming hole about kids who were still talking about the day at home or told me directly that it was “amazing”.  I was so happy to be able to provide this experience to my son and all the kids in our small town.

*Thanks to the teachers, administration, and students of the Anne T Dunphy School for letting us use the robotics kits and laptops for a day!

Lots of photos but check out this video of this second grader  testing his final LEGO egg carrier car.

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LEGO Education Master Educator Meet Up with Mitch Resnick

I was recently honored to be named a LEGO Education Master Educator (and an advisor to the group).   We met recently in Chicago for a day long event.  I got to chat a bit and hear the keynote from Mitchel Resnick, known as the inventor of the Scratch programming language.  He is the  LEGO Papert Professor of Learning Research at the MIT Media Lab and has been advocating the concept of Lifelong Kindergarten, the idea of bringing playful and creative kindergarten attitude to the rest of school and, indeed, to life.  Unfortunately, the push now is in the opposite direction, of pushing play out of kindergarten.  Mitchel is the intellectual heir to his mentor Seymour Papert, who pioneered the notion of educational technology with his LOGO programming language.  Papert also came up with the notion of constructionism, the idea that children create knowledge best in the context of creative  hands on activities.   Resnick  has created a model of projects, passion, play, and peers to help illustrate and define his notion of lifelong kindergarten.   Both Papert and Resnick has inspired my own practice of creating K-6 engineering experiences and also intensively studying the engineering processes of elementary children.


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PAEMST – Presidential Awards for Excellence in Math and Science Teaching

I received this award a few years back and I encourage others to apply.  It’s a great experience to video yourself, really analyze what you are trying to do, and get feedback from the NSF reviewers. Here’s some info on the award.

The Presidential Awards for Excellence in Mathematics and Science Teaching (PAEMST) are the highest honors bestowed by the United States government specifically for K-12 mathematics and science (including computer science) teaching. The 2017-2018 nomination and application period for K-6th grade is currently open.

The awards were established by Congress in 1983. The President may recognize up to 108 exemplary teachers each year. Awards are given to teachers from each of the 50 states, the District of Columbia, the Commonwealth of Puerto Rico, the Department of Defense Education Activity schools, or the U.S. territories as a group (American Samoa, Guam, the Commonwealth of the Northern Mariana Islands, and U.S. Virgin Islands). PAEMST recognizes those teachers who develop and implement a high-quality instructional program that is informed by content knowledge and enhances student learning. Since the program’s inception, more than 4,700 teachers have been recognized for their contributions in the classroom and to their profession. Presidential awardees receive a certificate signed by the President; a trip to Washington, D.C. to attend a series of recognition events and professional development opportunities; and a $10,000 award from the National Science Foundation (NSF). The National Science Foundation administers PAEMST on behalf of The White House Office of Science and Technology Policy.

Please consider nominating a talented science or mathematics teacher using the PAEMST website today. If you are interested in applying yourself, you can begin an application at www.paemst.org. The 2016-2017 nomination deadline is April 1, 2018, and the application deadline is May 1, 2018.

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Can You Teach Motivation?

I have been helping out at my son’s Suburban basketball team, mostly scorekeeping, but I did substitute for a coach one night.  I was working with the “bigs” on close to basket shots feeding them a pass with the kid turning and shooting and then rebounding and shooting again if they missed the first shot.  I noticed that the kids, especially the tallest kids, were not super motivated to jump, rebound, or to get the second shot in.  The two coaches have been noting the same things and discussing it with the team.  After they had a lackluster performance during yesterday’s game – not jumping, not rebounding well, not moving towards passes, etc. – one of the coaches basically told the team yesterday that he can’t coach motivation.

In my owning coaching, especially in baseball, I have definitely thought the same thing.   But I starting thinking about my Heffernan Fly Ball challenge experience.   I have been seeing more and more in my own coaching how what we practice and the drills we make up affect the kids when they come to games.  This is expressed well with a phrase I read in a Cal Ripken baseball coaching book, “Practice does not make perfect, perfect practice makes perfect.” (Ripken Jr, Ripken, & Lowe, 2007)

I was an assistant coach two years ago on a 4/5/6 Cal Ripken baseball team.  The coaching was very good especially on teaching baseball fundamentals and diagnosing hitting, pitching, fielding issues.  But the team was in a slump.  The team hit a nadir during one game when kids were missing lots of fly balls, making a lot of mistakes, and not hustling.  The lowest point came when the coach’s twins got into a physical altercation on the bench.  However, the other coaches’ attitudes bothered me more than the kids attitude.  The coaches were really yelling out when kids made mistakes and showing their displeasure when it happened – especially with their own kids.  I got to wondering if that was inadvertently increasing the pressure on the kids, which has the side effect of causing more mistakes, which further decreases confidence and causes even more mistakes.  This whole process, I was wondering, results in a hard to correct negative spiral.  I think this especially true in baseball when the spotlight is really on the player fielding, hitting, and pitching.

And was this really all on the kids like the coaches were saying?  I recall one of the coaches saying the same thing as the basketball coach – that they could not teach motivation.  While there is some truth to that and some kids are motivated despite what coaches do, as a teacher, I knew that adults can strongly influence all aspects of teaching and coaching, including social-emotional factors.

I learned from many years of training and performing with my two whippets in the dog sports of agility, obedience, and rally is that proofing can be the hardest part.  My dog Wyatt was great at home but it was much, much harder for him in actual trial setting, especially in the less action oriented sports like obedience.  Dogs can find it difficult to transfer their knowledge and their training to different locations, different equipment, and to busy or distracting environments.  Dogs can also be super sensitive to their handler’s changes.   Increased nerves can translate to the handler being slightly different – even though we are not necessarily aware of it.   What’s this all have to do with the fly ball issue the team was having in baseball?

Well, one of things I really liked about the baseball coaching on this team was that drills were turned into fun games and contests.  I later learned that this a big part of the Cal Ripken coaching philosophy.  I had a chance to lead a practice one day when the head coach was unavailable.  The practice field is opposite an ice cream stand where we would sometimes take the team after practices.  I got the idea to make a team challenge for fly balls that would increase pressure (but in a enjoyable and not a stressful way). The kids got the “proofing” but in a fun way.  Increasing the pressure in a fun way can help kids handle game pressure and also have more fun playing in actual games. As a team, the kids had to get a certain number of points to get various levels of ice cream – 100 points was a small cone, 125 was a small cone with sprinkles, and 150 points was a medium cone, 200 was a medium cone with sprinkles.  I then made a system for getting points.

1 – regular catch

2 – running catch

3 – shoestring catch

4 – diving catch

I added a point for an accurate throw back to me.  I also made a time limit, which was both practical but also a way to subtly increase the challenge to more closely simulate the pressure of a game.

I hit the fly balls to the kids and had them record their own points as a team – hopefully increasing their ownership and excitement in the drill.  Well, it certainly increased the kids’ motivation and they immediately bought into the idea and were encouraging each other.  One of things I noticed right away was that kids were really hustling to get to the ball, which had been a real problem in practices and hence games.   There was a marked decrease in the number of errors and a marked increase in good catches.  Some kids (see discussion of inadvertent side effects) were doing diving catches when they were maybe not actually needed (my own son being the prime example).  However, they were so into it they went for and earned the highest point level and we had a fun time at the ice cream stand.

I thought it went well and I was hoping some of it might transfer.  When the next game rolled around, I reminded the kids before the game of the fly ball challenge, specifically that they could catch and it could be fun and they should show the same hustle they showed during practice.  I was blown away by the huge difference in the fly ball fielding. Kids were running to balls and not making any errors!  I used the same challenge last year when I was a head coach of my own grades 4/5/6 Cal Ripken 40/60 team with similar results.

Getting back to basketball, I wondered about ways these kids could be more motivated, especially the bigs.  I did notice the team was super motivated when the coaches were occasional creating contest drills.  Would more contests help this team be more motivated, jump more, hustle more, etc.?  Well, I did not have much time but I tried to think of way to make our turn and shoot drill into a contest.  Many of the “bigs” were super lackadaisical about getting their rebound shot in.  I said if they missed a certain number of second shots, they had to do a lap.  Meanwhile, I did explain about “game speed” and perfect practice makes perfect.  But I think that talk needs to backed up with drills that expressly show the kids what is meant.  When I added the lap thing, the kids immediate perking up and got exciting but there was an inadvertent side effect of them slowing down and really setting up that second shot, which I did not want.  So as coaches we have to really watch for these inadvertent side effects.

I see this a lot when one part of the drill is the focus but we don’t look at the second part.  One of example of this was a drill we did when one kid shoots and the second rebounds.  In this case, the coach was focused on the shooting part but not the rebounding part and I saw that at rebound kids were walking with the ball and not even dribbling or passing after the rebound.   We certainly don’t want the kids traveling after the rebound but was what we were inadvertently teaching.  We have to always be thinking of what it should look like in a game and how drills should teach game speed and desired game behavior.

I am still trying to think of way to design the drill to make the whole thing fast including the rebound shot, if any.   Maybe have two teams, one on each side of the basket, complete to get the most shots (which might include second or subsequent shots) in a certain amount of time.  Then the kids would be motivated to make the whole process as fast and as accurate as possible.

So I think we as coaches can help teach motivation by how we structure our practices and drills.  However, I still agree that “you can’t teach height.”



Ripken Jr, C., Ripken, B., & Lowe, S. (2007). Coaching Youth Baseball the Ripken Way. Human Kinetics.


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Two Speeds at Once

This photo shows one of the common issues I see with our grade 6 make your own dragster project.  Frequently, kids try to have different wheels on the same car go at two different speeds at the same time.  Not sure if this has to do with causal reasoning or a lack of structural knowledge of gearing or something else.


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