Dec 4, 2015

#STEM Starts at Home: Turn! aka Spatial Skills Development

what to do 

Let your baby hold your finger, a spoon, or a toy like a rattle. Soon the clench will be paired with a wrist bend, and later turning and twisting the object around.
Image by lusi (sanja gjenero), via

what you are doing 

As your tyke turns objects, he or she becomes aware that things have different sides. Turning is a way to see these different views so a model of 3D objects can be built.
Visualization in 3D is part of spatial skills which are important in STEM success. You can think of spatial skills at this age in three main categories:
  • Placement: positioning objects in space. e.g. above, behind, between, inside
  • Features: ways to describe how objects are similar or different, and can fit (or not fit) together. e.g. triangle, corner, edge, round
Thus, the act of turning objects is the beginning of spatial awareness.


How you can grow 

Objects like spoons, forks, and rattles look different from different directions. Use them as starter experiences for your child to stimulate and build spatial skills.

As your baby’s small motor skills develop, move on to plastic cups or that ring of blank CDs you have left over from the start of the millennium. These make great nesting and stacking objects which develop the next level of understanding size, shape, and relation to other objects.

Large motor activities like turning, maneuvering around objects, pushing a cart, and going through doorways require your tyke to identify empty space, develop a sense of perspective, and make size and speed concepts real, useful, and concrete.

As your toddler shouts in disdain that he or she can’t go through a chair to pick up a toy that dropped, show with words and gestures that the problem can be solved spatially by going around or under the chair.

Tapping tykes on the head as they crawl under a table helps them remember (make a map in their minds) that something is up there. As their brain grows, they can relate the action of squatting down to get under with the idea that something is now above them.

You know you are successful 

When your babe starts to register these concepts, you know he or she is developing good spatial skills:
  • Up. My son was completely enthralled with the concept of up. We realized something was up (hah) when he would suddenly throw his head back and look straight above with a smile. It was as if he said “Hey, there’s something up there!”
  • Inside. I distinctly remember the day my son discovered that something could go inside of something else. It gripped his attention for quite a while as he put things in an empty pitcher and then took them out. Then he looked around for something else to stick his object in. It’s quite a wonder to watch.
  • Behind. Halloween was the time we first saw that our boy realized the concept of behind. He started chasing the tail of his costume as he spied the trailing yellow out the corner of his eye.
  • Mirror. So many parents tell me about when their baby first touches his or her face when looking in the mirror. When the babe then starts to touch other parts of the face and smiles when the baby in the mirror does the same, you are getting clues that some spatial skill development is going on.
  • Gestures. Even though my early childhood evaluation survey keeps wanting to see if my son can understand my words without gestures, I just can’t stop. Gestures are one of the first ways that babes start to communicate since speaking words are so much harder. But gestures seem to also be ways children can comprehend spatial relationships. Think about how you can describe with just words, the concept of above. But if you can use your hands, the concept becomes much clearer more quickly. Studies also indicate that children who use gestures tend to have stronger spatial awareness. So encourage your kiddo to talk with the hands. It may help develop STEM skills.

See also:

Nov 3, 2015

The T speaks to Manufacturing

I wish I could do more for the manufacturing folks. My heart has always been close to the manufacturing, despite my more "academic" education. It's why I took a job with a small engineering consulting firm after I got my Master's degree. I wanted to get closer to the actual production of real products.
image by mokra (Marcelo Mokrejs), via

Maybe it started with Sesame Street and Mr. Rogers who showed those great films on how things are made.

Whenever I talk with teachers, I remind them that the T is not just computers. It's that thing that we used to call (in my days) votech, industrial arts--and today, it's a missing skill set in industry. I talked with a local manufacturer who deplored the lack of "middle tech" (as opposed to "high tech"), and many students need to know about this option. They know they can do better than the production line unskilled laborers, but don't feel they have what it takes to be an engineer or scientist.

In a way, the military has been the best career opportunity for these learn-by-doing kids who get enamored with technology itself. A smart teacher can leverage this fascination with things (vehicles, light, computers, animation, etc) into a technology career.


Oct 6, 2015

Girls and STEM: Biased Teachers' Efffect

There's an interesting study that came out this year that might be of interest to those of you interested in making STEM more accessible to girls.  Lavy and Sand's paper, On the Origins of Gender Human Capital Gaps: Short and Long Term Consequences of Teachers' Stereotypical Biases, caught my attention because of the international nature of the research.
image by heribertosdb (Heriberto), via

According to an Education Weekly article,  the researchers had teachers grade Hebrew, English, and math tests taken by 5th grade boys as well as girls. Some teachers could tell the gender of the test taker; others couldn't. While the difference in blind and non-blind grading was statistically insignificant for both boys' and girls' tests, girls tended to get higher grades on gender-blind grading, and boys tended to score higher with gender-known grading. Then, the study apparently tracked girls' progress in math, both regarding their future test scores and math and science courses they took in high school. Yep, if the girls had biased teachers in 6th grade, their math test scores tended to decline, and they were less likely to take more advanced math and science courses.

Cynic as I am (who was schooled in the U.S.), I'm seldom surprised to hear about gender bias in American schools. However, Israel is a country that sees its women as equal enough to have required terms of military service for them as well as their men. The fact that bias issues exist so early in their system is interesting.

I haven't yet been able to lay my hands on the study's details, but if the findings are sound, it underlines the necessity for a two pronged approach to removing social barriers to girls and STEM:
  1. Not only do educational structures need to address mitigation of negative influences within their systems BUT ALSO
  2. Parents and influential adults in girls' lives need to support girls with constructive coping strategies
Why the latter? A few reasons come to mind:
  • Until educational systems can be free from bias, girls will encounter biased educators somewhere along their education. If not in elementary school, then it may be in middle school, high school, college, or even graduate school. Knowing how to cope with biased instructors can mitigate these situations.
  • If your child is lucky enough to be able to get into the most ideal educational situations, the STEM profession is still rife with bias. In a way, delaying exposure to this kind of tough reality until a woman is nearly mid-life may end up being more catastrophic. The study, Stemming the Tide: Why Women Leave Engineering, revealed an interesting phenomena with women engineers: if they disliked their particular engineering job, they were likely to leave engineering completely, as opposed to identifying the problem as being their environment. This was not seen in other competitive and demanding fields such as medicine or law. Knowing how to keep environment from influencing sense of identity is invaluable.
  • Biases plague most people for one reason or another. Resilience skills can be important for a full and happy life.
While I disagree with the final statement in Sabrina, the Teenage Witch's Trial By Fury episode regarding algebra (i.e., "and then you can forget it"), I do agree with the larger idea that handling bad teachers is a necessary talent. In fact, I deal with that when I'm in the workforce: The majority of my job is dealing with people who intentionally and unintentionally don't communicate technical information clearly.

A good school would constantly check its processes to increase gender-blind evaluations whenever possible.  For example, I used to do this by grading tests backwards, from the back to the front which was the only page with the name on it. I actually surprised myself on how often I guessed wrong on whose paper I was grading: some students did much better than I thought based on classroom performance, and some students who seemed on top of it, kind of spun their wheels.

A good teacher would strive to be a talent-scout more than a judge. When I taught, I tried to observe what was stumping students who struggled and tried to push the high performing students into areas that were challenges to them personally (oddly, public speaking was often such an area). By doing so, my testing and evaluation tools became ways to diagnose areas of strength and challenge, rather than discerning the "wheat from the chaff". Oddly enough, in my current job in industry, my manager has commented that I tend to understand why people were misunderstanding the situation rather than just saying the person was not sharp enough -- or worse, was a liar. By doing so, I can approach them as partners in solving the problem at hand, keeping lines of communication open. Not doing so can result in standoffs, shouting matches, posturing, or just not getting the job done.

A good parent (or influential adult) doesn't have to have the answers from personal experience (sometimes that personal experience may result in some post-traumatic stress!). Instead, a good parent can get children the resources they need: a role model, strategy books, or a process that can serve them for the rest of their lives. My parents supported me when I struggled academically with something as simple as getting me a planner to figure out my assignments and scheduling when I had to start them. But they never let a bad teacher be an excuse for not learning. They said things like "We know it's more important for you to know how to add rather than do it quickly, but after you know how, you can do it faster--and if that's what's required, that's what you need to practice."

Together we can help girls get over the barriers they encounter in their lives. And they will be the better for it.

Sep 8, 2015

Tips for engineers (and computer folks): Clarify, Verify, Quantify

When I have time, I try to jot down tips for the young engineering and computer science professionals. These might be useful for teachers, though, who want some insight into teaching foundational skills to their younger students.

I just cleaned up this blog post which was inspired by my husband who was training in a young engineer. We discussed the fact that there is not much instruction on how to have new graduates walk that delicate line between being rigorous in the engineering process and being helpful to customers.
image by Abyla (Javier Gonzalez), via

One thing that good engineers should do is stay grounded in reality. Thus, the trilogy of Clarify, Verify, and Quantify are important when considering problems in their systems/products. Time is money in the work world, and an engineer should use a logical process when troubleshooting and solving problems. This process can also be helpful for computer folks.

In the educational world, this is one aspect of "Critical Thinking". Let me know if you have questions about it!

See: Clarify, Verify, Quantify on the the Engineer's Playground Wordpress site for engineers and computer scientists, Because Engineering Should Be Fun.

Aug 4, 2015

#STEM Starts at Home: Go Outside!

Parents ask me, even before they become parents, what they can do to keep STEM open for their children. I always emphasize that they don't technically do anything different than what early childhood folks have been saying for years. Rather, they should make sure those activities are rich enough so that they can build STEM foundations. Here's one example: 

Go Outside! aka Starting Observation Skills

what to do 

Pack up your little one, even if an infant, and head out of the house. It could be to the park, to the zoo, to a mall, or to a restaurant. The latter may be especially good if its furnished with the ceiling fan.

image by Richard Sweet, via

what you are really doing 

By exposing your tyke to new sights sounds and smells, you're stimulating the senses which are essential for observation skills which are important for STEM:

  • Scientists observe how the natural world works, later making precise measurements and sharing these findings with others. Together, these observations are clues that help them uncover the laws of nature. 
  • Technicians use observation skills when troubleshooting systems, whether they are planes, computers, nanotechnology, or gears. 
  • Engineers observe how existing designs work and are keenly observant when troubleshooting their latest product.
  • Mathematicians use observation skills in conjunction with tools like graphs, charts, and computers to discover underlying patterns which they try to describe with equations and algorithms. This is how they can predict future behavior.

how you can grow these skills 

Keep pointing out interesting things that you see, things that catch your eye. Maybe you are drawn to animals, machinery, interesting smells or noises. As you notice things in your world, share them with your little one.

Reinforce your child's own observations. Infants will squeal or turn heads when something interesting catches their eye. Look around and try to see what your little one sees. As your child grows to be a toddler, he or she may start to make grunts, gasps, or even basic words like "bus", "bug", or "baby" to share what falls into view. Appreciate the shared observation with phrases like "Bus, wow, good eye!" or "How lucky we were to see that bug!"

As your child gets older, encourage a closer look, much like the Daniel Tiger song says. By doing so, you help your child see how things are put together or what may be hidden underneath. Lifting rocks, opening cases, or removing panels can show your tyke that there may be more to see than what's on the surface.

You can do this anywhere: looking up (in buildings as well as outside), on a park bench, or even just sitting in traffic. Many parents I work with have found a new appreciation for ceilings as well as road construction. Point out see what goes by, what sounds and smells exist, and what catches your fancy. I personally like pointing out funny shaped objects, things that move, and things with iridescent colors.

My son's squeal as a non-speaking infant/toddler was my signal to look quickly at the squirrel, bonfire, or excavation machines that passed by. I was surprised at how much I had been missing in my own neighborhood.

And being outside may provide even more benefits. Data shows that kids in urban areas have a higher risk for myopic eyes. Though there is debate about whether this is due to the lack of ultraviolet light exposure (for Vitamin D production), the fact that indoor light's intensity is limited compared to natural light, or the fact that looking at objects in the far distance allows the eyes to relax, the findings all encourage kids to get outside at early ages.

So the great outdoors appears to help the brain as well as the body.

See also:

Jul 7, 2015

#STEM Starts at Home: Tools for Toddlers

I recently got this question:
I'd like to get my 1-year old daughter some baby tools -- hammer, screwdriver, and wrench, and toy nails, screws, and bolts. She really liked imitating me with the screwdriver the other day when I was assembling one of her toys. I searched around on Amazon but only found things that (i) don't come with the nails, screws, and bolts, and a board to play with them on, (ii) have padded/squeaky hammer, screwdriver, and wrench that cannot actually be used, (iii) are large sets that take a ton of space, or (iv) are geared toward older kids. Any suggestions?
This is the part of my job that I love--giving advice on good resources out there.

One of the things I always ask in cases like this is: Where are your little one's motor skills? Does she wield a spoon pretty well? Does she feed herself? When she picks up other objects, do they all go in her mouth? Most children at this age still put things in their mouths so some tool kits are inappropriate. You want something that can handle the chewing and drooling without choking.

That being said, this tool box by Kidoozie is one that I got for a niece a while back when she was two (girls tend to be age appropriate for things like this a year later than the toy is listed). She loved using it. She would stand in the garage working with her father who is a carpenter.

When my son turned one, she gave it to him, and he has loved it at different stages. He first loved putting the tools in his mouth, but then he liked the shapes, turning the gears (they make music), etc. Then somewhere along with way he started hammering the nails (I think he and/or his dad broke it later) which would have one nail pop up when the other was hammered down. And he now likes putting the screwdriver in the screw heads and turning. A quarter turn is all that is needed to make a noise, and it works well with the first instinct of children to turn one way a bit and then back again. The drill trigger has broken, but that doesn't stop him from taking it and going to the doors and cabinets to apply the tool to "fix" them as he sees his dad do. So the short is, if your little one sees you using real tools, she can use these to imitate, and also build some motor skills, hand-eye coordination, shape sorting, etc.

Keep those questions coming!

Jun 2, 2015

KISS: A Story from Space

You're not a real engineer unless you like to KISS. Really. For those of you who are unfamiliar with the acronym, it stands for:
image by pitabox986 (Peter Miller), via

  • Keep
  • It
  • Simple,
  • Sweetie  (or that's what I say. Others use a more demeaning S word for some reason)
As an engineer, wielding the knowledge of science, the tools of math, and a wealth of technologies, it's all too easy to fall into the rabbit hole of "over-design" or over-engineering things.

There's a story we in engineering like to tell when remembering we need to keep things simple. From my research, it's not quite true, but it's a good story in any case:

Ballpoint pens work using gravity. The ink presses against the ball which then rolls to lay ink on the paper. But in space, alas, gravity doesn't work the way it needed to for the ballpoint. So, NASA invested in the development of a space pen--millions of dollars, so the story goes. It was branded "the space pen" and the pride of American ingenuity. Now the astronauts could write in space!

So it was stunning, the story continues, when the Berlin Wall fell and the secrets of the USSR were told. The cosmonauts had the same problem. But their solution? They wrote with pencils.

It's a gift to be able to realize you may be over-engineering the problem and even better when you are willing to KISS the problem again to keep things simple. Help your kids step back and make sure they are meeting the needs within reasonable constraints.

~ until next time, Yvonne

Read more:

May 30, 2015

Review: Robots 4 U

Having taught a lot of engineering/STEM curriculum, I am always on the lookout for highly flexible kits that truly have science, technology, engineering, and mathematics. As I walked the recent Mom's Expo, I was lucky enough to stumble upon such a kit.
courtesy of Robots-4-U

The I-ROBO kit made and used in camps by the Robots-4-U company is a promising blend of authentic materials and tools, physics concepts inserted right into the numerous scaffolded projects, and an engaging contextual framework of how robots relate with society and humans.

Okay, I think I've been hanging around educators a bit too long. Simply put, this seemingly basic kit looks a bit like a modern erector set with electronics and a microprocessor. The lesson book looks has cartoons to explain construction and STEM concepts. They remind me of comics I brought back from Hong Kong in the 70's, sort of pre-anime. What differentiates it from other "educational" robotics kit are:
  • Authentic materials: Plates, bars, and screws are used instead of patented snap-together pieces. But unlike the standard erector set, the projects speak to the product's Asian origins, composing not just machinery but also everyday devices like kid-sized glasses and organic creations like animals. You can also see inside the microprocessor unit; dispelling the "black box" is so important for the novice, and it plants the seed for learning more about the technology.
  • Tool instruction: One beef I have with kits is they often assume that the user knows how to use the tools. Being Montessori-based, the instruction booklet has engaging exercises that provide essential skills like using the wrench and screwdriver which are then built upon in future activities.
  • STEM-integrated: Another issue I have with some robotics curriculum is the lack of science foundation beyond simple machines (which is really more of an engineering concept than science in my mind). This curriculum embeds entertaining comics that discuss action-reaction forces and even the lift-weight-thrust-drag engineering science concepts behind projects.
  • Mechanical, then electronic, then computer: The activities in the instructional booklet develop in this manner: starting with simple static devices like glasses and moving into more complex items such as a helicopter which I'm told actually flies (!). This sequence is a standard evolution I usually do with my engineering and robotics courses as well because it seems to be the best approach to introducing true novices to thinking like an engineer. It's the way that humans developed fields of engineering, and it develops your budding mechatronics engineer (as we are known in the profession) with the ability to determine if the problem is best solved mechanically, electronically, or logically. Other robotics kits on the market often start with simple or set mechanical designs and focus only on the electronics and programming as the core place for creativity.
  • Time for play: And then, after the children make the project, they play with it. Imagine that! The product is part of a game, invites imaginative play, or lays the foundation for new ideas.
I know that most of the company's efforts are around camps, but their products look great for the STEM school, after-school, and even home-school markets. If you're looking for a creative way to make mobile mechantronic (robotic) devices, you need to check this out.

Until next time ~ Yvonne

May 5, 2015

Mom: A Child's Front Line Support System in STEM

image by gabriel77 (gabriel), via
This Mother's Day, I would like to talk a bit about my own mother. A mathematician, physicist, environmental scientist, and, at the end of her career, a chemist, my mom was a STEM pro.

Visits to her lab were what I did on my days off, before there was ever a "Take Your Daughter to Work" day. And cooking was a reminder of chemistry concepts from high school: "Put water in there," she would say as I burned my peppers and onion in the wok. "Don't you remember that the temperature stays constant at 100C when the water changes from water to steam?"

I told her once that it wasn't fair that she knew so much chemistry. Other mothers, I explained, tell their children "old wives tales" which their children would realize later were inaccurate or wrong. It would be a moment of maturity, when you realized your parents were just people, not all-knowing beings. But what about me, I told her? She tells me that this vitamin is important for this disease, and I'd find out later, she was right. When was my time to realize that my mother was fallible? She just chuckled and said to eat the favorite meal she had cooked for me.

STEM was not the only thing I learned from my mom. She also taught me grammar (using her Brighter Grammar books from Hong Kong) and had me read great literature so I could write better: Dickens was a great favorite of hers. She responded to ideas that I had with an action plan: for example, when I mused that there were a lot of kids in 12th grade who would be more than willing to tutor kids in other grades, she had me write a proposal and present it to the principal, birthing the volunteer tutoring program at our high school.

She also showed me the ways that one could be a mother, a student, and a professional. I appreciated the opportunities her "absence" due to work or class gave me to take care of myself, to do the laundry, to cook dinner, and to watch my sister when she had a long commute. My father helped when he could, and it made me realize that housework was something a family did, not just the women in the family.

Her life wasn't without issues. Our school didn't have a cafeteria because all the kids were to go home and eat a home-cooked meal. She told me each morning which friend I was to go home with for lunch. I thought they did it because they were my friend. I was extremely appreciative for the sandwich one made or the trip to Wendy's another provided. I found out only recently that she actually paid the parents to feed me, enough to take me out every day with their kid.

She told me once that she thought she would have made a good engineer. "You sure could have, Mom," I told her. She had the practical mind and the fortitude of spirit. "But, I couldn't," she said, "women weren't accepted into the engineering school. The girl who won firsts in math, physics, chemistry, and biology wasn't accepted into the engineering school. It was a clear message that women didn't do engineering." But I think she's happy that her daughter was able to, both due to her efforts and our changing society.

Thanks, Mom!

~ until next time, Yvonne

Apr 14, 2015

Grocery shopping algorithm, a joke

A fellow engineer told me this joke, and the computer scientist in me found it amusing...
A woman asked her engineering husband to go to the store for her to get a gallon of milk. "And," she added, "if they have eggs, get a dozen."
image by cannoncan (Karen Andrews), via

When he returned with 12 gallons of milk, she was agast: "What?!?"

"There were eggs," he replied.

Mar 31, 2015

Engineering Explains It All: The Numbers on Your Phone

What can engineering teach you? Interlace it with history and it can explain the world as you know it (or knew it).

I was having lunch with a friend and somehow phones came up. Suddenly, she said, "I never understood how that switchboard thing worked."
Image by Dan Shirley, via

So I explained that in the old days, phone were for the rich, with a direct line from one place to another, like the drawing room and the servants' quarters. If you wanted to connect two other places, you bought another phone line, which would connect, say the master bedroom to the servants' quarters. So some places, like the servants' quarters, would have multiple phone lines. This didn't seem weird as that's how the old bell system worked, when you would ring for the butler.

If one rich person wanted to connect to another rich person, then a line was set up from one house to another. Eventually, when more phones became prevalent, and one person wanted to anyone who happened to have a phone, the switchboard idea came into play. Basically, all the phone wires would come into the switchboard. Simply put, the switchboard provides a human a way of connecting two phones together so they can communicate.

Generally, speaking, a person would turn a hand crank on the phone to "ring" the operator at the switchboard. She (usually a she) would insert a plug into your line and connect so she could talk with you. Then she would ask you who you wanted to talk with. If you wanted to call up the grocer, then she would plug go to the grocer line, ring that phone line and make sure there was someone there. Then the operator would plug a wire into your line and the grocer's and thereby connect you.

A small town switchboard could have a number of lines coming in. If you wanted to call someone in another town, the operator would connect to that outside switchboard's operator. That operator would connect with the person you were calling, and then wires would be plugged into connect the phones up.

If you think of a city as a series of small towns, you can see that giving each phone a number, rather than a name, may make things easier for an operator in your area of the city. But if you wanted to call another area, you would also need to indicate the area of town you were trying to call in addition to the phone's number. Hence, the movie titled "Call Northside 777" referred to a phone number. Eventually, there were too many areas, and automated switching was developed where people could get automatically connected by typing in the number for the area, followed by the number for the phone. But how would people know which three numbers to enter?

Enter the idea of letters on the phone. With our example, Northside, you would find the first three letters on the phone (NOR) and press the corresponding number: 667. This was known as the exchange number, and this protocol explains why the old land lines in the same area of town often have the same first three numbers. We started to lose this idea as more phones came up in an area, and numbers that didn't correspond to the area name were added.

Other dialing protocols can be explained by the automatic switching, too. For example:

  • Dialing 1 for a long distance call
  • Area codes (in the old days) having a 0 or 1 as the middle digit

For those of us who remember landline phone numbers, this really sheds light on our world, and thereby gives us an instinct for reverse engineering phone switching technology. Pity the poor millennial who not only doesn't have this history to intuit how automated systems work, but also doesn't know why phones "ring"...

See also:

  • North American Numbering Plan, Wikipedia for explanations on the rules around phone numbers in the old days
  • Switchboards, Old and New, At&T Archives for pictures of the old switchboard systems and some trivia around the switching system (e.g. boys were deemed poor operators because of the pranks and cussing they did with the callers)

Mar 17, 2015

Tibetan Monks Go to College: STEM and Religion

Six years ago, I stumbled across a New York Times article about Tibetan monks and nuns learning science. It was part of the Dalai Lama's attempt to keep "modern and relevant" while honoring the Buddhist tradition. In a time when religion is often pitted as the antithesis of science and math, it was inspiring to see a spiritual leader articulate the commonalities, citing "investigative approaches with the same greater goal of seeking truth."
image by ndigit, via

Since then, more has been publicized on the experience of the monks as they journeyed to Emory University to learn more and of the professors who were challenged by students with limited English and formal education but who are "sophisticated adult learners" who are used to working through difficult ideas and analyzing contradictory observations and teachings. One of the most fascinating things is how do you teach students with no former experience with the scientific method.

You can see samples of the lessons and activities on their Science for Monks website, and a video about the experience at Emory University. While the monks certainly learned (and challenged) their science professors, the professors learned quite a bit from the monks as is documented by Chris Impey's Humble Before the Void which certainly looks like an interesting read for those interested in the intersection of religion, science, and philosophy.

So for those who have added R to their coursework in STEM, this project may provide an interesting resource and perspective.

Mar 3, 2015

Language and Math: Thoughts from Piraha Studies Regarding Language, Comfort, and Recursion

Back when I was teaching Computer Science, I ran across an anthropology article (Science News, The Piraha Challenge) about a research team who tried to teach the Amazon Piraha tribe math and reading. Two particular aspects seemed particularly relevant to me both in teaching computer science and later engineering and STEM.

image by mimwickett (Miriam Wickett), via


The Everett's, Daniel and Keren, worked with the Piraha in the late 70s to learn more about their language. In the early 80's the Piraha asked them to teach them to count and to read. Eventually, though, both lessons ceased. 

The article explains the discussion among anthropologists and linguists about language and culture roles in the situation. With math, the fact that the Piraha language had only words that roughly meant one, two, and many made simple arithmetic difficult for them. With both lessons, it seemed that practices required to read and do math conflicted with their "cultural conviction on how to converse."


Most notable was the belief that one should only talk from one's own personal experience. This eliminated language around "abstract concepts or ... distant places and times." In fact, trying to do so may have caused discomfort.

Think about it from a STEM point of view. The most basic mathematics problem is: "If I have two apples, and you give me another, how many will I have?" This concept requires thinking about something that does not yet exist in the real world--and in math, this is just the beginning of abstraction. If your student's culture feels this practice is wrong, success in the field will be difficult.

As a teacher, observing the student was just as important to me as communicating concepts and practices. When a student struggles, I always have to ask myself (or the student, if the right rapport is set up), "Why is this hard?" My job as a teacher is to then use this insight to make the subject make sense to the student. This is why teaching is an art, and really good teachers cannot be replaced by simple (or even complex) programs. 

This idea that a culture may actually feel that the typical practices of the subjects I taught would border immoral was fascinating to me. And perplexing. I don't think there is one, catch-all solution to it, but I share it here so other good teachers may at least consider it as they develop their lessons and teach their students.


One of the aspects the Everetts note is that the Piraha have no recursion in their language. There was some debate about this, but to me, the more interesting aspect is that recursion occurs in language.

My experience with recursion has always been in mathematics and computers. In fact, I was teaching a lesson on recursion the week I read this article, so I brought it up with my math majors, some of whom had already been introduced to it in their discrete mathematics course.

In case you don't know, in math, recursion is a process or definition that is really very simple: It has a general procedure that calls itself, using the next item in the series of numbers it will be applied to. It also has a termination condition. It's probably clearer with an example. Factorial is the most common example of a recursion function: When calculating the factorial of n, a number greater than 0:

  • See if n is 1. If it is, then the answer is 1.
  • If it isn't, then multiply n by the factorial of n-1
This means that 
  • the factorial of 1 is 1
  • the factorial of 2 is 2 times the factorial of 1 (which we see from above is 1) so it is 2 times 1 or 2
  • the factorial of 3 is 3 times the factorial of 2 (which we see from above is 2) so it is 3 time 2 or 6
  • etc.
In computer science, this concept is related to the stack data structure, and is one of the first standard algorithms taught. It was a very power concept in the early days of programming when memory was expensive because the code was tight, but the range was largely infinite.

But students always struggle with it. If you're a standard programmer (not a computer science major), you may be able to go through your whole life without ever using it. I've come up with a few techniques to explain how to design and decipher recursion functions, but there was always a struggle with the first grasp of the concept. If students don't feel that they have an inkling of the idea at the start, the rest becomes a struggle to memorize the bits and pieces they do get.

One of the key elements in recursion (and when implementing it in the computer) is that some information must be "held" until the next step is completed. In the case of the factorial, we know that factorial of 100 is 100 times the factorial of 99, but we have to hold that idea until we find out the factorial of 99, which requires us to wait until we figure out the factorial of 98, etc. Basically, we don't know the answer until we get the problem to be the factorial of 1, and then we can go back to all the multiplications we "held on to" until we got the answer.

This sounds daunting to a student. So I brought up this idea of recursion in the language. They were intrigued, and for some, it was a more gentle introduction to the nut graph of recursion.

Recursion in the English language can be easily seen in two places: 
  • Clauses: Consider the sentence "When I'm doing eating, we'll go to the store." You have to "hold" the data of "When I'm done eating" before you get the the main idea which is that we're going to the store. This makes me wonder if the Germans are particularly good at recursion because the active verb doesn't usually appear until the end of the sentence. Used to drive me bonkers. But in a way, it makes me realize that the action verb is very important to my understanding of the sentence. Perhaps the German mind soaks up more from all those other words and the verb is just a final concept to the mix.
  • Relatives: Consider the fact that the mother of your mother (a recursive relationship) is your grandmother. The mother of your grandmother is your great-grandmother, and then, it becomes just a matter of how many "great"s you need: great-great-grandmother, great-great-great-grandmother. The Piraha have a word for mother and then refer to their grandmother by given name. The language doesn't have this recursive relationship and therefore, it may influence the models and relationships for other ideas. 
Other studies seem to show strong links of language to STEM skills. Many studies I've been reading regarding spatial skills seem to indicate the importance of using spatial words early and often with young children. Even popular writer, Malcolm Gladwell, brought up language and math in his book Outliers:  The Chinese way of counting has a distinct pattern that correlates to the base 10 concept. Compare this to the English way of counting: The translated phrase for 11 is ten-one (not eleven), 12 is ten-two (not twelve), 20 is two-ten (not twenty) and 21 is two-ten-one (not twenty one), etc. This consistency of the language pattern may be helpful when learning numeracy.


Too often, I hear from colleagues that there is a battle between the literacy folks in education and the STEM ones. Research like this show that it's not an either-or, but a tight partnership. The next advances in STEM education need to happen hand-in-hand with the literacy education. Both are important, and they help each other. So why not work together?

~ Until next time, Yvonne

Related articles:

Engineer's Playground is often called upon by educators to provide ways to connect STEM with other content areas. Contact us if you would like to chat more about how STEM and literacy can complement each other.

Feb 17, 2015

Doubting Thomas: Science Attitudes Misunderstood

One Christmas, I was talking with my family about a friend 's cat who knew how the cross the street. She told me, "This cat will never get hit by a car. She goes to the curb, looks both ways, and then crosses when it's clear. I even saw her teaching a kitten the same thing!"

image by lusi, via
Most of my family chuckled. But my father, physicist, furrowed his brows and said sternly, "I don't know if I believe that.-- Can a cat even see to the end of the block?"

"Well, Dad," I challenged him, amused that it was the physics he found the cat geometry in question, not the decision making process involved with crossing the street or the fact that a cat would teach a kitten such sophisticated concepts, "that's a good problem for you to work out."

" I can't," he said, quite honestly. "I don't know how tall a cat is."

I found this very funny since this was a man who asked me at the dinner table how much energy was contained in the bags of leaves we had raked one autumn day. It became apparent that he expected me to make some gross assumptions like estimating leaves as a few carbon atoms that were then oxidized. The answer, he explained, was within an order of magnitude, which apparently was good enough.

"Try a foot tall for the cat," I told him, and he ran off.

In about 15 minutes, he came back with a smile, "It can see down the block, and the curvature of the earth won't come into play."

Since people lived for centuries believing the earth was flat, I was pretty sure a cat didn't see the curvature of the earth either, but I graciously replied, "Good to know." Dad really was a scientist... a doubter until he could prove it true to his satisfaction.

Challenging authority is the cornerstone to a good scientist. Good scientists don't swallow what they are told if it conflicts with their observations, experience, or logic. But they don't stick to their original thoughts out of stubborn ignorance. Instead, they go about verifying (or dispelling) it with proofs, experiments, and prototypes. The essay, Get thee to a physics class, waxes eloquently about this, and it's important to remember this aspect when teaching STEM.

Too many times, teachers feel that they have to have "perfect" science, engineering, mathematics lessons so that students will observe exactly what they should and make the proper (test-standard) conclusions. But sadly, science, engineering, and mathematical discovery are messy. New standards are emphasizing process more, and with good reason, because STEM knowledge is a living, breathing body, adapted when we observe, discover, or learn new things.

When I was asked to write about laser safety by Laser Classroom (Bringing STEM to Light), I followed all the best practices for STEM curriculum: No assumptions are made about the previous laser experience or knowledge. Rather than a list of regulations (to memorize), activities were used to develop "common sense" around the regulations. Then I rubbed the Engineer's Playground "secret sauce" on it: I added a "Where's the STEM?" section to show where the activities connected to science, technology, engineering, and mathematics; a "Historical Interludes" section which told the story behind a key idea in the activity (I'm particularly proud of the logarithms one); and a "Challenge Authority" section where students were invited to say, "Hey, I don't think that's right" to the activity procedures and conclusions. The latter, especially for a teen audience, I felt was critical.

So next time your doubting Thomas (or Thomasina) speaks up, don't get defensive, arm him or her with STEM to challenge authority.

~Until next time, Yvonne

Feb 3, 2015

Rotation: One of the Spatial Skills for STEM Success

photo by RWLinder (Robert Linder),
Spatial abilities are one of the most accurate ways to predict STEM success. One aspect is the ability to manipulate objects in your head: sliding, rotating, and flipping. Here are some ways to develop these skills:

Swish Match colored dots on clear plastic cards. My engineering team loves to play this over lunch.

Spirograph An oldie but a goodie. Creating a design gives tangible view of what happens when you rotate shapes.

Potter's Wheel What happens when you press here, here, and here? Potter's have a great sense of rotation, not to mention hand control.

More ways to develop spatial skills on the Pinterest Board.

~ until next time, Yvonne

Jan 20, 2015

What is #STEM? STEM Defined

image by RWLinder (Robert Linder), via
New to STEM? These are some frequently asked questions about STEM in schools: 


The simple definition is that STEM is actually an acronym, standing for : Science, Technology, Engineering, and Mathematics. But STEM has come to mean different things to different people:
  • Politicians, business, and the media: STEM is the pathway to economic growth and global competitiveness. The United States has been known throughout its history for innovative shipbuilding (e.g. Old Ironsides), weapons development (e.g. the Colt pistol, the Gatling gun), transportation equipment and systems (e.g. the Model T, the airplane), communication devices (e.g. the telegraph and telephone), and electronic devices (e.g. the electric light, the phonograph, and the computer). Each of these became export commodities and relied on science, technology, engineering, mathematics knowledge and skill to be developed and mass-produced. It is easy to see why there is a strong push from these sectors to have more students be versed in STEM. 
  • Schools and educators: "STEM" is being hailed as an opportunity to teach these topics with hands-on projects that put the learning into a meaningful context for the students. Additionally, schools have used this movement to put team-skills into the forefront, and many have connected with local industries and professionals to provide better career guidance for children, especially those from low-income areas who may not have been exposed to these lucrative careers. 


Sadly, too many times, we've seen schools say they are STEM, but in reality, they do Science and Math (S&M)--sometimes the same way as usual--, use Smartboards (and call it technology), and add a craft project to their curriculum (e.g. make a wind turbine or have students invent something), dubbing it engineering. Don't get me wrong; it's a start, but there's more that can be done by integrating the seemingly four distinct disciplines in order to glean the fullest potential of what STEM can give students. See blog post for more details on STEM schools today and in the future.


Integration is key... The focus can be different. In fact, the focus should be different for each school, depending on the student interest, teacher expertise and passion, and community values. Here are some broad-brushed ways to think about building a STEM school in an integrated manner:

Science-focused STEM. Activities at this type of school start with a question (the "research question"). All other activities then support the pursuit of the answer to this question: experience with relevant technology (tools, measuring devices, computer software) to observe or quantify; engineering devices that will constrain the variables and help answer the question; mathematical analysis and logical reasoning to make conclusions about the data. We like to call this the "Jacques Cousteau path": In his pursuit of understanding the world under water, he enlisted the help of Harold "Doc" Edgerton, an Electrical Engineer to develop time lapse underwater photography and side-scan sonar. >> See the MIT Video, Side-scan Sonar Technology video

Engineering-focused STEM. Activities at this type of school usually have a capstone project that starts with a need which students then break down into problems that must be addressed. This goal-oriented approach can be seen in any NASA-based story. Gene Kranz's memoir, Failure Is Not an Option describes how engineers teamed up with scientists, pilots, and ex-military to meet mission goals. At every stage, decisions had to be made based on data, laws of physics, knowledge of technology, systems thinking, and risk management. >> See the challenges Flight Control had to contend with while racing to the moon on The History Channel documentary, Failure Is Not an Option

Technology-focused STEM. Some schools start with a more tech-approach and the formal industrial arts curriculum (drafting, machining, etc). This approach succeeds in developing practical skills by creating existing devices, learning the common practices, and using this experience to make the technology run better, make it easier to maintain, or fix it so it works reliably. But a real STEM transformation to this "make a better mousetrap" approach would motivates students to learn the science needed to understand how the technology works, perfect the mathematics required to run the technology properly and safely, and some engineering design process practices in order to effectively improve the devices. History is filled with examples of how the person who was intimately familiar with the technology was able to bring it to the next level. >> See story of how the steam engine was developed on BBC's Connections - Ep. 6 Thunder in the Skies or this short history from The History Channel which describes some mechanical design considerations

Mathematics-focused STEM. Sadly, this approach hasn't really been developed as much as it could, possibly because so many people see mathematics as either completely theoretical or, as one mathematics professor put it, "a handmaiden to science". In reality, mathematical instincts (that all animals, including humans have) are the first step to using scientific observation to predict events -- for survival as well as entertainment and aesthetics. Engineers would just be tinkerers without mathematics, and technicians wield mathematics to make devices reliable, robust, and safe. I often tell my students that mathematics is like the "one ring to rule them all" and understanding it will help them be more efficient in their pursuits, no matter what they do. My guess, Britain or China will embrace this method first. For some reason, it seems to fit with the way my Hong Kong-educated parents. >> See stories of the power of mathematics in BBC's The Story of Maths

~ Until next time, Yvonne

Yvonne Ng is the founder and chief consultant at Engineer's Playground. Engineer's Playground is often called upon to help schools learn more about integrating STEM into their curriculum, leveraging teachers' strengths and interests and honoring the school's traditions and values. Contact us for more information or professional advice,

Jan 6, 2015

Making a Difference in #STEM: Start Early

photo by lauralucia (Laura M), via
Research shows that an early start is key to a more equitable education system: recent reports have shown that early childhood interventions can help close the achievement gap between low income and affluent students by age 8. Many of these interventions also develop traits and skills valuable in STEM, and introducing them early can help encourage underrepresented populations in STEM.

In the early years, think of STEM as the following:
  • Science is about observing the natural and designed world
  • Mathematics is the language to describe and quantify those observations 
  • Technology is about the tools and materials used to create designs
  • Engineering is about finding solutions to meet needs or problems at hand
With engineering ("the E in STEM") being required by more states, many more people--teachers, as well as students--will just be beginning with STEM. Feeds from our diijo list of resources can be found on the for Teachers and for Principals pages.

~ until next time, Yvonne

Yvonne Ng, founder of Engineer's Playground, will be presenting a workshop for parents and teachers on starting STEM early with children from ages 0-5. Registration through District 196 is open to all, or contact Engineer's Playground for other workshops.