Scientific equations and the metric system

Fancy images with cosines and fractions.

A formula with fractions. Can we just decimalize everything?

I’ve been told (as in second-hand information) that many countries that have switched to the metric system don’t really need to teach fractions anymore because pretty much every fraction can be decimalized. Additionally, I’ve had first-hand conversations with middle school teachers and students who find teaching and learning fractions is a nightmare. Do we really need fractions or, once we switch to the metric system, can we just lay them aside? Over time, I’ve come to question that and here’s my current thinking…

Ultimately, a fraction is part of a thing

We will always need the concept of a less than a full measurement unit. Just as a pound cake was known for its ease because it was based on the ratio of a pound each of butter, sugar, eggs, and flour, it was pretty crude in terms its result. Whether we only need part of a measure of fabric or a piece of wood that is less than a meter long, it is important that children learn (and adults understand) the notion of something that is less than “one” of something.

A fraction has a built-in “math problem”

Maybe some of the resistance to fractions is the inherent idea that it is, as its heart, a “math problem.” (Would we think about things differently if they were called “math challenges” rather than “math problems”? Let’s see…) A fraction is a division “quest.” It can ask a practical question, as in “If I have a half a cup of flour left in this bag and I need a whole cup for my recipe, how much more do I need to borrow from my neighbor to get the full amount needed?” It is a division “question” that needs to be solved if we pair it with anything else (as in add, subtract, divide…).

Consider the following two math “dares”:

combined

A traditional math “problem” on the left that includes fractions with uncommon denominators. On the right is the same math problem decimalized. The top number in the decimalized addition has only been carried two places to the decimal point, otherwise, it would go on forever.

When I hold up “flash cards” side by side with both types of problems shown above during my metric system demonstrations, almost invariably, people choose the one that has been decimalized because it eliminates the issue of uncommon denominators that are such a stumbling block for both children and adults. It also eliminates the steps to get to common denominators because all decimals already have common denominators in the form of 10s, 100s, 1,000s etc.

For the decimalized addition, just add up the columns as you would any math “action,” just making sure you keep track of where the decimal point goes in the final result. Pretty easy if the original equation is properly aligned as above.

In answer to the question “Can we get rid of fractions altogether?”

No. While most things will work just fine if you even go two or three numbers to the right of the decimal point, for some things it just won’t work since many decimals are frequently “rounded” and don’t fully express a numerical concept. While I am not a scientist, I do work with quite a few and when I posed the question of just decimals, “No” was the answer that came back to me. That’s because many fractions just don’t work as decimals for scientific formulas. Consider the fraction in the second math image. If you try to convert it to a decimal you have a problem because, technically, it trails on forever as in .3333333333333333333….

Scientists and mathematicians can’t work like that and need the compactness of fractions to visualize and express their work. (See the graphic at the top of this page for equation fractions.)

That said, let’s keep them where we really need them and stop needlessly torturing students, teachers and our population in general.

Even U.S. stock markets no longer report losses and gains with fractions down to the 16th. It changed a few years ago when the Securities and Exchange Commission ordered that all stock reports convert to the decimal system prior to April 9, 2001.

Why did it use fractions of quarters, eighths, halves, and sixteenths? According to the article from Investopedia, it dates back to the “pieces of eight” that Spain used some 400 years ago when it decided to exclude the thumbs for the purposes of counting…

Thanks for reading,

Linda

Metric System Temperature in Celsius and Rhyme

[Note: There is a poll at the end of this blog. Please participate!]

To me, the most difficult part of the using the metric system day-to-day is getting used to the Celsius measure of temperature.

I changed the weather app on my phone more than a year ago so it’s much easier for me to use Celsius now, especially when you consider that 0° C is freezing. I know what freezing is, regardless of what system is employed. At the other end, 100° C is boiling instead of our 212° Fahrenheit. Since it’s slightly imprecise (compared to what we use now), some countries compensate by using decimal measures for temperature so it’s sometimes reported as 18.3° C, for example. (In Fahrenheit, 18° C could be anywhere between 64.4° to 66°. Okay granted, now that I look at that it looks pretty silly–the middle 60s are still the middle 60s. The decimal point doesn’t really help me decide how many clothes I should wear when I go outside…)

During my research for this documentary I found several rhymes to help people adjust to the “new” (at the time) metric measures. I used one of them during my previous presentation at the MidSchool Math conference last year but had to apologize since it hit me as a little clunky. I told my audience that I hadn’t had time to write something better.

Given that I’m presenting next month at the same conference (slightly different topic than last year) I decided I needed to do what I said I’d do and try to come with something I thought worked a little bit better.

The poem I presented last year:

I thought this poem to learn degrees Celsius a little awkward

This bothered me a little since the construction is not parallel…that third line throws me off and seems out of sync (not written by a poetry major perhaps?)

On the U.S. Metric Association pages:

USMA

A bit better but I thought I’d take a stab at it as well. Here’s what I came up with (original to the best of my knowledge):

At 30 it’s hot
At 20 it’s pleasing
At 10 it’s cold
And 0 it’s freezing

I think it works because “pleasing” and “freezing” rhymes, “hot” and “cold” in the second and third lines shows a decreasing sense of temperature (as do the rest of the rhymes I came across).

Hey, you tell me. When the U.S. decides to convert to the metric system, which poem is the easiest to remember for you? I’ll leave the poll open a couple of weeks and will use the most popular version as I move forward with my project.

Thanks for your participation!

Linda

Let’s vote:

The MidSchool Math Conference

The next MidSchool Math conference is already in the planning stages

The next MidSchool Math conference is already in the planning stages

My presentation on Math and the Metric System: Using What’s Easy at the MidSchool Math conference went very well. The session had 50 people registered and while not everyone showed up, most folks did. Since the attendees were mostly math teachers I felt I had an opportunity to get them thinking about the metric system in new ways that they could take back their classrooms and hopefully their lives. The group was receptive and had lots of questions for me. They were also able to interact and ask each other questions about their metric classroom experiences.

Hands-on opportunities

I had scheduled some hands-on exercises using length and mass to help them get used to applying metric units. While length didn’t present much of a problem, only a couple of people used scales in the kitchen. This gave them a chance to play with some of the equipment I brought. (Let’s face it, pretty much every ruler and tape measure today has both U.S. customary and metric units on them but most people are so familiar with measuring cups that it doesn’t occur to them to use a scale in the kitchen though it’s far easier.)

I also brought some metric-only rulers supplied by the National Institute of Standards and Technology (centimeters on one side, millimeters on the other) and they cleaned me out of those—which I consider a good sign.

Avoid conversions!!!

A couple of folks on the U.S. Metric Association (USMA) listserve who communicated with me prior to my talk wanted to make sure that I didn’t encourage conversions during my presentation. Not only was that explicit in my presentation—twice no less—but I also pointed out that I’d gotten that feedback from USMA to try to drive the point home. I think it worked.

After all, the metric system was introduced at a time of widespread illiteracy and even unschooled french farmers and tradesmen learned it easily enough. It should be a cinch for today’s high-tech Americans.

One attendee told me she thought it was the best presentation she’d seen so far (I was in the afternoon on the second day) but I have to say that the keynote speaker on the first day, Dan Meyer, was extremely good. He stressed the need to engage kids studying math in the classroom in three acts and bring them along for a story where they really want to figure out what happens. Let’s face it, everyone gets more interested if there’s a good story involved. I think the audience heard him.

Testing my story structure

For my part, I got a chance to try out part of my story structure for the documentary on an audience, hear questions and find out what parts of the narration were of the most interest by their level of attention. There’s just nothing better than trying out your material on a real audience. I’m very pleased with the results but I will continue to refine and expand.

Since I did attend a couple of sessions other than my own, I also had a chance to engage with additional teachers and all seemed very interested in what I’m trying to do. It was only one of the other presenters who gave me pause when he suggested that the next generation would take care of metric conversion in the United States. (Only other time I’ve heard that before [good idea but not now] was in John Quincy Adams’ report to Congress back in 1821—haunts us every time we get serious about metric adoption by the way…) I quickly realized that there was no point in arguing the issue with him but would have loved to point out that in the 30 years since the U.S. Metric Board was disbanded no “next  generation” has come along so far and perhaps he’s part of the “next generation” that should do something. Ah well, I tried to be as persuasive as possible under the circumstances.

As should always be the case, the teacher and learner roles got reversed during my session and I walked away with some additional things to think about and research.

For instance:

  • I’ve been told the military uniformly uses the metric system but others have told me that’s not true. True status will take some digging.
  • When converting from miles to kilometers, what happens to the mile markers since they’re currently used to help drivers know how many miles to their next exit?
  • What’s the best way to convert existing recipes into metric?

The cost of conversion

Of course, the biggest unanswerable question I get asked is how much would it cost to convert to the metric system in this country. I don’t think anyone has a good grasp on that since it’s been so long since the question was seriously considered.

Aside from the cost of conversion errors, and time savings in schools and elsewhere on an individual basis, imagine how much time it takes to design things for multiple countries with dual labeling—including the use of more ink to print both sets.

Converting to the metric system will have a mostly one-time cost while failure to convert to the metric system continues to cost us, and cost us and cost us…

Linda

Metric System Presentation at March 2014 National Math Conference

The conference hopes to reverse the trend of declining math score in mid school

The conference hopes to reverse the trend of declining math score in mid school

Next month (March 28 to be exact) I’m making a presentation on the metric system at a national conference in Santa Fe called MidSchool Math thanks to project supporters with Imagine Education. The theme of the entire conference is Stop the Drop and refers to international testing standards that show in 4th grade, American kids are slightly above their cohorts in other countries in math but by 8th grade, they score slightly below. It’s the hope of the conference’s organizers to start to reverse this trend. During the three-day conference, sessions will cover a variety of topics from Mathematical Icebreakers to a keynote session on How to Make Kids Hate Math. My session: Math the Metric System: Using What’s Easy. So far, eight people have registered but there’s more than a month to go.

The cost of the conference is $475 or $525 (that whole early bird thing) and if you’re a teacher in New Mexico, you could be eligible for a stipend of up to $1,000 to cover the conference and its associated costs. Check it out or spread the word.

Having written on the subject of education and the metric system, I have a place to start to build my presentation content, particularly on the subject of Common Core State Standards for math as they relate to the metric system. My session will be an hour and fifteen minutes long so I’ll have time to cover lots of material and, with the assistance of our federal government in the form of the National Institute of Standards and Technology (thanks Elizabeth!), I’ll be able to supply attendees with some modest metric supplies and games to take back to their classrooms.

Total side note: I was just looking for meter sticks on Amazon and came across “One Meter (39-1/2″) Wood Stick Ruler.” Really? You’d think if you were looking for a meter stick (and not a yardstick), you wouldn’t need to have the inches spelled out for you. How much time is wasted in this country having to continually include both metric and U.S. customary numbers? Then I found this in a description: “Meterstick is lightweight and ideal for the classroom. It measures 1 inch wide and 1/4 inch thick.” Pathetic. Let’s please get our metric act together.

I plan to devote quite a bit of time to developing the presentation. When people walk out the door, I want them to say “Wow” but in a good way. That will take time, research, rehearsal and matching my subject matter to my audience. I realize that public speaking frightens a lot of people (some studies rate it as the number one human fear!) but I don’t currently have that problem. I say currently because at one point in my career I wasn’t making a lot of presentations but once I needed to again, I was able to relax pretty quickly. My largest audience to date: more than 500 people. The only caveat to my being relaxed is I have to know my subject matter. That shouldn’t be a problem in this case.

Luckily, I also have some teaching background and found that I’m pretty accurate about being able to estimate how much material I can cover within a particular time period. Of course, it’s always a good idea to have a little extra, so in case you find yourself running short, you can continue a little longer if needed. As the saying goes, “Always leave them wanting more,” but you also want to make sure people walk away feeling like their time was well spent.

I’m also hoping there will be a method for people to feedback on how I did. I find constructive criticism very helpful. While it’s unlikely that I’ll give this exact talk again, who knows what parts of it could come in handy as the project progresses.

It will be nice to get out and interact with the attendees and the other presenters. I’m sure I’ll learn things that will benefit the documentary in ways that won’t seem obvious watching the end product but if you follow this blog, you may see how they ultimately inform me.

I’ll be sure to share what I find out that’s interesting and fun…stay tuned.

Linda

Shortchanging American Children with Our Measurement System

While over the past year I’ve looked at metric adoption from a number of angles, the thing I keep coming back to again and again is how we’re shortchanging our children. Granted, my own daughter is almost 25 years old now so my own progeny concerns me less than our children as a whole and the generations that will follow them.

Students in the Lab with metric beaker

Metric units are used internationally for science

We are doing them a huge disservice every year that we continue to use U.S. customary units (for those new to this blog, we imported imperial units and then futzed with them so they no longer align with any other country in the world) in our education system. Metric units were designed to work together in very logical ways rather than the hodgepodge of units that make up our current measures.

Right now we teach our children both U.S. customary and metric units and under the new Common Core Standards (talked about this in a previous blog) measurement standards are dropped from the curriculum once students hit sixth grade. Still, every minute our customary units are taught in school is a minute wasted and that time would be better spent on other subjects. And every minute that metric units get second billing to U.S. customary units means that we’re ill preparing our children for careers in science, medicine and any activity that will take them out of the country or deal with others internationally.

Increasingly our children will study abroad—but they won’t know the measures used almost everywhere else in the world.

In fact, our children are less likely to stay within our borders during their education than at any point in our history and, according to the U.S. Department of Education,

Over 80,000 Americans study abroad at the college or university level each academic year. The number of U.S. students going abroad has increased by about two percent annually over recent years, and this type of study opportunity is now an established part of American academic life.

Of course, the minute most of our students hit the ground in another country they face an additional hurdle beyond language and culture: lack of familiarity with the metric system that almost everyone else uses. Luckily, the metric system is easy to learn but why make our children have to learn one more thing on the fly when they shouldn’t have to.

In fact, within the first month on this project I was flying to Washington, D.C. to visit friends and begin my research when I happened to sit next to a middle-school math teacher (one of many coincidences I’ve encountered on this project but that’s another blog).

She basically said that her students didn’t think it was a good use of their time to learn the metric system because they’d never use it again. She also said her counterargument was that it was like learning a second language and it might come in handy since other people use it.

Even as early as I was in this project, I offered her the following counterargument to use instead…

Sure, you don’t need to learn the metric system if you:

  • Never plan to leave the country;
  • Don’t plan on a well-paying job in science or technology;
  • Don’t plan on a well-paying job in medicine;
  • Don’t plan on doing anything associated with international trade (including manufacturing and distribution).

Students arriving here will have difficulty learning our illogical measurement system

Not only does our metric adoption hang up our students leaving the country, it also hangs up students coming to our country to study here and they mean big economic business:

(July 13, 2013) Association of International Educators released new economic data today showing that the 764,495 international students studying across the United States supported nearly 300,000 jobs and contributed $21.8 billion to the U.S. economy in the 2011-2012 academic year. Further analysis shows that for every 7 enrolled international students, 3 U.S. jobs are created or supported by spending in the following sectors: higher education, accommodation, dining, retail, transportation, telecommunications, and health insurance. 

International students must start scratching their heads almost the minute they arrive here because they’ve never encountered a system as messed up as ours. “Wait,” I imagine them saying to themselves, “I thought this country was advanced.”

While I’m not suggesting that students wouldn’t come here to study because we don’t use the metric system, it just makes it more difficult for them than it needs to be. International tourism is also one of the reasons Hawaii has considered adoption of the metric system to make it easier for travelers to get around once they arrive. To me, that just adds one more reason to change over to the metric system.

Those with our children’s interests at the forefront will assist with metric adoption

As this movement progresses, it will very important to let parents, grandparents, guardians, etc. know the disservice we’re doing to our current and future generations by clinging to our outmoded ways. Riled parents would probably be one of the most effective ways to give this movement some momentum—but they need to understand the issue first—something I’m hoping to help with.

Let’s give our kids a break and provide them with the best system available and help prepare them for today’s world—it’s the least they deserve from us even if the switchover will take a bit of effort on our part.

Linda

U.S. Metric Adoption and Common Core Education Standards

One thing I learned soon after starting this project is that our country is less the UNITED States of America than it is the United STATES of America. Having rallied against the British and its centralized government more than 200 years ago, our founding fathers made sure our Constitution gave limited powers to the federal government and put considerable control into the hands of state government. This includes our education standards.

While one might think that the Department of Education helps ensure that our children receive at least some basic level of education throughout our nation, such is not the case. In fact, the Department of Education:

  1. Establishes policies related to federal education funding, administers distribution of funds and monitors their use.
  2. Collects data and oversees research on America’s schools.
  3. Identifies major issues in education and focuses national attention on them.
  4. Enforces federal laws prohibiting discrimination in programs that receive federal funds.
    (http://www2.ed.gov/about/what-we-do.html)

You’ll notice that setting standards for what our children learn in schools is not within its scope—it’s up to the individual states to decide what children learn in what ways and even what constitutes a passing grade. (I don’t mean to imply here that the states are out to shortchange their children but they could if they so desired.)

While each state is able to set its own education standards, there has been progress toward the implementation of common, basic standards to finally provide some consistency in what’s covered within school classrooms across the country. The organizations behind this effort are the National Governors Association and the Council of Chief State School Officers.

Common_Core_

The Common Core State Standards Initiative is a state-led effort that established a single set of clear educational standards for kindergarten through 12th grade in English language arts and mathematics that states voluntarily adopt. The standards are designed to ensure that students graduating from high school are prepared to enter credit bearing entry courses in two or four year college programs or enter the workforce.

http://www.corestandards.org/

Adoption_mapAccording to the website: “Forty-five states, the District of Columbia, four territories, and the Department of Defense Education Activity have adopted the Common Core State Standards.” Those that have “not yet adopted” (the site’s wording) the standards are Alaska, Texas, Minnesota, Virginia, Nebraska and Puerto Rico. Work is still taking place for the standards and a visit to the Council of Chief State School Officers website shows that the publication Common Core State Standards: Implementation Tools and Resources is dated as recently as May 2013.

I’m happy to say that metric system is included in these standards.

Here’s what I found on the Common Core site for grades 2, 3, 4 and 5 under the sections called “measurement and data”:

Grade 2: “Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes and Estimate lengths using units of inches, feet, centimeters, and meters.”

Grade 3: “Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).”

Grade 4: “Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.”

Grade 5: “Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.”

From grade 6 and beyond, the “measurement and data” subheading no longer appears and other math concepts (such as probability) are listed.

So, at least the standards do include the metric system although it appears to be taught somewhat side by side with our U.S. customary units in at least grades 2 and 4. I suppose I could try to write something into the fact that for grade 3 the language says “standard units of grams, etc.” without mentioning U.S. customary units but I don’t think that buys much of anything. On the other hand, I could write into the fact that for grade 4 the wording “one system of units” could also mean that it could be interpreted to mean either U.S. customary or metric units could be used.

I’m writing about this subject for two reasons:

1. To raise awareness of the attempts to get some consistency within our country so we can best prepare our children for their (and our) future so that you can help support these standards—including when it comes time to press for elimination of U.S. customary units in favor of the metric system within the Core Standards, and

2) To make sure you know that while many powers were delegated to state control, Congress does have within its scope the ability to mandate our weights and measures. It states in the Constitution in Article 1, Section 8 that it is within the power of Congress:

“To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures.

The bottom line: I hope there will come a time in the future when this information becomes important.

Linda

P.S. I would like to thank any of my readers who helped back the Kickstarter campaign for the documentary on the kilogram. Amy met her goal and, as a result, has had the funds released to her to carry on her project. I wish her much luck and success with her efforts.