Takeaways from #NCTM14

Nothing is rejuvenating like spending a few days with like-minded people. I feel incredibly fortunate that I was able to speak with many innovative, passionate, and engaging math educators.

And… there’s more to it than that. Obviously, the people who are able to attend NCTM either have districts who are willing to foot part of the bill, received some kind of grant, or paid their own way. That is, the attendees are not representative of the larger math education population. But it seemed that I talked to two kinds of people: those who were content being there and those who were super hungry to connect.

I teach at a super small private school. We have about 220 kids in 6th – 12th grade. I don’t hear bullshit acronyms like “KWLM” – literally “kids we love the most” when talking about children who have not had success at school. I don’t hear kids being called “low” or “high.” I don’t hear these false classifications of children that have nothing to do with how they learn. Even a casual label like “lazy” is describing a behavior, not a person. I encourage you, if you hear a child being called by a label, call them on their shit. It can be awkward, but it can’t be a practice that continues or ignored.

End rant. Here’s a collection of takeaways I had.

The sessions by Christopher Danielson and Michael Serra respectively were the only two where I actually had to think mathematically. I think that it’s such a rich experience for math teachers to be able to be back in a learning environment with novel material. Students do it every day.

What I loved about Danielson’s presentation is that he didn’t know where it would lead: when students come up with their own classification system of hexagons, he doesn’t have a pre-defined notion of what we would create (unless he’s already come up with every possible way to classify his set of 14 or so hexagons.)

Michael Serra had created inquiry based materials which can be found here. We worked together in groups on some of his pre-created materials. I highly endorse the donut polygon problem set.

Recurring theme: Few people have a clear vision of what to do with technology in the classroom. I heard so many stories of computers, iPads, smart boards and other gadgets being stuck in storage because they were being used improperly or didn’t foster student learning (or both).

This was the first year I went to a talk on math and social justice. Rochelle Gutierrez’s sessions focused on the “unearned privilege” that those who can do math have in society. Math typically is heralded as the highest form of intelligence, and presents a high barrier to some. I really dug her point that “math needs people” as a converse to the traditional “everyone needs math.”

People I met put up with a lot of pressing questions. I don’t know how no one told me to shut the hell up all weekend. When asked about your craft, you people are much less defensive than I think I would be.

Steven Leinwand gave the sermon of the week. Among other items, he mentioned the “devastating impact of teacher isolation”; how standards and assessments are the bookends – necessary but not sufficient; and plugged the new Practice to Action text. I’m still confused why Practice to Action isn’t a free text, supported by NCTM, the Dept of Ed or some other professional organization. If the document is so important, why not put it in the hands of everyone? Maybe I’m naïve here.

“Don’t read off your slides. Don’t read off your slides. Stop it. Don’t read off your slides.” – me talking to myself and about half of the presenters.

Dan Meyer had a great presentation on lessons we can take from how video games are structured. He’s got a summary here. But what I really took away was a line at the end of his presentation. He pointed out that so many people are vying for kids’ attention: video game developers, shoe creators, wanna-be teen celebrities, musicians, etc. etc. etc. But what teachers are given (by law no less) is a captive audience. Students are “forced” to be with us for 180 days out of the year, and it’s a time that should be treasured and honored. It’s a time to innovate and connect kids with mathematical thinking instead of mechanical procedures.

I couldn’t have been more grateful for everyone who stopped by for my presentation. I was literally in the hallway grabbing anyone who looked at my sign in an act of shameless self-promotion. It was my first one, and I didn’t really feel nervous – it seemed like all who attended really wanted me to succeed.

I think that’s the vibe that should be supported by NCTM: we want you to be a badass and you can do that here at our conferences. Other than that, I’m still not sure why people come.

NCTM 2014 Slides

I embedded my slides from my talk about using non-traditional texts in my AP Statistics class. They might not be clear if you missed it. Feel free to hit me up on Twitter if you have any questions.

(I tried to embed this about 10 different times, but the heights were all wrong. Forgive the extra click)

Bringing the (Signal and the) Noise

Thinking quickly

I’m going to ask you a question about pizza, but I’m going to trust that you won’t look below until you agree not to do any calculations. By calculations, I mean on paper, in your head, or on a machine.

So don’t break our circle of trust.

Seriously, just move on if you’re tempted to cheat.

Ok, got the stragglers out of here. Without calculating, answer the following question

The largest pizza at East Side Pies has is fairly big. It’s 18 inches across. What is the area of the pizza?

a. About 254 sq inches
b. About 1017 sq inches
c. About 56.5 sq inches
d. About 740 sq inches

I…. couldn’t resist doing the mental estimation. It didn’t come to me naturally.

Now the rest is of this post is obviously speculation. I imagine that the rate of correct responses is somewhere in the 25-33% range, that is you might be able to rule out one of these questions pretty quickly. However, I don’t think there would be much difference if you asked a 4th grader or a high school junior.

If I have no real intuition about many, many little squares of pizzas, what does that say about my ability to “do” mathematics? To me, it shows how being able to calculate an area of some generic shape is a lower level of skill. If we made a Bloom’s taxonomy for math classes, I think calculation should be like level 2.

Questioning Wise Thinking

When I meet with parents at school functions, they want to talk about what their child is doing in class that’s unique, that’s cutting-edge. So often the question of the purpose of learning mathematics is brought into the public domain. I try to steer the discussion into the creative side of mathematics, how “thwarting” student assumptions and processes can lead to deeper mathematical connections. That message is hard to convey adequately. Most apologists of the historic math curricula give some derivation of the importance of learning logic as a great justification of learning mathematics. It’s a seductive argument, although when analyzed falls apart.

The discussion lacks nuance. Real world applications are tangentially connected to actual problems at best, at worst they’re deceptive to the point of turning knowledge into a set of oppressive devices.

And to flame the argument, when those with bigger platforms than most – the big voices in education –  describe what they think of the purpose of mathematics, I tend to listen. So when the great Ed Burger recently posted his “Truly learning math makes wise thinkers.” my ears shot up. This got some press in the local Austin and Houston papers. Below is my FireJoeMorgan-ification of his piece. Original is in bold and italics.

The question that educators and legislators in Texas should be discussing right now is not whether high school students should be required to take two years of algebra. This is an excellent example of investing time, money and effort to thoughtfully and carefully answer the wrong question.

Man I love Texas politics. Where else can we get a young state senator to filibuster for 8 hours and get a shoe deal out of it?

The right questions for all of us are: What positive and profound lifelong habits of effective thinking are we offering within all of our math classes?

Oh… at first I thought we were getting rid of SeaWorld. But, brother, I hear you. Also, can someone get on that whole “I can use your English state test scores to predict every other test score you take?”

And if the content of the algebra curriculum will be quickly forgotten after the last required exam (or even before), then why bother to offer any algebra?

Well… I’m not sure that doesn’t disqualify Pre-Algebra, Geometry, Algebra 1, Algebra 2, Statistics, Pre-Calculus, Calculus and pretty much every class I’ve taken at the high school level. In fact, If the metric we’re using to evaluate a class’s worth is “Do you remember the content after the last exam”, I don’t know what high school class this wouldn’t disqualify. We’ve changed the discussion from “should we keep Algebra 2 as a class” to “What are we doing with this whole standards and objectives based curriculum?”

Currently, too many of our math classes — as well as other classes — focus on mindless memorization and repetition that is designed to game a system focused on scores on standardized tests that measure the ability to perform a certain act — an act that requires neither deep understanding of the content nor the necessity to make meaning of the material.

Got it, repetition and memorization = bad. Deep understanding and meaning = good. Let’s store these equations for a bit.

Like magic, the moment the final exam is over, poof, the material is forgotten and magically disappears. Think it’s a joke? Math educators know otherwise. The overlap in middle school algebra, Algebra I and Algebra II is conservatively around 60 percent, and more realistically around 75 percent.

This small truth hurts. I understand redundancy when we’re talking about building ships to fly people to outer space. But the redundancy between all the Algebra curriculum reminds me of the painful waste of time when put into an overlap argument.

Our curriculum acknowledges its ineffectiveness at inviting students to make meaning of algebra: Those who study algebra in school are doomed to repeat it.

DOOOOMED I SAY! Also, what?

We need to replace our current math classes with meaningful mathematical experiences that teach students how to think through math rather than simply memorize formulas about math.

Ok Dr. Burger! I’m in. What does that look like? Does it involve teaching kids calculus at 5th grade? Does it involve something playful like sending students to the Desmos carnival?

By thinking through math, I mean understanding the material in a very deep way so that the student can appreciate and (ideally) discover connections between seemingly disparate ideas. Discovering relationships and patterns is not only at the heart of mathematical discovery but also the requisite trait to innovate and create in any space — from big business to the fine arts, from sports to technology, from politics to education.

This paragraph is meaningless drivel. Not once does Burger give any kind of non-jargon examples of what real learning, creating or playing with mathematics looks like.

In mathematics, we need to delve deep into the simplest of ideas until we see how complex they truly are. Only then can we pull back and see the bigger picture more clearly. One of the greatest triumphs of the human mind is that, by intent, we can take our current understanding and challenge ourselves to understand that much deeper—and, of course, that’s at the very core of education. These habits of the mind are what we need to be instilling in our students to enable them to become wise and creative leaders in an ever-changing, multifaceted world.

“Habits of mind” is utter filler and nonsense. “Habits of mind” is a generic approach that give nothing to looking at mathematics as something interesting or creative. “Habits of mind” is a desirable by-product, not the end goal.

Algebra provides a perfect example of this.

Algebra is a set of tools. Learning Algebra has little to do with making wise and creative leaders in an ever-changing multifaceted world. Learning when it’s appropriate to use those tools should be the outcome of mathematics education.

Calculus is one of the most beautiful constructs of humankind (of course, as a mathematician, I’m slightly biased).

Sure Calculus is beautiful. Let’s just start kids with that and then talk about the hyper-specialized cases that arrive in Algebra 2, right?

However, the whole subject revolves around just two basic ideas. So why do masses of students every year struggle with and eventually give up on calculus?

Kids ditch calculus? Or kids never had the chance to take calculus on account of Algebra and pre-calculus being so mind-numbingly boring?

The answer is because they never made meaning of the basic ideas of algebra.

Oh… I guess we agree here.

Even after manipulating the same equations for years in algebra, those students never were exposed to a curriculum that invited them to think through those equations and make them sing in their minds.

Ok Dr. Burger. Here’s where you’re getting me down. You are a textbook writer, the winner of many awards, and you’ve published a ton of material that has been some of the most popular written by a math educator. When you say students were never exposed to an interesting curriculum, this is where you put your money where your mouth is. What’s the interesting curriculum? What gets kids thinking? Where’s your advocacy really going to be powerful?

In my nearly 4,000 online math videos, I have attempted to make those ideas meaningful and, ideally, intuitive.

Awesome! We’re getting somewhere. I don’t really mind plugging your own work if it’s amazing. But then I tracked down a few of the videos where Burger tries to make ideas meaningful and intuitive.

Here’s an example:

“Something x plus something y equals a number.” “Standard form.” “x-intercepts”

Burger simply shows us how to graph the equation. There’s nothing playful here, there’s no higher wisdom to be gained. It is merely a process. It’s a context-less problem. It’s a rote memorization like he railed against at the beginning.

Damn it, I know where someone’s already going with this. Dr. Burger’s videos and general sense of style made him famous. His talks are incredible to go to, hell I’ve been to three in Austin myself. But these videos are dull and lifeless. They’re showing you how to do a hyper-specific process, and I can’t find anywhere where effective thinking comes into play.

This point can be applied to other subjects as well. In music classes, for example, students can simply memorize the finger movements in a piece.

Or watch a video of someone else doing it and try to copy them.

Or they could learn to hear each note and understand the structure of the piece.

Yeah, or that. That’s what the videos are for! Understanding structure.

My real beef is that so many talented minds go into the “let me show you how to do that” field, whether it’s making videos, apps or tutoring. And who can blame them? That’s where the money is at. No one is paying people to scaffold playfulness in math classes. They’re paying teachers to transfer information and skills to students.

In history classes, students can memorize basic facts about the Civil War such as the names of the generals. Or they could try to understand the background, competing forces and evolving social values that ignited the conflict.

Straw man alert! Who is saying history classes should be simply built around rote facts? What happened to the Algebra 2 framework which drew me in?

When teachers give assignments, they should always be asking themselves “What permanent benefit — what habit of thinking — will students get out of this exercise?” Teachers should craft assignments that promote long-term goals such as understanding deeply, learning from mistakes, asking probing questions, and seeing the flow of ideas. In other words, instilling lifelong habits of effective thinking.

Dude! Did you think you came up with that? Why is there no citation to Dewey, Piaget, Vygotsky or anyone else who have been saying the same thing 100 years ago?

And he came dangerously close to shamelessly plugging his book on effective thinking (which is on shelves near you).

Sure, I would be happy to see more students become math majors in college.

Pander to me baby!

But it is even more important to me that they learn to become wise, original and creative thinkers.

This is an empty wish. How exactly do students do so within any context, be it mathematics or somewhere else? I guarantee you, it doesn’t start with curriculum design or choices. It starts with teachers, parents, administrators and students all focusing on empowering students’ thinking. Without that, you could choose the most interesting content in the world, and it’s a lost point.

I’m not here to bash Dr. Burger. Like I said, I’ve cleared my schedule to hear him speak locally. What I’m objecting to is his empty jargon and recommendations around math education without even the slightest mention of what best practices actually look like. As a big voice in education, I dig the memorization = bad equation. But what else are you offering us? What’s your alternative?

End rant.

Thinking Like a Manager, an Economist, and a (sometimes) Mathematician

Every day I have a 20 minute commute, wherein I expect to be entertained! Dodging other commuters has an inherent challenge, but not the level of stimulation I crave.

I love Russ Robert’s weekly podcast series EconTalk. Through his series, I’ve learned how much wine my pregnant wife can drink, how potato chips fly 60 mph over a conveyer belt, and how incentives affect waste policy. His discussions with his guests are playful, inquisitive, and are a nice blend of education and entertainment. I have no training in economics, only Mathematics and education (sometimes at the same time).

I’m always jazzed to hear educators on the podcast… even though I usually have some strong reservations. Doug Lemov of Uncommon Schools and author of “Teach Like a Champion” was recently a guest. The direct link to their podcast is here. Their talk revolved around how to improve performance within schools and of teachers. Lemov framed his background by noticing a strong negative correlation between state-mandated test scores and poverty level (i.e. poverty went up and scores went down). However, there were some schools who systematically scored higher on the standardized tests. His work began by wanting to find the “industry secrets” of those schools.

They go on to discuss successful teacher techniques, systematic culture issues as well as the importance of education in a democratic community. I was incredibly inspired at some of the compassion, care and thought that Lemov had towards kids in the inner city. I don’t teach to that community, I teach at a private school in a fairly affluent community. And as an educator, I have some pretty strong beliefs with regards to mathematics education that I want to highlight no matter the demographics.

Making Teachers Great

Lemov begins by acknowledging that teaching is a performance profession. He mentioned that a good performance one afternoon does nothing to guarantee an equally good performance the next. Teachers are always on the spot. I agree that the discussion in teacher improvement must begin at that point. It gives light to how much preparation must go into every damn day. He offered up a few techniques for teachers. As I was listening, my cynical brain began lighting up. His book has 49 of these techniques, but he covered the following:

1. Call and response

Students are expected to call out certain concepts automatically. No need to invent the wheel here, Christopher Danielson already took care of this critique.

Without getting too philosophical, I still want to mention this: if schooling is a system of memorizing facts, it can easily turn into a tool of systematic oppression. But that’s another rabbit hole for another time.

2. At Bats

The idea of at-bats is simple – kids need to practice skills multiple times. They need to have opportunities to see them in slightly different permutations and practice with feedback, but not an overwhelming amount. This is probably an area where I am admittedly weak. At times I get stuck in the idea that we need to cover so many things that I don’t give students enough straight practice. As I reflect on my last semester, I realize that I selfishly emphasize co-creating concepts; this is a huge time commitment. Sometimes kids gotta practice.

The trap comes when we limit Mathematics to practicing skills. But we’ll come back to this in a moment.

3. Check for Understanding

This is a pretty straightforward technique. Teachers need to gain insight into what their students have learned and haven’t learned. Most educators would call this a formative assessment. It doesn’t have to be a big quiz or test. Lemov describes one way to check by putting up a multiple choice question on the board and having all the students raise their hands at once with their response. It’s feedback for the educator. I’m all for it.

Outcomes

Here’s where I get stuck. We get stuck in thinking of learning outcomes in a very narrow way. To most of those outside of the teaching profession, the only relevant teaching outcome is grades. If a girl is getting an A in Biology and Calculus, she is really doing well. If a girl is getting a C in Biology and Calculus, she is having a difficult time. The nuance of humanity is completely shuttled into a few digestible letters.

Lemov’s desirable outcomes seem to be tied to standardized tests. Forget for a moment that a recent study by Dr. Stroup found that about 10% of the variation in Texas test scores is accounted by previous scores. Forget that standardized tests are “insensitive to instruction.” Hell, forget that Lemov himself said that scores in all domains are highly correlated by students’ ability to read. My question is: what learning goals do we have for kids in math class?

My own most desirable learning outcome is that students think like a Mathematician. My short spiel on thinking like  a Mathematician is someone who can

  • Look at a problem in a novel context
  • Understand the structures of a problem
  • Think in extremes
  • Question assumptions
  • Experiment mentally (no getting our actual hands dirty!)
  • Make logical arguments to convince himself and others of a solution

My list doesn’t have anything to do with computations. I understand where leaders like Lemov come from – they are taking metrics like state-mandated test scores, and try to make his students successful in that way. The only problem is that we conflate doing well on these tests with thinking like a mathematician. In short, here’s an equation:

MATH != COMPUTATION

My heart breaks at one point when Lemov describes how often his kids practice math. He has his children practicing all the time, and he describes his kids at loving. When I think of loving math, my mind doesn’t think of things I can regurgitate facts like multiplication tables, trigonometric ratios or the power rule. I had a terrible experience when it seemed that college math was more memorization. I light up thinking of the time in 4th grade when I created a really strange algorithm for how to test divisibility. I think of my class in Combinatorics when I had to think about sets and functions without any assistance. Math is created, not memorized, and I sincerely hope Lemov’s kids aren’t crushed when they discover that fact.

The reification of those exams would be more interesting if we broke the SAT/ACT tests into: Reading fast, vocabulary, computational fluency and science trivia. So we get this idea that a kid knows how to do Calculus because he gets A’s in his math classes. He gets to higher levels of mathematics, and it’s a shit show. Because when someone is telling you how to find the nth derivative in multivariable Calculus, this beautiful creative process we call Mathematics turns into a chore. I don’t perceive mathematics as someone telling you how.

And I’m making huge assumptions here. Perhaps Lemov doesn’t have his kids “practice” Mathematics by asking them to calculate how to add or subtract repeatedly. Maybe he has them practicing estimation. Maybe he asks them questions where he genuinely doesn’t know the answer. But I’m guessing that most parents don’t view Mathematics in the same way Mathematicians do. They think of it as computations, or a set of rules to follow.

Improving Organizations

When Lemov discussed how he runs schools, I was incredibly impressed. He begins by creating powerful context: “The first obligation of an organization is that it makes its people better.” In all my discussions with administrators of any different organizations, this seems to be an undeniably underserved function. He said that a teacher should be observed every three weeks.

(!!!)

I can tell you that my admin team is pushed to the brink of responsibilities and time already, and I might be observed once or twice in a year. However, priorities are spelled T-I-M-E, and if managers aren’t looking to improve their team, they have to see what’s actually happening in classes. How to promote improvement in the teaching sector is not at all straightforward, but I’’ really appreciate his sentiment.

Listen to the rest of the podcast, there were some great other points when discussing schools as a system: the divide between admin and teachers, how incentives come into play, how autonomy and accountability have to live together.

So while I still have some qualms in Lemov’s approach to what math is, I loved hearing how he views schools as systems. And thanks for the invitation to reflect through writing.

Transversals, KenKen, and the Art of Making Puzzles

I’ve taught Geometry for four years now, and this year I’m completely writing my own course notes, essentially a textbook. I burned the boats, so to speak. And yes, it is because I’m a crazy person. But, also the books cater to these state standards which can be so very mind numbing. if I were to read through the TEKS (Texas standards for you outside the good nation), I would see dregs like this:

“111.41.C.5  Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures. The student is expected to: (A)  investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools.”

If the numbers at the beginning didn’t get you, the inane droning of vocabulary might have. But you know what? Puzzles in Geometry are badass. Kids like to do them, I like to assign them, they’re stretching, and they actually match up with class standards.

In the Beginning

Sometimes I start with low-level, accessible puzzles like this one from KenKen.com. They have to use some logic, some elimination, but nothing so taxing that they’re spent.

image

What I’ve noticed is that the “easy” (in quotes because it is banned in my classroom) problems generally only have one difficult spot – once a particular square is filled in, the rest of the puzzle becomes rapidly finished. Old Windows users, think of Solitaire when all the Aces through the 8’s are already moved to the winning area – from that point on it’s just a click party.

Back to Geometry

In that light, when I see puzzles like this… they’re a little on the soft side.

image

There’s not really any conundrum. The only way I can really have fun with a puzzle like this is by letting all the students solve for angles 2, 7 and 8 and then telling them they’re wrong (unless they’ve explicitly assumed two lines are parallel). So it’s off to Google (or Bing if any sponsors are reading this) to find better puzzles.

From the Discovering Geometry page we can see this one is an upgrade:

image

This puzzle is interesting to look at. Most of the students can solve these pretty quickly – they’re accessible and they can check themselves by looking at groups of angles that form circles. They feel great when they finish, but they’re not the most cognitively demanding puzzles. We can reinforce some vocabulary (what’s the relationship between angle f and the angle with 64 degrees?), but the only other meta question for me that really comes up is: Which angle is the easiest to find first? Or, how many angles does it take to get to angle c?

In my estimation, there are only a couple of points where kids can get productively struggle – probably around getting angles d and c.

So I keep searching, when I come across this:

image

Ok, here we have something interesting. If I was in my first year teaching this class, I might explicitly give them some of the angles (say, angle b is 40), and ask them to solve for the others. If I’m really devious, I might try to sneak in some Algebra components (what if angle f equals 4x and angle a equals –8x +20??), but I’ve been hearing some powerful arguments against that.

Now that we have a diagram, and I’m in a safe place in terms of my job, we can start to ask a different type of question, one that I’ve never asked before…

How many angles must you be given in order to find all the other missing angles?

I’m no Christopher Danielson, and I don’t know much about Hiele levels of proof in Geometry, but this is the kind of question that I’d like to give to students more often. The discussion was fascinating. About half of the students were convinced that you only needed one angle. The other half were convinced you needed two angles. Even though we haven’t used the word “similar” in class once, after talking with others, most students became convinced that angle a and f were congruent, as well as b and ace, and acb and e.

I can still play the devil’s advocate pretty well – even if the entire class was convinced the number of angles needed was “two”. I can simply give them angles a and f and say “gotcha suckers”. 

Yes, I have academic standards to which I am accountable. But this underlying level of communication, this “System 2” thinking where students move from instinct to a prolonged, effortful attempt at problems is my main focus.

I haven’t done it yet, but this problem is going to be on their next assessment. I haven’t even begun to work it out for myself because I’m interested in how students approach it.

“What information do you need in order to solve for all of the numbered angles in the figure below?”

image

Other thoughts:

How  does one make a good KenKen puzzle anyway? What makes one “easy”, “medium” or “hard”. I share with you the rabbit hole of information I’ve come across, or I could say – have you ever tried to make one?

Why are you lying to me Kia?

I bought a new car for the first time in  my life back in May of 2012, a Kia Optima. I had been driving the same Ford Explorer since I was a senior in high school… around February of 2002.

I know nothing about cars, and a little less about buying big expensive things. And, I am way too influenced by television. So when the NBA playoffs come around and I watch roughly 9,000 hours of games, my mind succumbs to ads like this:

or this

  

 

Owning a new car has been completely badass. My old car didn’t have fancy new inventions like Bluetooth calling, steering wheel controls or passenger seat belts. So I’ve really been digging it.

However, one new addition has really caught my attention. In the dashboard I have an electronic display that not only tells me the odometer’s readout, but also

  • My overall rate of fuel consumption (miles per gallon)
  • A mysterious “trip B”
  • My almost-instantaneous-fuel-consumption-rate (super curious to know what interval of time they’re using to calculate)
  • My estimated number of miles I can drive before I have to start pushing

I had no reason to doubt the face value of my overall fuel consumption rate reading. After all, the car knows how many miles I’ve driven and how much gasoline it can hold… But I started noticing a discrepancy earlier this year. So I began logging the readouts of the odometer, the gallons it takes to fill up, and the readout of the MPG from the dashboard. Here are my findings.

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(Note: The one entry with (???) comes from me forgetting to record that one).

Some aspects/questions of this table are extremely striking.

  • Notice how not once does the MPG indicated by the dashboard dip below the actual performance of the MPG.
  • Notice how large the discrepancy is between the two columns. Theoretically (and it’s not a lot of mathematics involved), they should be the same.
  • What factors are driving (no pun intended) the large variance of the difference between calculated MPG and the readout MPG?

And the last question that comes to mind: Is this a conspiracy? When I purchased the car, Kia advertised 24 mpg in city, and 35 mpg on the highway. Obviously, there are factors (A/C use, temperature, tire pressure, driving style, etc) that affect those numbers. But none of those have to do with the data points that the car should be using. The car should only be calculating how many miles were driven on how much fuel. Did Kia deliberately manipulate the calculations to offer drivers a better indication of fuel economy than is actually being performed?

Once, Harvard professor H. L. “Skip” Gates said, “Conspiracy theories are an irresistible labor-saving device in the face of complexity.” I don’t want to jump to the conspiracy theory just yet. But what could be the cause of such a large discrepancy of MPG? Is my Kia lying to me or is there some Mathematics that I’m missing?