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20 Replies to “Do The Math”
It’s one thing to offer videos that pose interesting questions, like:
“How far would you have to run to burn off a Big Mac?”
And it’s another thing to build a curriculum around them.
“With your help, we can put teachers in a position to teach math more effectively while engaging their students to become smarter, healthier and more curious. With your help, we can support teachers as they create a generation of young geniuses!”
You don’t have to know much to pick out the overblown and pandering marketing. Math to make you “healthier”? Create a “generation of young geniuses?” How about a math curriculum that ensures mastery of the basics on a grade-by-grade basis. Even top-down engagement loses steam when you get down to the hard work of mastering basics. Too many schools just go through the motions with curricula like Everyday Math which tells teachers to “trust the spiral”. As long as teachers see “active learning”, they don’t worry about mastery of skills because math, apparently, is some sort of vague thinking process.
“But math is much more than numbers and equations: math is a way of thinking. It can give us a fresh — a smarter, kinder, more insightful — way of looking at everyday life.”
No. Math is not a vague way of thinking. Math consists of specific skills, mastery of which is not devoid of understanding. Solving problems in math requires knowing which governing equation applies to a particular problem. It requires mastery of how and why that equation works, and it requires mastery of all of the possible ways that equation can be applied. Math is not just some simple Polya process where kids draw pictures and think.
Top-down engagement as a method for solving math education problems blames the kids. It assumes that all they need is little excitement and then everything esle will take care of itself. Trust the spiral. Trust the engagement. What is 6*7? How many one-thirds are in one half?
While I’ve spent a lot of time at home ensuring that my son has mastered basic math skills (who is now on the AP calculus track in high school), his lower schools assume that their Everyday Math curriculum works just fine. Many educators think that those poor urban kids just need more engagement to make them “geniuses”. No. Ask the parents of the best students what they do. We don’t just turn off the TV and model an interest in education. We teach and ensure that learning gets done. We do NOT trust the spiral. K-6 math curricula ruins kids. For many, a STEM career is all over by 7th grade, no matter how much engagement or Project Lead The Way they have later on.
“Rotherham believes dramatic improvements in America’s education system are integral to ensuring equality of opportunity and building a more equitable and just society.”
Math52 will NOT provide any dramatic improvement. All it will do is make “active learning” look better and mask the missing mastery of the basics. It will be used in high schools to make kids happier about math class, but not fix the missing gaps in their math skills, and it won’t open career doors.
Typical mischaracterization of traditional math as a teacher lecturing with students bored. Most middle school teachers will ask questions of their students, pose a problem, have them solve it. It’s nice to have interesting problems, but again, the idea that looking up data by yourself is better than having the data presented in the problem is at this point a cliche that inspires nausea and vomiting.
61% of students would rather take out the garbage. Was this question asked of other disciplines. How about whether they’d rather go to school or take out the garbage. How about reading Eduwonk’s Time Magazine polemics or taking out the garbage? How about giving us a break?
Interesting comments. A couple reactions:
I agree that a collection of videos by themselves cannot and will not transform math education. The benefit of the Math52 videos with respect to teaching, however, are the lessons that accompany them.
These lessons are not only engaging but mathematically rich. At Mathalicious, we offer lessons that explore the relationship between income and happiness, while introducing derivatives and integrals in eighth grade. Students explore how much Apple is charging for the iPad, and discuss linear vs. non-linear functions, solving equations, parallel lines and a number of other Algebra topics. The “Big Mac” lesson we mentioned? Common Core standards 6.RP.2, 6.RP.3 and 6.NS.3.
In terms of outdated critiques of traditional teaching, the stats are, unfortunately, all too real. As a former teacher and middle school math coach, I have seen many teachers struggle with how to engage students and teach math in a rigorous and meaningful way. I struggled, too. This isn’t necessarily the teachers’ fault. Many are new, many are overwhelmed, and most are teaching content that’s flat-out ineffective and perpetuates the notion of math as a series of random steps. It’s fine to be skeptical of Raytheon’s 61% stat, but to use this as an excuse to ignore the problem is problematic, indeed.
Math52 is one piece of a puzzle. Effective content such as the lessons that accompany the videos is another. To the comment, “Math52 will NOT provide any dramatic improvement. All it will do is make “active learning” look better and mask the missing mastery of the basics,” I’d encourage you to visit http://www.mathalicious.com/about to see what teachers and students have to say about this. A couple highlights: 95% of teachers say their students enjoy the lesson. 97% say it makes them better problem solvers.
Is this shameless pandering? Perhaps. Or perhaps it’s something that’s actually helping teachers engage their students, teach math more deeply and enjoy their jobs more in the process. Instead of dismissing this out of hand, you might consider whether it might actually be an honest — and promising — effort to help solve a very real problem.
After all, that’s what math is all about.
Why don’t you look at what teachers and students have to say about Saxon Math, and Singapore Math as long as you’re throwing testimonials our ways. Misrepresentation of traditional math is a time-honored approach to selling all sorts of supposedly new approaches to teaching math. That traditional math can be taught poorly doesn’t mean that it never is taught properly, with good results. Students need mastery of basic skills and problem solving procedures. Challenging problems are great, and that’s the purpose of multi-step problems that build mathematical reasoning and problem solving ability. The fact that a set of homework problems can be designed to provide scaffolding and discovery is beyond the ken of most of those who believe traditional math is all about rote.
Instead, what we get are ratio and division problems disguised as something exotic like income vs happiness and calories burned vs big Macs. Take a look at the type of problems that are in Singapore’s math books for 6th grade.
As far as Common Core standards, you seem to think these are without fault, but that’s another argument for another time.
Have you looked at any of the lessons on the site? I can appreciate your skepticism — I’m currently at the NCTM annual conference, and everyone in the exhibitor hall apparently has “the answer” — but why are you so confident that our lessons are just “disguises?”
The reason we’re able to introduce calculus in Grade 8 is not because or sorcery but because context allows students to develop both the conceptual and procedural fluency required for true mastery. Students differentiate non-linear functions, the use a video by Nobel laureate Daniel Khaneman to discuss the marginal benefit of additional income. Could you please help me understand what part of that you find objectionable?
We need students to become good at math, not something masquerading as such. NPR “Math Guy” and Stanford mathematician Keith Devlin uses our lessons as examples of how math should be taught. He’s no slouch. He’s also familiar with our materials.
Are you? If not, there are a number of sample lessons at the bottom of the homepage that should give you an idea of the mathematics that students are doing with their teachers. Happy to have a debate, but we would do well to be talking about the same thing.
Watching a video as “learning” has the same problems as depicted in the opening scene in the first video shown. Math is a participation sport. I tell my students that attending lectures will not cause them to pass the course — they must pull out problems and practice, practice, practice. The same is true in all grades, down to Kindergarten.
As Mr. Garelick says, we aren’t well-served by this caricature of teachers, who understand the need to engage students with lively topics that catch their interest. The problem lies in the transference of knowledge without any way of making it permanent — and in the belief that mathematical education is transference of knowledge (alone) in the first place.
Learning mathematics is more akin to learning a comprehensive skill like a sport, musical instrument or handicraft. It cannot be learned passively. Imagine “coaching” a soccer team by having them watch videos all day. Without practical drills, all the head-knowledge received, if retained, would be unusable on the field. In fact, it would not even be retained.
This fantasy that “having a conversation” after watching a lively and entertaining video will perform the function of practice, is also problematic. Conversations are good, but simply watching and then talking, while good for doing counselling or talking about societal values or history, it still misses the essential component of learning mathematics, which is the automatization of skills and the layer-by-layer addition of new levels of skill and sophistication.
Videos can be an excellent addition to this process, and can keep distracted students engaged. But they are no replacement for the process itself, and they can harm the process in whatever degree they replace the actual processes of math education in the class and at home. What is needed are well-designed learning tools that come with comprehensive exercise sets and feedback mechanisms that help students internalize the necessary skills as they are learned.
Anyway, since you’ve stolen the name anyway, why not check out my pal Hypatia’s blog, Do The Math, where she discusses this sort of issue and goes in depth about things that need fixing in math education?
Interesting — I do enjoy using this sort of thing as supplementary material — the cherry on top — but on the other hand, I’m a homeschooler and, relatively, have “all the time in the world” to spend on math any given week or year.
Back in the day when I was a student, I found that I really absorbed the the prevailing atmosphere that “Math is hard!” and “Math is boring!” and believed it because it was conventional wisdom and because I was young and stupid (as many of us are). At that age, I didn’t even know what conventional wisdom *was*, but I could pick up what I was supposed to feel about certain things.
It wasn’t until I was in college when — forced to *finally* take my required math classes that I had been putting off and putting off because “math is hard” and “math is boring” that I realized: Wait a minute — math is just fine and I am good at it. This was not any special project based class or anything like that, it was just plain ol’ College Algebra. Well, that caused a bit of a headache as I basically had to reboot my entire college plan (adding two years to the process) to accommodate the fact that, hey, turns out I like math and am pretty good at it. (But that’s a whole other story.)
What I’m trying to say is, I do enjoy a little “math appreciation” in our day, but I worry about too much of it replacing “actual math” instruction in the 5 hours a week our kids get in school. (My problems with current-day math instruction are the #1 reason we homeschool.) I think it inadvertently sends the opposite message that math IS hard and math IS boring because look what we have to do to it in order for your pretty little heads to get it.
“We provide classroom teachers with lessons that allow them to teach standards-based math using topics students care about…Instead of teaching fractions and percent, teachers get to teach “Is The Wheel of Fortune Rigged?”
Wheel of Fortune?
My Grandma Watches That (I’m sitting in front of a Wheel of Fortune episode now, oddly enough. Sitting, not watching.)
The idea that ‘real world’ problems are intrinsically interesting is simply not true. The real world is often boring, and I’m not sure what makes a word problem about Wheel of Fortune ‘real’ in any event.
The thing about forced fun is that it isn’t fun. When my son was 10, he told me, apropos of some fun math his teacher had sent home: “They don’t understand. When they make math fun, it’s more boring.”
@ R. Craigen:
We do not intend for teachers to show the videos to students, but rather to recreate the conversation and mathematics with their students. I agree with you that just watching a video would be fairly pointless…which is why we explicitly address this in the Kickstarter FAQs.
Teacher comment from Wheel of Fortune lesson:
“My students really enjoyed this activity. The student handout and the lesson guide for the teacher are wonderful. The students were engaged in this lesson the entire time. They really liked comparing the theoretical and experimental probabilities. It was a great lesson to demonstrate these probabilities.”
It’s very interesting to note how cynical all of these comments tend to be, and how they tend to address an issue/concern that doesn’t actually apply here. We’re trying to offer something that can help teachers. In the past three days, we’ve raised a little over $8000, much of this from teachers themselves: people with little disposable income but who are supporting the project because they recognize the problem and want to help solve it.
It’s easy to cast stones in blog comments. Before doing so, though, we would do well to make sure that the target exists in the first place. Otherwise we spend all our time railing against ghosts, and getting nothing done in the meantime.
These are great problems. But they’re not anything new in concept. A better use of your money would be teaching math teachers-in-training to frame more of the problems they use in class this way.
“It’s time for a change. It’s time for a fresh vision of what math can be…and that’s exactly what we’re going to offer with Math52.”
“Math52 is one piece of a puzzle.”
Which is it?
This is not a “fresh vision”. Top down, real world approaches have been used for a very long time. It hasn’t fixed test scores. Why? Because schools don’t ensure the basic skills portion of balance that they claim is still so important.
“math is a way of thinking.”
I already commented specifically on this error.
“Why Kickstarter? On the 2009 Program for International Student Assessment for math, American high school students finished 27th.”
Kids don’t do well on the simple PISA questions because schools never ensured mastery of basic math skills. Most current K-8 math curricula (for the last two decates) have spent enormous time on the real world problem solving portion. Besides, PISA is no guarantee of a STEM career.
So, what does Math52 add to the mix? It’s not a fresh vision. It’s simply some more real world examples that presume to be better than all of the other real world examples that have been used for decades. How does this fix the real problem of missing mastery of basic skills?
“97% say Mathalicious helps their students become better problem solvers”
Are they doing better on the PISA test? Are they getting into STEM careers? Can they now pass the Accuplacer test to get into a vocational school to become an electrician? Is the goal just to do marginally better in middle or high school math while ignoring systemic mastery issues in math?
You opened yourself up by claiming that Math52 is some sort of “fresh vision” for math, not just a fresh vision for real world problems in math.
I also have some specific comments about your video called “On Your Mark”.
Why would anyone think that height is a critical factor? What understanding of physics is that based on? Why wouldn’t someone at least say that it’s more like the length of the legs? What do you mean when you ask students to be problem solvers? Is this somehow devoid of content knowledge? Why would you look at average speeds for a race that is almost all about acceleration? How would your comparison change for a long distance race?
What problem are you solving? Are you trying to find the person who works the hardest while eliminating any advantages of genetics? If so, why would height be the key genetic factor? Why not weight?
What is your merit function? What physics is it based on? What is the definition of work?
That’s what math is about, not some vague sort of thinking process.
Why do we have merit functions? How can they be constructed? What are weighting values? How do we verify the function? How can we validate that it produces proper results? How can we do parametric sensitivity studies of the independent variables? Which variables have a dominant effect and which have a minor effect? Can you tell by looking at the equation? Can you model the acceleration portion and the steady state portion of any length of race and then see how the merit function changes when you change the race length variable? Problems don’t have multiple solutions, but they might have multiple choices of merit functions and multiple choices of weighting values.
As for the Bic Mac problem, Google calories in a Big Mac and calories burned while running a mile. Divide.
I hold double degrees in math and physics and my master’s in atmospheric physics. I am retired Navy and work at a university lab.
I could, if I like, spend every last minute of my waking hours TUTORING math and science students USING TRADITIONAL METHODS.
Parents demand this kind of instruction. It would appear to me that THEY are VOTING FOR MORE TRADITIONAL INSTRUCTION.
I simply cannot, as a math and physics expert, support any more of this hogwash math reform. These carpetbaggers have moved on from the flimsy liberal arts to math and science because they see big fat opportunities.
Parents are frantic for quality math and science instruction, and the publics, which have been OVERRUN by the latest bull crap math reform ideas, CANNOT DELIVER THE GOODS.
So, the private markets have responded with many TRADITIONAL MATH AND SCIENCE TUTORS.
The markets are speaking. Are the hogwash math/edu-reformers listening?
No, they are not.
@ Steve H:
“Why would anyone think that height is a critical factor? What understanding of physics is that based on? Why wouldn’t someone at least say that it’s more like the length of the legs? What do you mean when you ask students to be problem solvers?”
This is EXACTLY what happens in the classroom lesson. The question is “Do taller sprinters have an unfair advantage and should athletes run distances proportional to their heights?” Read: SHOULD they? There’s no right answer. Some students will say yes. Others will say no. Maybe it’s leg length instead. Maybe taller sprinters actually have more drag. What about weight? The goal isn’t to arrive at a conclusion. It’s to foster the conversation…and use math — proportions to calcula the distances, rates to find the new race times — to fuel it.
You’re arguing against asking the question in the first place. Why? No idea. I have no idea what your motivation is for spending so much time throwing rocks against people who are doing real work that real teachers are using with real students with real results. Mathalicious. Dan Meyer. I don’t know why you presume to be more of an expert on mathematics than Keith Devlin, or in pedagogy than thousands of teachers across the country.
But I do know that I’m having a hard time taking it seriously.
You got fired up about the Usain Bolt question, and you used that as a reason to rail against it. We posed a mathematical problem that got you excited, and you concluded that was a bad thing.
@ Steve H:
Incidentally, you seem to think that math is not a way of thinking but rather the manipulation of numbers. Not logic, but basic skills. I disagree. So do the ancient Greeks and Egyptians.
Problems can have multiple solutions, by the way. They’re called quadratics.
“people with little disposable income”
In my town average teacher compensation is $96,000 rising to $99,000 next year; benefits bring total compensation to $130k. Teachers have lifetime healthcare from first dollar (no co-pay) & pensions of, I believe, 80% of final salary, which the state DOE website explicitly encourages teachers to augment by leading after-school clubs & the like in the final years of their careers. Total funding for retirement comes to at least 1.5 million, almost none of which has to be saved by the retiree (this has now changed for new teachers). Pensions are guaranteed by the state constitution; 401Ks are not. Thus baby boom workers in the private sector, who need to save for their own imminent retirements, must fund baby boom teachers’ pensions instead.
If you want to see teachers with little disposable income, visit a community college, where students go to learn arithmetic and algebra after 13 years in public schools.
And, speaking of cynicism….
When my son was in 8th grade, he & his peers were coming out of two years with an ineffective teacher & an over-accelerated curriculum. They were very poorly prepared.
On back to school night, the “Math Lab” teacher – Math Lab featured real-world problems & “extension” activities – told parents he was aware of the kids’ difficulties & would be doing remedial teaching during Math Lab to catch them up.
He didn’t. Instead he devoted class time to Mathalicious-type activities & hired himself out as a tutor to students in the class at a fee of $80/hour. (This was 5 years ago; I’m sure his fee has risen in the years since.)
His clients’ grades on tests instantly rose from D’s & F’s to B’s & C’s.
Real-world problem solving inside the classroom, direct instruction in tutoring sessions at home. Same teacher, same students, same parents.
“Cynicism” isn’t the word.
A Mathalicious-type lesson, or an actual Mathalicious lesson? Again, we introduce elements of calculus in eighth grade. We have students use Wheel of Fortune to not only convert from fractions to percents, but to better understand what fractions mean. (And discuss experimental design and the difference between theoretical vs. experimental probabilities.)
There’s a lot of junk out there. I’ve seen it. But before you lump us in with that, I’d encourage you to look at our lessons. There are a number of free lessons at the bottom of the homepage that will give you a good idea of how we blend real-world contexts with deep, rigorous and meaningful mathematics. Just visit http://www.mathalicious.com
Okay. Good conversation, everyone. Clearly we disagree (or do we?) but I respect the passion. I think I’ve exceeded my blog comment allocation for the week. If you want to continue this, please feel free to email me at karim at mathalicious dot com.
“Problems can have multiple solutions, by the way. They’re called quadratics.”
Well, there’s my argument all scuppered, isn’t it?
“There’s no right answer. Some students will say yes. Others will say no. Maybe it’s leg length instead. Maybe taller sprinters actually have more drag. What about weight? The goal isn’t to arrive at a conclusion. It’s to foster the conversation…and use math — proportions to calcula the distances, rates to find the new race times — to fuel it. ”
“no right answer”
“foster the converstation”
No discussion of merit functions? No discussion of weighting values? No learning about energy or work? After a whole class period talking about this (probably in groups), what have they learned? What is the goal, some practice at guessing and expressing one’s opinion? Is the question a way for ninth graders to practice 5th grade math?
“We posed a mathematical problem that got you excited, and you concluded that was a bad thing.”
It did NOT get me excited because it wastes a lot of time for very little gain. There is no goal for learning about the math behind problem solving. The goal is not about learning specific content or ensuring mastery of skill sets. If you want to discuss general problem solving, you should look at the field of systems analysis. I taught a course in that for years. Math is not some vague thinking process. It defines specifics tools and skills. That’s the whole point.
“Mathalicious. Dan Meyer. I don’t know why you presume to be more of an expert on mathematics than Keith Devlin, or in pedagogy than thousands of teachers across the country.”
Invoking some sort of higher power is not an argument. That can be applied both ways. If there is “no right answer”, then why are so many educators fighting choice? Why do they claim “best practices”? Why are so many urban parents desperate to get their kids into K-6 charter schools that ensure mastery of the basics?
You are solving the wrong problems. You look at PISA and come to the wrong conclusions. You see only what you want to see. You are blaiming the student. The problem is not lack of motivation or engagement. The systemic problem is that kids are not mastering the basics in K-8. In spite of all of the talk of balance, curricula like Everyday Math just keep pushing kids along and trusting the spiral. That is a fundamental flaw. Educators unlink understanding from mastery of skills and then claim some vague thinking process for math. You claim the higher ground of pedagogy and mathematical understanding while looking at all the best math students in classes using direction instruction and large homework sets. These students are not robots who magically get answers correct with rote skills. Their parents ensured that these kids mastered the basics. They are the one’s going on to STEM careers. Colleges don’t care about Project Lead The Way. They care about math, physics, chemistry, and biology grades. As for problem solving, try sending questionnaires to the parents of the best math students and ask them what they do at home. It’s much more than turning off the TV.
The problem is the whole system, not just what walks into your classroom. The problem is not trying to make ninth graders happy about math after 8 years of bad curricula and low expectations. Even if that is the immediate problem, the goal should be ensuring skills that open doors, not playing at thinking. I taught college math and computer science for years. I saw the lack of skills. My conclusion was NOT that they just needed more interesting problems to guess at in groups and to practice fifth grade math.
I am impressed by what I see and read. Videos cannot replace teaching but clearly that is not the idea. The advantage of the videos is to bring a variety into the maths classroom and demonstrate practical applications and open up discussion. On that score there is validity. Clearly sound teaching cannot be replaced by videos and no excuses can be offered for shoddy teaching. BUT, supplementary approaches that support and bring extra to sound teaching must be commended. Sound foundations are essential but failure to provide such in the first six or seven grades leaves a child “handicapped” and leaves his/her later teachers a nearly impossible task to make up the backlog. Too often teachers teaching maths in lower grades do not understand the maths they are teaching, nor the critical importance of the early years. Where is the provision of on-going staff-development? This is not just a USA issue but a problem world wide with very few exceptions – AND its needs to be treated as both extremely serious and equally requiring urgent action.
Site one outlier on teacher pay and THEN extrapolate to the whole. I guess math was not your thing, eh?
Might as well insert your dissertation on the income gap and let’s use Steve Jobs. No doubt, you are a salesman, and your schtick is to called teachers overpaid and your product a real bargain: A SALES PITCH.
Go on-line and watch the Kahn Academy or Brighstormmath.com. Looks like direct instruction to me. Watch some MIT lectures. Looks like direct instruction to me. Watch some Stanford lectures. Looks like direct instruction to me. ALL OF IT IS FREE.
Mathalicious would be competitive if it were FREE.
ANY math instructor worth their salt knows what is going on here. School purchases videos when the same product is FREE. Teacher shows videos. Teacher is now extraneous to the learning process. Student watches Mr. Bolt run fast. Student is impressed. End of lesson.
And to Catherine. Cynicism is a form of cowardice: Everything stinks and I know it. Do not argue with me. Teachers are terrible. Schools are terrible. Yeah, some bravery there.
Not so fast. My children are both graduates from the very best UCs in science. They also attended the publics. An exception does CONTRADICT. But one exception does not make the rule.
Shame on you Catherine. Shame on you.