Monday, July 2, 2012

#mtt2k and my own version

Here's both an entry to the #mtt2k contest, and a humble submission for a better video that provides instruction for this concept.

Before y'all get out your flamethrowers and head to the comments, I'd like to say a few things. I'm neither vitriolic, panicked, nor bitter about Khan Academy. I think it's a great resource and it's an excellent place to see a demonstration of procedures. I send my own students to it during exam review time, and they report that it is helpful.

Where Khan and the Gates Foundation overextend their claims, though, is when they suggest that the Khan Academy can serve as standalone instruction in Mathematics. Enduring learning requires productive struggle and time to noodle out unfamiliar problems, posed by a teacher who knows what you're ready for, and can provide expert scaffolding. Lecture-only instruction focused on mastering procedures is an impoverished substitute for doing Mathematics, and it doesn't matter if that lecture is in person or in a video.

Given that, I do think that the instruction provided in the Khan Academy could be improved with some better planning and basic pedagogical technique. It's already a good resource for some purposes, and I'd love to see it get even better. It's my hope that the key players involve will calm down, cut the drama, and work together to improve the available resources. It's math, people. Not the opera.

I made a video intended to instruct on the coordinate plane. Although I'm certain it could be improved since it hasn't been subjected to editing by anyone but me, I think it's better than the Khan Academy offering. First, it provides motivation for graphing quantities in two dimensions. Second, it asks questions of the viewer at key points, with the idea that the viewer would take a moment to think and respond before continuing. Here you go:

Peter Tompkins said...

Hi Kate,
I agree that this provides something not found in KA. There is a reason to engage in the process. The model builds on an understandings of fun and expensive- (nice low entry point). I would use this but pause a few times for class discussion, students suggesting other example etc.
Thanks

Doug Dahms said...

Kate,

"Khan and the Gates Foundation... suggest that the Khan Academy can serve as standalone instruction in Mathematics. Enduring learning requires productive struggle and time to noodle out unfamiliar problems... Lecture-only instruction focused on mastering procedures is an impoverished substitute for doing Mathematics..."

This is true and a common misconception of the KA model. Projects and investigations (applied, long problems) are really a part of existing KA pilots and even more will be developed and distributed over the next few months over the KA site.

See http://tinyurl.com/6o57a37 and watch the next video starting from 3:30 http://tinyurl.com/dxe2bpt More examples here http://tinyurl.com/c5yco35

In the fall, KA plans to launch its Computer Science curriculum, which will serve as a gateway into math and science ed, as it will include interdisciplinary projects into various subjects that makes for even deeper learning.

With respect to the Coordinate Plane, video, I agree with your remarks and actually, a crowd-source-esque tool is planned to be incorporated into Khan Academy such that teachers and others and customize their videos/exercises/projects/activities. I expect that as far as multiple representation with Coordinate Planes, go Khan talked about teaching Coordinate Planes during a summer camp by including that within the context of programming and robotics, so that should provide some concrete experience for students.

Timon Piccini said...

I really like it (I was secretly wishing you had a thicker NY accent "I'm mathing here!" but that's my small town, Canadian raised, stereotyping flaring up!).

I'm wondering if the jump to negatives wrt this example is too quick. I do not know if this is nitpicking, but I wonder if we could delay showing the numbers,in your example, or make the number connection more natural. When I think of inexpensive I think close to zero (not negative). In fact I would think of expensive as negative (I am losing money). Where would I put "a job" on this graph?

I want to reiterate, I love the set up, but I am unsure if it naturally leads to positive and negative numbers. Perhaps instead money gained, money lost? Then you don't get the clear distinction among the activities that you have selected, but I feel as if negative should have a "loss" concept, and positive should have a "gain" concept. Those are my two cents (buh-dum-csh).

Also the pop-up video style of the critique video is AWESOME! Super constructive and helpful for everyone.

Doug Dahms said...

On a positive note, I found the following paragraph (if your claim is genuine) very wise and inspiring:

It's my hope that the key players involve will calm down, cut the drama, and work together to improve the available resources. It's math, people. Not the opera.

Given the sarcastic nature of videos other than yours, I doubt many MTT2K players are *truly* seeking beneficence. If true, yours is the minority opinion among critiques and a 180 degree flip from "Make-politicians-take-tests-Kate". Kudos for that.

Christopher Sears said...

Are you using an on-board microphone? I started to use a USB microphone that I picked up used at GameStop for \$10. It really helps with reducing the background noise from a computer.

Kate Nowak said...

Timon, I agree, the negative expensiveness is a problem. I dont think it's nitpicking, it's a valid criticism of the lesson.

Christopher, thank you, I learned a lot about ppt animations doing that project. I used a rather nice USB microphone actually, an audiotechnica 2020 with a pop filter.

Kate Nowak said...

Doug, a few things: I looked at the links you shared. Thanks. However, watching procedures acted out followed by long applied projects is still not what I am talking about. In the problem-based learning I and others use with my classes, we don't show them procedures first and then give them a project that uses it. They work on unfamiliar problems first, and discovering and learning concepts happens naturally as they make sense of the problem. It's an important difference. And I feel impossible to replicate or simulate with video delivery. I try to understand your perspective and I do genuinely value the work that KA has done. Please try to understand mine and don't dismiss it with "we already thought of that, see? Projects."

I still think the politicians should be pressured to take the tests, because they don't realize the destructive nature of a bad test. And some of these tests are really, really bad, for all kinds of reasons that others have reported on better than i can. Also, the companies getting rich off them are not trying to help kids learn, as I feel KA is genuinely trying to help kids learn.

I think the confrontational tone of some of my colleagues has been beneficial in instigating some reporters to look at the KA video offerings with a more critical eye. Without the brilliant use of the mystery science theatre format, this discussion wouldn't have even started. I also think that no one is going to listen to you if they think you are attacking them. I don't want to attack KA because I think they are on the same side and their motives are ones we would mostly agree with. At the same time, I think they should admit their videos have lots of room for improvement.

mr bombastic said...

Nice non-emotionally fuelled critique of Khan for a change! Great point about using color with purpose – especially for this topic. I like your variations on the square question. It is hard to judge which question is more useful when you don’t know your audience.

I agree with Timon that the natural interpretation of expensive/inexpensive doesn’t involve negative numbers. For me, that is a huge blotch that ruins some nice ideas in your video. I think a modified version of your video could be a really nice initial introduction (6th or 7th grade) that only involves the first quadrant.

Nit-picky things: Abscicsa & ordinate seems awfully formal. How about x & y coordinates or cost and fun coordinates. You and Khan both list off the four combinations of signs for the coordinates and the corresponding quadrant. I think many students see that sort of presentation and view it as a rule to remember instead of something that is obvious if you think about it. I like Khan’s crudely drawn coordinate plains and so forth because he is drawing and writing in the same way as the students.

I think your point about motivation gets back to the purpose of Khan’s videos. To me, they serve as a reasonably clear presentation of the steps of a process, with some mathematical justification for the steps. I can see that being useful to many students, and apparently, that is what a lot of students want. I think that is probably a reflection of how unsuccessful many teachers are in their attempts to provide motivation for the math.

@Doug, I don't find your examples compelling. The idea for many of us is to incorporate interesting problems into the lessons that teach the skills. We are trying to motivate the need for the skills through a question that piques the interest of the student (this is how a typical Japanese lesson procedes). I, and I think many others, find it very challenging to come up with such questions. Boring lectures on skills followed by interesting projects is better than just boring lectures. But, why not try to replace the lecture part with something that is more engaging? There are many students that can benefit from Khan. But, I just don't see how a large role for Khan is compatible with a very good to excellent classroom teacher.

Here's the thing...Kate gets teaching...why does she get it...because she has actually taught in a classroom and knows what to anticipate from students. She knows where they will make mistakes and where you will here those questions "why do we do this?" (as seen in the pop up video) She is what I like to call a "seasoned" teacher.

Looking at Khan's video he gets math...yes he (mostly) understands how the math fits together in that little world of math. What KA is not getting is the teaching part that comes along with the math part.

The only way to learn about this teaching part is to DO IT...get your feet dirty...dive right in and go through the same process we all did..those horrible first years of teaching then it getting progressively better at a rate of 2%/yr (if you're lucky).

This is one of my biggest gripes in education as a whole...there are a lot of people making decisions for us as teachers and our students who have NO IDEA about this teaching part. They don't listen to these children who struggle and WANT to do good but just need that WHY to get it...they aren't good memorizers so they need that notebook as a comfort blanket when they take their test...The list goes on and on....

My point is...looking at the two videos you see a definite difference when it comes to teaching. It is like Sal is the first year teacher just using that textbook to get him through this year but Kate is that teacher who is experienced and knows what to expect from students. She anticipates those questions and has her own responses to get kids back to what she wants them to discover. It is unfortunate that more people don't come into our classes to observe the art of teaching. I think more people would realize the difference that KA is offering students. I would also like to reccomend that Sal get into a classroom and actually teach these concepts like we do..because I feel as though his videos would not get as much criticism as they are now because he will be learning, like most teachers who made it past 3 years, how to make the "lectures" more relevant to what students need/want.

As ancient Hawaiians said: "Ma Ka Hana Ka `Ike" Through doing one learns.

Megan Hayes-Golding said...

I love your MTT2K video because it's the first I've seen that doesn't attack Khan's mistakes. Everyone makes mistakes and at the rate he's been producing videos, they're going to be some. Whatevs.

The real critique (and I think we're on the same page here) is that Khan Academy is not a teacher-replacer. It's a tutorial resource. A wonderful tutorial resource. The lack of production value in his videos give them an in-person-with-a-tutor feel. My students tend to watch Khan videos and TL;DW slickly produced films. (I wouldn't have believed it except that I watched it happen in my class.)

Khan Academy videos could improve if Sal Khan attended a strong MAT program. He needs to learn educational theory and practice teaching an entire class. His style -- tutoring -- is different than instructing an entire class. Or hire people to make the videos who know these things.

Why would KA want to expand beyond their sweet (tutorial) zone?

On another note and since we're crowdsourcing here, I imagined I was a student watching both Khan and your videos. What do I do with these points from my homework: (5,0) and (0,-2)?

Megan Hayes-Golding said...

I love your MTT2K video because it's the first I've seen that doesn't attack Khan's mistakes. Everyone makes mistakes and at the rate he's been producing videos, they're going to be some. Whatevs.

The real critique (and I think we're on the same page here) is that Khan Academy is not a teacher-replacer. It's a tutorial resource. A wonderful tutorial resource. The lack of production value in his videos give them an in-person-with-a-tutor feel. My students tend to watch Khan videos and TL;DW slickly produced films. (I wouldn't have believed it except that I watched it happen in my class.)

Khan Academy videos could improve if Sal Khan attended a strong MAT program. He needs to learn educational theory and practice teaching an entire class. His style -- tutoring -- is different than instructing an entire class. Or hire people to make the videos who know these things.

Why would KA want to expand beyond their sweet (tutorial) zone?

On another note and since we're crowdsourcing here, I imagined I was a student watching both Khan and your videos. What do I do with these points from my homework: (5,0) and (0,-2)?

Fawn Nguyen said...

I love your pop-up critique: constructive, non-emotional, and cute as hell.

While it's not natural to equate expensive/inexpensive with +/- (and I don't have a better idea!), I just love how you start with concrete examples that use the four quadrants so effectively. Stopping to ask for an example that would fit in Q4 is wonderful, and your 4 choices make the question an easier entry, and all 4 choices make me think about their placements -- more practice for me.

Maybe the original labels for expen./inexp and fun/not-fun could fade away when the coordinates are placed in; this may help to disassociate the quality with the quantity. You've already done a beautiful job of engaging the learners in why they should care about the quadrants.

The word "project" is so overrated and somehow escapes scrutiny by its name. I know there are math teachers who do lots of math "projects" that are worth squat in student learning because as you have pointed out, projects that FOLLOW procedural instructions are nothing more than dressed up exercises.

Thanks, Kate.

Christopher Sears said...

I have a suggestion for the horizontal axis in your video. It should be "income". Positive income earns money and negative income spends money. Positive income and positive fun would be a fun job like movie actor or professional basketball player. Positive income and negative fun would be most jobs.

mr bombastic said...

How about fun on one axis and healthy on another.

enzuber said...

The contrast between the two videos is incredible. Thanks for the clear demonstration of different ways to do maths videocasts.

Tastefully done.
Great pop ups.
Wonderful combination of praise & constructive feedback.
Tactical questions posed to Kahn and lesson that would help with a lesson revamp.
Very simple, eloquent and powerful.
Lastly, I love the constant question of 'why?' Why are we doing this... a typical question posed by a student.
I love it Kate. Thanks!

Mark Carstens said...

Nice work, Kate! Your integrated observations made entertaining an otherwise frustrating viewing experience. I teach fourth graders so, from my perspective, there was so much missing (for me) in Khan's explanation for pretty much everything that I found myself living vicariously through your comment pop-ups. :)

For example, isn't an ordered pair, firstly, an intersection point of two lines -- one x and the other y? Why not start with that as the basis for the x,y values? Maybe it's because my kids (9-10 year olds) and I venture another coordinate grid system -- latitude and longitude -- before we we hit ordered pairs and functions, that I have a different frame of reference. Plotting points out of thin air with the little ones is a recipe for pedagogical disaster, a sea of glazed-over expressions and guaranteed deluge of questions before any work can be done. Been there. Done that.

Your running commentary did two other helpful things for me beyond providing a conduit for my frustration; they provided a patchwork fix (mending some holes in Khan's workflow) and inspired reflective thinking that would help guide future versions of this...instruction.

For example, I can see myself using these videos to inform parts of my lesson protocol. And though the the Khan Show sacrifices the "why" in favor of a single prescription for the "how," the conversation, in affect, has been started. So, when I create my own version (iPad>Doceri>Macbook>projector), it'll be  a remix that suits my protocol and my students better. By this standard, Kahn videos -- as flawed as these might be -- have value, albeit as a source of instructional input.

Then again, Kate, if I could count on your editorial cleanup as an iterative step, so much the better! ;)

Sue VanHattum said...

Dave Marain just posted on the issue of why we use coordinates. His activity can't be done as a video, but maybe something like it could be included.

Michael Paul Goldenberg said...

@Sue: I believe it's Dave Martin, not Dave Marain, you've linked to.

GregT said...

So, firstly I'll just agree with a lot of what has already been said - nice pop-up style in the commentary, good questions posed (and wouldn't it make more sense to use a different colour per quadrant rather than it being arbitrary?), and I liked the follow-up by giving value to the variables, so to speak.

Two follow-up thoughts on your video, or perhaps rhetorical questions or possible improvements, I don't know. First, towards the end when showing the co-ordinate signs, the quadrants were listed off 1-4-3-2. Why not 1-2-3-4? Secondly, why was "Expense" horizontal, and not vertical? Let me explain what I mean there...

The horizontal is generally the "independent" variable, or the one we control and handle while measuring the vertical "dependent" variable. As much as I'd like to say I control the expense of gas, I don't. But I COULD control how much fun I have with the experience. So shouldn't "fun" be horizontal (under my control) while "expense" is vertical (measured by society)? I mean, I guess it's not measured based on the amount of fun I'm having (one hopes - "hey, he's having fun, charge for it!"), so there's no correlation, but we usually speak of "cost per independent variable". Well, food for thought, maybe?

Kate Nowak said...

@Greg I don't know why 1-4-3-2 instead of 1-2-3-4. Does it matter? I don't have an answer to whether it matters. Wondering if you think it does, and why.

Exactly zero thought was given to forcing this context to be appropriate for representing a dependent relationship. For this purpose, I was going more for two distinct, easily-graspable, intuitive, spectra to describe an activity.

@mrbombastic - Sorry to take so long to reply. I included the vocal words abscissa and ordinate, because the kids I made the video for were expected to know those words.

Sue VanHattum said...

(Thanks for catching my mistake,Michael. I read too many blogs. I don't think I realized those were two different people. Yikes.)

SiouxGeonz said...

Welp, the *original* contest asked for critiques of Khan's movies. I think that makes sense -- people keep assuming that they are good!
It's only in the comments under the comments that we get to the "we want 101 bloggers to put out something better." Working on one myself...

GregT said...

I don't have an answer as to whether it (quadrant order) matters either. At the same time, I can just see the question... "So why do we label the quadrants counterclockwise?" (Particularly if they're then listed off clockwise.) Which is why I bothered to bring it up -- wasn't sure if you were going for an angle there.

As to the rest, I think you accomplished the purpose, I easily grasped the axes interpretation. Again, it was all very well done, there were just those two things that left me musing.

Anonymous said...

Am I the only one who thought Kate's alternative video less good than the original? This material is taught to 9yos here (all 4 quadrants - they do 1st quadrant much earlier, not sure when). Please don't tell my 9yo who may have to have braces when he's much older that this is expensive and unpleasant, kthanks? It's not maths, and it's not helpful. Overall this version seemed very slow, patronising, and in places confusing (it insists on doing movement in one direction and then the other, whereas Khan correctly points out that it doesn't matter).

Can't see the commentary, since this popup stuff people apparently liked doesn't show up at all on my setup - I only see the original, with no commentary.

Kate, It is quite amazing to me that your perspective (that seemingly the rest of the teacher's here share) utterly dissociates the math, something already abstract but still accessible, by a layer of a bewilderingly obtuse second abstraction.

Expensive/Inexpensive, Fun/Not fun. Really?

Do you use math like this in your life. Does anyone? It becomes a primary mystery why someone is insisting on mapping exp/inexp, fun/non-fun onto x and y axis that completely distracts from the math.

No wonder kids find KA video refreshing. This is why. He rolls up his sleeve and immediately enters the subject matter. He is messy, and unrehearsed, but you are completely with him in examining the subject matter itself. I am not a kid, and even I was fascinated by the sudden immersion in quadrants and axis. With your video, I was just puzzled by what we could possibly be up to up here. With the KA video I stuck till the end. With yours, I was eager to leave.

It is ok to just teach math. Perhaps it is your method that needs to be re-examined. I am sure you are a great teacher being burdened by a strange pedagogical methodology.

Best wishes,

Mark Carstens said...

A commenter whose opinion reads like a Khan Academy proxy, sweeping generalizations and all?  Coincidence? Y'all be the judge. ;)

At any rate, it's clear (at least to this reader) that comparing the original Khan video and Kate's mtt2k version is an "apples and oranges" proposition. It ventures the destination of understanding the coordinate plane from two very different directions

Khan's version is keenly focused on addressing the coordinate plane procedurally through worked examples; without (or assuming the existence of) a foundational frame of reference. There's plenty of "how" but not a lot of "why."

Kate's version establishes a frame of reference for conceptual understanding through analogy. And then, once established, demonstrates through a series of examples how this plays out within the context of that reference frame.

So, my first question would be, "Do worked examples alone lead to conceptual understanding?" In other words, the frame of reference is the work itself; is this enough?

Next question, is does fun/not fun, expensive/inexpensive an effective analogy that provides an accessible frame of reference for most students?

Before venturing either answer here, let me say that, in my experience, some kids -- those who've learned to grasp procedures as the briefest means to an end -- would appreciate Khan's "jump in the saddle and ride" style and may be able to repeat the procedures, but without understanding the conceptual infrastructure behind them. Others, whose eyes glaze over when you throw them into the procedural (calculations) without an underpinning or who prefer an analogous frame of reference (like Kate provides) to introduce a concept, are more open to the procedure *after* the foundation is established.

With that said, to my way of thinking, the question of which video treatment is more appealing (or, dare I say, "better") is secondary to the more meaningful question, "What interactions took (are taking) place *in the classroom* before and after (either) video is viewed?" The argument, then, shifts from evaluating the standalone quality and effectiveness of (any) video to "Which approach best supports what I do in the classroom?"

At the end of the day, where you stand depends on where you sit. If we focus narrowly on the procedural, that is all our efforts will yield. That's short-sighted, in my view.

I'd rather find and use teaching tools that are inherently more flexible and provide a broader frame of reference. So, for me, more than reinforcing a narrow view or "the one way" of solving a math problem, I need a means of integrating divergent thinking and analogy into math instruction. Videos like Kate's offer this.

Michael Paul Goldenberg said...

One of the hardest parts about watching this and other critiques of Khan Academy videos is having to listen to Sal Khan's monotonous voice. It's dead-souled presenters like Sal that can make the most fascinating topic immediate cause for suicide. Sal sounds only slightly less dead than my former insurance agent from Met Life. Talking with him on the phone made me want to jab giant knitting needles into my ears.

Chris Hunter said...

Mark suggests we are comparing apples and oranges.

We are not.

http://reflectionsinthewhy.wordpress.com/2013/03/04/plotting-uses-of-technology-for-learning/