This is winding down.
I’m mostly content with the two-part definition I set up two weeks ago. I’m also satisfied that pseudocontext is much less of a problem than real context that’s either a) poorly represented or b) poorly examined. Any final comments, questions, or challenges, get them on the record ASAP.
This winter I’m taking “The Design of Technologies for Casual Learning” with Shelley Goldman so I ran a quick survey of math apps for the iPhone and iPad. Scratch off all the drill and test-prep software and you have a lot of apps that are trying to make use of some kind of context. Do they represent pseudocontext or not?
Could you swap out “peacocks” for, well, anything without changing the implications of the problem? It fails definition #2, “operations that have nothing to do with the given context.” See another example.
The iLiveMath family includes iLiveMath Oceans, iLiveMath Animals of Africa, iLiveMath Animals of Asia, iLiveMath Speed, iLiveMath Trains, iLiveMath Entomology, iLiveMath Ford Cars, iLiveMath Farm Fresh. Each one is stuffed to overflowing with pseudocontext. Also, at $4.99 each, you’d wish they’d spellcheck this stuff even a little. (These are the promotional stills, incidentally.) Produced by a company called iHomeEducator, this stuff is obviously pitched at homeschoolers, which, as a homeschool graduate, kills me.
Fails definition #2 again. What does 2 x 2 have to do with a tiara?
Ditto the others. You don’t really “use math to defeat” the boss. You’re doing math and the game rewards you by defeating the boss. I will break out the parade if someone can point me to the iPad game where you really use math to defeat the boss. That sounds awesome.
Dress Up Math
The operation, at last, matches the context. It fails definition #1, though, because there’s no way that pink blouse costs $4.00. Even I know that.
Mellyme, a five-star review of iLiveMath Animals of Asia:
This app is a very good concept and it works well in practice. It’s multimedia approach to word problem drills is genius. Kids can learn about various animals while doing math. The videos provided are great as well. Give at least one of this company’s apps a try. I have bought two from them-my daughter loved them both.
Okay, so here we go. Students can find pseudocontext interesting. Students can find real context boring. Reasons for the latter include poor representation and poor examination. Reasons for the former include social and academic pressures, enthusiastic teachers, and idiosyncratic student tendencies from which it’s really unwise to generalize to “all students” or even “my students.”
The problem with pseudocontext isn’t the risk of boring the majority of your classroom. It’s the message that this is how the world works and this is how we apply math to it. Pseudocontext teaches students – even the students who tolerate or even like pseudocontext – a lesson that is very hard to unlearn.
TomDecember 11, 2010 - 7:16 pm -
From what I recall* you’ll find Tabula Digita’s stuff pseudocontext taken to an entirely new level. Think Ninja Math but in a full blown video game environment.
It would be interesting to see your take on it.
*I haven’t played all their games, nor played them extensively. We did not opt to purchase.
ElenaDecember 12, 2010 - 1:52 am -
I like to tech too!
I very much enjoyed your video, I could watch the video on the blog of Annarita Ruberto here the link:
I would like to link your blog to my blogroll here:
Elena from Italy ;)
Jim EllisDecember 12, 2010 - 4:25 am -
The evil pseudocontext is all over these examples for sure. But I have a few questions here.
1. In the Ninja Math example, is the point of this game to teach the skill of single digit number addition?
-I would guess not. This seems to be a stage in learning where the concept is understood, but the learner (and or teacher) are looking to add to rote memory. Myself, I’ve got 6+8=14 locked away in my own rote memory. I don’t spend much time contemplating the act of adding in context or in symbolic math. I just simply do it. We know rote memory skills to be important when these students reach such topics as algebra. For example, I don’t want my students contemplating the nature of negative numbers and how to use them when they are designing/solving an equation. The attention should be on the rhetorical or symbolic algebra. The analog version of this might be flash cards. I can’t say that I disagree with this tool (or flash cards) when used at the proper juncture of a students learning.
2. Dress Up Math’s screen shot doesn’t give me enough information to understand what the problem is all about, but I find your effort to match your pseudocontext definition to this activity rather flimsy. “The operation, at last, matches the context. It fails definition #1, though, because there’s no way that pink blouse costs $4.00. Even I know that.”
My question to you is one of cultural relevance. Can you tell me for sure that the places your students shop include items that cost much more than this?
-Recently, I got a few long sleeve workout shirts for 2 Euros (about $2.60) when shopping in Vienna’s main shopping district. I also happened to see several of my affluent students in the same shop. I’m more concerned with the body image messages young girls would get from the character about what is a desired figure.
Finally, I must admit that I don’t care so much for these games either. Why can’t analog solutions do this same task just as well? You don’t have to plug in a sibling/parent/classmate or teacher who is working with you on flash cards or is actually shopping with you. Nor do my analog tools such as flash cards require charging.
Daniel SchabenDecember 12, 2010 - 7:47 am -
OK . . . I want to take the classes you take. I am pretty sure this class is not something I can take here in Nebraska yet. Keep posting, great reading for a Sunday morning.
MyleneDecember 12, 2010 - 12:33 pm -
I’m curious to look at the issue from the other end: what harm does pseudocontext do? What harm does badly-applied real context do? (Are the 2 kinds of harm different in kind or only in degree?) I know what harm I *suspect* it does. Can we document it?
I read a study recently and have been wondering if it answers these questiosn. It documented university physics students’ “common sense” assumptions about motion (http://modeling.asu.edu/r&e/Hestenes_CommonSenseConcept.pdf). It’s 25 years old but I fear still relevant. Conclusions:
– the majority of students entering university hold beliefs about motion that date back to somewhere between 200AD and 1200AD
– When told, during in-depth interviews, that these ideas are incorrect, most students justified their beliefs with increasingly complicated rationalizations
– When presented with physical evidence that contradicted their theories, most students continued to defend their beliefs and further argued that the demonstration must somehow be inapplicable (wrong context??)
Examples of common student assumptions:
– a moving object to which no force is applied will slow down
– heavy objects fall faster than light ones
– a ball swung in a circular path, then released, continues on a circular path “for a short while” before transitioning to a parabolic path
– a puck moving in a parabolic path across an air table would eventually go in a straight line “if the table were long enough”
Here is my theory so far: when math classes distort students’ intuition about the real world, it may not prevent them from doing well in further math courses. It prevents them from doing well in any other course where math is used.
Here is what the authors conclude: “If such misconceptions are not corrected early in the course, the student will not
only fail to understand much of the material, but worse, he is likely to dress up his misconceptions in scientific jargon, giving the false impression that he has learned something about science.”
Pseudocontext at work? I would love to know your thoughts.
louiseDecember 12, 2010 - 1:15 pm -
computer uses, math in context, yes – it’s a game. No it’s not made specifically for an ipad. I had students playig these secretively, as it was obviously not studying coordinates (the assigned task).
I still think we need to teach math and intro physics together, so that students see what really happens. Now that digital cameras are so available, let’s get to the slow motion effects and really measure what happens.
LauraDecember 13, 2010 - 8:45 pm -
Dan, I am a die-hard WCYDWT fan. I’ve been intrigued by the ongoing PS conversation over the past few months.
I have to agree with (3) Jim. When I first saw your examples of Princess Math or Ninja Math, I’m not convinced those games are relaying the dangerous message of pseudocontext: “this is how the world works and this is how we apply math to it.”
I teach second grade, so I work with math learners who are beginning to understand how numbers work. I’m also guiding them toward the realization that knowing what these numbers are when you add them up is something that’s important to know if you want to do other math. And it’s important to know quickly. I stress fact fluency to parents and kids alike, and if a princess tiara (or ninja kick) is going to entice one of my students to practice their facts, then I’m all for it! I may be assuming too much, but I’m not under the impression that students are inferring that tiaras or ninja moves are real world applications of 2+2.
Now, the iLive math (with their peacocks and whatnot) claiming that their software will help the user learn more about animals….that IS a gross misrepresentation of how math applies to the animal kingdom :)
MarcieDecember 14, 2010 - 8:20 am -
Vernier has great apps for data collection!!! You can then use video analysis in the app to find all sorts of wonderful, exciting things.
Ever wondered how fast the QB at the game really throws the ball? There’s an app for that (using a little graphical analysis, of course).
RickDecember 26, 2010 - 11:58 pm -
“The operation, at last, matches the context. It fails definition #1, though, because there’s no way that pink blouse costs $4.00. Even I know that.”
Maybe they mean wholesale.
gasstationwithoutpumpsJanuary 1, 2011 - 1:02 pm -
My immediate response to “there’s no way that pink blouse costs $4.00” was “Well, he obviously doesn’t shop at Goodwill or the Salvation Army.” It is quite common for a blouse to cost in that price range at the thrift stores. (I buy all my dress shirts at thrift stores, for about $5 each.)
The shoes are not at thrift store prices, but the rest of the prices are.