Opening up things a bit
Having come back from Educon 2.1 I realize that I have to be (far) more collaborative. Not my nature being an introvert but, having tried to blog every year for the past 10 years, I'll try again. Since I can't always talk about CAS, I've opened this up a bit and we'll just look at anything (mathematics U education U technology) that crosses my desk. It'll also help me avoid filling up my colleagues' mailboxes.
A little off topic
MathML Strengthens Digital Math Texts
Digital texts are moving beyond simply putting pages on a computer screen.
In Kentucky, a small pilot study is demonstrating the benefits of this textbook technology for students with different learning styles. Instead of re-creating a complex math problem as a static image file, digital texts that use math markup language, or MathML, are able to speak words and equations while highlighting corresponding elements on a computer screen.
MathML-enabled digital texts helped the study's very small cohort of students struggling with printed text outperform peers who used traditional print texts. Many students said that before MathML, they'd see a problem but not know how to say it. Hearing the formula and how to say it was a big help to these students.
From ASCD http://ascd.typepad.com/blog/2008/10/mathml-strengthens-digital-math-texts.html
Digital texts are moving beyond simply putting pages on a computer screen.
In Kentucky, a small pilot study is demonstrating the benefits of this textbook technology for students with different learning styles. Instead of re-creating a complex math problem as a static image file, digital texts that use math markup language, or MathML, are able to speak words and equations while highlighting corresponding elements on a computer screen.
MathML-enabled digital texts helped the study's very small cohort of students struggling with printed text outperform peers who used traditional print texts. Many students said that before MathML, they'd see a problem but not know how to say it. Hearing the formula and how to say it was a big help to these students.
From ASCD http://ascd.typepad.com/blog/2008/10/mathml-strengthens-digital-math-texts.html
The fence question
So I assigned the classic fence-against-the-river question to my group (you have 200m of fencing, what's the largest rectangular area you can contain where one side is not needed against the river). We had just started quadratics so they have no real background in it at all. One student solved it thusly:
1) He made a table of values for a few fences:
Then, he turned to Maple. We had done a unit on linear systems and did a few questions on finding lines of best fit... so he used the Curve Fitting Tool to find the best fit parabola, then found the vertex of the parabola and hence the best area.
Then he found the vertex of the parabola by zooming:
Almost every other student did it the traditional way of setting up the equation, graphing and finding the vertex. I thought it was a nice bit of synthesis from the previous unit to approach it in this fashion!
So a little further
Well, we're into quadratics now. The one section is doing really well incorporating Maple into their learning process -- they fluidly jump back and forth between Maple & OneNote. The other class more stubbornly holds on to doing everything by hand/calculator. I keep struggling to move this section to a more exploratory model but they will have none of it.
Maple still perplexes us from time-to-time... the switching between independent & dependent variables based upon alphabetical order is one of the more irritating ones. It will graph it in the desired order but as soon as you change the window (axes, zoom, etc) it switches the order! I've gotten around it by choosing my variables appropriately but when they experiment the students don't always think to (nor should they have to).
Maple still perplexes us from time-to-time... the switching between independent & dependent variables based upon alphabetical order is one of the more irritating ones. It will graph it in the desired order but as soon as you change the window (axes, zoom, etc) it switches the order! I've gotten around it by choosing my variables appropriately but when they experiment the students don't always think to (nor should they have to).
Variables
Well, we've used the Curve Fitting Tool for the past couple of classes. Lesson learned: it's best to be descriptive in your variables because using x and y is not conducive to the CFT (it wants to use x as the regression variable).
We're on to quadratics now; I wish the spreadsheet tool was a little more flexible than it is and followed Excel notation ... having to add the tilde before the cell reference is clumsy. I also wonder if there's a way to have the column filled by a list variable?
Oh... and results on the survey coming up.
We're on to quadratics now; I wish the spreadsheet tool was a little more flexible than it is and followed Excel notation ... having to add the tilde before the cell reference is clumsy. I also wonder if there's a way to have the column filled by a list variable?
Oh... and results on the survey coming up.
The test
Things that immediately pops up....
Having them able to use the TEXT to describe their variables and present their solutions neatly. We focused so much on the math work that I didn't do enough on using the text component to explain the setup and solution. Sigh.... only so many hours in a class is one excuse, but it is an excuse, I should have done it. Goal for the next unit.
And another thing... having them use the HELP function in case they got stuck during a test.
They are also spending a long time (relatively speaking) per question on the Maple as opposed to the written portion. They finished up the written part (3 algebraic solutions, 1 graphical, 2 analysis questions) in about a half hour, then took another half hour to finish up 1 graphical & 1 algebraic question in Maple. Something is up there... going to survey them to see what they thought.
Having them able to use the TEXT to describe their variables and present their solutions neatly. We focused so much on the math work that I didn't do enough on using the text component to explain the setup and solution. Sigh.... only so many hours in a class is one excuse, but it is an excuse, I should have done it. Goal for the next unit.
And another thing... having them use the HELP function in case they got stuck during a test.
They are also spending a long time (relatively speaking) per question on the Maple as opposed to the written portion. They finished up the written part (3 algebraic solutions, 1 graphical, 2 analysis questions) in about a half hour, then took another half hour to finish up 1 graphical & 1 algebraic question in Maple. Something is up there... going to survey them to see what they thought.
Leading by the nose? Or breaking a path?
Well, we did a bit of direct instruction (not Direct Instruction, which is completely different... kinda like variables in poorly designed programming languages) where, in order to lead them through using Maple to get a least squares line for a set of data, I had to go through with them step-by-step. For one, I didn't plan enough time to write out instructions & film them ... 2nd, I wanted to be able to discuss WHY we were doing each step with the students.
It went VERY well... in fact, I had a number of students say "I really like using Maple" and most were actively engaged. I did have one student get frustrated and say "I hate Maple" but a caveat: he's not the most focused student and tends to make sloppy errors. His adjacent seatmate helped him make corrections.
They also wanted to experiment a bit... one student didn't want to write all the years 1989-1992 so wanted to write that Year:=1989..1992. I said there was a way to do that so I'll have to work that idea in later.
I'm really hoping that they are open to experimentation... they seem okay with the "button pushing" process but, of course, I really want them to focus on mathematics problem solving.
It went VERY well... in fact, I had a number of students say "I really like using Maple" and most were actively engaged. I did have one student get frustrated and say "I hate Maple" but a caveat: he's not the most focused student and tends to make sloppy errors. His adjacent seatmate helped him make corrections.
They also wanted to experiment a bit... one student didn't want to write all the years 1989-1992 so wanted to write that Year:=1989..1992. I said there was a way to do that so I'll have to work that idea in later.
I'm really hoping that they are open to experimentation... they seem okay with the "button pushing" process but, of course, I really want them to focus on mathematics problem solving.
And they find another one...
Well, we've been graphing now pretty successfully.... when we get to this simple little example:
d = 230t
d = 200t+170.
Plot the first, drag the second on to the grid, no problem. Then, we try to zoom/translate to approximate the intersection's location.
Well, Maple decides that we aren't going to get it. When you don't use x/y as your independent/dependent variables, then even when you specify an implicit plot of t/d, as soon as you do any manipulation Maple reverts the graph to d/t. In fact, regardless of your initial setting of independent/dependent variables as soon as you use the zoom or translate tool Maple resets the variables in alphabetical order.
So... I was warned through research that using a CAS system would require better understanding of mathematical expressions and their equality. I just didn't expect to have to deal with Maple's idiosyncracies (or is it errors?). In the future, I guess my variables will be in the correct order... I wonder if the students will notice?
d = 230t
d = 200t+170.
Plot the first, drag the second on to the grid, no problem. Then, we try to zoom/translate to approximate the intersection's location.
Well, Maple decides that we aren't going to get it. When you don't use x/y as your independent/dependent variables, then even when you specify an implicit plot of t/d, as soon as you do any manipulation Maple reverts the graph to d/t. In fact, regardless of your initial setting of independent/dependent variables as soon as you use the zoom or translate tool Maple resets the variables in alphabetical order.
So... I was warned through research that using a CAS system would require better understanding of mathematical expressions and their equality. I just didn't expect to have to deal with Maple's idiosyncracies (or is it errors?). In the future, I guess my variables will be in the correct order... I wonder if the students will notice?
2nd foray
Having done graphing with Maple the other day, we worked a little bit with solving systems of equations by substitution. One of the students mentioned that instead of assigning names by typing "L1:=y=3x+2" you could avoid the first equal sign and just use a colon.
Well, that was okay for graphing, since you just right-clicked and chose plot. However, it doesn't work because the assignment to L1 isn't made, so when you tried to do a substitution into L1, it didn't exist.
Some of the students in the 2nd section had a challenge with the 2nd line they dropped on to the graph only had domain -10 to 10... wasn't sure why that was happening.
The second section does algebra on Friday ... and we'll do more algebra with it next week!
Well, that was okay for graphing, since you just right-clicked and chose plot. However, it doesn't work because the assignment to L1 isn't made, so when you tried to do a substitution into L1, it didn't exist.
Some of the students in the 2nd section had a challenge with the 2nd line they dropped on to the graph only had domain -10 to 10... wasn't sure why that was happening.
The second section does algebra on Friday ... and we'll do more algebra with it next week!
Dipping a toe in...
Okay... well we made an attempt at Maple 12 today... just a brief introduction to graphing. I deliberately did it by assigning names to the equations
L1:=y=3x+2
Then I chose to have them graph it implicitly. I'm trying to plan ahead here, so that I can use the names of the equations when they start to solve algebraically by elimination.
Unfortunately, Sharepoint requires them to download and save the file and THEN open it ... it won't open directly :(
L1:=y=3x+2
Then I chose to have them graph it implicitly. I'm trying to plan ahead here, so that I can use the names of the equations when they start to solve algebraically by elimination.
Unfortunately, Sharepoint requires them to download and save the file and THEN open it ... it won't open directly :(
So it starts...
It begins tomorrow. Well, actually, it doesn't because the students don't have their laptops tomorrow so we will just do a "welcome back to school, I'm your teacher, here's a little activity" without involving any technology.
So it will actually start on Tuesday. I'm hoping to get the permission forms approved by admin by then so they can get home, signed & returned by next Monday. Then I can formally start recording observations! In the meantime we'll introduce Maple 12 and see how it goes. More, much more, to come.
So it will actually start on Tuesday. I'm hoping to get the permission forms approved by admin by then so they can get home, signed & returned by next Monday. Then I can formally start recording observations! In the meantime we'll introduce Maple 12 and see how it goes. More, much more, to come.
Out to the students
We've distributed out to the students instructions on how to install Maple on their laptop before they arrive in class. Normally (and in the future, one hopes) this will be part of the tablet image that goes on to the computer before the student receives it or gets repaired but the IT department has been swamped. The process is easy (agree to everything, basically) but it does take about 20 minutes.
One of the big concerns with Maple is that it is a huge program; it takes about 30 seconds to get up and running. One wishes that there was some kind of staged loading, so that it would pop up immediately and then bring in things over time. The context menu pops up rather slowly, too, but much faster than previous version. If we're going to make the change so that this is the mathematical scratchpad then the faster things are, the less chance the tech gets in the way of student problem solving.
One of the big concerns with Maple is that it is a huge program; it takes about 30 seconds to get up and running. One wishes that there was some kind of staged loading, so that it would pop up immediately and then bring in things over time. The context menu pops up rather slowly, too, but much faster than previous version. If we're going to make the change so that this is the mathematical scratchpad then the faster things are, the less chance the tech gets in the way of student problem solving.
Subscribe to:
Posts (Atom)