Great Video on Changing Education Paradigms

This is a great video from RSA animate that brings Sir Ken Robinson's talk to light. It seems to me that technology will be an essential part of changing the way we do education.

Mathination

I stumbled across a new app today called Mathination. This app takes different expressions and equations and allows students to manipulate them by hand. For example, a student can drag variables and numbers around and see what happens to the expression or equation. Dragging a number across an equation changes its sign:

 

 Then, squeezing the 7 and 2 together yields a 9:

Then, dragging the coefficient 3 underneath the 9 automatically gives us x = 3.

Mathination also allows the user to expand and factor expressions, and square root and square equations. 


I have mixed feelings about this app. On one hand, I think it is a great way for students to explore solving equations and simplifying expressions. However, on the other hand I think that this app does not help students understand why these algebraic steps are correct. For example, dragging the 3 to the other side of the equation to isolate x does not help students understand that dividing by 3 on both sides gives us a 1*x, which is equal to x.  


The app also allows you change the equation or expression in ways that do not lead to solving or simplifying, for example I was able to change this simple equation:

Into these:

Before finally isolating a correctly:

I actually think Mathination will be most helpful in the classroom for exploring these equivalent expressions and equations that lead students off the path of simplifying/solving. Instead of having students practice the right way to solve/simplify, Mathination gives them the freedom to explore the algebraic rules to become convinced of the most efficient method for simplifying/solving. Mathination also takes arithmetic proficiency out of the picture, allowing students the freedom to explore within the time constraints of the curriculum and school day.   If you have read some of my earlier posts, this type of conceptual exploration is what I have been looking for!


I think I will use this app with my Algebra I students when we get to rational expressions - not to teach the skill of simplifying expressions or solving equations, but to explore the rules for simplifying and solving after we have already practiced using pen and paper. I will keep you updated on how it goes!

Doodling in class

I first saw this video on the blog iLearn Technology, but I felt it deserved some attention on my own blog.  (If the video doesn't show up, you can see it here)

I love this video. I love how it shows mathematical inquiry for the sake of curiosity, something that is missing from a lot of secondary math classrooms (including my own on some days!) This video reminds me why I love math, and why many of my mathematics professors in college loved math.  I think we would have more students that loved math if we could somehow get students interested in these seemingly unimportant but interesting problems. How can we create a more inquiry-based curriculum, and how can we encourage more intellectual curiosity in our classrooms? How can the iPad help with this? 

I guess this goes back to what I was discussing yesterday - that while the current mathematics apps on the iPad help with routine practice, there are not a lot of apps out there that are promoting mathematical curiosity or concept building at the secondary level. I will keep looking!

Designing apps?

Right now I am at a bit of a "teacher's block" when it comes to using the iPads in my classroom. I have a repertoire of about four activities that I can match to various learning objectives in my class, and there are a few great conceptual math apps out there (trigonir being one that I have used in my PreCalculus class), but there are not enough interesting, demonstration-like apps out there to help secondary math students really understand the math they are working with. I would love to see something more like the demonstrations available through Mathematica Demonstrations Project. Wouldn't it be amazing for students to be able to manipulate a parabola on an iPad and see how the coefficients and constants change? Or, to be able to push around a function and see how it affects the graph of the derivative?  The mathematics apps that are available right now are mainly focused on giving example problems and practice problems, and telling the student whether they did the problem correctly or incorrectly. While this is fine, it is not using the full capacity of the iPad!

All of this makes me want to learn how to program apps and see if I could create what I am envisioning. Have any teachers looked into the programming process? I would be curious to hear about it if you have! Also, feel free to comment if you know of any more demonstration or concept-building math apps out there.

Notetaking on iPads

Yesterday I experimented with having students take notes on the iPads.

I initially thought that notetaking with the iPads was unrealistic, and while I still think that it won't become a daily thing for us, there are some benefits to having it as an option.

We used the app Noterize (which I really like - very user-friendly with a lot of capabilities) in combination with the website dropbox.

One barrier to notetaking on the iPads was the fact that each student does not have his or her own personal iPad. How will the notes get from the shared device to a personal device or binder? We solved this problem with dropbox. Dropbox is an online storage service that allows you to store up to 2 GB for free. Noterize has a built-in way to download or upload photos from Dropbox.

The reason why I decided to use the iPads for this particular set of notes is because we were looking at several large graphs and word problems. Instead of photocopying several pages for students, I thought it would be easier to have them write on a set of slides with the graphs that I have created.

Students downloaded a PDF with the slides on them (the notes outline), then were able to take notes on the screen. They then uploaded their finished version of the notes to their own dropbox account.

The notetaking process went OK - as always, there are a few kinks to work out. Like any new skill, writing on the iPads by hand takes some getting used to, which means that taking notes took longer than I would have liked. However, because it is so simple to erase and because there are so many colors to use, I found most students took much neater, clearer notes than normal.