As I renew my commitment to blogging and change the focus of this blog, I thought I would start with an updated "about me".

I am a secondary math teacher and am starting my sixth year in the classroom. Of my five completed years in the classroom, three of them have been in urban DC and two in suburban Silicon Valley. I am starting at a new (suburban) school in Los Angeles this fall.

My experience in DC focused on teaching Algebra I to English Language Learners. I learned a lot about clarity and differentiation in those first few years - some of my students had never been in a formal school situation, while others were well prepared for Algebra I.

My move to Silicon Valley gave me the opportunity to experiment with iPads in the classroom, and inspired me to use more technology in my classes. This blog previously focused only on my experiences with iPads in the classroom, but now I will open it up to my reflections on teaching and education in general.

I hope you enjoy reading my blog!

# Infinitely Many Solutions

Adventures in teaching high school math

## Wednesday, July 20, 2011

## Thursday, March 24, 2011

## Tuesday, March 22, 2011

### Notetaking on the iPads #2: with freshmen!

Yesterday I did something I never thought I would do when I first started this experiment: I took notes with my freshmen on the iPad! I thought I would never do this because I assumed that freshmen would be too impatient, too distracted by the other features of the iPad to actually focus and learn. Well, you know what happens when you assume.

I think it helped that I chose a topic that was particularly conducive to taking notes on the iPad: systems of linear inequalities. My students in the past have had difficulty visualizing the solution space where the two linear inequalities intersect. The iPads, along with the app Noterize (which is quickly becoming my favoring notetaking app) helped students visualize this solutions space clearly.

The app has a highlight function, so students could highlight the solution space for each inequality in a different color, and then they could see the solution space for the system of inequalities clearly when the two different colors overlapped.

I also found that some of my messiest, most disorganized students took the neatest, most meticulous notes on the iPad. Usually these students were boys. I do not know why this happened - maybe it was because they had the opportunity to erase, or because it seemed more permanent or special than simply writing on paper.

I think it helped that I chose a topic that was particularly conducive to taking notes on the iPad: systems of linear inequalities. My students in the past have had difficulty visualizing the solution space where the two linear inequalities intersect. The iPads, along with the app Noterize (which is quickly becoming my favoring notetaking app) helped students visualize this solutions space clearly.

The app has a highlight function, so students could highlight the solution space for each inequality in a different color, and then they could see the solution space for the system of inequalities clearly when the two different colors overlapped.

I also found that some of my messiest, most disorganized students took the neatest, most meticulous notes on the iPad. Usually these students were boys. I do not know why this happened - maybe it was because they had the opportunity to erase, or because it seemed more permanent or special than simply writing on paper.

## Monday, March 7, 2011

### Update: Algebra I iPad Textbook

Here is a small update on how the HMH-Fuse iPad Algebra I Textbook Pilot study is going.

There is not a lot of data yet on whether the iPad classes are doing better than the standard textbook classes, but so far it sounds like this teacher and I are drawing the same conclusions: The iPad is not a cure-all, but it does make learning more fun for students. It gives some students (usually the most uninterested) an opportunity to be interested in the material.

One thing that this teacher is doing that I might try is using videos in the classroom. It seems like a great way to differentiate instruction, something that I have not yet accomplished using the iPads. I will keep you updated on how that goes!

There is not a lot of data yet on whether the iPad classes are doing better than the standard textbook classes, but so far it sounds like this teacher and I are drawing the same conclusions: The iPad is not a cure-all, but it does make learning more fun for students. It gives some students (usually the most uninterested) an opportunity to be interested in the material.

One thing that this teacher is doing that I might try is using videos in the classroom. It seems like a great way to differentiate instruction, something that I have not yet accomplished using the iPads. I will keep you updated on how that goes!

## Sunday, February 6, 2011

### Article on iPad use at University of Notre Dame

Here is an article on University of Notre Dame students using iPads in a project management course.

Overall, both the professor and the students had a positive experience with the iPad. Students said it was easier to collaborate and share ideas, while the professor felt less of the "wall" between him and his students that comes with the vertical laptop screen. One of the main complaints from students was not being able to write in the margins of articles, which can be done (at least on PDF files) through apps like Noterize or iAnnotate.

Overall, both the professor and the students had a positive experience with the iPad. Students said it was easier to collaborate and share ideas, while the professor felt less of the "wall" between him and his students that comes with the vertical laptop screen. One of the main complaints from students was not being able to write in the margins of articles, which can be done (at least on PDF files) through apps like Noterize or iAnnotate.

## Monday, January 31, 2011

### 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.

## Tuesday, January 25, 2011

### 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

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

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!

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!

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