Updated "About Me"

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!

Tablets in science classrooms

Here is a video about using tablets in science classrooms. (Via Mindshift). Exciting!

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.

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!

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.

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. 

Mercury News Article on iPads in Schools

Take a look at this article in the San Jose Mercury News discussing the use of iPads in schools in the Bay Area. While the article does not mention my school, it does share my belief that iPads or another form of tablet will become a large part of the secondary classroom soon.

Online Resource about using iPads in Schools

I just found this website, Livebinders, which provides a way to organize online materials in a binder. This website would be very helpful for organizing and sharing online resources for any topic.

One of the binders shared on the website is called iPads in Schools, and has a ton of blogs and other websites dedicated to the topic. It will take me  a few weeks to get through all of the resources collected here!

Collaborative learning with Shareboard

Shareboard is an app that allows up to four iPads on the same wireless network to share the same blank screen. Anything that one iPad user draws or adds to the screen shows up on the other iPads.

A typical problem in Algebra I is that students try to skip steps and do an entire problem in their head. A way to combat this lack of work-showing is to have pairs of students take turns writing consecutive steps of a problem on the same piece of paper. This way, students are forced to follow common process so their partner can understand what they did and what to do next.

I decided to use this same idea, except on the iPads. It worked well using shareboard. Each partner wrote in a different color, so it was very clear that they were switching off writing consecutive steps. It allowed for a more in-depth discussion about the problems, because the partners were looking at the exact same work in front of them.

I plan on using shareboard again, especially for topics where I find that students tend to not show enough work. (perhaps simplifying radicals?)


Here are some examples of the student work:

App Review: Sundry Notes

Description: Sundry Notes is a notetaking app. You can type, write by hand, import pictures, and even add sound recordings. It is free.


In the classroom: I originally downloaded Sundry Notes thinking that students could use it to take notes, but after playing around with it I found that the inking was slow and would make for a very messy, painstaking process of taking notes. However, this app is ideal for students who are creating something - a poster, a project, a summary of anything. The fact that you can import things from the internet, draw, type, and even add sound recordings allows for a lot of creativity on the part of students. It also have a very intuitive user interface, whereas some of the other notetaking apps with the same capabilities are not as user-friendly.

Recommendation:  I would recommend this app for project/picture/poster making, but not for notetaking. The search for a good note taking app continues...

Here is a sample from Sundry Notes:

 

Notice how you can add sound recordings:

iPad Algebra I Textbook

This year, Houghton Mifflin Hourcourt is piloting an Algebra I iPad textbook in select California public school classrooms.

The e-book, called the HMH Fuse: Algebra I, is more than just a pdf of the paper textbook. The e-book contains self-tests where students get feedback on how well they understand a section, videos where a nerdy-looking teacher figure explains concepts, and demonstrations where students can see how changing the m in y=mx + b affects the graph of the line. Here is a video that shows how the textbook works.

I will be interested to see the outcomes of this pilot project. How will the student learning with the e-books compare to the student learning with the regular textbooks?

Regardless of the outcome of this particular experiment, I do believe that this is the way that all textbooks will be going very soon.

Tech Blog: iPad Curriculum

There are some amazing education technology blogs out there.

iPad Curriculum  reviews different applications available through the itunes store that could be used in the classroom. One of my favorite apps mentioned is edupad, an app that allows teachers to create their own applications without knowing any code. While this app has not yet gone live, I will definitely be checking it out when it does.

Instant Feedback

Today I used an app called eClicker with my Algebra I students, and it worked like a dream.

Let me start off by saying that teachers are constantly trying to get and give instant feedback. The sooner a teacher knows that some of her students are not "getting it," the sooner she can adjust her teaching methods. Similarly, the sooner a student knows he does not "get it", the sooner he can reflect on his work and find his mistake. (sidenote: my use of pronouns is arbitrary.) The eClicker app allows for super-fast feedback, both for students and for teachers. I plan to use this app a lot more.

Before class I entered six practice problems into my eClicker Host app, and during class students could access my questions for using the eClicker student app. I would send all 30 of my students a question, and they would have two minutes (or more, I could decide the length of time) to choose an answer choice. Here is an example of one of my questions:

After the minute, each student would see if they chose correctly, and they could see a bar graph of the % of students that answered each question, with the correct answer highlighted:

  

This app is the zenith of  instant feedback, both for students and for the teacher. The "host", or teacher, also gets a list of students with their specific answers, so I can pinpoint the five percent that answered "A" instead of "B".

Here is the bar graph from another question I gave to students. Based on the large percent of students that got this problem incorrect (and based on which answer choice most of those students chose) I can clearly see that students are confusing an undefined slope with a slope of zero, and I can review the concept right then and there: 

This app has other possibilities too that I am only beginning to brainstorm. I could possibly use it for quizzes (no grading necessary)? Or have other students create questions using the Host app for each other? What are your thoughts?

"Poster" Project - Derivative Review

Last year I did a review project where different groups of students were assigned different derivative rules to summarize and then present to the class. This year, I decided to try the same project except with students using the iPads instead of posterboard and markers. Students had the choice of using a few different apps (my opinion of the different apps to follow), and each group of three or four students got two iPads to create their summary on.

Students needed to include: (1) A description of the derivative rule, (2) An example (both graphical and algebraic), and (3) some key ideas and common mistakes associated with the rule.

Overall, the project went OK. Students were certainly excited about using the iPads to create something, although some of the applications were difficult to figure out and it took some time for students to learn how to use various apps.

Take a look at these examples:

These students did a great job of incorporating typing and the iPad's touch screen.

Some students used more than one "screen shot" for their project, like this group:

Being the first time that the students did something like this, they did a great job. The best part is that we can take their finished pictures and make them into a powerpoint presentation that students can access from our class website, so they can go back and refer to it while they study for our test on derivatives.

iPad as a reader

While it is probably the simplest way to use the iPad in the classroom, today I used the iPad as a reader. We needed to review some trigonometry in my calculus classes, and our textbook does not have a good trig review. So, I found a great pdf file online that I linked from my website. Students were then able to access the 17 - page pdf (which had great pictures and examples) without my needed to print and copy all of those pages!

Students enjoyed being able to zoom in on different parts of the pdf. And the best part: students were focused on the lesson, not distracted by having the internet and iPad applications in front of them!

First Day

Yesterday was my first day testing out the iPads with the students. I passed them out to my Calculus students in the last 10 minutes of class, just so they could get acquainted with some of the different apps that I had put on them.

I also posted a simple set of rules for iPad use:
1. Do not download any apps without permission (they wouldn't really be able to anyway - they would need the school's itunes password)
2. Do not go to any websites that are not related to what we are doing as a class.
3. Do not change any of the iPad's settings.

Students mostly seem excited about having them in the classroom, although they also seem to think that the iPads will not have much impact on their learning. (I got a lot of "we are going to use them to learn? To learn math??" type questions)

We will see when we use them tomorrow!