iPad App - Mathspace

As I mentioned in my last blog, it is not very easy to find math apps for high school students. Thinking it would be more difficult the second time around, I was surprised with how quickly I found an amazing app. The app I came across is called Mathspace.

What is Mathspace?
Mathspace is an online tutoring program that provides instant feedback and helpful hints along the way for students. Offered in a range of topics, Mathspace is great for guided lessons that students can work on at their own pace. In this app, users are given a series of questions that they can work out on their own and submit for feedback. Mathspace tracks your progress and gives you recommendations based off of your learning profile. I have been playing around with the app, so now when I go to start a new worksheet, they recommend modules for me to do based on what I have learned.

On the right, you can see a screenshot of the recommendations pop-up on Mathspace. Based on my learning profile, it is suggesting that I work with Algebraic terms and factoring. If I feel comfortable in these topics, it gives me the option to choose my own from a multitude of choices. In these modules, it tracks your progress and gives you points for the day's work.

How Does it Work?
To begin, you start off by creating an account. You can create a free account as a student and join with a class code or create a teacher account and receive a free 7-day trial to view Mathspace from a student's perspective. Once your account is activated, you can explore all of the content Mathspace has to offer. From a teacher's perspective, they can create problems for their students to work on and provide instant feedback to each student. Teachers can track a student's progress and even can communicate directly with the student's parents about their progress.

Upon download, I was instantly hooked. Though this app is more of an online tutoring service than a game, I am so addicted to using it. I first started playing around with the app to test its features and see what it can do, but I ended up really enjoying doing the math problems. I'm a math major, so I enjoy doing math for fun. I like to do the different Algebra worksheets to test my memory on the content.

Part of the reason why I enjoy this app so much is because it allows you to draw out your solutions. As you can see in the picture on the left, there is room for scratch work. So, in the blue and red writing, I worked out the factoring of the problem. Then below in black, you write your solution and Mathspace changes it into typed writing for you to submit. Also in the lower submission space, you can scratch out your writing if you made a mistake or need to start over. Based on how you're progressing, Mathspace will tell you your strengths and weaknesses.

Features of the App

From playing with this app the last couple of days, I have certainly run into more good things than I have bad things. One great feature of this app is that it makes you submit your answers in their simplest form. For example, if you look at the picture on the right, you'll see that the first answer I submitted has a yellow check next to it. This means that the answer is correct, but it can be simplified further. Once a student sees the yellow check, they know their answer is correct, but they now have to work further to simplify. The answer below it has a green check. This means it is in its simplest form. This feature is great for students because it will get them in the practice of submitting all of their work in the simplest form, which is something that all math teachers love.

What is quite possibly the best feature of this app is the hint feature. If students are stuck on a problem, they can click hint to receive a little tip on how to solve the problem. So, say I was stuck on the problem above. I could click hint, and Mathspace would tell me to cancel out the common factors from the numerator and the denominator. This feature is great because if you are working on these on your own at home, it is just like asking the teacher in class.

The only negative I have found from Mathspace is that there is not a lot of advanced content. The content on Mathspace is great for average level students, but there is little to no content for advanced or gifted students. Perhaps in an update on the app, they could add some word problems to trigger more intellectual reasoning rather than computational work.

How can I use Mathspace in the Classroom?
As mentioned earlier, teachers can use Mathspace to create online lessons for their students. As a future teacher, I could assign homework for the class as completing a certain amount of online worksheets and marking their progress. This will work great for students because they can work at their own pace and receive instant feedback.

In my future classroom, I plan to encourage all of my students to download this app and to tell their parents about it. Their parents can encourage to do extra math work on their own time to better their knowledge.

I can also use Mathspace as a token economy and reward students if they score a certain amount of points for the week. This will motivate students to want to use the app and train them to see math exercises as a way of leisure and learning.

Reviews
In the App Store, Mathspace is rated 4.5/5 stars. Most of the reviews for the app are positive, saying things like it is great for building student's confidence in math. Being able to work at their own pace and receiving hints along the way allows for students to want to persevere through tough problems.

Overall, Mathspace is something I will certainly use in the future. I see it as a great tool for fostering learning and allowing students knowledge to expand. I recommend this all to all students and all math teachers.

References
Mathspace. (2011-2016). Mathspace. Retrieved from https://www.edsurge.com/product-reviews/mathspace-product

Mathspace Pty Ltd. (2016). Mathspace. Retrieved from https://itunes.apple.com/us/app/mathspace/id586612052?mt=8

Mathspace Pty Ltd. (2016). Mathspace. Retrieved from https://mathspace.co

iPad App - EzyTrig

In my search for a useful app, I wanted to find an app that I could picture myself using. Knowing that I wanted to find an app for math, I searched for something that was easy to use, yet beneficial for students. At first I struggled to find an app that fit what I was looking for. I kept coming across different math games, but I wanted to find an app that high school students would use. Some of the math games were cool apps, but I couldn't picture using it as a high school student. I continued my search and then I came across EzyTrig.

What is EzyTrig?
EzyTrig is a user-friendly app designed to help students understand Trigonometry. Free in the App Store, EzyTrig focuses on the use of the Unit Circle, which students are able to access easily. In this app, students are given the image of a unit circle and can rotate the angle to show the relationship between different angles. The app is interactive because the user is allowed to set the circle at any angle they want in order to see the corresponding value. There is a wide variety of settings that students can adjust to create exactly what they need in order to help them solve trigonometric problems. EzyTrig is a great tool for the classroom because students can can always have access to the Unit Circle at their fingertips.

Why is EzyTrig Useful?

For the readers who are unfamiliar with Trigonometry, the Unit Circle is a vital tool for assessing relationships between radians, degrees, sine, cosine, and tangent. As seen to the right, the Unit Circle is used as an easy way to compare angles of a triangle. Many teachers will want their students to memorize the Unit Circle because it simplifies problem solving in Trigonometry, but in reality, the entire Unit Circle is too complex to memorize. That is where EzyTrig comes in handy, because it offers an accessible and interactive view of the Unit Circle for students.

Features of the App
Below, you can see two screenshots taken directly from the app. On the left, you see the main feature of the app, the Unit Circle. Here is where you can rotate the angle that the circle is set at. So, if a problem on your homework asks for tan(45), you can set EzyTrig to 45 degress, as seen below, then you can notice that the answer is 1.

Another great feature on EzyTrig is the ability to toggle settings between radians and degrees. For everyone who has ever taken Trigonometry, you recall constantly switching between degrees and radians. So, on this app, students can easily adjust which format they need to be in.

In the upper left hand corner of the app, there is a chart of the common trigonometric values that constantly come into play in Trigonometry. This feature can be seen above on the right. This will be very useful for students when they need to quickly look up certain values.

Out of all the great features of this app, there is one thing that this feature is missing. While there is an option on the main screen to toggle between radians and degrees, the Exact Values chart leaves out the corresponding radian values to the degrees on the chart. In order to find the radian value, students would have to know which degree is equivalent to the radian value they want to look up. Other than that, this app seems to have everything a student could need while taking Trigonometry.

For a deeper understanding of the features of this app, watch this tutorial video below.

How can I use EzyTrig in my classroom?

When I took Trigonometry in high school, it never crossed my mind to download an app to help me with the material. Nowadays technology is so much more relevant in the classroom, so many teachers are leaning towards incorporating measures of instruction, such as apps, that students can relate to.

As a future teacher, I plan to encourage all of my students to download this app. Whether they are on their own or in the classroom working on problems, they will be able to access this app. This app will allow them to further their understanding of Trigonometry by viewing first hand the relationship of the Unit Circle. Students can enjoy playing around with the app and testing its features, while simultaneously learning the functions of the Unit Circle.

Reviews

In the App Store, EzyTrig is rated 5/5 stars. All of the reviews say it has a nice representation of the Unit Circle and that it is great for visual learners. I find this to be a great app that will be very useful to high school students. They can use it at their leisure to better their understanding of Trigonometry.

I would have liked having this app when I was in high school because I tried to memorize the Unit Circle and that proved to be very difficult. I tried coming up with little memorization tricks but there were just too many values to keep track of. With this app, I could've manipulated the angle on the circle to correspond with my homework problems to allow for an easy assistance to solve problems. Overall, EzyTrig will be huge time-saver for students and very beneficial to the growth of their learning. 

References

Bourne, M. (2010, Sept. 23). Unit Circle: an Introduction. Retrieved from http://www.intmath.com/blog/mathematics/unit-circle-an-introduction-5166

Dill, W. (2016, Apr. 27). Explain Everything: EzyTrig [video file]. Retrieved from https://www.youtube.com/watch?v=bNzW9l3v9E8

KGiants, (2016). Ezy Trigonometry. Retrieved from https://itunes.apple.com/us/app/ezy-trigonometry/id654848143?mt=8

[Untitled image of a Unit Circle]. Retrieved September 10, 2016 from http://teachers.henrico.k12.va.us/math/ito_08/07BasicTrig/7-1angles.html