Saturday, May 2, 2015

The Last Blog Post of the Semester

I always assign myself to be the last blogger for the semester as it is a good time to reflect on the course. Having taught this course three years in a row, I have come to realize that this course is very difficult to teach. I have to admit that because it is difficult, I get frustrated and don’t plan assignments as well as I should. For my end of the semester reflection, I have decided to make two lists—things that went well and things that need improvement. 

Things that went well: 
  • I enjoyed having and using a textbook for the reading assignments. Previously, I just had to find assignments online and the book was helpful for making this part of my job easier. I would recommend this textbook for any general technology course for teachers, Educational Technology for Teachers by Dr. Gregory Francom at Northern State University. 
  • Students did a great job improving the online iPad app rubric that was created by the Spring 2013 class. I was very impressed with the students with the first assignment. They were to use the online iPad app rubric to evaluate some iPad apps. They observed and shared that they thought the rubric didn’t work well for all apps. They offered suggestions and we worked together to create an improved online app rubric, 
  • I utilized an assignment from the textbook on Project-Based Learning and modified it to create a Project-Based Learning Assignment. I think it was a good assignment and will likely make improvements to it before using it again next year. 
Things that need improvement: 
  • I often assign students a technology tool (TI-Nspire, Excel, Geogebra, etc.) and ask them to teach us how to use that tool to teach mathematics content. I really need to create a rubric for these assignments and make it more clear what I expect them to do. I think this would improve the class a lot. 
  • This course is always a small group of students so I generally have a laid-back attitude in the course. I feel that this semester that caused some of the students to not take things as seriously as I would have liked. I need to be more firm at the beginning of the semester and set clear expectations.

Tuesday, April 28, 2015

Calculator Literacy

Anyone who has ever taken a math class (especially at a college level) is aware the calculators are a very contentious topic. Should students be allowed to use them? Are they a crutch? Would they be allowed to use them in the “real world”? Some teachers allow only scientific calculators with the most basic operations. Others have an “anything goes” policy, letting powerful TI-Nspires into the classroom. Others still ban them entirely, requiring everything be done by hand. Since I will have to make the same call some day as a teacher of mathematics, the issue of calculators is one close to my heart. 

When I was in high school, I remember being allowed to use calculators and even being required to buy a graphing calculator (I want to say it was the TI-84 that was the most current model at the time). I also distinctly remember resenting these calculators because I had no idea how to use mine. Once I got to college, some of my professors actually took the time to show us how to use calculators and make them do what we needed them to— whether it was manipulating matrices or using Newton’s Method to find zeroes more efficiently and accurately than by hand. I have been attached to my calculator ever since and have ranted tirelessly about how important calculators are.

Consider this: what real world career is going to INSIST their employees do not use calculators? Sure, they will want them to know the math, but certainly calculators will be available to the employees and they would be encouraged and expected to use them. If one of the reasons we teach math is because it is so useful in life, then it seems silly and arbitrary to not allow the most ubiquitous math tool available. I was 100% on this side of the fence for a long time.

The most obvious problem with this train of thought is that it relies on people knowing math before they use a calculator. Too often in my field experience or in my work as a math tutor, I see people relying on calculators for simple operations. “What is 1/3 times 1/3?” or “What is 20 times 1/5?” gets me a blank stare and a hand slowly creeping towards their calculator. Alternatively, and perhaps even more frustrating for the student, people make order of operation mistakes when inputting things into their calculator and don’t realize it is wrong. -3^4 is NOT the same as (-3)^4, but because their mathematical foundation isn’t solid, students don’t realize that the answer they’re getting back doesn’t make sense.

So should all calculators be banned? Should we just make sure that students can do all the mathematics by hand so that they don’t have to turn to a calculator? That seems not only like an extreme overreaction, but frankly not helpful. The further in math you go, the more complicated the calculations get. If I’m trying to find inflection points of a function, I want my mental workbench focused on inflection points— not on arithmetic that I can pass off to my calculator. The question then becomes how do I let students who can appropriately use calculators benefit from them while making sure others don’t use it as a (frequently misleading) crutch?

My current thoughts on the situation would be some form of calculator literacy education. Calculators themselves are here to stay and used so widely that it would be pointless to pretend they don’t exist and ban their presence. Instead of demanding that every student does every problem by hand so that when they get to an instructor who does allow calculators they have no idea how to use one, why not educate students on how to best utilize them? If every math class spent a tiny amount of time showing the right way to use calculators to aid your solution process, we might see fewer mistakes, less resentment towards arithmetic, and better numerical literacy concerning things like PEMDAS and exponents and the like. Learning how to do the math on the calculator would only follow after learning how to do it by hand and the principles the mathematics are founded on. 

My goal as a future instructor is to help prepare my students for the rest of their lives, so it seems only logical that I would help them understand how to make their calculator their friend instead of their enemy. However, I still have a lot of mixed feelings on calculators and hear a lot different takes on the issue. How do others handle the issue of calculators?

Monday, April 20, 2015

Khan Academy in the Classroom

            Khan Academy was implemented by nine study sites (20 schools) and a research brief was done on three of these nine sites. Khan Academy is a website which includes instructional videos on math, economics, history, and art. The teachers at the study sites used Khan Academy to review material and work through the problem sets on the Khan Academy website. Some of the teachers use Khan Academy for a reversed classroom setting, where the students learn the concepts at hoe work through the problems themselves and come to class with questions. The students said that using Khan Academy helped get immediate feedback, filled in gaps of past instruction, the students started holding themselves accountable for their performance, and allowed teachers to spend more time assisting individual students. At one of the sites, during the first year of the study students were spending about 22% of their instructional time on the Khan Academy activities, but during the second year it went down to 10%. The schools at this site changed the setup of their math instruction where it is all self-paced, self-directed approach so the use of Khan Academy was at the discretion of the students. Though, with students using it for their purposes they found it was being used in a more personalized way. The benefits of this style of teaching listed above also come with some negatives. Teachers at these sites noticed there was a lack of alignment between the content to grade-level curriculum which made it difficult to utilize in the classroom. This negative also made it hard to organize the content, because there was no clearly mapped grade-level content. 

            We talked about having a flipped classroom in our Technology for Mathematics class. Overall, our class agreed that using a flipped classroom is extremely beneficial to students, but having personalized videos would be the way to go. Using websites such as Khan Academy to direct the learning of students makes it seem as though the teacher isn’t the one with the knowledge of the content, but the video is. It takes a lot of the respect away from the teacher.

Sunday, April 12, 2015


As educators and students, we hear all of these warnings about copyright, but how much can it really hurt us? I mean how many times have we actually heard of schools getting in trouble for copyright? Recently in class, we had a discussion about copyright. We went on and on about how it is bad, but with every bad, there was an exception for it to be okay. This is such a vague concept that it is hard to take too seriously. What is considered proper for educational use? What websites can we use in class? How is the proper way to have your students read an article that you, as an educator, think is appropriate? I was left with so many questions that couldn't even be answered, because of all of the exceptions. It is also hard for me to take this to seriously, because throughout my educational career, almost all my teachers would copyright. Most of the time they didn't even realize that they were doing it. I have educators that constantly copyright. Have they heard these long talks about how bad it is? I assume so. Just like any student that has to listen to these conversations about copyright, it is hard to take it seriously when your teacher telling you not to do it, is doing it themselves. Even after they preach the fact that it is bad, they still fail to take it seriously, so why should the students? It is like telling students not to smoke, but the health teacher is outside of school smoking where the students can see. If educators are going to tell students not to do something, they should at least follow the same rules and find ways to avoid copyright.

Monday, April 6, 2015

How safe are we really?

It is no secret that technology is taking over this world, but are we getting too comfortable with what we put on the internet. Last week in our technology for teachers class, out professor asked us to Google our names and see what comes up. It was startling to see what came up when I did that. I ask whoever is reading this to do the same and the results may surprise you as they did me. In this day and age we do not realize what we are putting up on the web for everyone to see. We had an assignment earlier this week to respond to this doxxing article Dr. Vestal sent us. If you are not familiar with doxxing it is when someone puts up personal information about someone else, like their address, phone number and other personal information like that. While I was responding to this article I was doing some research about computer hacking to see how often and easy it was for someone to find this information about someone. I found an article about a 15 year old who hacked the pentagon because he was bored. Obviously this is an extreme case but if this kid could hack the pentagon he could really get any information he wanted from anyone he wanted. More and more of our information is going up on the web and more and more people feel comfortable with putting it on their. I remember watching this TED talk about hacking and the speaker had his laptop out showing the crowd what he could do with it. Credit cards now have these computer chips on them and he could wave this device he created and all the information went straight to his computer within seconds.He could also hack the hotel menu on the TVs and order PPV for free. What was ever crazier was that he could hack other guests in the hotel and mess with there cable and other electronics in their room. I cannot remember the name of the talk but it was very interesting and I would recommend it. I guess it is inevitable that as technology gets more sophisticated there will be people out there trying to exploit it. 

Saturday, March 21, 2015

3D Printing!

3D printing is incredible. With a little bit of programming, anyone can print a plastic model of just about anything. The sky is the limit. But these 3D printers also have a lot of educational applications, especially in a math classroom. One of the great things you can do with a printer is make figures of 3D graphs. 3D graphs are nearly impossible to draw by hand, and students can have a hard time visualizing the graphs even with graphing software. But holding a figure of the graph in their hands gives students that extra dimension and they can really see what’s going on. Another thing you can do is create 3D figures to use as visuals when teaching about volume and surface area. You could create loaded dice and regular dice, then have students use probability to figure out which is which. Really the possibilities are endless.
                Recently, I found out about another advancement in 3D printing, which is a 3D printing pen. Here is a short video describing the pen: This is so cool! You can actually draw in three dimensions. You can instantly create outlines for different shapes. I sometimes struggle with drawing decent-looking 3D objects like boxes or pyramids on the board. But with this, I could draw shapes in 3D and my students would be able to see it right away. It would be really fun to give pens to students and have them create things. They could create and compare different shapes or look at the perimeters of different shapes and how much plastic it takes to make them. Using the pens helps excite and engage students.
                Currently, costs may be a prohibiting factor. A quick search on Amazon showed that base models of 3D printers run around $500 while more advanced models go for much, much more. Currently, 3D pens run about $100-$150 each. However, like most technology, as 3D printers and pens become more and more commonplace, the prices are likely to drop and more schools might buy into them. 3D printers and pens have so much to offer that I can’t wait until we can all use them in the classroom. 

Sunday, March 8, 2015

Cells Phones in the Classroom?

I read an article about cell phones being used in the classroom. Though, all the articles I read mostly had cell phones being used as polling agents. Here is one of the articles I read . I have experienced cell phone use in a classroom when I observed a Geometry classroom. The teacher didn't not promote the use of cell phones, but if his students lacked a calculator he allowed them to use their cell phone. The only time he would not allow the students to use their cell phone is when they were getting to more trigonometry based criteria. The only reason he wouldn't allow them the use of their cell phones was that the accuracy of the sine function and cosine function are extremely off within the scientific calculator of a phone. I also experienced one within my Middle School Applications class this semester where we all took a poll with our phones. I was pretty excited to find a cheaper way to get in polls without having a clicker (which is a required device within some of the classes at SDSU). The way Jen Weber had it set up in the classroom was very easy. It was just a location to send a text message to. There was far less technical problems with the polling than my experience with the clickers. One of the downfalls with a phone is that the clicker lights up the moment you send in an option to the poll, where with the phone you are unable to tell if your message was registered.
Thinking about active use of a cell phone in the classroom makes me a bit weary as a future educator, because during my high school years I had a lot of class clowns within my classes. If they had the option of using their cell phone in the class, they would most likely pull too many pranks using their cell phones, one way or another. I do like the idea of using a cell phone enough in class that students will start to view their own cell phone device as a tool for the classroom and not a distraction. For this idea to work the use of cell phones must be thoroughly planned within the lesson plan, because if not worked in just right I do believe students will take advantage of the use of cell phones. If cell phones are not being used for polling, but being used as a calculator instead, I feel more students will use their device for a distraction and not for learning. More teachers seem to be moving toward technology into the classroom, but I hope the teachers are using discretion on when a cell phone is used within the classroom. 

Tuesday, March 3, 2015

How much Technology is too much?

Recently, I got the chance to meet some wonderful 7th graders from Mickelson Middle School in Brookings, SD. I was very excited to meet with four girls to discuss reading for my Middle School Philosophy class that I am taking. At the end of our meeting, I got the chance to ask them some questions about middle school, and what they could change. Immediately, I made sure to ask them about the Digits Program that they are working with.
I am familiar with the Digits Program mainly from observing the classes and tutoring some of the students. My first two years of college, I was required to observe 8th grade mathematics. As soon as I got to the class my first day, I was shocked at what I saw. Everything was technology base, EVERYTHING! The lesson that the teacher taught was on a smart board and through a program that provided a step by step lesson. The homework was all online. The tests were online. Even the analysis of the students at the beginning and end of the year was online. I don't want to sound like I am old by any means, but this was never something that I was introduced to at the 8th grade level. My junior and senior year of high school was when the smart boards started to show up in my school, but we never based all of our curriculum on the technology.
This leads me back to my encounter with the 7th grade females. At the end of the session, I asked them about the digits program. They didn't really care for it. They didn't seem interested to talk about it at all. So I pushed the subject a little bit more, and finally got the response that I was expecting. One young lady said, "I usually just wing it, and most the time I get the right answer." As a future educator, I was very upset about this response.
So, when is using technology too much? Digits is a program that allows you to answer more than one time on the  homework, so if the students don't get it right the first time, then they got another chance. The second chance comes with a way to solve the problem. The second chance also comes with the exact same question with different numbers. This leads to guessing the first time, waiting to see how to do it, and then plugging in the new numbers that they gave you. Programs like Digits also lead to a lack of students showing their work and no proof of knowledge to actually figuring out the answer. When I tutored, this was a huge barrier for students to break. They would refuse to write the questions down and figure them out with paper and pencil. This was frustrating because I never had physical evidence of them knowing how to do the work. Is it always just a guessing game with these programs? I don't understand how they use this technology and not require work to be shown for EVERY assignment, not just for tests. If students get into the routine of constantly showing their work, they will be more prepared for the tests, because there will be no doubt that they know how to do it.
I understand that technology is growing, and won't stop. Educators need to adjust with the technology though. The rise of technology is to make the world faster, keep everyone moving. With education, including all the latest technology needs to be less of a focus then making sure that students are still learning in the same way and using the technology efficiently. This takes a lot of focus from educators to track the students, but in the end, it will be way more beneficial then just "winging it".

Thursday, February 19, 2015

Refreshing Our Statistics Knowledge

Last week in Math 371 we took some time to cover basic concepts regarding statistics. Dr. Vestal shed some light on a disturbing issue regarding some teachers in our area. She mentioned the week previous that teachers struggle to retain main statistics concepts, which leads to struggling to teach stats in a high school. It is easy to see how future teachers such as myself could forget such material. We are only required to take two stats classes as a math Ed major, both of which are usually taken as a freshman and sophomore. For that reason, she assigned our class to take some concepts from the “For Dummies” series, which involved our TI-nspire, to teach to the class in teams of two. We are still learning to effectively use the nspires but are becoming easier and easier to use as we use them more. It has been a couple years since I have had to work with any statistics based concepts so it was a good refresher for when I have to take the second level of Stats. I worked with Jessica and we were tasked to create a dot plot on our calculators and then convert it to a histogram. As this was only a brief presentation of the more simple concepts, I cannot imagine that this is the last we see of stats in this class.

I am going to take a step away from traditional learning to an idea that could potentially change the way we learn in the future. One of our assignments was to read out of our ebook, Educational Technology for Teachers. In the reading, it discussed different forms of technology to use as methods to assist teaching. One of them was augmented reality. If you do not know what this is, augmented reality or virtual reality is a way to visualize a real world scenario using goggles. I have been intrigued with this idea since I hear about oculus rift, one of the first, truly revolutionary ways to see into a different world. I was excited to see this in the reading because it has enormous potential to help teachers teach, and excite students to learn. As it may not have potential applications for mathematical use, who knows what the future could hold. It could have the potential for you to visualize a xyz-plane in front of you, which could help students who struggle in Calculus III. I am personally still a firm believer in not incorporation to much technology into a math classroom, but I am excited to see what the future has in store for us.

Friday, February 6, 2015

Technology: A New Outlook

This week in class, as with many other weeks this semester (and the previous ones too) our class discussion has turned into a conversation and even somewhat of a debate about the benefits and conflicts of technology in education.  The great thing about these debates is that everyone contributes and we all have varying opinions. 
One specific struggle that continually comes up and we face more and more each day, as math educators, is the challenging question:
“When should and should I not use technology?”
If anyone is looking for the answer, our class is not the place to find it.  However, we have learned new ways to consider the use of technology.  Through research, class discussions, evaluations of other teachers, and even self-reflection, we have learned which questions to ask ourselves before choosing to use technology.  For some people these questions come easier than for others, as do the answers.  Yet, for some of us, knowing the right questions to ask and the most effective ways to evaluate technology still doesn't make the decision easy enough!
We grew up in a time that was only beginning to embrace technology – much of which didn't reach our middle or high schools.  The people who taught us used little or no technology when giving us lessons.  Yet, soon enough we all will be earning a college degree.  So, we learned just fine without technology – shouldn't students be able to do that now?
On one hand, we have a negative outlook on technology from bad experiences both in secondary schools and college.  Many of us have had teachers that ineffectively use Web Assign, PowerPoint, and online grading/lessons.  Many of us have even misused technology as students – graphing calculators, Wolfram Alpha,, and many others.  We fear that our students will misuse these things in the same way or even worse – that we will ineffectively use technology in our classrooms.  These concerns drive much of our dislike for technology – and maybe rightfully so, but what our class is realizing is that technology is a necessity in the world today, and it’s not going anywhere.
We are learning to embrace technology and that instead of asking, “Why do I have to use technology today?” we should ask, “How can technology enhance learning today?”  We have come to realize that technology not only helps students to dive deeper into the content, but can help students think abstractly and visually, making students stronger thinkers and problem solvers, and making us better teachers.
Although we all can think of many reasons not to use technology and most of my class will still side against it, we are beginning to open our eyes and see the possibilities of our classroom of the future – technology and all.

Friday, January 30, 2015

Refreshing Our App Survey Rubric

This week in Math 371, we spent our time revamping the app rubric survey made by the class a few years ago. We felt the old survey was a little vague and not all the questions applied to the specific type of app we might be reviewing. Our new survey includes a lot more branching than the original, since we wanted to make sure we were asking relevant question based on the kind of app. We now have separate sets of questions for apps that are games, resources or tools. While we easily agreed on the types of questions we wanted to ask, we had a tougher time wording our questions. We wanted to make sure our questions were worded as precisely as possible to avoid any confusion. This led to some lengthy discussion, but we finally created an outline of all the questions we want in our survey. Dr. Vestal is working on putting all of our questions into QuestionPro, and the only thing left for us to do is to decide how we want to score and weight each question. I can’t wait to see our final survey!

In other exciting news, we got to check out TI-Nspire CX CAS calculators this week! I've only had an hour or so to explore the calculator, but I’m thoroughly impressed by what I've seen so far. I’m amazed at the simple fact that I can graph in color with this calculator. This calculator even does things like evaluate indefinite integrals for me. I feel like I could spend the next year of my life playing around with this calculator and not know everything it’s capable of doing. From a teaching perspective however, I’m not sure it’s alright to give students a tool that does all kinds of work for them. Calculators can easily become a crutch for students. When they get to an exam or quiz where calculators aren't allowed, it becomes really clear who’s been relying on their calculators too much. Maybe we need to regulate the use of calculators and only let students use them after they show proficiency in doing the work by hand. On the other hand, if students do have access to calculators like these ones, maybe teaching students focuses less on computation and finding answers and more on applying knowledge to solve more complex, real-world problems. Next week, everyone in class is going to share interesting tools and applications they've found on the calculator, so I look forward to seeing more of what this calculator can do.

Thursday, January 22, 2015

Math Technology Students Review iPad Apps

The assignment in Math 371 last week was for each student to review three iPad apps.  Below is a summary of each review, including the grade level, the function of the app, and whether or not the student would use it in his/her classroom.  One of their best comments was that they feel like the online iPad app rubric that the Math 371 class created 2 years ago needs to be modified.  So that is their homework for next week.  Stay tuned...

Chad Blackwelder
IQ Gym
middle school to high school
      This app was made to improve your mental math skills for the user. There are three main categories add/subtract, multiply and division, with three subcategories below each: Challenge, Survival, and time attack. It gets increasingly harder as you work through the levels, to a maximum of level 99 for each subcategory. No real goal other than to improve mental math.
     I do not think I would use this app in the classroom. This app focuses on how to memorize multiplication tables and addition, as opposed to actually learning why 3*8 is 24. It seems like this app is for someone who just wants to work his or her brain for a while instead of a learning app.

Math Ninja
Later Elementary to middle school
     Math Ninja is a game that forces you to fight enemies that are attacking your tree with a variety of weapons. You use math as a way to earn money, to get better weapons, and to defeat the boss.
     I would consider trying this in my classroom if I was in a middle school setting. It could possibly have some benefit of getting the kids to do math in their heads instead of a calculator, but it could possibly get repetitive.
Khan Academy
For all grade levels
     Khan academy was created to give students, who struggle in a subject, a complete video walkthrough of different concepts. To something as simple as basic subtraction to solving first order differential equations.
     I would definitely consider using this app as a second source of information for the students. Maybe have them watch them on their own time outside of class to see the material for a second time. I watch these videos now, so this app is very powerful to the user. 

Jessica DeNeui
Graphing Calculator by Desmos
     This is a two-dimensional graphing calculator. The program plots functions and creates tables. You can add sliders and set limits to manipulate variables for an equation. Sliders also allow you the opportunity to animate your graph. The program comes preloaded with example interactive graphs of a variety of basic functions.
     I would use this app. It’s really easy to use and understand. It graphs really well, although you can only graph one variable at a time. I really like the idea of the sliders and being able to manipulate constant terms in the equation, and I think it really helps students understand how manipulating constant terms affects the function and graph. 
TanZen Lite
     This is an app for tangrams. This lite version comes with 45 free tangram puzzles. The player can choose to have a pattern for the puzzle or create the picture based on a thumbnail. Once all the pieces are in place, the app saves your work.
     I would use this app if I didn’t have access to real tangrams. I think using the app makes it more difficult to measure the perimeter of the shapes, which is something that’s easier to do with the physical tangrams. I do like that you can choose to have the template of the puzzle rather than just the thumbnail. Some students really struggle with creating the puzzle with just the picture, and the templates would help them complete the puzzle.
Educreations Interactive Whiteboard
     This app is partly whiteboard app where students can use their fingers or styluses to write on the screen. This app also allows you to create a video recording that captures writing and talking. Teachers can create classes and give their students a code to the class, where students are able to watch the recordings. You can also share your videos with the public and access other people’s work.
     I think I would use this app. While there are parts of the app that are locked and cost money to upgrade to, the basic app is still pretty functional. I like using white boards because it’s a quick way to check what students know. Using the app instead of actual whiteboards definitely helps save time since you don’t need to pass out boards, markers, and erasers. I also think the video component could be really helpful. If students are working on homework and projects at home and have questions, supplemental and review videos can help them find answers if I’m unreachable. Overall, I think this app is pretty nifty. 

Jamie Formanek

     This app connects students to more than 1,700 videos of all different sorts, from education and technology to music and business. It gives the students a chance to see all the new ideas coming out into the world.
Shady Puzzles

     Shady puzzles is a puzzle game which requires you to shade the rows and columns using the criteria given. It is a critical thinking game which challenges your problem solving skills.
Number Line

     This app is a tool to help students’ visual number sequences and model strategies.

Carissa Hilmer
Triangle Solver
     Given 2 angles and one side, the app quickly calculates the remaining values for the remaining sides and angles.
     I don’t think I would use this app in my classroom. It is not appealing nor does it give the students a chance to actually learn what they are solving. It is basically giving a student a calculator to solve 1+1=2; it is something that they should know how to find the solution without typing it into a solving calculator. 
Equation solver
     By entering an equation with one variable, the app will not only solve the equation, but also provide a step-by-step solution
     I still believe that face-to-face interaction with other students and teachers in order to solve equations like this would benefit a student more. If I were to pick an app to recommend to students that need help at home, I would consider this one because it uses reasoning for each step. It is not just giving the students an answer. 
     This app is for both educators and students. It is an easy way to communicate and also looks like Facebook, so it will grab the attention of students at any age. There are places to post homework, grades, and even communicate with other educators for ideas. 
     This is an app that my teacher used in my high school Pre-Calculus class. It was an app that was easy to navigate because it relates to Facebook, which also makes it more appealing to upper level students. I think I would use it because it also has ways for educators to communicate and to get different ideas on lessons or how to solve problems in class.

Jenna Stephens
12th grade (Calculus)
     This app gives short tutorial lessons for calculus topics. It is organized based on different topics in the general order that most classes would follow the content. It allows students the opportunity to mark whether they understand or still need more review of the content, to go through again later.

     I would use this app in a calculus or even pre-calculus class as supplemental material. I think this would be a good way for students to review the lesson, or possibly even to preview the lesson. I could make some of the videos mandatory for all students to watch after a hard lesson, or just leave the choice to the students as an opportunity for free “tutoring” after class. 
Math Splash Bingo
     This app lets the user choose between the four basic operations and gives a bingo card for that operation. The user has the option of choosing easy, medium, or hard. Once the student clicks start, the game shows a multiplication problem and the user finds the answer on their bingo card. If they guess the wrong answer, it goes to the next problem with no feedback. If you guess the right answer, you get an animal bingo marker over that spot. Once you get 5 problems right in a bingo, you win.
     I most likely would not use this app in my classroom, because it is an elementary level app. Also, this app may rely heavily on memorization of multiplication facts which is not what common core is all about! Also, students can click a number and just happen to guess their way to a bingo without solving any problems.
Although I would not likely use it, it may be useful as a review before a quiz, or could be a good homework game for students to play with their parents at home. (As a teacher, I may consider sending home a list of fun games and apps – including this one – that students could use at home to practice math with their students.)

Rose Fairfax

SAT [∞]
Middle School to early High School
     You play through levels answering questions about specific math topics, eg “Properties of Integers” or “Coordinate Geometry”. You get points for correct answers as well as quick answers. The goal is to beat the levels and get points.
     I would not use this app. Not only does it claim to be free while locking the majority of its content behind a pay wall, but it ultimately is about getting points and being right. Since mistakes are an extremely important part of the learning process, I cannot see this app having much value in a classroom aside from a fun way to review things a student might already be expected to know.
yHomework – Math Solver

Middle School to High School
     Solves simple arithmetic as well as decently complex algebra problems. User inputs the problem (eg 9x +5 = 14) and hits solve. The app then solves the problem and gives a detailed walkthrough of how to arrive at that answer. At the bottom of the solution page there is often the option to change the method of solving (addition versus substitution for systems of equations, for example). 
     I would use the app. Although it can be used to do all the work for the student, it can also walk them through answers instead of just computing a number with no explanation. It is also easy to use and has a tutorial at the beginning to ease in all users.

MyScript Calculator
Elementary through Middle School
     The user writes with their finger or a stylus. They can enter simple calculations like addition, subtraction, multiplication, division, etc, or they can enter simple algebraic expressions using “?” to denote unknowns. The app automatically balances the equation and solves for the unknown.
      I would maybe consider using it. It’s a bit more intuitive than a calculator, especially for younger students, and encourages understanding order of operations because of the way the app interprets what is written. (It also encourages neater handwriting.) However, it is very limited in its solving abilities and would be little help for things with complicated expressions or things requiring simplification. Sometimes its AI solves problems in a bizarre way or gives an answer that doesn’t follow throw and seems wrong. For example, it solves 9x + 1 = 10 by subtracting 1 from 10, not substituting in a 1 for x.  This would be the first step in SOLVING the equation (subtract one from both sides), but it just stops there, which would certainly be confusing for students who have newly learned this material. That said, I remember stuff that translated my handwriting for me being a really cool sell when I was in school so it may make learning to use calculators more enjoyable and reduce “I pressed the wrong button” errors.