Final Thoughts

As I conclude this research project, I want to revisit my initial question that I stated on day one.

How can technology be used in math classrooms to benefit student learning?

Breaking down this question, there are two main parts…1) uses for technology in the classroom and 2) benefits to student leaning.

1) Uses for technology in the classroom

Technology can be used for so many different aspects of the classroom. First, a very key part of any classroom is communication. Teacher need to communicate with students, students with other students, teachers with parents. There are so many apps out there that allow file sharing and messaging abilities to allow for this part of effective learning. If a child only learns at school, he or she will not develop much. Learning has to take place in a variety of places such home, school, church and sports.

Technology must also be used to transform active learning into interactive learning. This includes the creativity and innovation aspects of a classroom. There are hundreds of thousands of online interactive manipulative for math teacher to use in their classroom. These are especially helpful when the teacher does not have the specific manipulative to represent the problem accurately. I found quite a few resources for teachers to use that help make student be interactive in their learning. A classroom that uses only lectures and worksheets to learn, is not actually learning. The student have to comprehend and apply the lesson in order to retain it.

Another aspect of learning that we discusses was creative thinking and problem solving. The internet is a slew of apps and websites that make any problem easier. Whether it be organizing a project or drawing out each step, there is something that can help. In the classroom, teacher can use to make mind map with the classroom, share that map with every student using Dropbox, then leave each student to create their own notes from it using Penultimate, without ever printing a piece of paper and taking a chance of losing said paper on the bus ride home.

2) Benefit student learning

Much of this was covered in the previous section, partly because it overlaps so much. There is a right and a wrong way to use technology in a classroom. The right way facilitates student learning, deeper thinking, and longer retention. The wrong way hinders learning, plain and simple. Technology should be used to make student think deeper into a question, explain more above and beyond the question asked, and communicate with self-confidence. Interactive learning forces students to actually become a part of the lesson. Strong student learning occurs when students are engaged and see the potential in lessons and activities. With so many student having personal technology on them 24/7, using technology in the classroom is one of the only ways to reach them. Student will learn better when they can connect school work with real life.


Research projects like this is exactly what interactive learning is. I was in charge of the lesson that I was to teach myself. Like the “Mathmaticious” music video, I had to take an idea and run with it. A project of this sort would have been very difficult without technology. Learners can take simple, broad topics and expand on so many different aspects of them. Spending a little time each week made it not to overwhelming. I would have never thought to have compiled so much information about such a topic.


Creativity in Math

The topic for this week’s assignments were critical thinking, problem solving, and decision making. Some of the description for this included planning and managing projects that help develop a solution or complete a project. The standards for this sections also included using multiple processes and diverse perspectives to explore alternative solutions.


Regarding mathematics, almost every problem that is present can be solved in multiple ways. When I saw this description of critical thinking and problem solving I immediately thought back to a project I did in my AP Calculus class senior year of high school. At the end of the year, before the big test, we were told that we have to make a notebook that contained everything we had learned the entire year. Immediately my jaw dropped. There was no way that I could remember everything that we learned, let alone have time to write it down, in detail, and explain example problems for each topic. I would have to organize my thoughts, know that I have included everything, and because everything I do has to be perfect, it had to be in order. So, with that said, I basically had to write it all out before I put it in the notebook.

Now, you might be asking what this has to do with the rest of my blog, implementing technology in a math classroom. I have an answer for that! There are so many apps and websites out there in the technology world that could have made this project so much easier to accomplish. Below I have made a list of some of the problems I had with the project and some solutions I found that made use of the thousands of apps and website available for students.

1. Problem: When I was brainstorming all of the topics we had covered, I was drawing a metal map of all the different branches. I had to organize the topics it main concepts and then the different concepts that branched off of the main ones. This got very confusing with so many ideas running through my head.

Solution: is a website that allows students to visually see the connection they are making. With this application, I could have seen more clearly the branches I made and easily put them in an acceptable order. Because this is digital, I could easily change and edit the bubbles and ideas I had created. This would have been a great starting point for me to get my ideas down without having to worry about it being perfect the first

2. Problem: I had to carry around a notebook to place that I could possibly have time to work on it. Because it took so much time to complete, I would take it to dinner a work on it during the hour wait time. Carrying an actual notebook became troublesome and added another thing to keep track of.

3. Problem: When I would finish a few pages, I would often time think of something to add in between the pages. To solve this problem I had to staple in a page, which looked very tacky.

Solution to 2 and 3: A virtual notebook

The Penultimate app allows you to take notes on your touch screen device, which can be done virtually anywhere. The app gives you the experience of writing on paper but allows you to edit the document with ease. You can import images and documents onto your paper for better notes. The apps automatically syncs with Evernote so your notebooks can be seen on all your devices. Because the notebook is digital, you can add pages in between already completed pages.penultimate

4. Problem: After all the students had created their notebooks, we would swap with other student and studies theirs to get a different perspective on some of the topics and study for the AP exam. I was always afraid that the other student would lose mine or damage it while they had possession of it. I understood the reason we were switching and looking at others’ but I was protective over what I had spent so much time on.

Solution: Dropbox

Dropbox is a web-based document storing site that allows you to upload files and share them with a link to the Dropbox sites. If we would have made the notebooks on a virtual notebook app, we could have shared them with each other using Dropbox, or several other sites that are similar to Dropbox. I would have been able to access many students’ notebooks anywhere I wanted on any internet enabled device.



So, now that I have present some problem and solution to the math notebook problem, I want to explain how it connects to last week post about interactive learning. Quoting myself, “Interactive learning encourages the students to be a part of the lesson instead of being an observer of the lesson.” This notebook project forced me and the other students to become the lesson. My teacher did not stand in front of us for two weeks reviewing all the topics that we had covered. She made us be interactive in our learning. The technology that I have provided would have been great resources for the class to use to help aid us in the project. It would have been an appropriate measure regarding the project and the class material.

Interactive Learning

This week I wanted to follow up on one of the articles I mentioned last week about implementing the right kind of technology into a classroom, specifically a math classroom- “Thinking (and Talking) About Technology in Math Classrooms” by E. Paul Goldenberg



Through many searches and browsing through blogs and presentations, I came across the video “A Brief History of Technology in Education”

In this video a few lines stuck out to me. They explain that the hype inside classrooms use to deal with how teachers presented information. Now, it has shifted to how teachers access information. Because of the new technology (including the internet) “you can make active learning interactive learning.”

Interactive learning is what I am focusing on. Interactive learning encourages the students to be a part of the lesson instead of being an observer of the lesson. The amount of technology that is out there available for teachers to use is incredible.

On the same site as the previous video, I found the following video about math. This student has used a great deal of technology to make this video. He has became a part of the lesson and surly is not sitting on the sidelines watching. The creativity and originality that went into this is out of this world, and is a prime example of interactive learning. The video can be used as a review tool, as a way to review many of the topics covered in mathematics course.




Through some more searches, I found a blog written by an elementary teacher aspiring to earn a master’s degree in mathematics education. He has compiled a few resources for teachers to use as a way to engage and enhance math lesson in the classroom. All of these resources are ideal to use as enrichment tools, not to solely teach the lesson. The virtual manipulatives (as mentioned in Goldenberg’s article) can increase the variety of the problems students can think about and solve.

“The National Library of Virtual Manipulatives (NLVM) is a site with many virtual manipulatives. The site is organized into five mathematical categories (Numbers and operations, Algebra, Geometry, Measurement, Data Analysis and probability) and by different grade levels.” This site also contains interactive online units for teachers that are based on the national standards. With tools to track student progress in online programs, teacher can get a sense of where students are and how they are benefiting, or not, from the online interactive tools.NLVM

Some other online tools that are mentioned are:

A+ Click – helps students of all grade levels practice problem solving skills and to use creative thinkinga+click

Math Pickle-gives teachers a way to play mathematical games, solve puzzles, and have math competitions in their classroommath pickle

Education World-offers professional development, lesson plans, and resourceseducation world

Super Kids-offers worksheets, games, and “brain food” for studentssuperkids


Day One

Initial question: How can technology be used in math classrooms to benefit student learning?

I started out with a simple Google search of “technology in math classroom”. Most of the results were school websites, textbook websites, or education development organizations. Below I have summarized some of the results I found.



“Thinking (And Talking) About Technology in Math Classrooms”

E. Paul Goldenberg, Education Development Center, Inc.

“With technology, what changes is the pool of problems to choose among and the ways they can be presented. Some problems are too hard to be posed in a pencils only classroom. Some lessons require students to experiment with certain mathematical objects and see how they respond. Some require visual representations—graphs, diagrams, geometric figures, moving images—that respond to students’ questions, answers, or commands.”

“Computers can provide interactive “virtual manipulatives” where physical [manipulatives] do not exist. As always, the value of a tool depends on how it is used. If physical or electronic manipulatives are well designed and well used, they can increase the variety of problems that students can think about and solve.”

This article focuses on the when it is appropriate to implement technology in the classroom and the benefit they can serve. As quoted above, technology can be used to widen the scope of questions and topics learned in a lesson. Goldenberg explains that certain tools can be useless if they are not used correctly. For example, an interactive white board that display what is drawn on it onto a larger projector screen is useless if the teacher is sitting in the front of the classroom using it for him/herself. The value of such tools come in when it is used for multiple students to share drawings at their own seats. This can create more learning for students because they are able to see other students’ processes, rather than a teacher’s one explanation.



Teaching Today

“Integrating Technology into the Mathematics Classroom”

Teri Willard, Mathematics specialist

 Calculators- study aids, inverse function explorations, function families, compare values, program calculators

Computer software- geometry drawing programs, spreadsheets, word processing, presentation programs

Interactive white boards

Digital video cameras

While Goldenberg’s article focused on why technology should be used, this article focuses on some of the different uses of common technologies. Most classrooms have calculators, computers, white boards, and cameras. But the question is, how are they being used? Are calculators used to add, subtracts multiply and divide? Or are the full functions being used to study inverse trigonometric and liner functions along with visualizing function families on a graph? The internet is full of free geometric drawing programs than can show relationships between polygons such as interior angle size and number of sides. Students can use the computer to make presentations for test reviews rather than working a bunch of book problems.




“Common Core in Action: Math in the Middle School Classroom”

Monica Burns

  • Using Technology to Instruct

“When it comes to hooking students and grabbing their attention at the beginning of a lesson, video tutorials can be powerful. Instead of giving a lecture to teach new material, the instructor can field questions and facilitate a discussion after students watch a concise tutorial on a particular topic.”

Resource- Khan Academy: free, high quality video tutorials on variety of subjects

  • Using Technology to Explore

Use interactive whiteboards to allow student to show what they are doing during a lesson or project. They can be used to model drawing of different shapes and when using an iPad, it is very easy to move around the classroom for multiple students to use.

App- Geometry Pad: provides a coordinate plane for polygons and graphing and allows for writing space for explanations or answers to questions

  • Using Technology to Assess

An important part of Common Core Math Standards is solving real-world problems and applying lesson to real-life tasks. So, have students show this using technology! Have students create a “lesson” teaching you want they are to have learned. Record them working through a problem and explain as they go. Use this as assessments rather than a multiple choice test where they could guess and get answers right. Using technology to asses allows you to actually see what each student has learned

Apps- Educreations, ScreenChomp, Doceri,

Shared by the George Lucas Educational Foundation, Monica Burns wrote about a specific Common Core skill and how to integrate technology into the classroom while teaching the specific geometry standard. She focused on three main parts of a lesson- instructing, exploring, and assessing. Each step has different ways to use technology, each of which stresses the content of the specific common core standard.