Month: January 2016

Relative Advantage of Instructional Software in an Algebra Classroom

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Software Search

There are five types of instructional software, each classified by the teaching function that it is designed to assist: drill and practice, tutorials, simulations, instructional games and problem-solving programs. All have varied uses in mathematics, and many fit into more than one area. They range on the spectrum from fully directed instruction to total inquiry-based learning. Which is most useful will depend on the lesson and the audience.

Drill and Practice:

Drill and practice is an example of directed instruction and is one of the most common forms of software available for mathematics classrooms. There is little higher order thinking involved, and it is rarely integrated into the curriculum. Students solve problems or answer questions and receive immediate feedback, something that our students have come to expect, if not demand. It allows them to practice basic skills, an area in which many of my students have deficiencies. Some programs offer badges that students earn or levels that they complete as they progress in the program, increasing student motivation. Drill and practice allows teachers to differentiate instruction, allowing each student to focus on personal areas of weakness. Constructivists view drill and practice as outdated and of little use in contemporary classrooms, however special education teachers find them to be an appropriate tool that allows students to work on basic skills in a more engaging manner (Roblyer, 2016). Examples include IXL and AAA Math.

Tutorials :

Tutorials are commonly used in flipped classrooms.  Videos show step-by-step solutions to various math problems. They can be used to differentiate instruction, either for small groups or a single student.  These videos can also be created by the teacher for the students in that class.  Tutorials can be watched as a stand-alone or as entire curricula, allowing students to self-pace. Linear tutorials progress along the same path for every student, regardless of how the questions are answered, while branching tutorials adapt that path based on student response (Roblyer, 2016).  My students are more engaged and less frustrated if the software branches, allowing them to relearn and practice skills that they have not yet mastered.  I usually post at least one video for each new concept that I teach, on our Google Classroom page.  This allows my students to “make sense of problems and persevere in solving them”, one of the eight shifts in Common Core Mathematics. My students are quick to give up, so anything that I can create or provide to help them learn this skill is valuable.  They can watch the video, stopping and rewinding as many times as necessary to try to solve the given problems.  I have also created my own videos using my document camera.  Khan Academy and Virtual Nerd are both examples of tutorial software that I use regularly.


I love using “What would happen if….” scenarios. My students rarely show curiosity in math, how it relates to them or to their world. They view it as a chore to either get through or give up on. Simulations allow me to attempt to foster that curiosity. These are computerized imitations of real-life or imaginary situations. Students can adjust different variables to see what effect each has on the outcome of the problem involved. This type of software allows students to conduct an experiment without having to purchase materials or leave the room. Simulations allow students to see how math is connected to other subjects, such as science (radioactive half life), and social studies (population growth and decay). Simulations increase student engagement and understanding. Simulations have been found to work best when paired with other activities, such as hands-on learning (Roblyer, 2016). (Desmos is an online graphing calculator with many interactive simulations included on the website. Glencoe offers many virtual labs that tie to math, such as punnet squares for sex-linked traits. PhET is a simulation site offered through the University of Colorado, Boulder. The SERC portal offers simulations that tie math and social studies.

Instructional Games:

According to Roblyer (2016), “instructional games are software products that add game-like rules and/or competition to learning activities (p.92). There is a long history of using instructional games in mathematics classrooms. I can remember using Number Crunchers almost twenty years ago as a reward for students who finished their work early. Students enjoy playing them, and it allows them to practice basic skills. Unfortunately, the students who got to use these games rarely needed that extra practice and the ones that did need it rarely got to use them. When I use games in the classroom, I tend to either use them as skill and drill or for review. The biggest advantage is that kids love to play them and will easily engage in the lesson. They are difficult to use effectively in my classroom because of the wide levels of ability. It is difficult to find games that are not competitive, which can leave my struggling students behind. I work around this by forming carefully selected groups that compete against each other. Jeopardy works well with larger teams, as do many of the games created by Gina Wilson, of All Things Algebra. I have also used Cool Math, Fun Brain, and Math Playground with individual students.

Problem-Solving Software:

This type of software fits well with the constructivist theory and common core. According to Roblyer (2016), there are two main areas: content-area skills which work within a given subject area, and content-free skills, which focus on more general problem solving skills. Students are given a problem that they need to solve, usually involving a real-life scenario. These allow for application of knowledge to new situations, something that my students have difficulty with. There is a distinct lack of problem-solving skills that allow them to answer those higher ordered questions on Blooms Taxonomy. This is not a type of software that my students can handle independently. When I use these, I do a lot of modeling and whole group work, or small groups within the whole group. I have found that unless I lead them through it, most of them will give up and lose focus. I ask many leading questions to try to get them headed where they need to go. Some will get there, many will not but the overall experience is worth the frustration. If we work through a task together, my students are more focused and engaged. Being able to tie the math to real life situations allows them to see the connections in a way that they can understand and be curious about. Desmos has some great teacher created activities built into their program. Geogebra is another great site, as is Geometer’s Sketchpad and Yummy Math. Dan Meyer is a huge proponent of project-based learning and has many tasks and activities on his blog.

I have used all five types of instructional software with my classes to varying degrees of success. My students tend to do best with drill and practice and instructional games. These can be tailored to each student’s level and allow them to feel successful with minimal help. While I agree that there is a time and a place in my curriculum to use these, I much prefer the simulations and problem-solving software. Even thought my students struggle with it, by making it a group effort, we struggle together. They learn more from these programs because they are forced to think. Sometimes I wonder if we make our special education students think enough. I watch so many teachers “GPS” our kids to death. Do this. Now do this. Now this. They just blindly follow the steps without ever putting any real thought into the process. They don’t ever wonder why. My students tend towards apathy. They lack curiosity. By fighting our way through a problem, I am modeling “I wonder what happens if…”. When I hear a student ask that question out loud, I know I am on the right track.


Roblyer, M. (2016).  Integrating Educational Technology into Teaching (7th ed.). Massachusetts: Pearson.

Relative Advantage Chart

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Pros and Cons

I see many teachers in my district attempting to use technology simply so they can say they are using it. Other teachers avoid technology completely. Because my district is a 1:1 district, the expectation is that we will be infusing our lessons with access to websites, apps and other learning experiences that in the past would not have been possible. This can be very overwhelming. Relative advantage is a way for teachers to decide if any given method has benefits that outweigh the current method of instruction. While there are many instances in my classroom that the use of technology will make something easier for either myself or my students, there are other instances where it will not. Last year I attempted to use Castle Learning with my students for a weekly assignment of ten questions. The expectation has always been with these assignments that after my students use all available resources to help themselves, they can then come and work through their mistakes with me. This allows me to reteach concepts they have not fully grasped and gives them the ability to put a perfect score in the grade book. The relative advantage of this was less than zero, after all was said and done. My students struggle to copy things from the screen, so I had to print out the worksheets after I created them. They also needed those worksheets so they could go over the problems with me. After we did all the corrections, they then had to upload their responses so I could regrade them in the program. I ended up tripling my workload and frustrating my students. This is a case where technology was not an advantage. I still use technology to create the assignments, but each student has a paper copy that they complete the work on, and which I grade by hand.

This assignment made me more thoughtful about how I am integrating technology in my classroom. It can be difficult to use some aspects of it in a math classroom without adding extra work. I need to continue to be aware of the advantages vs. the disadvantages.

Relative Advantage Chart

Vision Mission Statement

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School 2.0

Our world is changing exponentially.  We are more connected, more tech-savvy and better informed on global events.  As teachers, we see the results of this in our classrooms every day. Students lives revolve around technology.  They are texting, sharing, downloading and communicating throughout their waking hours.  Except when they are in school.  Education has been slow to embrace this new world. “We have not yet become good enough at the kind of pedagogues that make the most of technology; that adding 21st-century technologies to 20th-century teaching practices will just dilute the effectiveness of teaching” (Keeling, 2015).  The skills they need.  Instead of teaching students what to learn, we need to teach them how to learn.  My students constantly ask me why they need to learn algebra.  The truth is, they don’t.  I am a special education math teacher in charge of getting my high school students through the state exam so they can graduate from high school.  None of my students will ever need to know how to factor a quadratic equation in their future lives.  Nor will they need to put an equation into y=mx+b form. I am teaching them how to think.

My school has a fifty percent poverty rate.  All of my students live in poverty.  They are all on the wrong side of the digital divide.  Many of my students have no access to the Internet outside of school.  Few have cell phones; even fewer have smartphones. To level the playing field, every student in my high school has a Chromebook provided to them. All of my students use them almost exclusively to message each other via Google Hangouts and watch videos on YouTube.  It isn’t that they refuse to use them for collaborative projects, or to help themselves.  They just do not know how.  Shockingly, over half of my students had no idea how to access their school email, compose a message and send it.  They require exposure, not just to mathematical concepts, but also to technology.  Without this exposure, my students will continue to fall behind their more connected peers.  Technology can and will help students become better problem solvers.  With this in mind, one of my roles is to provide a technology-rich learning environment.

Many classrooms are still driven by the objectivist method of teaching. The teacher is the “sage on the stage” imparting knowledge through direct instruction. Students are seen as vessels to drink in all that the teacher has to share with them. Classes have been taught this way since the beginning of education, and while the elders of society like to state that it worked for them, that it was a good solid education, they are not seeing the big picture.  In the words of Marc Prensky (2001), “Our students have changed radically. Today’s students are no longer the people our educational system was designed to teach.” What has worked in the classroom in the past no longer prepares students for the jobs they will be working in the future.  Employers need workers who can function in this increasingly connected world.  They are looking for employees that can think and problem solve. This epic shift is forcing teachers to adopt a more constructivist style of teaching. Inquiry-based learning is student-centered, leaving the teacher as the “guide on the side”.  Learners are expected to drive their own knowledge through project-based learning.  These classrooms look very different.  The teacher is not the focus; the learning is. These teachers facilitate instead of lecturing.  Students are not seen as a blank slate but as the sum of all their life experiences and prior knowledge. Constructivists believe that these experiences should drive project-based learning, making learning more meaningful. This method of teaching helps students learn problem-solving skills, flexibility and perseverance.

The best classrooms offer a blend of these two methodologies. According to Roblyer (2016), “Proficient technology-oriented teachers must learn to combine directed instruction and constructivist approaches and to select technology resources and integration methods that are best suited to their specific needs” (p. 49).  Technology in the mathematics classroom makes abstract ideas more tangible and approachable for students with learning differences.  By making the math more accessible, learner engagement and confidence increase. My students can spend more time applying what they do know, while relying on technology to help them overcome what they don’t know.

Keeling, B. (2015, September 15). Technology in classrooms doesn’t always boost education results, OECD says. The Wall Street Journal. Retrieved from

Prensky, M. (2001). “Digital natives, digital immigrants” On The Horizon, 9.5, 1-6.

Roblyer, M. (2016).  Integrating Educational Technology into Teaching (7th ed.). Massachusetts: Pearson.


ID Job Description

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My first assignment in the Instructional Design class was to create a fictitious posting for an Instructional Designer.  Educators and Instructional Designers are often lumped together but while there are some overlaps, the jobs are actually quite different.  Going into this project, I assumed that I had no design experience at all, but as I read, I realized that I have done some work in this area.  It did not include technology because this was many years ago but the experience did give me some interesting and valuable insight into this task.

ID Job Description for Educational Designer

I Am…..

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The introductory assignment for EdTech 541 is to write an I Am poem that follows a given template.  I found this to be an task.  I was very anxious at first as I am not a poet, nor do I enjoy poetry.  Once I saw the template, I calmed down.  This I could manage.   I spent about a week writing and editing this assignment and what I noticed was that the words and tone changed according to my moods and thoughts.  My final submission seems a little dark and melancholy, but that has been my frame of mind lately.  My life is in a state of flux right now, and it is making me uncomfortable.  The anniversary of my mother’s death was a couple of weeks ago, adding to my general unease.  All of this came out in my poem, and though I tried to make it a little lighter, it refused to cooperate.  The image I chose was the Chinese symbol Sho Shin.  It stands for Beginner’s Mind and refers to one’s open-mindedness when learning new things.  I feel that this is a good description of my character.  I pride myself on my ability to adapt and change.  I love to learn.