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 Constructivists view drill and practice as outdated and of little use in contemporary classrooms, however special education teachers find them to be an appropriate tool that allows students to work on basic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 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.
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.
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.
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.
I had a hard time with this assignment. I couldn’t decide what I wanted to do so I finally just picked something and went with it. I’m not super happy with it, more because of the Quest itself rather than the design. This class really stretched my level of creativity which has never been very high. I think that had more to do with my apathy towards this assignment than anything else. I think I just need a break. Even better, I need to learn when something is good enough and not spend extra unneeded hours agonizing over the smallest detail. I tend to drive myself crazy.
I had the most fun completing this assignment but it was also definitely the most challenging. I am getting more comfortable with templates and enjoyed picking through the code and seeing what I understood and what I didn’t. I am also getting braver with adding new code and being able to figure out and fix errors.
While I enjoyed creating this activity, I found working across all the platforms very tedious. Keeping the CSS straight in my head was difficult, and I found it easier to plow through it rather than work on it for awhile and then take a break. It was hard to remember where I left off. I also struggled with how to create an activity for my students to complete outside of school as most of my students do not have mobile devices or internet service. I decided that for those with no device, they can try to use their school Chromebooks to take the pictures. If that doesn’t work, I can do an after school session and take them out to the football field, letting them use my devices to complete the assignment. As far as internet goes, there are hotspots all over town, including the neighborhood elementary schools, so that should not be as much of a problem. Where there is a will, there is a way…..
The content I chose for this assignment lent itself well to the parameters involved. My classes are small, so I needed a task that would accommodate a small amount of groups without being overwhelming. We teach solving systems of equations three different ways. Each group will become an expert in one method, and then teach that method to the rest of the class. This activity is definitely something I will use with my classes.
I struggled with making the table, but not inordinately so. It took some adjusting to get it centered on my page and once again, I had difficulty finding colors that made sense to me. It is interesting to note that as nervous as I was about learning to code, I am really enjoying this class. While I am finding it challenging, I am also enjoying it immensely. I think writing the content to go on the pages is more difficult for me than the actual coding. Go figure!
As an Algebra teacher for special education students, I initially wanted to do a concept map on the different methods of factoring, as this is an area that is heavily tested on the NY Regents Exam and my students struggle with this concept. But honestly, my students struggle with most of the algebraic concepts. Abstract concepts are very difficult for them to grasp. I am constantly asked, “When will I ever use this?” and that’s a tough question because I know that none of my students will ever use the majority of this material again. My answer to this question has always been that I am not teaching them math. I am teaching them how to think, and problem solve. If I can get them to try to help themselves without immediately giving up, then I feel that I have done them some good. With this in mind, I created a concept map of places on the web they can go to help themselves when they get stuck. These are all great sites that I would like them to get comfortable going to with a problem. I use VirtualNerd a lot for flipping my lessons. The videos are short, concise and easy to understand. Desmos is our go-to calculator for homework as my students cannot afford a graphing calculator. The MathBits couple is amazing. They live near me, and I love to go to their workshops. They also are the brains behind regentsprep.org, a site that every NY teacher is familiar with. I am not as familiar with Khan Academy, but I have used some of the videos. I really liked the result of this assignment. Both the coding and the content flowed easily from start to finish, so I must have been on the right track!