The lesson that I plan on integrating technology with is one in which the students will be exploring graphs of polynomials and how they relate to the different parts of polynomial functions. For instance, by finding the leading coefficient and degree of an expression of a polynomial function, one can predict the shape and behaviors of its graph. Students will be looking at different polynomials and finding patterns between their graphs and the parts of a polynomial. Instead of using the traditional graphing calculator, students will be be going to the back of the classroom to use the Desmos graphing devices on the computers to complete questions like those on the following handout:
Desmos is a free online graphing device that has many of the same features of a Texas Instruments graphing calculator. Therefore, as a math teacher it is quite easy to integrate Desmos into classroom for many math concepts can be modeled via graphs and the act of graphing is essential for a deeper understanding of certain mathematical conceptual knowledge. For this particular lesson students will be using the graphing device to clearly see graphs and accomplish their learning objective: students will be able to identify a polynomial function graph based on the parts of a polynomial and vice versa.
One of my main reasons for using Desmos over the typical Texas Instruments graphing calculator is that with Desmos, students can save their work, unlike the calculator. Overall the computer application is also easier for students to collaborate and investigate with for multiple students can see the visuals of the graph at once. This is really important for this particular lesson since students are asked to work in groups to see patterns that aren't easy to see individually or without discussion. Another characteristic that separates Desmos from the TI-83's available in our classroom are that program begins to create graphs as students type in numbers and variables. If you make a change to a number, the graph is quickly redrawn on the computer. This way, students can make these changes and the impact of the changes they make in real time; this gives them immediate feedback and of how the graph changes under certain circumstances which is pertinent to and enhances the objective I am trying to reach and overall a powerful way for students to learn math.
What makes Desmos even more remarkable is that students can also download the application on their phones and tablets. This may be something that I consider having them do before implementing this lesson since it may help some students engage even more so he may be distracted by the computers or want to work alone. By having students download the application to their own devices, there is a chance they would play around with it during their time after school. This could really extend their learning to places outside of the classroom, which is one of my overall goals as a math educator specifically.
I am happy to see the effort you've put into explaining your rationale for using Desmos, Caitlin, and in identifying where it gives you and your students added value. I was especially intrigued by your observation that, as contrasted with the TI-83, Desmos facilitates collaborative work. Your vision for the lesson goes beyond what could be a nice, but rather general observation, to seeing how the students are engaging in conjectural work in your lesson that could and should have a collaborative dimension in order to maximize the learning opportunities. I don't know how often your students get the opportunity to engage in this kind of collaborative "figuring out," but I would strongly encourage you to include in your lesson writeup your observations about how your conjectures about the kind of work Desmos would facilitate actually played out.
ReplyDeleteCaitlin,
ReplyDeleteI think your idea of a collaborative lesson using Desmos is great! I remember from our experience at Scarlett Middle School how Ms. Racine always tried to incorporate partner work or small group work with her lessons. The students seemed to be more engaged this way rather than working on math problems individually. I did notice that you wrote about using Desmos to teach math concepts; however, I wonder if you feel that students may become overreliant on technology (calculators, computers, etc.) to do problems and they don’t get the practice necessary to develop fully their math skills. Do you also have students graph polynomials “old school” style with graph paper and a pencil? Could Demos be an efficient tool for feedback to see if students can graph and make predictions about polynomials correctly? It’s certainly a struggle for teachers to determine when technology adds to learning and when students become too dependent on it.
Hey Caitlin,
ReplyDeleteI like your idea to use Desmos instead of the typical calculator. Mentally, for me at least, this would be less intimidating that using a graphing calculator. I say this because for most of my education I have used a non-graphing calculator, and when I got to pre-calc in high school I had to get one and I hardly knew how to use by new sidekick. However, most people these days are much more familiar with a computer, even if they don't have one at home. By directing students to a domain to acts like a graphing calculator on a computer you may be taking some of this intimidation out of the equation. However, I would say maybe not to use Desmos all of the time because moving forward students will probably need to know how to use a graphing calculator in some capacity. In the end though, I think this lesson will prove fruitful. Best of luck!
Caitlin,
ReplyDeleteI love this idea! Using the graphing calculators for calc class was one of the things I enjoyed in math class, I can only imagine home much more fun this would be if students use a computer tool and are able to carry their work around on phones etc. I like this idea because many times in math it is important to be able to reference older examples of work so that you know that you are not repeating mistakes etc. I found this to be especially true when dealing with graphs. Im assuming they can also print these results which can give students who like paper representations of math work an option, which was the case for me! I found visually representations of math work to be the most helpful to me. I am excited to see how this pans out!