Title: Slower Algebra Students Meet Faster Tools: Solving Algebra Word Problems With Graphing Software
Author(s): Michal Yerushalmy
Journal Name: Journal for Research in Mathematics Education
In this journal article, they conducted a study on middle school students to see how each pair used the graphing tool to solve word problems. In this study, they conducted three groups, three pairs of successful students (U25), three pairs of average students and three pairs of low successful students (L25). Each group was given the same word problems to complete. Both groups had access to the computer and graphing tool. The graphing tool is a software with capabilities similar to a basic graphic calculator that presents two-dimensional graphs and numerical values for any single variable expression. As each pair completed the word problem, there were interviews being done as they worked. The interviewer was not allowed to give the answers only to assess their thinking process. The main goal of the interviews was to observe the processes by which the L25 constructed mathematical meaning while solving traditional word problems with the function graphing software. From this study, they noticed how each pair had a different approach when it came to using the graphing tool. Some students wanted to use the tool to get an answer, others use the tool to check if their answer was correct and others students just wanted a visual representation of the function. Overall, the tool was part of the students’ reasoning and argumentation and was used to reflect on conjectures.
Question: How can we guide students to use graphing tools properly to solve algebra problems?
Graphing tools were constantly used in classrooms, and students were encouraged to use them. The techniques involved in using the graphing tool were practiced routinely in the eighth and ninth grades, including values, reading linked representations of function, and reading the values at intersection of two function graphs. Graphing tools are very helpful when students are dealing with functions. But if a student does not use them properly or over rely on these graphing tools, it may cause them just use the graphing tools to get the answers of the problems instead of trying to reason and understand the concept behind the problem. So, in order to help student to use the graphing tools properly, we need to set rules that they can only use them when they complete difficult operations and to confirm conjectures. Also make the assessment “uncheatable,” students need to be able to understand the concept, validate it and apply it. That is goal of solving a problem.
- Should middle school students be allowed to use graphing tools in class?
- What kind of graphing tool are helpful for middle school students?
- What are the benefits for students to use graphing tool in the class?
- How do you know if your students are over relying on graphing tools?
- How does a graphing tool help a teacher teach her/his students understand algebra?
- Should you allow student use graphing tool during the test?
The audience for my project will be Calculus 2 students. I am assuming that students should know the following: being able to solve systems of equations, being able to integrate, and being able to use simple Maple commands, such as the plot command and the solve command. The reason why I chose to do a worksheet is to get students to practice the content. I used Maple as a way to check their work. I didn’t want students to rely too much on Maple to do all the work. Students should also be able to solve a problem by hand.
After reading the article and watching the video, not only did it amaze me but it also frightened me. It’s a weird mixture. On one side, I put myself in the student position and I’m all for it. We need better teaching methods. But when I put myself in the teacher position, I see a decrease in wanting teachers.
Watching Sugata Mitra experiments and seeing his plans for the future made me change my vision of learning. It made me realize that children are capable of learning something new without the help of a teacher. These group of children were able to use a computer even when they did not understand the language. It also made me realize that his plan will bring some sort of equality among students. His idea is to transform classrooms into a room where all students would have access to some sort of technology. That means that not only the “rich” people will have access to best resources. Now referring to the article, I don’t entirely agree with the idea that teachers will be replaced with technology. The reason why is that as humans, we need to have some sort of interaction between each other. I understand that letting students learn on their own is good strategy but students cannot always work independently. Communicating with others is an essential tool that we are taught in classrooms. Learning this skill will be beneficial for us in our future careers.
This article didn’t really make feel depressed nor hopeful. I would say I was in the middle. I was more amazed on how learning is changing drastically. If this was to come true, which is possible considering the increase of technology, as a future educator it would be a good idea to have some sort of a back-up plan. I should develop technological skills meaning to become more of an “expert” in using technology.
Overall the main idea of this article was using technology in classrooms to teach language. It demonstrated both the pros and cons of involving technology in the classroom. The pros of using technology when teaching language is that there will a variety of different teaching styles in the classroom, more independence among the students and as well as getting students to get more involved with others. As Ellie Paull stated, “they add another string to my bow as a way of presenting new information and checking their understanding.”Although these pros seem to be very convincing to prove that technology is a good tool to be used, but there are some cons as well. By using technology as big a part of your lesson you’re going to deal with a lot distractions, as well as setting up the technology tools, and sometimes even help explain how to use it. These technical difficulties might take away from the main objective.
Now my opinion about technology being used in classrooms can go both ways. I do believe that technology should be more involved in classrooms. As I see it, everything around is becoming more of using technology rather than the old style. Getting students to get more of early hands on is great, as long as it can be balanced out with the main objective.
Personally I didn’t use the rubric for my presentation. This was actually my first time looking at the rubric. Overall I thought the rubric was very easy to understand and it set clear standards. For me, I don’t like using rubric even though I hear it’s a good tool. I’ve had teachers used rubrics with me before but I don’t like using them. I feel like it puts a bit more pressure on me to get my work, presentation in this case, to be perfect. With this rubric it wasn’t as “picky” as other rubrics I’ve seen in the past. Which to me personally is okay. I also thought did rubric was appropriate for this presentation. As well as for our future presentations.
The form we used to submit feedback to our classmates was actually really entertaining. I actually thought that this was a good idea. It kept me focused on the presentations and I felt like I was actually being useful rather than just being an audience for the presenter.
My topic as you can see is solving a system of linear/quadratic equation. During this lesson I will demonstrate how much easier it is to use desmos when it comes to solving a system of equations. I will explain step by step how the system is to be solved algebraically and of course demonstrate the pros of using desmos when it comes to solving it graphically.
Hey guys! As you can see my name is Evelin but you can call me Eve whichever you prefer. I was born in California but I was raised in Brooklyn, New York. The reason why we moved to New York was because we didn’t have any family members in Cali. All of my family was and is still in New York. I can speak both English and Spanish.
I’m a very stubborn person so I don’t like to give up easily. Especially when it comes to solving math problems. I’ve always loved math ever since I was in elementary school. I’d like to thank my 5th grade teacher, Ms. Carter, for that. She showed me little tricks to make math fun and easier. Since then I enjoy solving all types of equations. The second person I would like to thank for inspiring and motivating me would be my ex partner. She was awful in trigonometry so in order to help her out, I would go the extra mile just to help her pass the class. I would study the topics more, even practice solving new problems each day. Every time I would tutor her, I would get a satisfaction feeling. It made me feel great.
I’ve haven’t had much experience with technology in math class. The only technology I’ve used are scientific and graphing calculators. This semester I’m being introduced to a software called Maple.