Fall 2016 - Professor Kate Poirier

# Author: Evelin

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

Published: 2006

In this journal article, they conducted a study on middle school students to see how each pair used the graphing toolÂ to solve word problems.Â  In this study, they conducted three groups, three pairs ofÂ successful students (U25), three pairs of average studentsÂ and three pairs ofÂ low successful students (L25). Each group was given the same word problems to complete. Both groups had access to the computer and graphing tool.Â  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 aÂ 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 tryingÂ 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 themÂ when they complete difficult operations and to confirm conjectures. Also make the assessment â€śuncheatable,â€ť students need to be able to understand the concept, validate it and apply it. That is goal of solving a problem.

Discussion questions:

1. Should middle school students be allowed to use graphing tools in class?
2. WhatÂ kind of graphing tool are helpful for middle school students?
3. What are the benefits for students to use graphing tool in the class?
4. How do you know if your students are over relying on graphing tools?
5. How does aÂ graphing tool help a teacher teach her/his students understand algebra?
6. 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.

Â Â Â Â Â Â Â Â  After reading the article and watching the video, not only did it amaze me but it also frightened me. Itâ€™s a weird mixture. On one side, I put myself in the student position and Iâ€™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. Â

Â Â Â Â Â Â Â Â Â Â Â 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 â€śrichâ€ť people will have access to best resources. Now referring to the article, I donâ€™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.

Â Â Â Â Â Â Â Â Â Â Â  This article didnâ€™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 â€śexpertâ€ť in using technology.

1. IfÂ $\triangle{ABC}$ is a triangle with circumradius R, then

$\frac{BC}{sin(\angle{BAC})}$=$\frac{AC}{sin(\angle{ABC})}$=$\frac{AB}{sin(\angle{ACB})}$=2R

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 differentÂ 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’reÂ going to deal with a lot distractions, Â 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.

My topic as you can see is solvingÂ a system of linear/quadratic equation. During this lesson I will demonstrate how much easierÂ it is toÂ 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.

https://www.desmos.com/calculator/cnz0mup3n5

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 weÂ moved to New York Â was because we didn’t have any family members in Cali.Â All of my family was and is still in New York. I can speakÂ both English and Spanish.

I’m a very stubborn person so I don’t like to give up easily. Especially when it comes to solvingÂ  math problems.Â Â 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, evenÂ 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.

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