Title: Map, Scale, proportion, and Google Earth
Author(s): Martin C. Roberge and Linda L. Cooper
Published: April 2010
This article is based on the concept of using sources such as Google maps and Google Earth in order to teach students proportions in terms of large and small-scale scenarios. The tools are used in a pedagogical sense, by enabling students to use what they already know about places, ratios, and measurements and apply it to real life situations where they make connections with geography and proportional reasoning calling for a higher level of thinking. So, not only are the students learning how to read a map, use its key to measure the distance between places or objects, but they are able to convert the maps measurements to real ground measurements through proportioning to get approximates of distances with a very small margin of error. This activity also forces students to look past the ideas of proportionality typically taught in the classroom by making them use their reasoning skills to come up with the basic format taught in the class and other ways that also lead to correct answers.
Question: How do can we incorporate a tool such as Google Earth into our lesson plan without it being overwhelming to our students?
In order to incorporate a tool such as Google Earth into our lesson plan we can guide our students to recognize the different types of images on the computer from different perspectives and then zoom in and out and encouraging the students to think about what words can they use in order to describe what is happening as you manipulate the picture of the object in relation to size and distance. Once the students realize the action that you are doing you can relate this to “zooming in and out,” on a phone or computer (everyday activities), and then introduce maps of different scale factors starting out with things that are familiar—such as, their neighborhood, the area surrounding their school and once they grasp the concept of proportions based on a large scale, then we can broaden the area of the map based on an entire city, then region and so forth using a smaller scale this way the students will not be overwhelmed with converting the measurements on the map with real life measurements. This really forces students to critically think and analyze each situation and also forces them to create and answer many questions on any type of picture.
- What is the relevance of using a source like Google Earth in a mathematics classroom?
- How can we adapt the activity for a younger audience (6th graders)?
- How can we adapt the activity for an older audience (high school students)?
- What are some ways to access students learning using Google earth as a pedagogical tool?
- What other concepts can we have students learn by using Google earth?
- What other ties does this topic have to other fields in STEM?
My audience is trigonometry students in high school or college. I am assuming that they know and understand how to graph trig functions and the basic form for a sinusoidal function and its components:
|A| = amplitude
B = cycles from 0 to
D = vertical shift
C = horizontal shift (“phase shift” when B = 1)
The content is delivered, supposedly following a lesson in trigonometric functions, using maple as a pedagogical tool for expressing the translations of the sine and cosine functions with a change in C representing a horizontal shift, demonstrating how to transform each of the trigonometric functions to the other.
Maple is an appropriate tool for demonstrating this concept of trigonometry through an in-class lesson, because it enables you to do calculations, graphing, labels, and input text without any problems and easily correct errors, or change in equations, functions, or graphs.
I agree with the assertions the article makes about the classroom being geared towards a more technological based learning because the schools are implementing technology more and more in the classrooms. But, as the article expresses the notion of a teacher’s job being replaced by the computer in as little as ten years from now is a bit extreme. I think we have a long way to go before there is a program that will bring to the students the same or an improved method of teaching students what is needed for the real world and to encourage the same students to be innovative. I highly doubt that the school system would take the risk of fully implementing a computer ran classroom in order to experiment with young children in order to see if the method of teaching is more effective than the old fashioned way of teaching as a teacher being the main source of instruction in the classroom.
I am a little worried about the way the speaker in Ted Talks spoke in a way that discredits the job of an experienced educated teacher. For there is no way a computer can assess the needs of the different types of children that enter a classroom with different needs and levels of learning. My favorite quote from the article is, ” There is a profound difference between a local expert teacher using the Internet and all its resources to supplement and improve his or her lessons, and a teacher facilitating the educational plans of massive organizations,” I say this because I like the idea of teachers getting ideas from other sources in order to maker the classroom more engaging for the students but I do not think the sole purpose of computer software to be as the main source of learning for students. A student can not ask a computer certain questions that has never before been asked or addressed while a live teacher can help a student arrive to an answer without the use of technology. This type of learning places too much responsibility on the students, especially younger students who need guidance from adults. Computers are just not well rounded when it comes to learning, because even in my own experience I tried using videos like Khan academy but it only showed me the basic concepts of what I needed to know, when my professor actually figured out the way I was thinking and was able to determine the fault in my logic.
I find that technology will be a major tool for learning throughout my career but I do find that I as well as my future colleagues have to have a firm foundation n our field of learning in order to be effective teachers because what happens when the computer crashes. We have to be prepared and not be too dependent on technology to teach our students things that we already know. While I feel technology can never replace a good or even mediocre teacher I do find that it is important to stay knowledgable about the advances in technology by taking technology courses (as we are doing now), reading informative articles about new and upcoming innovations in technology, and keeping on top of studies done by professionals that is monitoring the effects of technology in the classroom. I think the home should be the place where a self organized learning environment is key for when the teacher is not around and the parents are not as informative as we’d like them to be to guide in learning at home, but a teacher should never be replaced with a computer.
1. Angle Bisector Concurrence Theorem:
This article discuss the difference between the traditional classroom and the inverted classroom of university leveled courses. The traditional classroom entails the student teacher relationship, where students come in receive a lecture, take notes, and may ask questions. Then they take the information from the classroom and show what they learned through take home assignments. These assignments are submitted and students are assessed by the professor to determine whether or not the students are learning in any given course. As noted by the author, this cycle repeats itself. The author posits STEM courses tend to be an exception to the traditional classroom and they lean towards a more inverted classroom where most of the transmission of the material is learned at home rather than by the professor during class time, unlike the traditional classroom, leaving more time for assimilation of the material given. This type of learning structure is becoming more and more common among grade levels K-12 along with college leveled courses. These courses that include lab time, project, or problem-based learning tend to be highly effective in prepping students for real life experiences in their field of study.
The author used a study done by the creator of Matlab, a pedagogical tool used for problem solving, particularly for engineering students. The creator designed a course surrounding Matlab and the computer program was deemed to be more effective than the previously used programming textbooks. The students where able to be assessed quickly at the start of a class, followed by hands on learning using Matlab, which is helpful in learning codes for computer programing and input. Although, according to the study, the students had mixed feelings on the computer program in terms of how much they found it useful in areas outside the course. As noted by the author, the thought of an inverted classroom places the learning on students and has great promise for deepening students learning when used effectively.
I have concluded, from years of experience, that an inverted classroom is a highly effective method of teaching and learning. I find that technology is all around us and we should use it to our advantage. I have learned that students tend to respond better to hands on learning, which I call active participation, than a lecture from a professor. Also, students do not have to worry about the pressure put on them to finish take home assignments or referring back to their notes to finish a task they should of learned during transmission. I find that the material sinks in more and the students get a chance to share and learn from one another.
I picked this article because it spoke on the computer program Matlab. I have taken an introductory course for engineering and the main program we used was Matlab. I found it to be very helpful and easy to use. I enjoyed using the tool and did very well in the course. We also did our homework and assessments using the program. Like the students in the study, I have not used Matlab outside of the course but then again I am not an engineering major. Still, I found the course more enlightening because of this program and would recommend other professors to find a way to implement it in their technology and math courses. More over, I believe learning should be fun and sometimes our new advancements in technology can be geared to achieving that goal. Even though, nothing beats an experienced professional guiding students to meet their potential a more hands on learning experience may be the key to a more effective learning experience.
I believe that the rubric was a fine guide for us to determine the grades for our classmates. Still, I felt funny grading some of our classmates on topics I have never seen before because I was not sure if their presentation was good or not being that I had no previous experience in the topic so my scores reflected that. Some of the students I felt knew what they were talking about, even though, their presentation could have been clearer, such as, the clarity of their speech – for some I could not understand them or they were using the wrong words to explain their topic or present their work on the slides. Although, they knew how to use desmos and technology better than me. I think writing and English skills should be of more importance when teaching all subjects in the classroom, and that goes for me as well. These skills can be a serious barrier between students and teachers that must be improved, because the teacher may have a brilliant mind but it has to come through when they are teaching. So I believe column 4 which uses the word eloquently should be used when determining all aspects of a presentation because it is very important to be clear. I hope I don’t sound too judgemental but this is also something that I am working on. Also, I like the feedback I got from my classmates because I did not realize that my back was facing them the majority of the time, so I appreciate their honesty and I will use their constructive criticism ion order to improve on my presentations.
Hello everyone, as noted I am Tyniqua HInton. This is my fourth year at City Tech, and getting to this point in my academic career has been a trying task. I started off in a remedial math class my freshman year due to the fact that I graduated high school in June 2001. So, I forgot the majority of everything I learned and was not prepared for college math courses as yet. Therefore, I was not able to begin a major in math education until I was able to complete the prerequisites required to get into the major. It took me two and a half long years before I was able to be a math major.
My first two years at City Tech was amazing, I did well in every class receiving a majority of A’s which I was invited to be in our school’s Honors Program. My favorite subjects were every history and English class I have taken, but I always looked forward to my math classes I never surpassed an opportunity to take one or attend a workshop. I learned to love math in my freshman year of high school where I had a dedicated group of teachers and a gifted tutor who taught math in the most enlightening way which gave me a new understanding an appreciation for the subject. As a result, I received a 97 on my math regents in the 11th grade, still, I felt my school failed me because they did not offer me any additional math classes that would of better prepared me for college. I never saw trigonometry until I attended a college trig class which I struggled to receive a B. I had more difficulty in math when I started my calculus classes which has proven to be my most challenging subjects. Even so, my passion for math has not changed, I am always willing to learn and I am looking forward to teach everything I learn about teaching middle school math to my future students. I believe middle school is a very crucial time in a students academic career, for the reason that the students are introduced to more abstract or complicated topics that requires a higher level of thinking and they need a teacher that is willing to understand that all students are unique and have their own way of learning so we have to add a little bit of everything to the learning experience to help develop the blossoming minds of adolescents.
I had a bad experience during my middle school year, I was introduced to the concept of the variable and my 8th grade teacher taught it in a way that was not catching for me. When we came into class all the work was previously written on the board as he proceeded to teach from the back of the classroom and spoke like the man from the popular dry eyes commercial. As a consequence I failed math the entire year, but due to the city wide exams that all New York city students are required to take I passed the eighth grade and my poor grades for that class did not leave me behind and I continued to go to high school. Thanks to my mom who got me a brilliant tutor and all of the extra math classes my high school gave me I excelled in mathematics throughout high school. Hopefully when I graduate I could put to good use all of my past experiences along with my present ones and become an awesome teacher. Also, I ran an after school program and summer camp for the past nine years, but I resigned last August in order to finish school. Currently I became certified by the Department of Education to be a paraprofessional at New York City’s Public School, this will be helpful to me because I will learn hands on what is required to be a teacher.
I will use desmos to graph a quadratic function showing the points of intersection on the x-axis. Additionally, I will show how to get the roots of the equation manually using the quadratic formula.