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Project#4: Research Article – By Armando and Tyniqua

December 13, 2016 / Tyniqua / 0 Comments

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.

Discussion questions;

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 (6^th 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?

Reminder – Research Article Choice Due

December 11, 2016 / Kate Poirier / 0 Comments

If you and your partner haven’t already claimed a research article that you’ll present on Thursday, please indicate your choice ASAP as a comment on this post.

Final Exam – Maple Component

December 8, 2016 / Kate Poirier / 0 Comments

As discussed in class, the final exam will have a Maple component. In order to ensure that you have the relevant Maple skills, there are two sources of information:

Your classmates’ Maple Anything projects, download them from here,
Professor Douglas’s Maple worksheet here.

Final Project – Peer Feedback and Submission Instructions

December 8, 2016 / Kate Poirier / 0 Comments

Here is a link to the peer feedback for this morning’s presentations. This spreadsheet will be updated with the feedback from this afternoon’s presentations when it’s ready. (Edit: the spreadsheet has been updated.)

Your revised projects are due via email to Professor Rojas and me by tomorrow (Friday) night. Please send both of us all your files/links as a single package. (In case there’s a problem, use both of my email addresses: kpoirier@citytech.cuny.edu and kate.poirier@utoronto.ca.) If you used GeoGebra for your lesson, upload the file to GeoGebraTube and include a link to that worksheet in your email.

I strongly suggest making revisions according to the feedback you receive today. This is your chance to learn from your presentation to improve your project and to improve your grade on an assignment that’s worth a lot for both of your MEDU classes! I especially recommend making revisions to address feedback about different cognitive levels and potential issues students may have, and to address incorporating technology into the lesson.

Final Project Peer Feedback

December 7, 2016 / Kate Poirier / 2 Comments

Once again…

here is the link to the rubric for you to use to score your peers,
here is the link to the form for you to enter your scores and feedback.

Calculators…finally!

December 5, 2016 / Kate Poirier / 0 Comments

One of the most familiar technological tools in the classroom is the last we’ll discuss in this class: the graphing calculator. You are probably already aware of at least the basic functions of whatever calculator you have used in your own classes, but you might not have thought about the calculator as a pedagogical tool.

I’m of two minds about graphing calculators. On one hand, they are surprisingly powerful machines and, when used the right way, they can help a student understand a concept or an example without being distracted by rote computation. On the other, they’re clunky and old fashioned; we have much more powerful and user-friendly tools available now (for example, the software we’ve discussed in this class).

I found this 20-year-old report from Texas Instruments about the role of the calculator in math education, and figured I would hate-read it while I was procrastinating. After all, the report was put out by the same company that has had a near monopoly on calculators in classrooms for years…so it’s not exactly unbiased. However, the report discusses the exact same themes we’ve been discussing all semester! Take a look at the five myths mentioned near the beginning of the report; do they sound familiar? Familiarize yourself with the content of the rest of the report; you could replace the words “graphing calculator” with any other kind of technology essentially throughout the whole piece.

In addition to the benefits of using the calculator as a pedagogical tool, you should become familiar with the pitfalls as well. There is a nice chapter on Lies My Calculator and Computer Told Me from Stewart’s Calculus book. The examples listed in it aren’t the most relevant for us (many of them deal with rounding errors) but the chapter contains a nice quote:

Computers and calculators are not replacements for mathematical thought. They are just replacements for some kinds of mathematical labor, either numerical or symbolic. There are, and always will be, mathematical problems that can’t be solved by a calculator or computer, regardless of its size and speed. A calculator or computer does stretch the human capacity for handling numbers and symbols, but there is still considerable scope and necessity for “thinking before doing.”

Complete the following exercises:

Imagine you are trying to help your students understand $\lim_{n \to \infty} (1+ \frac{1}{n})^n$ . Try substituting larger and larger numbers for $n$ in your calculator. What do you expect to see? What do you notice?
Graph the function $f(x)=\sqrt{4-\ln(x)}$ on your calculator. What behavior do you expect near the $y$ -axis? Do you see it on the calculator’s graph? Compare the graph your calculator gives you with the graph Desmos gives you.
Graph the functions $f(x) = \sin(10x), g(x)=\sin(100x), h(x)=\sin(1000x)$ on your calculator. Do you see what you expect to see? Do you notice anything weird? What happens if you graph the same functions on Desmos?
Graph the function $f(x) = \sin(\ln(x))$ on your calculator in the window $[0,1]$ for $x$ and $[-1,1]$ for $y$ . How many roots does it look like there are in $[0,1]$ ? Change the window to $[0,0.1]$ for $x$ and then to $[0,0.01]$ for $x$ with the same $y$ -values. What has happened to the roots? Try graphing the same function in Desmos.
In the standard window on your calculator, graph the piecewise defined function $f(x)= 3x - 2$ if $x < 1.5$ and $x^2$ if $x \geq 1.5$ . Ask the calculator to tell you the derivative at $x=1.5$ . Is this what you were expecting? Try graphing the function on Desmos.
Use the equation solver on your calculator to solve $\frac{\sin(x)}{x} = \frac{1}{x}$ . How many solutions do you expect?

Project #3 Peer Feedback

December 5, 2016 / Kate Poirier / 0 Comments

Here is the feedback you gave each other for your Maple Anything project. Official grades will be posted shortly.

Update: You can now see your grade and feedback for Project #3 as a (private) comment on your Project #3 OpenLab post.

Final Project – Lesson plan and presentation – due Thursday, December 8

November 30, 2016 / Kate Poirier / 0 Comments

As announced in Professor Rojas’s class, your final project for the learning community (both classes) is a lesson plan together with a 10-minute presentation. You may choose any topic from the middle school curriculum and you may choose any technology that you like, but it must be used in a pedagogical way. Make sure you answer the question: How is using this tool helping my students understand the lesson better than if I had not used the tool?

Presentations will be held in Professor Rojas’s 8am class and in our 2:30pm class.

Include a copy of your final project on your ePortfolio. Share a copy of your lesson plan as well as the technology component with me.

For the technology part of the presentation, we will be using the same rubric that we have used for projects throughout the semester. Professor Rojas will score your lesson plan separately for her class.

Portfolio Assignment – due Tuesday, December 20

November 30, 2016 / Kate Poirier / 0 Comments

Throughout this semester you have completed a variety of projects and homework assignments. The ePortfolio feature of the OpenLab is an excellent way to showcase you and your work. You should keep your ePortfolio updated as you generate more work and accomplishments that you are proud of.

Create an ePortfolio on the OpenLab if you haven’t already. (To do this, view your own profile, click the link to edit your profile, and then the link on the upper right of the screen to create a Portfolio.)
Set up your ePortfolio site with information about you as a Math Education student.
Create a page in your portfolio called Technology in Math Education. On this page, include a copy of each of your projects from this semester and copies of any other homework assignments that you would like to show off. Organize the content so that it is easy for your audience to see what you have done.

Keep in mind that you are not generating new content for this page, you are simply putting the work you have already done into one place. Feel free to edit the copied versions of your projects, if you please. (For example, you already posted a description of your Maple Anything project, but you can’t upload Maple files to the OpenLab. You may wish to add screenshots to your description when you copy it onto your portfolio page so that the reader has a better sense of your project.)

Project #4: Research Article – due Thursday, December 15

November 30, 2016 / Kate Poirier / 12 Comments

For project #4, you and a partner will report on an academic journal about technology in math education.

Instructions

Choose an article from one of the journals listed below. The article should be around 10-20 pages long and should have been published between 2006 and 2016.
Your article must be approved by me. Comment on this post with your choice; include the title and author(s) of the article, the journal name, and year of publication. Each pair must choose a different article, so make sure to check others’ posts before you claim yours. Post your claim by midnight on Friday, December 9.
Submit an OpenLab post with the following:
1. The title and author(s) of the article, the journal name, and year of publication.
2. A 1- or 2-paragraph summary of the article.
3. Details about one important point made by the article. Write this as a question with a short essay response. (The reason for writing it as a question and response is that these questions will serve as inspiration for one of your final exam questions.) Make your question and essay response as clear as possible as it will serve as a study guide for your peers.
4. One discussion question about the important point from the item 3 above (or more discussion questions, if you like).
5. Add the category “Project #4: Research Article” to your post.
Together with your partner, prepare a 5-10 minute presentation based on your OpenLab post and prepare to lead a short discussion with the class about the important point you chose to report on above.

Due date: Thursday, December 15

Journals

Journal for Research in Mathematics Education
Educational Studies in Mathematics
Mathematics Teacher
Mathematics Teaching in Middle School
For the Learning of Mathematics
Research in Mathematics Education
Mathematics Education Research Journal
The Australian Mathematics Teacher
College Mathematics Journal
Journal of Mathematics Education at Teachers College

Journal access

These journals may be accessed through the CityTech library. You can view them online from anywhere by following the directions here.

MEDU 2010 - Technology in Mathematics Education