Category: Uncategorized (Page 2 of 3)

The test has four components. CHOOSE THREE OF THE FOUR TO COMPLETE. Read the instructions for each component carefully. While some components require the use of a computer with access to the internet, you may not access webpages other than the ones linked below and you may not communicate with your peers or anyone else during the test.

1. Geometry component

Answer the questions in the space provided on the paper. (Here’s a link to the PDF if you’d like to view the paper on the computer.)

2. Written component

Click on this link to access the instructions and linked form. Do not submit until you are happy with your answers.

3. Desmos component

1. Click on this link to access the Desmos activity.
2. Do not sign into your Desmos account; enter your name when asked.
3. Complete the activity by answering the questions on each page. Your work is automatically saved. You will be able to go back and edit your previous answers during the test as long as you keep the browser tab open.

4. GeoGebra component

Complete using the GeoGebra desktop app. Save your response as a GeoGebra (.ggb) file with your name as its filename. I will save your file to my own drive. (Save a copy of your file for your records.)

1. Place 6 points A, B, C, D, E, F in the plane so that A, C, and E lie on one line and B, D, and F lie on another line.
2. Color the two lines black and color the 6 points A, B, C, D, E, F gray.
3. Create the lines and and color them red. Let L be their intersection point. Color the point L red.
4. Create the lines and and color them green. Let M be their intersection point. Color the point M green.
5. Create the lines and and color them blue. Let N be their intersection point. Color the point N blue.
6. Use the drag test to see how the configuration of lines and points changes as you move the free points around. Pay special attention to the points L, M, and N.
7. Make a conjecture about the relationship between the points L, M, and N. (Hint, it may be helpful to hide all the lines and perform the drag test again. You may like to add Geogebra elements to test your conjecture; if you do, make them a different color.) Create one text box containing the statement of your conjecture. Be explicit and precise. Use full sentences.
8. Does the drag test consist of a proof of your conjecture? Why or why not? Create a second text box containing your answer.

According to an article “Teaching Math Using Technology” by David Moss, he explains how technology is useful for students, parents, and teachers to do math. In his article, he include many helpful websites that students and teachers can use in classroom or at home to enhance their understanding of mathematics. There are websites that offer teachers many lesson plans, however sometimes it is a kind of hard to determine the value of some lesson plans.

By reading this article, I found many websites that I think will be helpful for me and for my future students as well. I think it is a good idea to use some of these websites to help students understand mathematical concepts more because students currently engage better to the topic when they use technology. Also, students can have fun learning math by playing math game instead of playing any other game that is not useful.

Teaching Math Using Technology

Your midterm exam will be given in class on Tuesday, November 7. More details will be announced in class.

There are lots of ways to consume information about technology in the classroom. Later in the semester, you will be reading and presenting formal research papers in the field. For this homework exercise, you’ll perform a much less formal review. Submit your findings as a post here on the OpenLab.

Instructions

• Find an article or a blog post anywhere on the internet that discusses technology as a pedagogical tool.
• Before you write your review, include a link to that article/post as a comment on this post to claim it as yours. Make sure none of your classmates have already chosen the same article/post.
• Write a one- or two-paragraph summary of the article. (Write your summary so that when your classmates read it, they’ll know what the main points of the article are, and can decide whether they would like to read the article for themselves.)
• Write a one- or two-paragraph statement expressing your opinion about the points made in the article. (You don’t have to be super precise here; you can discuss the points in the article whether you agree or disagree with them based on how they relate to your own experience.)
• If the website where you found your article/post is not that of a well-known media organization, include one sentence about the kind of website it is. (For example, if you choose a blog post, the “About” section of the blog should tell you a bit about who the post author is.)
• Submit your review, along with a link to your article/post as an OpenLab post. Title your post ” Review of [title of the article/post you’ve chosen].”

How to choose an article/blog post

You have some flexibility in terms of what you choose to review, but there are some rules you must follow:

• Read a few different articles or blog posts before selecting one to review.
• The article/post you choose must express an opinion about technology in the classroom, report on an academic study about technology in the classroom or discuss specific strategies for using technology as a pedagogical tool.
• The article/post you choose should support its arguments with evidence.
• The article/post you choose cannot simply report on a type of technology being used, or how widespread its use is. It cannot be a “how-to” guide for using a particular technology yourself.
• The article/post you choose cannot be published by a company that is writing to promote its own product.
• The article/post you choose should be long enough that it is insightful in some way.  Your summary/opinion should tell us why it is insightful.
• The article/post you choose should be short enough that a fast reader could read it in under 15 minutes. (For example, you should not review a scholarly research article.)
• If you have an article/post in mind and aren’t sure whether it is appropriate, link to it in the comments on this post and explain why you’re unsure. Leave enough time before the deadline to choose something else if I determine it’s not appropriate.
• The article/post you choose should be written in English. If you find something that’s written in another language and that you’d really like to review, link to it in the comments on this post and explain why it appeals to you. Leave enough time before the deadline to choose something else if I determine it’s not appropriate.

Some resources

Note: some of these websites require a subscription to access articles, but will provide a selection for free to non-subscribers.

The Chronicle of Higher Education

Inside Higher Ed

New York Times Education Section

Los Angeles Times Education Setion

Washington Post Education Section

Slate

Math with Bad Drawings

dy/dan

Here are links to some of the Geogebra projects that last year’s students created. Take a look at these for inspiration!

• The Theorem of Menelaus by Jodel Delectable
• Ptolemy’s Theorem by Abdelmajid Ihda
• Morley Theorem by Gary Zhang
• Desargue’s Theorem by Armando Cosme
• Napolean’s Theorem by Josiel Nunez
• Simson’s Theorem by Mei Zhu

(pronounced LAY-teck) is a commonly used language for typesetting math. There are many ways to use to create professional looking documents (most involve installing an implementation on your computer) but you can also use  to type math right in your OpenLab posts.

Professor Reitz has some great instructions for using on the OpenLab here (scroll to “Typing math on the OpenLab”).

It can take some getting used to, your homework is to practice by submitting a comment on this post. Don’t worry about typing something that makes any mathematical sense, just try typing anything. Play around and make a giant mess in these comments. If something doesn’t work at first, don’t worry; just try again. (Note that your first OpenLab comment will have to be approved before it appears.)

You can mouse-over something to see what LaTeX code was. For example, mouse-over this: to see what I entered.

If you submit something that LaTeX doesn’t understand, it will display “formula does not parse” but you can also mouse-over that to see what was submitted.

Other resources:

• The Not So Short Introduction to 
• The Comprehensive  Symbol List
• A shorter symbol list
• Overleaf (writing full documents and collaborating online)
• The Project (an overview)

Chapter 0 of the Venema text has 11 short sections. Not all sections have exercises.

For Tuesday, read all 11 sections and complete all exercises in sections 0.3, 0.6, and 0.8 (8 questions total).

For each new geometric object introduced, try constructing the object in Geogebra. For each theorem stated, try performing a construction that illustrates the theorem when you apply the drag test.

NOTE: Since Tuesday follows a Thursday schedule, we’ll meet in G-208 (our usual Thursday room).

F-BF4

Inverse functions and their graphs

In this lesson, I want my students to explore the function and their inverse graphically. I am going to insert the function and its inverse in Desoms and I am going to insert x=y to help student to visualize the symmetry.

I will use 4 different pairs of functions and their inverse to make sure that students grasp the idea of function and their graphs.

then I will choose a random point from the function’s graph and show the student the inverse of that point and how that is connected to the inverse arithmetically.

The Transformation of the graph of quadratic function ax^(2) when a=1>0

In this lesson, i want to teach the transformation of quadratic function x^2 .I want to start the lesson by recalling quadratic equations, what is a quadratic equation, its standard form and when does a quadratic equation become a quadratic function. My goal for this lesson is to compare the original function y=x^2 with the graphs that we will get by shifting them horizontally and vertically , which at the end will make students to understand the point called vertex and the formula that helps to find a vertex. I also with use the blackboard plug values in the function, so I may ask students any question related to that.

Here is how the graphs on Desmos will look:

In this lesson I will  give Examples about the inequalities  making sure that my student knows the different between the symbol  >,< or bigger than or equal or less than or equal  ,I will make sure they will knows where they have to shade in order to find the solution , where up the line or down the line, the line should be solid or should be dash line , and of course I will make them under stand the graph it self and how they use desoms  in order to solve the inequality equation.