Author: Kate Poirier (Page 2 of 6)

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.

Rubric and feedback form links for Maple project

November 29, 2016 / Kate Poirier / 0 Comments

Rubric

Feedback form

HW #11 — WeBWorK — due Thursday, December 1

November 23, 2016 / Kate Poirier / 2 Comments

Homework #11 has three parts:

Here is the paper version of the problem set. Print it out and show all your work in the space provided for each question.
Here is the link for the WeBWorK version of the problem set. Enter your answers in the space provided before 2:30pm.
Here is link for the short questionnaire for you to complete after you complete the problem set. Read the questionnaire before starting the problem set.

Your username and password for WeBWorK are your last name with the first letter capitalized. Usernames and passwords are case sensitive. (If your last name has a hyphen, delete it to form your username and password.) Let me know if you have trouble accessing your account.

The questions on the paper version and WeBWorK version are identical. The whole assignment should take you under an hour to complete. You can complete all questions using material that you learned in Calculus I (MAT 1475) or below. (No MAT 1575 material is required). Everyone who demonstrates a clear and honest effort for all questions will receive full credit for this assignment. You must work independently on this assignment. Calculators/aids are not permitted. You may use the internet only to access WeBWorK.

Why are we doing this?

WeBWorK can be used effectively as an instructional tool in many different ways. As a teacher, creating sets from existing problems is straightforward, and there is a large library of existing problems to choose from. However, creating new problems is less straightforward (uses the Perl programming language and LaTeX). You should be aware of how this tool works, at least from the student side, in case you want to use it in the future. If you would like to create your own WeBWorK set to use as part of your final project, let me know and I’ll create a teacher account for you.
By completing this particular assignment, you’ll be helping me collect data for one of my responsibilities at CityTech outside of MEDU 2010. Thanks! 🙂

Desmos Activity Builder

November 17, 2016 / Kate Poirier / 1 Comment

If anyone is interested in using the Desmos Activity Builder for their final project, log into teacher.desmos.com with your Desmos account. It’s pretty straightforward to start building activities. Let me know if you have any questions.

On the midterm, you experienced the Desmos Activities from the student side; I created the activity using the Activity Builder on the teacher side.

Project #3: Maple Anything – due Tuesday, November 29

November 17, 2016 / Kate Poirier / 0 Comments

We’ve already discussed guidelines for your Maple project. They are collected here and will be updated should the need arise.

You have complete freedom with respect to mathematical content. You have almost complete freedom with respect to your use of the tool; your project is to use the tool to help your audience understand the mathematical content and must satisfy the following two conditions:

It must demonstrate knowledge and/or skills in the software itself. (For example, it must use both the computation and typesetting features, not just one or the other.) Why are you using this tool instead of another one?
It must use Maple in a “pedagogical” way. How does your use of the tool help your audience understand the mathematical content?

The project itself consists of three components:

Your Maple file(s)
- Optional: other documents you use for your project (for example, PowerPoint slides)
A written description of what your project is all about:
- Who is your audience?
- What knowledge are you assuming your audience knows?
- How is the content delivered?
- Why is Maple an appropriate tool for this content and this delivery?
A 5-minute presentation explaining what your project is about; include your Maple file(s) and/or screenshots of them.

Your Maple files will be collected over email and/or via USB stick in class. Your written description is to be submitted on the OpenLab (don’t forget to add the category “Project#3: Maple Anything” to your post). Your presentation will be given in class and will be scored by your peers according to our standard rubric and form.

Ideas:

lesson (like Project #1)
In-class activity (like Project #2)
Homework assignment
In-class assessment
Something completely outside the traditional school/classroom model (see, for example, the project described in the TED talk video from Homework #10)

Due date: Tuesday, November 29

Maple tutorial

November 14, 2016 / Kate Poirier / 0 Comments

There are different Maple tutorials available around the web, both for beginners and for advanced users. Of the tutorials I found, I thought Maple’s own was the clearest and easiest to use.