Fall 2016 - Professor Kate Poirier

Category: Projects (Page 1 of 4)

How can computer-based learning help students learn fractions? [Mei] [Admajid]

  • Title: Conditions for Effective Use of Interactive On-line Learning Objectives: The case of a fraction computer-based learning sequence

Authors: Catherince D. Bruce & John Ross

Journal: The Electronic Journal of Mathematics and Technology

Year of publication: 2006

  • This paper focuses on the challenges of students’ understanding about fractions from students’ perspectives and teachers’ perspective. Not using factions daily is one of the factors that makes it difficult to embed the significance of learning fractions as part of students’ life. The success of supporting students’ understanding lies on the design of instructions. The traditional teaching methods lack the emphasis at students’ conceptual understanding with little connections to students’ existing knowledge. However, technology-assisted learning is introduced as a successful model in enhancing students’ understanding with challenging math concepts.

The paper takes a main point on a computer-based learning package named CLIPS-Critical Learning Instructional Paths Supports. The package consists of its own characteristics and learning tasks for students. Even though students make meaningful progress in understanding of fractions under CLIPS, there are limitations and exceptions that students would not benefit from the program. Through case studies, the paper concludes the importance of building the direct relationships between online learning tasks and in-class learning tasks. The necessity of having in-class activities that are within students’ zone of proximal development. The full participation or involvement in the CLIPS will make a difference, and the pair work between students will support each other in completing the CLIPS tasks. Last but not the least, since the CLIPS program is computer-based learning, students can keep their own pace and go back for checking their work. The educators believe that students go with the sequence order to understand the content better than those who were absent and chose the tasks randomly.

  • Why do you think learning fractions is challenging for middle grades students in your own opinion?

First of all, there are different ways to represent fractions: division sign, colon, and fraction bar. Fractions are divided into proper fraction, improper fraction, and mixed fractions. They will have questions involving mixed fractions, but what they need to do first it to convert them to improper fractions to make computation easier. If a teacher cannot make his or her students understand the meaning of proportionality, it is going to be extremely hard for students to complete a task associated with fractions or understanding the significance behind ratio. From the reading, I learned that a computer-based learning might be a possible way to assist students to have a better understanding of something that was not clear to them through vivid images and audio. At the same time, there are challenges to implement technology in a classroom. The learning objectives from the sites should be correlated to the lesson itself. Schools need financial support to provide students’ access to computers. There are also technical issues along with computers that might happen in the classroom, which will make it unsuccessful for students to keep a consistent attention during the tasks. In conclusion, I agree that students need some technology in their learning if students can use it wisely with their goals of learning in mind.

When students are learning fractions, they will be able to understand what a ratio is. How to complete a ratio table is considered one of the basic and important tasks for students when they learn fractions from my observation experience. Thus, there are a lot of definitions that students need to know in order to understand fractions.

Without access to the reading, I learned that students struggle to factions because they are familiar with whole numbers. They are good at simple operations with these numbers, but students will have difficulty with whole numbers with different signs. They are likely to make conceptual errors when they subtract negative whole numbers. It is going to be a higher level when students learn fractions.

  • What are the strategies that you think can help students build a good habit of using internet?

What are possible ways that we can negotiate with students’ parents’ involvement with students’ online assignments at home? (like sit there with the students for half-hour)

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

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

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.

  1. 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.)
  2. Set up your ePortfolio site with information about you as a Math Education student.
  3. 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

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


  1. 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.
  2. 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.
  3. 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.
  4. 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


  • 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.

Project#3 Maple on Trigonometric Functions

In this presentation, my audience will be my classmates who took the mid-term exam. I am sure that all of us took it and my topic is how to use Maple to graph trigonometric functions with various amplitude, period, phase shift, and vertical shift. Also, how can we graph them in the same x-y coordinate.

I assume that my audience still remembered how they used sliders in Desmo activity to change the features of a trigonometric function. My content will be using a different software to solve a same problem. So, after this class, I believe my classmates will have some insights for further tasks associated to Maple. Maple is an appropriate tool for this activity because it might be new to some of us and using it show something we learned is a good practice.

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

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:

  1. 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?
  2. 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.


  • 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

Simson’s Theorem [Zhu, Mei]

“Simson’s Theorem: A line that contains the feet of three perpendiculars from a point P to the triangle ABC is called a Simson line for triangle ABC. The point P is the pole of the Simson line.” In other words, given a triangle, a point P outside of the triangle, we will be able to construct the perpendiculars from the point P to the sides of the triangle. The feet of the perpendiculars will lie on a line, which we call it Simson line.

Hi, everyone, I hope my worksheet will help you understand the theorem. To be honest to all of you, the actual work  took for me to finish this was not easy. I almost lost all my work when I tried to make some changes of the wording. I even tried to reproduce the worksheet online, but the internet was off when I tried to save. Fortunately, I finished it. Please find the link below and give me some suggestions on this. Thank you very much for your attention. :)))


Project #2: Rubric and feedback form and HW#9

On Thursday, we’ll begin going through everyone’s dynamic worksheets. Once again, you’ll submit scores and feedback for your classmates’ work. We’ll refer to the same rubric as we did for Project #1 (though keep in mind that “presentation” means something slightly different now than it did for that project). The feedback form has been modified slightly, so make sure to read the descriptors for each category.

It will take around 10 minutes to review each project, so we will not finish during Thursday’s class. Homework #9 is to finish submitting feedback for all the projects. Your forms must be submitted by 11:59pm on Monday, October 31 (this is instead of the usual Tuesday deadline, so that I can compile responses so we can discuss them during Tuesday’s class).

GeoGebra construction steps slideshow

Recall our sample GeoGebra dynamic worksheet on Ceva’s Theorem. When you open the worksheet, it automatically takes you to slide 25/25 in the slideshow, but you can jump to slide 1 and scroll through them one by one. What you’re seeing is actually the construction of a single dynamic worksheet, one object at a time. (In this case, I think it is extremely helpful to see the dynamic worksheet built up like this, rather than just seeing the end result.)

If you’d like to add this feature to your own dynamic worksheet, all you have to do is turn on the Navigation Bar for Construction Steps.

In the desktop app:

  1. Click on the View menu
  2. Select Layout
  3. Select Preferences – Graphics from the top of the window (the icon is the overlapping green circle and blue triangle)
  4. Under Navigation Bar for Construction Steps, select Show (you can include the play button too if you’d like to automate the slideshow)

Then, when you upload your GeoGebra applet to the online GeoGeobra worksheet that you’re constructing, the navigation bar will appear as it does in the Ceva sample linked above.

I hope this helps with your GeoGebra projects. I can’t wait to see them!

Project #2 – GeoGebra Dynamic Worksheet – due Thursday, October 27

Due date: Thursday, October 27, 2:30pm

Individual are assigned below. You may trade topics with a classmate if you wish.

Your assignment is to include the following two items in an OpenLab post:

  1. The statement of the theorem/result that you have been assigned, written in LaTeX, in the body of the post. You may copy this statement word-for-word from the text, or paraphrase it. Either way, it must be complete and precise.
  2. A link to a GeoGebra dynamic worksheet (uploaded to GeoGebra Tube) that helps students understand the statement in your post. The dynamic worksheet should be completely self contained. Think of the worksheet as playing the following role: You are teaching a geometry course and will be absent for one class. The lesson for that day is the topic you have been assigned for this project. The substitute teacher assigned to cover your class does not have a background in geometry, so your students will have to learn the topic exclusively from your dynamic worksheet. Your worksheet must take advantage of the benefits GeoGebra has over traditional paper worksheets (for example, you can make use of the drag test).

You may also include extra details either in the body of your post or in the dynamic worksheet, if you think they will be helpful. For example, you may include hints for the proof of your statement (why is the statement true?) or you may include helpful applications. These are optional and should only be included if they help students understand the statement.

Add the category “Project #2: GeoGebra Dynamic Worksheet” to your post.

There are many resources available online for help creating dynamic worksheets. Here’s one. Read Chapter 3 of the Venema text for other helpful tips. As a sample, here is the dynamic worksheet on Ceva’s theorem that we explored in class.

Once again, your classmates will be asked to score your worksheet and offer detailed feedback. This will be similar to the rubric and feedback form for the Desmos mini-project. Details will be announced later.

Topic assignments:

  • JODEL: The theorem of Menelaus (Venema Chapter 9)
  • MEI: Simpson’s theorem (Venema 11.6)
  • MAJID: Ptolemy’s theorem (Venema 11.7)
  • JOSIEL: Napoleon’s theorem and the Napoleon point (Venema 12.1)
  • GARY: Morley’s theorem (Venema 12.6)
  • SONAM: Circumscribed circle and circumcenter (Venema 4.1)
  • EVE: Extended law of sines (Venema 4.1)
  • TYNIQUA: Angle bisector concurrence theorem (Venema 4.2)
  • LUIS: The medial triangle (Venema Exercises 5.1.1 to 5.1.4)
  • ARMANDO: Desargue’s theorem (Venema 11.2)




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