Fall 2016 - Professor Kate Poirier

Author: Mei Zhu

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)

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.

We need technology so as teachers [Zhu, Mei]

The article and the Ted Talk are new and fresh to me. At the beginning of the reading, I felt a little depressed and worry that in the future the role of teachers will be questioned and eliminated by people all over the world. For me as a future Mathematics teacher, I could not stop thinking if this became real, how I am going to face it and make a decision. However, if I were ten years old right now, I may change my dream to be another profession instead of teaching. Too late I am not a teenager anymore, and I could see myself changed through schooling. People are humans with brains to think and reasoning, with nose to smell, with eyes to see, with ears to hear, with mouth to talk, and with our hands to work. If students learn things at home alone or as a group in a room in front of the big screen, how long are these students’ interest of learning going to last? In the video, we can see that students feel excited and read after the “teacher” in the screen asked them to do so. I believe this is going to be a good success for very poor countryside that people cannot afford technology like smart phones or TVs. When a thing that can talk and even responds their questions, students will feel excited and wish that they could see the “robot” every day.

I still remembered the first time I saw and touched computers in my elementary school in China. We had to share computers with each other. I was scared to touch it because I was afraid that I would break it if I did not use it properly. I just sat there and watched my peers surfing. Even though I learned how to use computer in my junior and high school life, I did not learn actual computer skills until I came to college. I bought my first laptop when I was enrolled in BMCC because my friends all have one. I used it to translate, to search articles, and to watch some YouTube videos for learning purposes or entertainment. Technology helps us many things, but it cannot be a substitute of education. Instead, we should use it as a tool to checking our learning.

I met a girl from Hunter who never got her K-12 education in school. She had home schooling and passed the GED test. After that, she finished her Bachelor degree and also her Master in Hunter. I intended to ask her some questions and her opinions when I got this reading assignment. Even though she was a home schooling with no teachers in her teenage life, she also disagrees with the idea that technology can take the place of teachers. She told me that she was not able to do some chemistry experiments in her kitchen although she got the materials and watched videos. Also, she told me that she felt a little afraid when she entered college because she never learned how to get along and socialize with other people. She loved reading and writing, but she hates Mathematics and gives up easily when she could not solve the problem and returned to reading. From her experience, I learned that even though children can learn by self-organization, but there are some limitations that can be solved in school. For example, when a student is doing an experiment at home with instructions from the video, it is hard to prevent dangerous incidents happening if there is no instructor around.

I agree with the idea that teachers are sometimes act as a facilitator, but it is not always the case. There are so many roles that a teacher has and so many duties they need to handle. In a class, we are not just learning content knowledge but also learn how to get along well with others. We also have some activities that are not curriculum relevant. The host takes the fact that Mathematics is universal around the world, but he ignores the important part of reasoning. Even though some students know how to do the operations of Mathematics, many of them do not know how to express their opinions. They need the communications and practices with people not just staying for hours in front of a big screen. Every piece of learning needs connections. If a subject is unrelated to students’ life, students will get bored easily. Also, we learn and understand things differently. We also learn from our mistakes and the people around us. Assuming that everybody studies at home, how they are going to communicate with others and express with thoughts. Teachers not only taught us knowledge but also taught us living skills. I learned how to control myself when I was depressed, I learned how to manage my time, and I learned how to be a responsible person. There are so many things that we learned from teachers, our peers, and ourselves. Without formal education, we may not be able to define these behind every school day.

Also, in real life, it is kind of impossible to have children like in the video that they enjoyed reading with a teacher in the screen unless they feel it interesting and important. For example, I will follow after the instructor read like the one in the video because I know I need to improve my English speaking skills. Look around us, how many children know how to play Ipads and some parents feel very proud of them. They think their kids are smarter than them because in such an early age, they already commanded the skills of technology. They never think about the negative impact, even they realize it they will have nothing to do with it because it is too late. I saw my 3-year-old nephew playing his Ipad on the floor. He talked to himself and followed the behaviors inside the video with no concern that I am around. He will get mad when I chose a channel for him. We can predict that, if students self-learning at home, who is going to be the one to assist if their parents both work.

In conclusion, we need teachers and we also need technology. As teachers, we should learn corresponding technology skills to better equip ourselves. For instance, as a Mathematics teacher, he or she should be able to teach students how to use some math software to learn something outside of school. Teachers should be able to make students believe that computers are not only for entertainment but also a good place to learn and explore more things.


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. :)))



HW#3: Review of [How Does Technology Influences Student Learning][Zhu, Mei]

The implementation of technology in the classroom has a positive effect in students’ learning process and outcomes. This paper claims that explicit learning standards and objectives support the effectiveness of technology greatly. Taking advantage of technology in the school work, students will be able to apply content knowledge to real-world situations and be more interested in the text. Also, the paper addresses the involvement of technology develops students’ higher-order thinking skills by utilizing technology as a tool to present their works with a full picture with events. Lastly, the paper discusses the advantage of technology in preparing students for the workforce by enriching the experience of communicating ideas and information.

I agree with the statement that the combination of technology and learning standards will strengthen students’ understanding of the content. From elementary to high school, the most advanced technology is calculator. When I entered college, I learned more software to learn Mathematics. I learned how to use Maple during my first semester in college for calculus class. I found it very useful to plot complicated graphs, to calculate integrals and derivatives of a function, and to make a conclusion based on the results. Gradually, I started learning Geogebra for my Geometry and Modern Algebra projects. Using technology as a tool helped me understand the concepts better and saved me a lot of time in drawing pictures with measurement. Recently, I do not have any experience of applying technology in real-world situations; however, I believe that people do use technology to solve life problems. Except social interactions with the social media, people can use computer to make a model and to test outcomes. I learned to use R to make a random walk model by assigning different variables in a research. I guess that it may be the starting point of applying technology into real life.

I am definitely with the last point that technology brings work opportunities. For example, we can write the software we are expert in onto our resumes. As future teachers, learning to use more software and being able to convert among them will help me to become a more flexible teacher. Students might get bored with paper worksheets, so teaching students to use technology to study and have fun might be a good approach to raise students’ interest in learning.


Project#1 – [Transformations of a polygon in a 2 – coordinate plane]

In this lesson, I am going to introduce the three basic transformations of a polygon in a 2 – coordinate plane using Desmos as a tool to present the work. I used Desmos to create polygons starting with creating points. Typically, I worked on basic transformations of a triangle: translation, reflection, and rotation. I used the table to create the points of a triangle. Also, I changed the point style to segment style so I can have the sides of a triangle. Then, I will use two main methods to do these transformations either by moving the points or writing out the coordinates of each point.

This is the Desmo link:




Yet, the summer ended. We are back in class, and my head and mind reset in motion and gear up to get in motion. I still have so many things to learn to improve myself to be a well- prepared person with critical thinking about teaching.

I come from China. Chinese is first my language, and I also speak some proper Spanish. I was grown up in a small town, and my family lived in a small place in a small town. Life was hard; public education was not accessible for every children because the cost was too high. Especially, my family, me and my two sisters, it was very difficult to pay for the tuition and all expense. My parents had to work very hard to support us to stay in school.

Now in America, as an immigrant, language was my first priority problem when I came here. English was difficult for me to transfer my thoughts clearly as I wanted to. After ten days’ going back and forth to the Department of Education and high school, I began my first day in American high school. Fort Hamilton High School – the most beautiful and advanced one that I had never seen in my hometown. I was excited about everything surround me especially the people who speak American English. The supervisor of the Language Department arranged me in an ESL class. I felt comfortable when I saw Chinese in the class.

When I was little girl, I used to dreamed to be a police woman many times, also a supermarket owner, a lawyer, etc. As time passed by, when my headmaster in high school asked me what I want to be in the future, I answered that I wanted to be a dedicated person that can contribute to the society. Gradually, I found the dream being a police woman fades out. And the dream to be a teacher is taking place.

I chose to be Mathematics teaching because I realized that learning Mathematics can be productive if we learn by hands-on approaches with open minds. It is not about reading and doing homework assignments, which is not enough for learning Mathematics.

I love the MEDU 1021 class very much. Before I entered this class, I did not know that teaching has so much fun by hands-on activities. That was a Mathematics class but more about how to teach and learn mathematics by working together. We worked on the problems in groups and then shared with the whole class; we learned by group discussions. We listened and gave feedback to other peers; we learned by critical listening and thinking. We presented our topics and responses to “students”; we learned by actual practice ourselves as future teachers. In this class, each of us learned at the same pace because the content knowledge is within our pre-knowledge. We learned more from ourselves as we made progress. The least I love about Mathematics is rote memorization of formulas because I think that is the most difficult part for me to learn something new.

I learned Maple to compute and graph in Borough of Manhattan Community College. Also, I learned some basic coding in R in the summer’s Mathematics research from Prof. Bessonov. In this class, I want to learn some software that are being widely used in secondly schools. I have seen a teacher in City Poly High School who used her cell phone to scan students’ answers and presented the bar chart in the class. I believe that must be a new program because my teachers from high school never taught class that way.

In CityTech I have learned many requirements and internships which will help me to succeed my dream of teaching profession, and school has opened many doors to many programs such as Peer leading, Noyce, CSTEP, PERC, I will need the school to assist me in my future plan that I wish to be a teacher after graduated from here. At the same time I will continue to pursue my Master degree in teaching. I will need a lot of help and guidance here in CityTech. Shortly, I want to pass the required certificate tests before completing my Bachelor’s degree. Besides learning, I also love swimming even though I just learned how to swim this summer. I found it very interesting and healthy.