(Read the disclaimer at the end of the chapter)
Kwong’s Pride and Honor
Kwong, a grade 11 student, was sitting alone in the school cafeteria. One could easily tell from his face that he was angry, sad or perhaps both. When his girlfriend Jun saw that he was distraught, she joined him and started talking. She was almost sure that Kwong’s grief concerned what happened in Ms. Clementine’s class. Jun also knew about the high expectations of Kwong’s parents and how strict they were with him.
Ms. Clementine was a very good Math teacher who would retire in two years. She was also a disciplinarian. She hated it when a student did not respect her, or for that matter if they disrespected any other teacher. Many students were using smart phones in her class when she was talking to the class. She sternly told them to get the ear buds out of their ears, and she threatened to send them to the vice-principal if they used the phones in her class again. She also gave them a long lecture indicating the possibility that a prolonged use of phones decreases the ability of people to think. She went on to tell them that such an action could lower their academic performance. Even though she was talking to the whole class, Kwong thought she was addressing him alone.
Jun: Hi Kwong. Are you still thinking of Ms. Clementine?
Kwong: How could she? Why did she pick on me?
Jun: Don’t be so sensitive. She was talking to everyone, not just you. Don’t take it personally, Kwong.
Kwong: No, she picked on me. She could have easily sent me to the vice-principal’s office. If my mom finds out about it, I would be in trouble and could lose all my privileges.
Jun: So don’t tell your mom.
More students from the class gathered around Kwong and Jun.
A bystander student: Kwong, Ms. Clementine was mad at you today.
Jun to the bystander student: Go mind your own business. It’s not like you have the best reputation in the school. Just go.
Moving forward
Johnny: Kwong, I am sorry that we all sat there without challenging Ms. Clementine. She didn’t give us any evidence for what she said. We should have asked her for a proof. We all just sat there scared like a herd of dears in front of a lion.
Kwong: But why did she have to pick me? At least 15 students in the class were using smart phones with ear buds.
Jun: Johnny is right. We should have challenged her.
Kwong: She looked so angry. She would have sent me straight to the vice-principal’s office if I had raised any doubts about what she was saying. Yes, for sure (almost sobbing and incoherent due to anger).
Jun: So what are you going to do – moan for the rest of your life? My parents taught me to do whatever it takes to regain my honor.
Kwong: What do you mean by whatever it takes? What can I do?
Johnny: I have an idea. I don’t know if you are up to it.
Kwong: Johnny, you and your ideas! I don’t know about them (pause). What do you want to say this time?
Johnny: We could challenge Ms. Clementine without actually questioning her. We could say that we want to test the impact of smart phone use on academic performance.
Kwong: Johnny, you may have something. What do you have in mind?
The Science fair proposal
Johnny: We could tell her that we want to enter the Science Fair and we need her to guide us through it. The project would be “The Relationship Between Smart Phone Use And Academic Performance.”
Kwong: How will we do this project?
Johnny: You have many friends in class including Jun and me. We could do a survey.
Kwong was a little calmer by now and started playing around with his phone. Suddenly he had a Eureka moment and said: You know I can get my phone history on demand. I can check my total phone use between any two dates.
Johnny: That’s great. Anyone who has a smart phone should be able to find their total phone use in the month of the exams in the last semester.
Jun: Why don’t we divide up the class, find out who knows who, and then do the survey. I know a lot of students in the school in grade 11 – some who take higher math and others who don’t. We all have friends in the class. Can we do the survey?
Kwong: First, let me talk to Ms. Clementine.
Johnny: It’s a good idea. Otherwise she might get angry thinking that we are doing this behind her back just to show her up.
During his next free period, Kwong approached Ms. Clementine.
Kwong: Ms. Clementine. I am sorry for what happened in the class. We have decided to make up for it. Jun, Johnny and I will do a Science Fair Project to show you that we are serious students.
Ms. Clementine: The deadline for the registration and school presentation for the Science Fair projects is only a week away. How will you be ready? Have you done any experiments? Did you talk to any of your science teachers? I am not sure how I can help.
Kwong talked to the teacher
Kwong: Ms. Clementine. The project is “The Relationship Between Smart Phone Use And Academic Performance.” We will survey all the students of grade 11 in our school. There are many of us who together can do the survey fairly rapid. After the initial data collection, it will become an analysis problem, and we hope that you will guide us through it as a Math teacher.
Ms. Clementine had mixed feelings about it but she couldn’t refuse a student asking for help in Math. So she agreed.
Smart Phone Usage And Academic Performance: The Survey
Kwong got back to Jun and Johnny. They found that between them they knew everyone in grade 11. So they divided the work of talking to their friends. The students were told that this was an unofficial survey to help Kwong with the Science Fair, and that it had nothing to do with the school. Nobody’s name or any other identification would appear anywhere even in Kwong’s work. They were also told on how to get their own phone history data. As soon as they got the data, they would send it to Kwong’s phone as a text message along with their grade point average in that semester.
With the power of having good helpful friends and the smart phone technology, Kwong had the data from all 175 students within 48 hours. He sent the data to his laptop. Now the question was what to do with it. He converted the phone usage data to hours of phone use per day. He arranged the data with the increasing number of hours of phone usage per day. Then he graphed the data, transferred the graph onto his phone and arranged to meet with Jun and Johnny before school.
Kwong met Jun and Johnny in the cafeteria. Johnny and his girlfriend Sara used to walk to school together and so she also came. Sara told Kwong that she would go away if they minded her being there. Jun replied that they would be very happy for her to see what they were doing. Kwong also nodded in affirmation.
Kwong: I have made two graphs. First, I want to show you the one that I am excited about. See the graph for 35 students on my phone (Fig. 7.1). It shows that the grade point average improved of the students with their phone usage. So, Ms. Clementine was wrong (he said this with an air of smugness).
Jun: It will be great to do a Science Fair presentation. All the students will be excited.
Johnny: Yes, there is a definite correlation between the grade point average and the extent of phone usage.
Kwong: I forgot to tell you that one or two exceptional students, whose marks were very high, are not shown in the graph.
Sara: I guess one of them would be me but more interestingly, the graph is only for 35 students. Johnny, didn’t you say that Kwong had the data for all the 175 students?
Kwong: Yes, yes. I did tell you that I had two graphs. What if we did the Science Fair using only these 35?
Sara: Are these 35 taken at random?
Kwong: No. I arranged them according to the increasing phone usage. These are only the first 35 out of the 175.
Johnny: Show us the second graph. A report based only on the first 35 would be dishonest. It could get us kicked out of the competition and even from the school.
Jun: Kwong, Show us all the data.
Quadratic relationship
Kwong: Okay, here is the graph with all the 175 students – including the three outliers (Fig.7.2). This graph is not so exciting. It goes up a little bit and then down, down and down.
Johnny: Sara, now I see you there with the 98% average in the last semester. You are one of the outliers.
Sara was fidgeting with her phone and probably didn’t hear them but then she suddenly blurted: Kwong, you will have to analyze the data if you want to get on Ms. Clementine’s good side or do well in the Science Fair competition.
Kwong: What do you suggest?
Sara: These data could form some kind of a parabola. I am not sure, but it may fit into a quadratic relationship.
Kwong: What’s that?
Sara: In general, it is written as y = ax2 + bx + c. We haven’t done this in class as yet but I looked through our book in the holidays. When you showed us the graph, I did an Internet search using my phone. You can analyze the data online at this site. Do you have the raw data on your phone?
Kwong: No, but I have it on my laptop. How do we go about the analysis?
Sara: Here, let me try. Let’s remove the outliers, feed the data here onto this website and hit execute. Hey, it calculated it in less than a second. The data fit y = -2.4x2 + 9.6x + 76.8.
Kwong: Thanks Sara. May be you should be on our team for the Science Fair.
Sara: I have a lot work to finish. So, I am not sure.
Jun: You can be there as an advisor. We are going to need someone to answer all the tough questions too. So please, join us. Advise us and the three of us can do all the leg work.
Sara: I’ll think about it, but for now we have a class.
Kwong asked to talk to Ms. Clementine.
Kwong: Ms. Clementine, we have completed our survey and I have the data.
Class discussion of the data
Ms. Clementine: You said that it would involve analysis. So tell the whole class about your data. Maybe someone can help.
Kwong to the class: For a Science Fair project, we did a survey of the whole class. You know about it because all of you participated in it. The overall result is this graph of the relationship between the academic performance of students in the last semester and their smart phone usage in the month of the exams in that semester. You can see, the graph goes up, peaks and then comes down. Sara showed me a website that calculated the relationship. It fits the quadratic function y = -2.4x2 +9.6x + 76.8. Thank you all for your participation. That’s all we have for now.
Ms. Clementine: I think you should get Sara to participate in the Science Fair project. Will you do that Sara?
Sara: Yes, Ms. Clementine. They had already asked me. I was thinking about it. If you think that it would be good for us, I will be happy to work with the group.
The Science Fair Presentation
Kwong and the team prepared a poster for the Science Fair and the school approved it. Kwong showed the graph for the survey of the 175 students, the fit of the data into the equation y = -2.4x2 + 9.6x + 76.8, graph for the equation with the y = 0 points and also the co-ordinates of the vertex.
Here are the title and the abstract of the presentation.
“Smart Phone Use Increases Academic Performance.”
We surveyed 175 students of grade 11 in our school. We asked them the total time they used the smart phone in the month of the exams in the last semester and their grade point average that semester. The data fit a quadratic relationship y = -2.4x2 + 9.6x + 76.8. This shows that, on average, the academic performance increased when the phone use was up to 2 hours/day. The maximum average increase in the grades was almost 10%. However, excessive time spent on using the phone decreased the grades.
After the Science Fair, Kwong had this conversation with Ms. Clementine who asked him how the Science Fair went.
Kwong: Many students from different schools came to see our poster. The poster was very popular at the Science Fair and we won a prize too. The judges grilled us though. It’s a good thing that Sara was there to answer questions. Otherwise, we would have crumbled.
Judges’ questions
Ms. Clementine: I am sure the judges were fair and doing their job. What were some of the questions?
Kwong: Some of the questions were:
You get both an increase and a decrease in grades with the cell phone use. Why do you focus only on the increase? Isn’t it misleading?
Your data are only for one month – the month of the exams. Doesn’t your school also use grades for your assignments and midterm tests throughout the semester?
You have shown that there is an association between grades and cell phone usage. What is the logical explanation?
Your title is Smart Phone Use Increases Academic Performance. Is an association between the grades and the cell phone use really a proof of causation or is it just a coincidence? What experiments need to be done to prove that the concept in your title is a valid one?
If the experiments you want to carry out are not allowed due to ethical reasons, how would you go about testing the validity of your concept?
Do you think that the vertex of 2 hours is applicable to every student individually?
How did you determine the outliers? How do you explain them?
You indicated that you tried a quadratic fit because the graph looked curved. Did you see if the data would give a better fit using a cubic or a higher power polynomial?
Ms. Clementine: That’s good. That means they showed interest in you and prepared you for the future.
Disclaimer
No-one should use the data here as a guide for the appropriate time for phone use. This is a fictional story. The data were made up as were all the characters. The data were created solely to explain the concepts of quadratic equations. The values of y were generated using the equation -2.4x2 + 9.6x + 76.8 and then adding random numbers between -5 and 5 to each data point.
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