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LESSON 6: Conducting Mini Surveys (Days 9-14)
DAYS 9-11 (2/27-3/3) Conducting mini-surveys
We started class by going over the homework (Appendix H). Most of the students were able to identify situations that were experimental or theoretical. The thumbtack worksheet presented a bit more problems. First, students didn't realize that they should be using the table to predict what would happen in 50 and 100 trials. Thus many students concluded that the tack has a 50/50 chance of landing on its side vs. top. Of course, on the last question of the homework students argued that there is a possibility of finding the theoretical value for the thumbtack. However, they did mention that they may need an expert in thumbtack dynamics to be able to calculate the chances of it occurring without testing it. This reiterated to them the importance of realizing that a theoretical value has already been proven, in some cases without being tested. Rather, by analyzing all the possible outcomes. The thumbtack discussion lead us into taking a closure look at experimental probabilities.
Teacher: I know that you guys have mentioned many times before that an experimental probability, with further testing, can get us into a theoretical probability. We know this is indeed true from the thousands of research project that are carried out every day in hopes of reaching a theory. Even with this thumbtack discussion, you guys believe that nothing is exactly impossible-and that there could be a way of finding the theoretical value. Moreover, we know that experiments can help us make predictions. So like if you experimented with this thumbtack, you may be able to predict the next outcome. Have you guys ever conducted an experiment before? Or collected data? Most of the students have collected data in their sciences class. Teacher: Okay, do you guys think data is valuable in conducting an experiment? Class of course confirms this question. Teacher: Well, than what is the data used for? Justin: To find if what ever you are testing is true. Matt: Or like you have to gather data to explore something-like when we write papers. Teacher: Nice example Matt. Have you guys ever done surveys or been in one? Brian: Sometimes in the mall they stop you and ask you questions. Ame: Have you guys ever been stop to watch a preview for a new movie-my parents once did. Teacher: I did that once too. Then they make you fill out the survey! Why do you think surveys are performed? Morgan: To find out like what's your favorite movie. Teacher: They definitely have a goal. Some surveys measure the populations' opinion on certain topics-for example politics. Let me ask you a question. Do you think that these surveys and opinion polls arrive at a theoretical or experimental probability? Class: "experimental" Teacher: How come? Kacy: Well, its like they are measuring peoples opinion and stuff like that-so there is not one definite outcome. Teacher: I agree. Christian: Okay, its like we are conducting an experiment or a survey so obviously that will only get us an experimental value. Teacher: Oh, what was I thinking to ask that question (class laughs)! Of course you guys know this already. Great than, if we know that surveys, opinion polls and even scientific research is based on carrying out experiments or tests and collecting data-what will it help us do in the long run? Class: "we will know what will happen", "we will know what the general trend is". Teacher: So what if it will help us know this? Brian: Than you will know what happens in general or even what will happen in the future. Like before the election, the opinion polls already told us who is going to win. Teacher: Nice job Brian-these surveys and research will allow us to predict what may happen. Like suppose I wanted to know what CD's 8th graders listened to. What would I need to do to conduct this survey? (At this point I write the topic on poster paper, and begin writing what the students offer). Morgan: You'll need to break it up into music groups-cause there's like a million CD's 8th graders listen. Teacher: I agree-okay so let's offer some music groups-now what? Kacy: Go out and ask 8th graders. Teacher: okay-how many? Brian: well, probably the whole class-cause that's 100 people and than you could speak for the entire 8th grade. Christian: No, If you asked 50 that's pretty good. Teacher: okay both of you have some good points-will your results vary depending on the # of people you ask? Class in general agreed that the number is important. Teacher: Okay so suppose I asked 50 people and a got all the results, now what? Class: "get the percent of each music group", "ratio". Teacher: Right, so we need to compile our results into fractions or ratios so that we can form a conclusion of what percent likes what. How would you present your data? Class: "Bar Graphs", "graphs", "charts", "list". Teacher: Okay, wow, you guys are like almost experts with this stuff. I just have one more question for you? Has anyone heard of the term bias before? Most of the students have heard the word used. However, they had a tough time trying to explain what is meant. Many of the students used the phrase "the results were swayed or unfair". Lina; Well, let's say I had someone who decided to ask people whether they preferred to bungee jump or water-ski. Do you see a problem with that question? Class thinks for a moment but doesn't come up with much. Teacher: How many people here have bungee jumped? (0 students), How many water ski (4 students). Mmm. Well, guys what's the problem with this question. Matt: Oh, not everyone has tried both. Teacher: Good, so how does that effect the question? Brian: You are like asking them to make a choice-but probably most people will lie and say they have done both. Teacher: True, or you could be forcing the question. People will have to say one or the other even if they haven't tried either of them. Do you think you'll get trust worthy data? Class: "no" Teacher: So in a way the question was biased or swayed to force people to picking one or the other. How could we change this question to eliminate the bias? Morgan: You can ask two questions. Like how many people water ski before and how many bungee jumped. Matt: yeh, but than you don't know which one they prefer. Teacher: Good point Matt, it's like you changed the question Morgan-but you could do that if you wanted to know how many 8th graders have done those things. Anybody else? Brian: You can put another option that says-I can't answer the question. Teacher: That's one way. Anybody else? Christian: You can put a choice that says "neither" because maybe there are people who did do both and hate it. Teacher: Very good, I didn't think of that one. Thanks. Ame: Actually you could put an option that says that you haven't tried either of them. Teacher: Another good suggestion. You guys got the hang of it. Suppose I took this question and went to survey the elderly community. What do you think of that? Are my results going to be telling the truth? Class: "no way", "old people haven't done that stuff", "actually they may only have water ski-but I don't know if they would remember that". Teacher: So than you're saying that the elderly population wouldn't be telling me what most people prefer. Good. See who you survey is also very important. If you only surveyed 8th graders-your results would change as well. So we need to be thinking about how we can make our question fair as well as how many and who do I survey. Now having said this, I think you guys are ready to do your own survey. I want you guys to have an opportunity to collect your own data and arrive at your very own experimental probability! You can't ask for a better assignment. |
I passed out the Data Collection Worksheet (Appendix I) to start the students off with what the assignment would be for the next few days. I explained to them that they could get into groups of 2-3 and come up with a question they wanted to explore. I wanted them to feel free to do whatever they were interested in. Moreover, I wasn't giving them guidelines as to how many people they should survey nor how to phrase their question. I felt that through their own investigation they will arrive at their own methods and conclusions. The discussion above, gave me more than enough proof that the students did not need their hands to be held. Moreover, this discussion acted like a model of things that they should think about when they proceed with this assignment. The whole point of this section is for students to be able to apply what they know.
The first part of this exploration, I wanted the students to only survey their math classmates. This would allow them a chance to test out their question as well as compare their predictions.
Appendix J was given to students on the second day of this assignment, 2/28. Since, I was going to give them time in class to work on their survey and compile their results, I wanted them to stay on task. App. J was to be turned in at the end of class.
Appendix K is the survey presentation requirements. This was given to them on the second day as well. It outlines the presentation expectations as well as the grading system. Students used this sheet as a check list. They needed to be prepared to answer each of the topics listed on the sheet.
The students really enjoyed doing this assignment. Topics that students chose include things like: sports, colors, actors/actresses, movies, soda, fast food restaurants and of course, music. Many students chose a number of athletes to use in their question for sports. For example who is the better player: Rodman, Jordan, or Grant? Many students asked if they could survey teachers. Because this was a substantial question I left it up to them-but I also reminded them to prepare to talk about it. What was most interesting to watch is that after practicing their survey question on their math class, many students revisited their question to rephrase or even take away or ad more choices. In other words they were critically thinking about what they were asking. By the third day, students began to realize that only surveying their friends wasn't going to give them a representative sample. Students would comment: "your friends are like you, so we have to get more people".
During the class presentations, the students had some amazing posters and well thought out explanations. In fact, they are still hanging up in the classroom. The students wanted them to take home, so my cooperating teacher and I decided that it would be best to leave them at the school. As you can see the students were proud of their work. Each presentation was interactive amongst the presenters, the class, and myself. Everyone was expected to participate and most everyone did. By the 2nd day of presentations, the students were assuming the role of the teacher in asking questions to the presenters.
DAYS 12-14 (3/4 - 3/7) Survey presentations
The following are some excerpts of what took place during the presentation:
Which brand of shoe do you like the best? Nike, Reebok or Adidas?
This particular group, knew that their question was forced in the sense that they did question how many people really have tried all the brands.
Charlie: We decided to limit our question to these 3 top brands b/c if we didn't we would have too much data to deal with and most likely people would fall into one of these 3 categories anyway. Teacher: Good point Charlie. Let's try to talk about these brands from a marketing view point. Why do you think people choose these shoes? Larry: Well, when we asked people what brand they prefer, I don't think they were necessarily talking about a comfort level. Charlie: yeh, like these brands are influenced by famous people. Miken: Not everyone has tried each shoe to compare. Teacher: I agree, I chose Reeboks only because I own a pair. |
What is your favorite subject in school?
Matt: I had students choose from Math, Social Studies, English, Science, Gym and Foreign Language. Classmate: Why didn't you put lunch? Matt: Because everyone would pick it and that's not really an academic subject. Teacher: Did students tell you why they picked the subjects they chose. Or better yet, what do you mean by favorite subject. Matt: My interpretation is that it is a subject that you do well in and enjoy. I think that's why lots of people chose Gym. But I also think that your favorite teacher will make you choose your favorite subject. I could see where the word "favorite" is maybe too broad-yet I look at the results and it seems to confirm what I thought most students would do. |
Which artist do you like best in the rap group Wu-Tang?
Teacher: Do you think there are any biases in your question? Rich: Yeh, we know that some people don't know who the group is. Tom: Also, when we surveyed people, they were just picking one of the choices-and we knew they really didn't care or have a preference. But if we did this survey in like New York City with a bigger population -more people will know the band-we'd get better results. Teacher: What would you guys do different next time? Rich: I think we'd have people listen to the music, so that they can become familiar with it. Plus, we would first ask people if they knew the group or not and if they didn't than we'd move to the next person. |
What's your favorite sport?
Dave: We think that one of the big problems with this question is that it varies within the seasons. Rob: Ms. Maine you know how you asked us to do our math class first-well that's only 18 people. I put the math class in a pie chart and than I took the 50 people we did and put them in a pie chart-and look at the difference. I can see how the more people you have the better numbers you get. Teacher: Very nice analysis Robbie. By any chance did you find that taller people were choosing basketball? Dave: Well, it's tough to say, I mean what is tall to me, may not be tall to Robbie. Kyle: Wait look at some of the NBA players. The point guards are short. Teacher: Wait a minute Kyle, if we are talking NBA-I think the majority of the players are "tall". Dave: yeh she's right. But still in our survey I don't think I could see that relationship-maybe if I went to the high school it might happen-those guys are taller. |
Needless to say the students really came up with some intuitive thoughts and ideas. One of my students drew 4 pie charts on what is your favorite sport. The charts comprised of what 25 adults said, what his math class said, what 60 8th graders said, and the last one put all the population together. His charts gave us a great look at what happens to results when the sample is varied. Another group ended up distributing their survey question at the mall to get a random sample! I think one of the most impressive points in this whole survey section is that the students really took ownership of their own learning. They only asked questions to verify their thoughts. I'd say that my assistance ended up to be more support than anything else. The students had displayed some critical thinking with their questions and how it fits into the bigger picture of trying to predict what the general population will say.
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LESSON 7: Article research and commercial analysis (Day 15)
DAY 15 (3/7) Article analysis
By the last survey presentation, the students had a solid understanding of what they have been exploring. Thus, rather than beating a dead horse and taking away the excitement of what they had mastered, I decided to close this section up by taking a look at some articles and consumer advertisements. Appendix L was passed out and my intention was to pick and choose some articles or excerpts to analyze as a group. I had students read the articles aloud in class. At some points I'd ask students to stop reading, so that we can interpret some lines that may be a little more difficult to understand.
The following are a few articles that were discussed:
Teacher: How could it be that Ann Landers comes out with a poll that says 70% will not have children, while the national poll comes out with 91% will have children? Mike: First of all the national survey has to have more people in it. Teacher: yeh, but my gosh, how many more people to get the complete opposite result? Brian: Well, how many people can respond to this anyway. It depends on how many people got the article in the first place. Teacher: now you are on to something Brian. How did Ann get people to respond to this article? Jessica: Well, she just put it in her column and whoever wants to respond will do it. Teacher: Jessica is about ready to nail it!-Can you give me a little more. What kind of people responded? Jessica: People who hate their kids. Ben: Oh, I get it its like a question that normal people don't have time to deal with. So all the people with kid problems responded-it's like a huge bias. Teacher: Do you guys see a problem with what the health magazine is trying to do? Matt: Not everyone is a reader of this magazine-how many people own health magazine anyway-probably like all the doctors and nurses and medical people that take care of themselves. Teacher: Okay, so perhaps the readers are from a select population. What else? Ame: They are trying to lie because they told people who take lots of vitamins to respond. So the 93% is from people who take lots of vitamins as oppose to what the regular people do. Teacher: I agree-they are swaying the results. Christian: How could someone say that it's the vitamins that improved your health. I mean I know they are good for you-but some people could be naturally healthy. This is a rather difficult article for 8th graders to read smoothy. However, the contents of the article is in their level of understanding at this point. I had students read the first paragraph and than conducted a discussion with them: Teacher: What would it take for you to conclude that airbags save lives? Ben: First you'd have to find out how many people died in car crashes. Christian: All cars have seat belts but not all have airbags so obviously more accidents are going to happen in cars with only the seatbelt-so its like hard to track it. Kristin: You know those airbags don't save kids because they are too little to reach the airbag. Justin: How the heck are you suppose to know if people were wearing their seat belt in the first place? Tim: yeh, like what if they were wearing the seatbelt and have an airbag but died anyway. Teacher: All of you have some good points and it is exactly these points that you guys have mentioned that are in this article. I knew you guys didn't even need to read it! Does everyone see why the title of this article makes sense. |
The students like talking about these kinds of controversial topics-such as the airbag. I know that in a math class it doesn't happen very often. I'm glad these students caught on to allot of the biases that such everyday articles portray. I assigned the last page of the packet (Appendix L) for homework.
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