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Make thoughtful, substantive comments to the 4 blog entries (AT LEAST 5 SENTENCES EACH). The comments should be related to topics and issues discussed in the blog entries, and should further the mathematical thinking (by making connections, asking questions, answering questions posed, etc.) This is not a place for merely complimentary posts – though you may certainly include compliments as well
BY CHRISTINE PALMERAMA
We began this course with a look at basic statistical vocabulary and sampling techniques. We identified what a population was and how to determine what kind of variable we were studying. We also looked at how to effectively sample from a population using various kinds of sampling techniques. I’ve enjoyed the various activities that we have engaged in and have learned a good deal from my colleagues in seeing the different perspectives that we bring to the discussions. One of the biggest “take-aways” for me is how truly difficult it is to create a statistical study that has no bias or potential problems that could arise. There are so many things to consider and one must continually think of what problems could happen in order to make a plan to avoid them. Being in groups and discussing the various assignments reminded me of how helpful it is to collaborate and work as a group. Since I teach statistics myself, most of the content of the course was familiar to me; however, working on statistic research and analysis myself and with a group is something I usually have my students do. It is good for me to go back and be the student again and remember what it feels like to come up with ideas, do my own research and data collection, and go through the process of actually doing the project. As a teacher, it is good to switch roles sometimes and be the student!
As far as the content so far, I enjoy looking at the various data sets and creating a “picture” of the data by graphing, finding the measures of center and analyzing the shape of the data. This is such an important first step. It amazes me how much information we can gain by making more than one graph. Each graph shows different aspects of the data in different ways. Where a histogram may show the shape of the data well, a boxplot quickly shows how the upper and lower 25% of the data fall as well as the middle 50%. I also really liked making graphs of two data sets side-by-side in order to compare their different properties. With our raisin data, it has been helpful to see all the graphs and get a holistic view of the data we collected. The study of the difference between the mean and median has also been good. It’s great to understand how the mean can be influenced by extreme values whereas the median is more resistant a measure of center. The median does a great job of showing the position of the very middle of the data whereas the mean lets you know the kind of value one could expect from the data. All in all, I look forward to the rest of the weeks when we get into even more analysis of the data and use it to test hypotheses.
BLOG COMMENTS:
BY RANDY JEAN SPARKLE
I was somewhat dreading this class when I enrolled in it because the only real memories I have of Statistics was when I took it as an undergrad and it was combined with Probability. Probabilities are one of the few mathematical topics that just doesn’t click with me…I can’t see it like I can other branches of mathematics. I think by the time that I got to the Statistics part of the class I had kind of checked out and don’t remember much of anything. This was back in 1977 and I have trouble remembering what I did yesterday:) The only real experience that I have had with Stats in my teaching career has been teaching measures of central tendencies to my Algebra 1 students.
It was nice that once I started the class many of my fears were alleviated because some of the material did come back to me from undergrad work. I have really enjoyed learning to use the technology associated with Stats as this was not around when I was taking it. It makes it so much easier to make the dot plots, histograms and box and whisker plots using the technology available. By using the computer or calculator it has made it easier for me to concentrate on what the data is really telling me. I did have to try and teach box and whisker to my Algebra 2 students this past year and I really didn’t do a very good job…went through the motions on how to create all the parts but was not able to relay to the students what it all meant. I could find all of the different quartiles but was not able to tell my students what they were used for. This past module has been very enlightening to me and I can now do a much better job as a teacher.
I wasn’t really sure what the point of counting raisins was going to be at the beginning but have now found out how much information can be gathered, sorted and reported from such a simple task. This is something that I would be able to use in my class for this coming year as a great hands-on project and I really think that my students will get much more out of something like this as opposed to just finding values from problems in the book. I have always struggled with finding hands-on projects for the upper level students while still trying to get through everything that needs to be covered in the curriculum.
I know that there is much more to come in this class and I am now actually looking forward to the coming weeks and how much more I will be able to learn. I can’t thank my group enough for the help and guidance that they have given me these past three weeks. I have not always been a fan of group work, especially online, but getting feedback and different ideas has made me a huge believer of the group concept.
BLOG COMMENTS
——————————————————————————————————————————————BY KATHERINE LEYLA INGER
I must admit that after having taught AP Statistics for the past five years, a lot of this material has been review for me. That being said, I have learned some new techniques for teaching certain topics. For example, I really liked the article which we read in the first week. When I am teaching Statistics, I always tell my students that the information that the general public sees on the news is coming from research using statistics. However, the news does not report p-values, types of hypothesis tests, potential sources of bias, and other statistical analysis, because most people will not understand it. I think it would be very beneficial to my students to read a scholarly article that actually reports all of the facts. Specifically the article that we read because it also identifies several types of bias.
Another reason that I really liked that article is that it showed the link between tobacco sponsored research and independent research. Most consumers do not even think about this when hearing the results of a survey. I usually explain to students in all of my classes that this is the reason that it is so important to learn statistics. People should be aware that although one study may find that, say drinking coffee is good for you, there is some other study out there which finds that it is not.
In addition to the article, I enjoy the group discussions. Honestly, I was dreading them. I hoped to just be given a set of math problems and post answers to them. Contrary to my initial reaction, they are very insightful. I have learned a lot from reading discussions. Normally, I use a lot of group work in my classes. I try to monitor conversations, but sometimes I think the strongest person in the group just ends up doing the bulk of the work. Although the group work generates conversations, I think that everyone must contribute equally to an online discussion. Maybe I will try to set something up for my class this year.
Collecting our own data is one other part that I enjoyed in this course. In past years I have done an M&M activity with my students using the colors of M&Ms. Quantitative data seems more interesting in terms of outliers and possible human error in the recordings. I think I will use the “how long is a minute?” activity in my classroom.
One article that made me reflect on my teaching and understanding was the Mean and Median: Are They Really so Easy? Up to now, I have been teaching my non-AP students so that they could pass the MCAS. This article brought up new ways to teach the same concept to see if students really understand the material. I think that is one of the themes of this course: to see topics in different contexts to ensure that we fully understand them.
The only question that I really still have is the difference between a sample and observational units. I cannot think of a time when these two would differ. I would love if someone could share that with me!
BLOG COMMENTS
BY MEGAN TRINA PARIS
Before I began this course I was very nervous about what to expect. I thought I would be doing a lot of work that I had not been doing before. However, so far I have had prior experience with the things that we have covered in the course. I have not gone into as much depth with each of these concepts, but I had some knowledge. The thing that has been new is the idea of really analyzing and dissecting the data. In prior math classes I have had to graph data and create box plots, but I have not been asked to analyze data at the level that we do in this course. I have been trying to go beyond stating the obvious with data we have analyzed, but I feel as though I still need practice with analyzing data.
There have been many terms covered in this class that we use to describe data. Some of the terms we have discussed describe similar aspects of data, but in a different way. As an example, when talking about the center of data, median or mean can be used. It depends on what exactly the data is describing and what the person who is analyzing is looking for, to decide which to use.While statistics gets us to look at data and analyze the data in parts, it also causes us to think about what the data actually means. In the raisin data, we found some specific points and parts of the data, but we used that to describe what that meant in general. We used all of the small points to make a generalization about the difference between store brand and name brand raisins.Each week of working we have been learning more about how to gather data in the best way and then using the data we gathered to create our own graphs or plots. Then using the plots we created we analyzed and described the data. I have really learned a lot about statistics because of working from the beginning to the end like this.
In my own thinking about math I have learned to look deeper and compare more. There has been so much to see in histograms and box plots, more than I thought there was. I think that this change in my own thinking will help me to be a better teacher. I can teach my students to look deeper into the math they are doing. We don’t have to just be talking about statistics either. Just using the practice of looking at data and finding a way to describe it has helped me in other areas of math. I have developed some stamina in my thinking and look for patterns in what I am doing. I hope that I can use this to help my students take an interest in math and be excited by it.
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