There have been a mind boggling number of posts on Reddit since it was created, but which ones have done best? This visualization shows the 200 highest-scoring posts of all time from the site.
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I chose this artifact because I think that the context would be a good way to catch students’ attentions. I think that health supplements are a very relatable topic for secondary students. Furthermore, our job as teachers is not only to teach our students academic lessons but also other important lessons in their life. The age of secondary students is a crucial time to for people to be practicing good health habits.
Before working with this visualization in your classroom it would helpful to briefly dissect the graph as a class. At the end of the document it explains that this image is a ‘balloon race’. The height of the balloon determines how effective the health supplement is with respect to the specified condition. In the interactive version of the map a user can click on the bubble in order to get the exact statistics of the health supplements effectiveness. The size of the bubbles in this graph corresponds to the popularity of each health supplement.
This artifact is has very versatile mathematical applications. The most basic mathematical idea present in this artifact is the concept of ratios. Students could compare the ratio popularity with respect to the diameter or area of the circles. There is a link to a Google document that contains more numerical data about this graph: https://docs.google.com/a/vanderbilt.edu/spreadsheet/ccc?key=0Aqe2P9sYhZ2ndFRKaU1FaWVvOEJiV2NwZ0JHck12X1E&hl=en_GB#gid=0. Although this Google document has been transformed from the original data according to an unknown scale, it gives the reader a chance to discover the relationship between the quantitative and qualitative data.
This artifact could also be used to build statistical literacy. An interesting aspect of the graph is “worth it” line. As a student in a statistics classroom I remember being challenged with deciding a proper confidence level or margin of error. Students could analyze the bubbles positions on the graph (i.e. distance from the worth it line) with the score that the health supplement received in the Google document. After discovering the relationship between the two, students can make conjectures about whether they agree or not with the artifact. This gives students the opportunity to cultivate their critical literacy. I would challenge my class to take a health supplement that is presented as not “worth it” and find a condition that is positively affected by the supplement. Students could pick a few specific health supplements at various positions in the graph to closely analyze. Through this analysis they have to explore the exact numbers taken from the studies linked to each individual bubble. After researching and comparing the data students would need to take the stance of agreeing or disagreeing on the value of the supplement.
I chose this artifact because I thought it was an interesting visual display of population growth, and it was interesting to see how the authors predicted future population growth to continue but to level out around 2050. The video format of the argument was helpful because the information was accompanied simultaneously by the visual representations of the data. In addition, I was intrigued by the alternate form of displaying a line graph and bar graph in the form of a circle. I also thought that the statistical ideas behind the construction of the graphs would be interesting to explore.
While the majority of the mathematical literacies involved in reading this argument involve reading the graphs, in order to fully understand the statistical argument, the students would need a strong statistics background to understand the statistical modeling involved. If the teacher supplements the artifact appropriately, the students could explore a range of statistical concepts. Nevertheless, the way the argument is presented, the primary challenge for students is understanding the layout of the information, which is considerably different than most graphs. In this way, students learn that there are many ways to represent data, beyond the types of graphs taught in school. Students should also increase their graph reading abilities through reading of this argument. Students must understand what the variables are for each graph, and how the axes are laid out. Students should also understand the difference between the population size and the annual increment and how these two factors are related, as demonstrated by including them on the same graph. Students should be able to observe the trends in the data, including how the graphs visually demonstrate the decrease in elapsed time between each billion people. Students must understand what it means for "the momentum of population growth to slow almost to zero". This involves concepts of acceleration and rate of change, rather than just the amount of change itself.
Nevertheless, I think this artifact could be useful in a mathematics classroom. In order for students to completely understand the argument in this video, I think it is essential for them to understand how it was constructed. For this reason, a lot of the statistical literacies involved in constructing the argument could also be involved in the reading of the argument. I would use this video to help teach students the concept of rate of change as demonstrated by the acceleration of population growth and eventual steadying out of population, i.e., an acceleration of zero. I could also use this artifact to teach students about statistical modeling. Students could guess how the data for 2010-2050 was constructed. This could lead into a discussion of different types of models and how one would go about choosing a model for a set of data. This could also lead into discussion on using data to make arguments and could be used to teach students to read graphs critically, not just accepting everything that they see and hear. I would see if they had questions about the argument, and then discuss some of my lingering questions with respect to the construction of the argument.
This artifact does not require much contextual supplementation, considering that the focus is on population and fertility rates. While "fertility rate" may be an unfamiliar term for students, it is explained as "children per woman" in the video, which should clarify the concept. The video does mention the "Baby Boom" in the 1950s. The increase in population from this decade on is in part attributed to this phenomenon, so it may be helpful for teachers to make sure students understand what it is. Students may be curious as to why the fertility rates of Iran are included in this video and if there was anything happening culturally or otherwise that would have caused such a quick decrease in fertility rates.
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This video is about range and measures of central tendencies (mean, median, mode). Students in this classroom are very enthusiastic while they recall the meaning of mean, median, mode, and range using chants.
Here are the chants that they go through:
"Mode means most"
"Median means middle, order first then find the middle number"
"Range subtract the lowest from the highest number"
"Mean add them up and divide by the the addend"
After hearing each of these chants I cannot even get them out of my head so I am sure students will not be able to either. I may use this as a short review for mean, median, mode and range.
This teacher engages all of the students in such an amazing way! By using a song and dance about math the students are learning about mode, median, and range and in a fun and exciting way.
Students love watching YouTube videos. I chose this artifact for it’s mathematical richness. Not only does this artifact serve as a great way of connecting distribution in algebra to multiplication but it also stresses various values in mathematics. One mathematical value that I want to stress in my classroom is the idea of multiple representations. For every math problem there are multiple ways to find the solution. Finding connections between these representations will lead students to a better conceptual understanding and procedural fluency because different representations can stress different parts of the procedure. Another mathematical value presented in this video is that math is consistent. Many students believe that the procedures presented to them in math class are simply pulled out of thin air. Math is consistent because it is a logical system created out of deductions.
Every algebra teacher hopes and begs that his or her students enter the classroom with a solid foundation of math skills. After all, it is nearly impossible to factor quadratic equations without knowing multiplication tables. One way to use this video in your classroom is directly after introducing the distributive property and multiplying binomials. With this video students will be able to make connections between multiplying two numbers versus two binomials. Initially, multiplying two binomials can be very difficult for students. It is helpful to connect this idea with something students already have a handle on. After watching this video having “number talks” with the class would reinforce the ideas. For example a teacher could introduce: (15)(12) = (10+5)(12) = (10)(12) + (5)(12)
If you are already using area models or algebra tiles in the classroom this is a great way to reinforce that idea. If not, this video could serve as an introduction to using them as another way to represent multiplication. In the video the student says, “Don’t let notation get in the way of your understanding”. This is an important thing to pull out of the video for students. Students need to realize that all of their understanding of how arithmetic works when they get to algebra is applied in algebra. The only difference is that variables are being using instead of numbers.
Another great quote to pull out of this video is “You can make up any rules you want as long as you are consistent”. In order to reinforce mathematical consistency a teacher could challenge the class of students could make up their own symbol. This symbol has to be something mathematical. This symbol can be a relationship like pi or e, or this symbol can be an operation like multiplication or division. Students will be challenged to represent their consistent symbol with at least 3 representations (arithmetic, geometric, symbolic, graphically…etc). When everyone has constructed a symbol students will have to define their peers symbols. A great question to ask during this activity would be “What happens if two people have the same symbol to represent different things”, “Is there anything in math that does this?”
I chose this artifact because I believe all secondary students can relate to it in some way. Most likely, every student you my classroom will be a part of some social networking site. Thus, this context can serve as an initial bridge between students and mathematics. However, before begining it would be important to review the definition of a social networking website. Furthermore, some students may become distracted by all of the websites that they have never heard of before. In that case, it may be productive have a conversation about this before working with this artifact. Simply explain that the students will most likely not know every website on this sheet. Challenge students to use this knowledge to make mathematical explanations and justifications (i.e. the website they do not know have less visitors).
The best part about this artifact is that not only is the content relatable for students, but it has contains strong mathematical ideas that will help foster mathematical and statistical literacies in a classroom. First of all, it takes document literacy to deduce the information the artifact is conveying. This artifact is interesting because it displays 4 representations of the same information. The first column is a pictorial representation. Each boy/girl figure represents 1% more visitors to that social media than the other gender. The second column shows the percentages of boys/girls that visit these websites. The third column shows the actual number of million more monthly female or male visitors. Next to this is a bar that shows a visual representation of this number of visitors. This bar makes it easier to compare the number of more visitors between websites.
One main mathematical idea in this representation is ratios and percentages. The idea of ratios extends beyond obvious comparison of female to male visitors. For example, students could find the ratio between the bar length in the 4th representation and the number of million more monthly visitors. In order to create a better conceptual literacy of the relationships between ratios and percentages I would ask students to find relationships between the 4 representations.
In a classroom with more advanced mathematical backgrounds it would be interesting for students to create their own study. This would help build critical literacy in the classroom. Begin the discussion of this artifact with the questions. Do you think this information is accurate why or why not? What makes a study/artifact accurate? After discussing this have students conduct an “accurate” survey of their own. After students gather information have them represent their results in at least three ways. Here are some key questions to ask your class:
1. How do the 3 columns of statistics (pictorial, %, and million more) relate, and how are they different?
2. Given one column would you be able to produce the other three?
3. What is the central focus of this document?
4. Do you agree or disagree? Why?
5. Would a sample at our school produce similar results?
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