We associated "probability/independence" with the second article,
“No, CBS Sports, The Patriots Have Not Found an Edge on Coin Flips.” In 2015,
CBS Sports claimed that the New England Patriots were winning coin tosses at an
“impossible rate” (Chase, 2015). The author disproved this claim by calculating
the probability that a single team in the NFL wins 19 or more tosses out of 25
independent coin tosses (the Patriots’ record at the time).
Lastly, we chose “sample size” for our last article. “Moneyball Shows the Power of Statistics” explores how Billy Beane’s baseball team was
built on statistics. The team did not do well at first, and Beane blamed their
bad record on a small sample. The author of this article tested the claim that the
size of the team made a significant difference in the team’s record.
Heather and I explored the different types of graphic
organizers we could use to teach these vocabulary words and decided we liked the Semantic Map and Frayer model
the most. The Semantic Map helps students activate and organize prior knowledge
before reading a text. The Semantic Map is revisited during and after reading (McLaughlin, 2015). I
like the Semantic Map a lot and have seen it effectively used in English
classrooms. Semantic Question Maps are a specific type of Semantic Map that
encourage students to raise questions about a focus word (McLaughlin, 2015). I cannot remember a time where I've seen the Semantic Question Map implemented, but I think it could also work well, especially for tricky concepts like bias (Is this data biased? How can data be biased?).
I decided to further explore the Frayer Model. The Frayer
Model is used to “identify and define unfamiliar concepts and vocabulary” (Richardson).
The focus word is written in the middle of the graphic organizer, and the four
surrounding boxes are designated for definitions, essential characteristics,
examples, and non-examples. There are several variations of the Frayer Model. One such variation requires students to explore synonyms instead of essential characteristics. This version encourages students to explore synonyms through both words and pictures.
When using the Frayer Model with my students, I need to first
explain it to them. I will tell students that the Frayer Model is an effective way to organize and reflect on new vocabulary. I want to use the Frayer Model to explore independence in Harvard Sports Analysis' article "No, CBS Sports, the Patriots Have Not Found an Edge on Coin Flips." When I think of the word "independent," I sometimes picture the scene from Rudolph the Red-Nosed Reindeer where Rudolph meets Hermey and they state that they will "be independent together." I didn't really understand the irony of this scene until I rewatched the movie years later. I think it's a humorous example, but I cannot assume that all of my students have seen the movie, because not all of my students will celebrate Christmas.
Instead, I will connect "independence" to an idea that I know every student has learned about (probably multiple times) in their K-12 careers, the Declaration of Independence. While the Revolutionary War was much more complicated than "hey, we're declaring independence," I can still use this idea as a reference point. I also like connecting math concepts to topics from other disciplines, such as history. During the late 18th century, the thirteen colonies were independent from Great Britain (more or less), just like two events can be independent in probability. I will ask some students to share their own associations of the term "independence" before we move on to the next step.
As a class, we will complete a Frayer Model for independence. Students will be expected to record their own explanations and examples for the focus word. I will periodically check in with students by completing a box at a time. I have included my example below.
I will work with students to provide them with visual representations of independence. Personally, I like the version of the Frayer Model with four compartments, so I do not plan on giving students an extra box to draw an image. However, I do want them thinking about the mental picture they associate with their focus word (in this case, independence). If we get a chance, we will share some of our mental pictures and associations with the class. In my opinion, the best representation of independence is with a sort of Venn diagram. I will show students the image I associate with "independence" from a probability perspective, which is shown below.
After I have explained the Frayer Model and worked through a example with the class, I will read the title of the article aloud (“No, CBS Sports, The Patriots Have Not Found an Edge on Coin Flips”). As a class, we will brainstorm a few statistical terms that relate to coin flips. These can include words related to independence. The list might include terms like probability, dependence, and statistical significance. I will ask students to volunteer some of the words they came up with and write them on the board. Each student will choose a focus word, and then pair up with a classmate. Students will share the word they chose with a partner before diving into the article. They will complete the Frayer Model during and after reading. Once they have completed the Frayer Model, I will instruct students to work with their same partner from before and do a think-pair-share.
Richardson suggests that "students play games to reinforce and review new vocabulary" (Richardson). Before this week, I never really thought about reinforcing vocabulary every week with games and other review activities. However, I really like Quizlet. I was introduced to Quizlet in high school and have continued using it in my higher education career. I like that students can make or use study sets and take them wherever they go. Quizlet also has a lot of interactive review games. I plan on giving my students a few minutes every week in class to review vocabulary on Quizlet.
Richardson suggests that "students play games to reinforce and review new vocabulary" (Richardson). Before this week, I never really thought about reinforcing vocabulary every week with games and other review activities. However, I really like Quizlet. I was introduced to Quizlet in high school and have continued using it in my higher education career. I like that students can make or use study sets and take them wherever they go. Quizlet also has a lot of interactive review games. I plan on giving my students a few minutes every week in class to review vocabulary on Quizlet.
References
McLaughlin, M.
(2015). Content Area Reading: Teaching
and Learning for College and Career Readiness. Pearson Education.
Richardson, F. “Frayer
Model: Vocabulary Strategy.” National
Behaviour Support Service. Retrieved from http://www.nbss.ie/sites/default/files/publications/frayer_model_-_vocbulary_strategy_handout__copy_3.pdf
I agree that Venn diagrams are extremely helpful in understanding probability concepts. I wish comments let us post images, because I tried doing your Frayer model with sketches and fewer words. That's just how my brain works - I need fewer words on a Frayer model, or it doesn't help me boil the concept down to something I can remember or use to help me study. I used a sketch of a die for the example with a note that the probability of rolling an even # is the same on the first and 1,000th roll. For non-examples, I wrote Dependent Events and drew a sketch of a jar with the one red and 3 blue marbles in it, with a note that the probability that the 3rd marble drawn is red would depend on what came out of the jar first. Not all students will draw or sketch, but you can provide that option in the main Frayer model without having to include the extra space. Frayer models are great for math, and there are so many ways we can use them. I love that they can be effective both for students who like words and for students like me who prefer the process of choosing and making a sketch to solidify a concept.
ReplyDeleteAs always, I’m once again impressed by your work. I thought you did a very thorough job with this week’s assignment. I loved that you developed this into a cross curricular idea and got student to think about a math vocabulary word in a way that they could relate to. Getting students to think about past experiences with the word will create a solid foundation for learning it in a new context. You did a wonderful job describing the Frayer model and mentioning it comes in several different variations. Your example is awesome and students will easily be able to follow your directions. I wish some of my teachers could have introduced activities like this for us in school. Even those this is tedious work, the students will benefit from thinking about the word in so many different ways. I also liked that you mentioned that you would like for your students to think of a visual representation of the word as well. We saw that there are many strategies that incorporate visuals when discussing new words. This can be key to getting students to remember words long term. Great job creating nice resources, this will benefit you greatly when you get into the classroom. Finally, was impressed with your connection to online resources like quizlet. Although you’ll have to be careful of which quizlets you use in the classroom, this can be a fun way to engage students with learning new terms since there are several games associated with the review cite.
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